Why Fiscal Stimulus Programs Fail, Volume 2: Statistical Tests Comparing Monetary Policy to Growth Effects [1 ed.] 3030647269, 9783030647261

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Why Fiscal Stimulus Programs Fail, Volume 2 Statistical Tests Comparing Monetary Policy to Growth Effects John J. Heim

Why Fiscal Stimulus Programs Fail, Volume 2 “The book is well laid-out and designed. The topic is very important and timely given the economic conditions that are currently present. Additionally, the analysis provides an important examination of what not to do during economic downturns and how to ensure that monetary policy will have the impact that is hoped for. The topic of the book is extremely important and the Federal Reserve should read the book themselves. I am confident that this book should be a key part of any macroeconomists’ library and should be read by policy makers. This book proposal does offer an important and original contribution to the field. The book offers an exhaustive analysis of the accommodative monetary policy issue, which, if covered at all, is largely just a theoretical issue in macroeconomic books. This proposal shows that Keynesian monetary policies did not fail; what failed was the Federal Reserve’s use of accommodative monetary policy which were not large enough to overpower the crowding out impacts. The analysis provided in this book illustrates that if loanable funds are increased sufficiently and appropriately, Keynesian macroeconomic policies will work. The importance of this finding cannot be overstated.” —John Polimeni, Albany College of Pharmacy, Albany, NY, USA

John J. Heim

Why Fiscal Stimulus Programs Fail, Volume 2 Statistical Tests Comparing Monetary Policy to Growth Effects

John J. Heim Department of Economics State University of New York Albany, NY, USA

ISBN 978-3-030-64726-1 ISBN 978-3-030-64727-8 (eBook) https://doi.org/10.1007/978-3-030-64727-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Paul Hohenberg, brilliant economist, distinguished scholar, long time mentor and friend.

Preface

This is the fourth of a five-book series on the hard science underlying Keynesian mechanics and its policy prescriptions. In all these books, initial results found in testing a specific sample covering a certain period of time are discarded unless the results can be replicated in most or all other time periods, ensuring that our results are good science, not just attractive sounding theories or potentially spurious statistical results typically obtained when testing only one model for only one period of time. The need for a series of science books like this is obvious: over 80 years ago Keynes coined his famous theory that the economy was fundamentally demand, not supply, driven, and that because of this, deficitfinanced government fiscal spending and tax cut programs could stimulate the economy. Yet, to this day, there is no unanimity of agreement within the economics profession as to whether they work. This, I believe, is because positions many economists hold on the issue are not generally empirically based at all, but based on theory alone, or are based on endless numbers of limited empirical studies of (say) investment, with no two models tested containing the same variables, or testing for the same time period, or testing for more than one time period. Nary a thought given to the fact that you don’t have a scientific result unless you have replicated; i.e., verified that the same model yields the same results in all or almost all time periods.

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PREFACE

If this continues to be the way economics is practiced, evaluation of whether economics policies work will not have a sufficiently scientific basis to be anything but an intellectualized version of “he said/she said” arguments heard in divorce courts, where there often is a lack of empirical evidence to allow us to determine which is the truth. You can think of this purely theoretical or faux empirical approach as a version of the “talking heads” economics we hear on talk radio and TV. By contrast, of the four science books mentioned above, the first is a well-tested, well-replicated, 56 equation empirical model of the economy (“An Econometric Model of the U.S. Economy”, 2017), which compares the fit of well-known DSGE, VAR, and Keynesian models of the economy during the same post-estimation period of time. It concludes the Cowles (Keynesian) Model best explains the variation in the economy since 1960 and does so equally well for each decade during the 50-year period studied! In the same book, similar results are found for the key equations in the Keynesian model: consumption and investment. The models explain approximately 90% of the variation in those variables since 1960. And again, the same models explain the data as well in one decade of the 1960–2010 period as another, indicating the model is good science, not just less empirically based “talking heads” economics. The second book, “Crowding Out Fiscal Stimulus” (2017), uses the standard economic models for investment and consumption from the first book to test whether deficit-financed Keynesian stimulus programs worked over the 50-year period, 1960–2010, controlling for all other variables which could also affect consumption and investment levels. Surprisingly, it found little or no evidence stimulus programs did work. The reason for the failure, examined in detail in books 3 and 4, was that deficit financing “crowded out” borrowing-based private consumption and investment. This was due to the need to finance the deficit from the existing, limited, pool of loanable funds, reducing what was available for consumers and businesses to borrow. This typically kept Keynesian stimulus from working fully (if at all) from 1960 up to the start of the Quantitative Easing program in 2008. Again, results were found replicable in several time periods sampled, and were also replicable using a variety of models. The third book, using from 6 to 18 different sample periods, reiterates the testing to see if deficit finances stimulus programs cause crowd out, and affirmed they do.

PREFACE

ix

But the main focus of the third book is on why accommodative monetary policy by the Federal Reserve did not offset this crowd out problem, and ensure attempts at Keynesian stimulus did work. After all, the empirical soundness of the underlying demand-driven theory of GDP determination was well established in the first of these books (and in earlier large scale econometric models developed by Kline, Eckstein, and Fair), and it implied fiscal stimulus programs should work. And later additions to the theory established that should crowd out problems arise, they could be offset by “accommodative monetary policy” by the Federal Reserve. This means the stimulus programs would work if the Fed increased the pool of loanable funds available to private borrowers by the amount it was reduced to finance the deficit. This book concludes the main reason fiscal stimulus programs haven’t worked was the systematic decisions by the Fed, from 1960 to 2007, not to increase bank reserves, i.e., implement accommodative monetary policy, to anywhere near the extent needed to offset the deficit. The third book also finds other problems that limit the effectiveness of the Fed’s accommodative actions. These problems were more “policy analysis” oriented, rather than econometric. They involved the Fed’s stubborn insistence on implementing the accommodative policy through securities purchases mainly from investment banks, who sell securities for themselves or others, mainly to raise money so they can buy other securities, not to finance consumer and business loans to buy real goods and services, the business of retail commercial and savings banks. This third book also looked at whether endogenous growth in the loanable funds pool, due to rising incomes and saving, an increasing marginal propensity to save, could help offset the crowd out problem caused by deficits, and concludes it can. This explains why in some periods, fiscal stimulus programs seem to work, despite inadequate Federal Reserve action to increase the pool, while in others they don’t. Hence, depending on the period picked, the results provided good evidence for economists on either side of the argument about the effectiveness of Keynesian stimulus programs. It helps provide an explanation why the economics profession has found it so hard to become of one mind on this topic. The fourth book, which is this book, explores in great detail how well different combinations of increases in loanable funds, some by the Fed (exogenous increases), some endogenous, actually offset crowd out problems. It also tests different definitions of loanable funds to see which definition of system liquidity works best to define how well crowd out can

x

PREFACE

be offset. It concludes the total national savings plus foreign borrowing provides the best definition of what increases in loanable funds offset crowd out. It also concludes endogenous growth in the loanable funds pool, generally through economic growth, is several times more effective than Federal Reserve—induced (exogenous) growth. This is presumably because endogenous growth in loanable funds is more likely to be used for loans to purchase real goods and services, raising the GDP, and not the result of liquidity added to the system (exogenous growth), mainly being used to buy other securities. The fifth book, not yet started, will be an effort to determine if the “neoclassical synthesis”, the theory most commonly used to show how the economy moves from the Keynesian short run into the classical long run, can be empirically verified to exist, or whether it is just another “talking heads” theory looking nice on paper, but without much empirical support. When completed, I hope these five books will provide good reason to reclassify macroeconomics from a series of different, essentially deductive, social science philosophies, poorly grounded in empirics, into a branch of practical science, namely engineering science. Toward that end, we may be making progress: The first citation of the 56 equation econometric model book, noted above as the first of this series of books, was in an engineering journal sponsored by the Institute of Physics, and dealt with production functions. Engineers do a lot of economics. It is a good sign the engineering field is finding it can confidently rely on well-replicated economic results developed using the scientific method. The more this type of economics is done, the more the engineering world will accept economists into its fold, and not just think of them as “another group of social scientists.” Numerous discussions over the years with Paul Hohenberg (professor emeritus, Rensselaer Polytechnic Institute) on monetary policy, especially as regards the Federal Reserve’s role in stimulating the economy, have been extremely helpful in shaping this book. Also very helpful were discussions with Ken Kuttner (Williams College), clarifying the mechanics of how the Fed performed its role in implementing monetary policy. I am also deeply thankful to my wife Sue for her constant support during the three years this very time-consuming project was underway. Albany, USA October 2020

John J. Heim

Contents

Part I 1

2

Introductory Chapters

Introduction 1.1 The Crowd Out Problem and Accommodative Monetary Policy 1.2 Individual Chapter Contents and Findings 1.2.1 Estimating Crowd Out’s Actual Effects 1.2.2 Total Loanable Funds as a Crowd Out Modifier 1.2.3 Exogenous Loanable Funds Modifiers (FR Securities Purchases) 1.2.4 Endogenous Loanable Funds Modifiers 1.2.5 Summary Chapters 1.3 Summary of Key Findings References Literature Review 2.1 Summary of Findings 2.1.1 Stocks and Bonds 2.1.2 GDP 2.1.3 Inequality 2.2 Detailed Findings 2.2.1 Assessment of Monetary Policy Effectiveness in the Business Press

3 3 6 8 8 9 9 10 10 12 13 13 14 14 15 15 15 xi

xii

CONTENTS

2.2.2

Assessment of Monetary Policy in the Academic/Professional Literature 2.2.3 Comparisons of Findings of the Professional and Business Press 2.3 A Comparison of Cowles, DSGE, and VAR Methodologies Used in Literature Review References 3

Methodology 3.1 General Methodological Issues 3.1.1 The Importance of Replicating Results Before Publication 3.2 Other Methodological Issues Specific to This Study 3.3 GDP Deflator Methodological Adjustments 3.4 Reconciling Differences in Signs, Significance Levels of Tests in Different Time Periods 3.4.1 Mixing Periods of Budget Deficit (Crowd Out) Increase and Decrease 3.4.2 Statistical Insignificance Caused by Lack of Variation in the Data 3.4.3 Left-Out Variables 3.4.4 Multicollinearity 3.4.5 Insufficient Sample Size 3.4.6 Spurious Results Indicating Insignificance 3.5 How Should a Change in Loanable Funds Be Distributed to Tax and Spending Deficits 3.6 Other Model Specification Issues: Different Deficit Modifiers Tested References

Part II

4

19 33 34 37 41 44 49 50 53 54 55 67 70 71 72 73 73 74 78

Theory of Crowd Out and Accommodative Monetary Policy

Theory of Crowd Out and Accommodative Monetary Policy 4.1 Under What Conditions, Federal Reserve Purchases of Government Securities Can Work to Stimulate the Economy

81

81

CONTENTS

4.1.1 4.1.2

Overview Detailed Analysis of the Crowd Out and Accommodative Monetary Policy Processes 4.2 A Formal Model of the Effects of Fiscal Stimulus Programs, Their Crowd Out Effects, and How Accommodative Monetary Policy Can Offset Crowd Out Effects, Allowing the Fiscal Stimulus to Work 4.2.1 Crowd Out Effects of Deficit Financing 4.2.2 How Accommodating Monetary Policy Offsets Crowd Out Effects 4.2.3 Should We Use Accommodate Monetary Policy to Offset Crowd Out? References

Part III

5

xiii

81

83

87 89 90 104 105

The Effectiveness of Accommodating Monetary Policy Mechanics

The Role of Primary Dealers, Investment Banks and Foreign Banks in Federal Reserve Efforts to Change Bank Reserves and the Money Supply 5.1 Primary Dealers Dominate Auctions 5.1.1 What Type of Bank Does the Federal Reserve Purchase Securities from: Investment or Depository? 5.2 Loss of Efficiency When Using Investment Banks and Brokerages to Implement Accommodative Monetary Policy 5.3 Primary Dealers Who Are Domestic Vs. Foreign Corporations 5.4 The Failure of Accommodative Monetary Policy before Quantitative Easing (QE) and Its Success After; The “Pushing on a String Problem” 5.4.1 Effectiveness of Accommodative Monetary Policy 1960–2007 5.4.2 Effectiveness of Accommodative Monetary Policy 2008–Present

109 110

111

116 117

120 120 128

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CONTENTS

5.5

Historical Data on FR Purchases of Government Securities, Reserves, M1 and the Monetary Base References

Part IV 6

7

Does Crowd Out Really Occur?

Does Crowd Out Really Occur? Initial Empirical Evidence—One Time Period 6.1 Consumption 6.2 Investment 6.3 Conclusion References

137 139 141 142 142

Does Crowd Out Really Occur? Empirical Evidence—Replication in Many Time Periods 7.1 The Heim (2017b) Study 7.2 The Heim (2017a) Study 7.3 Crowd Out Findings in This Study References

143 143 144 146 148

Part V

8

128 133

Increases in Total Loanable Funds—Do They Reduce Crowd Out?

Initial Tests of Whether Crowd Out Can Be Offset by Increases in Loanable Funds 8.1 Methodology for Testing Increases in Loanable Funds as an Offset to Consumption Crowd Out 8.1.1 Separating the Positive and Negative Effects of an Increase in Loanable Funds on Consumption 8.2 Taxes: Another Variable that Has Both Positive and Negative Effects on Consumption 8.3 Methodology for Testing Increases in Loanable Funds as an Offset to Investment Crowd Out 8.4 Conclusions References

151 152

154 156 158 161 161

CONTENTS

9

10

11

Which Models Best Explain How Changes in Loanable Funds Offset Crowd Out? 9.1 Effects on the Consumption Function 9.2 Effects on the Investment Function References Do Loanable Funds Modify the Crowd Out Effects of the One-Variable Deficit (T − G)? 10.1 Consumption Results When also Including (S + FB) as a Separate Variable 10.2 Consumption Results When Not Including (S + FB) as a Separate Variable 10.3 Investment Results When also Including (S + FB) as a Separate Variable 10.4 Investment Results When Not Including (S + FB) as a Separate Variable 10.5 Comparing the Effects of Exogenous (FR Purchases Induced) and Endogenous (Economic Driven Change Induced) Loanable Funds Growth 10.5.1 Effects on Consumption 10.5.2 Effects on Investment 10.6 Conclusions Reference Do Loanable Funds Modify the Crowd Out Effects of the Two-Variable Deficit (T ), (G)? 11.1 Testing the Two: Variable Deficit Consumption Model 11.1.1 Mixing Crowd Out and Crowd in Periods May Distort Results 11.2 Consumption Models Without Stand Alone (S + FB) 11.3 Crowd Out Effects on Investment Using Stand-Alone Loanable Funds Variable 11.4 Crowd Out Effects in Investment Models Without a Stand-Alone Loanable Funds Variable 11.5 Chapter Summary References

xv

163 166 172 177

179 179 186 188 195

199 199 201 204 210

211 211 239 257 260 267 274 281

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CONTENTS

Part VI

12

Does M1 More Accurately Define the Extent to Which Crowd Out Can Be Modified Than Total Loanable Funds? 12.1 Testing the Consumption Model 12.2 Testing the Two-Variable Deficit Investment Model 12.2.1 Investment Models with a Stand-Alone Loanable Funds Modifier 12.2.2 Investment Models Without a Stand-Alone Loanable Funds Modifier 12.2.3 Investment Models Without a Stand-Alone Loanable Funds or M1 Modifier, but with a Business Cycle Control Variable 12.3 Comparing Model Results with (Table 12.5) and Without (Table 12.4) GDP Control 12.4 Summary of Chapter 12 Results Reference

Part VII

13

14

Comparing M1 and Total Loanable Finds Effects on Crowd Out

285 286 296 296 304

306 309 311 318

Exogenous Increases in Loanable Funds (Fr Security Purchases): Effects on Crowd Out

Alternate Ways of Modeling How Deficit Variables Modified by Accommodative Monetary Policy Reduce Crowd Out (Bernanke, Mankiw Definitions of Accommodative Monetary Policy) 13.1 Effects of FR Securities Purchases on Consumption 13.2 Summary of Results and Conclusions for Chapter 13 References

321 324

Does Modification of the Single Variable Deficit (T – G) by FR Purchases Better Measure Crowd Out, Controlling for Endogenous Loanable Funds Growth? 14.1 Summary of Consumption Test Results for Different Sample Periods

339

336 338

342

CONTENTS

Summary of Investment Test Results for Different Periods 14.3 Summary of Chapter 14 Consumption and Investment Findings and Conclusions Reference

xvii

14.2

15

16

17

Does Modification of the Two-Variable Deficit (T) (G) by FR Purchases Better Measure Crowd Out, Controlling for Endogenous Loanable Funds Growth? 15.1 Testing the Two-Variable Deficit Consumption Model 15.2 Testing the Two-Variable Deficit Investment Model 15.3 Summary of Chapter 15 Results from 2 Variable Deficit Models Reference Do FR Purchases, Used as Deficit Modifiers, Reduce Crowd Out, Controlling for the Level of Private Saving and Foreign Borrowing 16.1 Summary of Consumption Test Results for Different Sample Periods 16.2 Summary of Investment Test Results for Different Periods 16.3 Conclusions 16.4 Have FR Securities Purchases Been Pro or Contracyclical? References Do FR Security Purchases, Used as 2 Variable Deficit Modifiers, Reduce Crowd Out, Controlling for Private Savings? 17.1 Testing the Two-Variable Deficit Consumption Model 17.2 Testing the Two-Variable Deficit Investment Model 17.3 Summary of Chapter 17 Results from 2 Variable Deficit Models Reference

345 352 355

357 358 364 370 373

375 380 385 390 394 401

403 404 414 420 423

xviii

18

19

CONTENTS

Do FR Purchases Reduce Crowd Out Effects, Controlling for Other Types of Loanable Funds? 18.1 Testing the Two—Variable Deficit Consumption Model 18.2 Testing the Two-Variable Deficit Consumption Model 18.3 Adding a Separate Loanable Funds Variable to the Consumption Model 18.4 The Consumption Model Without a Separate Loanable Funds Variable 18.5 Testing the Two-Variable Deficit Investment Model 18.5.1 Crowd Out Effects in Models with an Endogenous Loanable Funds Control Variable 18.6 Crowd Out Effects in Models Without an Endogenous Loanable Funds Control Variable 18.7 Chapter 18 Summary and Conclusions Reference Effects of Accommodative Monetary Policy on Crowd Out Before and After Quantitative Easing. Does “Pushing on a String” Occur?

Part VIII

20

425 425 425 428 431 433

436 441 445 448

449

Endogenous Increases in Loanable Funds: Effects on Crowd Out

Is Endogenous Total Loanable Funds a Better Modifier Than Total Loanable Funds? 20.1 Testing the Consumption Model 20.2 Investment Models Using the (S + FB) or (S + FB) - (Tr + a) Modifier 20.3 Summary and Conclusions Reference

453 454 464 473 477

CONTENTS

21

Comparing Various Stand-Alone Endogenous Loanable Funds, and FR Securities Purchases Variables Models 21.1 Statistical Significance of the Total Loanable Funds Variable When Added to the Standard Consumption Model 21.2 Statistical Significance of the FR Security Purchases Variable When Added to the Standard Consumption Model 21.3 Statistical Significance of the Combined Loanable Funds and FR Security Purchases Variable When Added to the Standard Consumption Model 21.4 Statistical Significance of Separate Loanable Funds and FR Security Purchases Variables When Added to the Standard Consumption Model 21.5 Statistical Significance of Separate National Savings (Instead of (S + FB)) and FR Security Purchases Variables When Added to the Standard Consumption Model 21.6 Statistical Significance When Separate Loanable Funds Net of FR Security Purchases and Separate FR Security Purchases Variables When Added to the Standard Consumption Model 21.6.1 Investment Model Tests 21.7 Statistical Significance of the Total Loanable Funds Variable (S + FB) When Added to the Standard Investment Model 21.8 Statistical Significance of the FR Securities Purchases Variable (Tr + A) When Added to the Standard Investment Model 21.9 Statistical Significance of the Combined Loanable Funds (S + FB) and FR Securities Purchases Variable (Tr + A) When Added to the Standard Investment Model 21.10 Statistical Significance When Separate Loanable Funds and FR Securities Purchases Variables Are Added to the Standard Investment Model

xix

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484

487

489

491

493

496 498

498

502

503

506

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CONTENTS

21.11

Statistical Significance of Separate National Savings and FR Securities Purchases Variables When Added to the Standard Investment Model 21.12 Statistical Significance of a Separate Endogenous Loanable Funds Variable (LF - FR Purchases), and a Separate FR Securities Purchases Variables When Added to the Standard Investment Model 21.13 Summary of Chapter Results and Conclusions Reference 22

23

24

Total and Endogenous Parts of Loanable Funds as a Stand Alone Deficit Modifiers: Comparison of Cptrs. 11, 18, 21 and 24 Test Results 22.1 Comparing Chapters 11 and 18 Stand-Alone Loanable Funds Variables 22.2 Comparing Chapters 11, 18, 21, and 24 Results on What Type of Loanable Fund Best Offsets Crowd Out 22.3 Chapter 22 Conclusions Difficulties Comparatively Testing Total Loanable Funds and Endogenous Loanable Funds Only in the Same Model Comparing Endogenous and Total Loanable Funds Modifiers to Deficit Variables 24.1 Testing the Two-Variable Deficit Consumption Model 24.2 Consumption Comparisons in Models with a Separate Loanable Funds Control Variable 24.3 Consumption Comparisons in Models Without a Separate Loanable Funds Control Variable 24.4 Testing the Two-Variable Deficit Investment Model 24.4.1 Investment Comparisons in Models with a Separate Loanable Funds Control Variable

508

511 513 518

519 519

521 523

527

529 530 533 536 539

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CONTENTS

Investment Comparisons in Models Without a Separate Loanable Funds Control Variable 24.4.3 Investment Comparisons in Models Without a Separate Loanable Funds Control Variable, but with an Added GDP Control Variable 24.5 Summary and Conclusions Reference

xxi

24.4.2

545

547 551 553

Part IX Summary Chapters 25

26

27

Summary of Introductory. Literature Review, and Methodology Chapters (Cptrs 1–3) 25.1 Cptr. 1. Deficits, Crowd Out, and Accommodative Monetary Theory 25.1.1 Actual Accommodative Monetary Policy—Chapters 4–5 25.1.2 Accommodative Monetary Science Chapters 6–24 25.2 Cptr. 2 Summary—Literature Review 25.3 Cptr. 3: Methodology Summary of Crowd Out Theory and Accommodative Monetary Policy Theory (Chapters 4–5) 26.1 Chapter 4—Theory of Crowd Out and Accommodative Monetary Policy 26.2 Chapter 5: The Effectiveness of Accommodating Monetary Policy—The Mechanics Summary of the Science Showing “Crowd Out” Exists and Accommodative Monetary Policy Can Offset It 27.1 Do Changes in Federal Reserve Security Purchases to Offset Crowd Out and Stimulate the Economy Lead to “Pushing on a String” Effects? (Chapter 19)

557 557 558 558 559 559

561 561 562

563

564

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CONTENTS

27.2

Does Stimulative Fiscal Policy Create a “Crowd Out” Problem that Reduces Consumer and Investment Spending, Causing the Fiscal Policies to Be Ineffective? (Cptrs 6, 7, 10–11) 27.3 Does Growth in M1 Offset Crowd Out as Well as Growth in Total Loanable Funds Pool? (Cptr. 12) 27.4 Can Increases in the Total Loanable Funds Pool, Either Endogenously, or Exogenously Through Accommodative FR Increases in Bank Reserves, Offset the Crowd Out Effects of Stimulative Fiscal Policy? (Chapters 8–9, 10–11, 19) 27.5 Are Alternatives to the Total LF Variable Better Crowd Out Modifiers? (Cptrs. 12–24) 27.6 Comparing the Effects of Endogenous and Exogenous Loanable Funds on the Real Economy and Financial Markets? (Cptrs. 10, 20, 21) 27.7 Total Loanable Funds Compared to Alternative Modifiers Reference

565 565

565 566

569 571 574

Part X Overall Conclusions, Definitions and Engineering Equations 28

Overall Conclusions

577

29

Acronyms Used to Define Variables in Equations

581

30

Summary of Engineering Quality Equations in This Book 30.1 Do Deficits Really Cause Crowd out? 30.2 Changes in M1, or Loanable Funds: Which Affect the GDP’s Components More?—Using Full Structural Models to Control for Other Variables’ Effects (Table 12.5)

585 586

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CONTENTS

30.3

30.4

30.5

30.6

Index

Which is the More Accurate Measure of Consumer Crowd Out? The Size of the Deficit alone, or the Deficit Minus any Same Period Increase in the Pool of Loanable Funds? (1 and 2 Variable Deficit Models Tested) Which is a Better Measure of Investment Crowd Out? The Deficit, or the Deficit Reduced by any Same Period Growth in the Pool of Loanable Funds (1 and 2 Variable Deficit Models)? Do Endogenous or Exogenous Increases in Loanable Funds Have the Most Success in Reducing Crowd Out? 30.5.1 Comparing Endogenous and Exogenous Loanable Funds Effects on Consumption—Initial Model 30.5.2 An Alternative Model Comparing Endogenous and Exogenous Effects Do Increases in Loanable Funds Increase Consumer and Business Borrowing? Does Increased Business Borrowing Decrease Consumer Borrowing? (Results Taken from Heim 2021; Equation Numbers are from that Book)

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593

595

595 597

602 605

List of Figures

Fig. 2.1

Fig. 2.2

Japan monetary base and CPI inflation (Note The monetary base has grown by a large amount in Japan since January 2013, with little or no ultimate effect on inflation. The temporary increase in inflation in 2014 was primarily due to an increase in the consumption tax. Sources Organization for Economic Cooperation and Development and Bank of Japan) U.S. versus Canada real GDP (Note Canada and the U.S. are subject to the same basic macroeconomic forces, but over this period the Fed conducted QE and the Bank of Canada did not. Canada actually had slightly better real GDP performance. Sources Bureau of Economic Analysis/Federal Reserve Economic Data (FRED) and Organization for Economic Cooperation and Development)

24

24

xxv

List of Tables

Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 3.7 Table 3.8 Table 3.9 Table 3.10 Table 3.11 Table 3.12 Table 3.13 Table 3.14 Table 3.15

Calculating 2013–2017 real GDP using estimated values of the base year 2005 chain deflator Simulated regression data Changes in regression coefficients and t-statistics associated with loanable funds changes Average yearly increases (+)/decreases (−) in deficits by decade Yearly changes in the deficit in the 1990s Simulation of deficit and surplus effects on sign of government spending coefficients Effects of spending deficit growth on consumption Effects on consumption of loanable funds growth less than spending deficit Effects on consumption of loanable funds growth greater than spending deficit Effects on consumption of declining spending deficit Trends in crowd out significance, and movement in other variables Ratio of standard deviation/average yearly change in standard consumption function variables Single variable deficit significance in standard consumption model (multi-decade samples) Coefficients of modified T ,G variables and stand alone (S + LF) when (S + LF) distribution varies Modifiers tested and test location by chapter

53 56 59 59 61 64 64 65 65 66 68 70 72 74 77

xxvii

xxviii

LIST OF TABLES

Table 5.1

Table 5.2

Table 5.3 Table 5.4 Table 5.5

Table 5.6

Table 5.7

Table 5.8

Table 5.9 Table 7.1 Table 9.1 Table 9.2 Table 10.1A Table 10.1 Table 10.2

Table 10.1AA

Firms from which permanent treasury security purchases were made as part of the quantitative easing program (Q1: 2016; Q1–4: 2014, 2012; and Q3–4: 2010) Permanent treasury security purchases as part of the quantitative easing program (Selected periods Q3: 2010–Q1: 2016) Q4: 2014 purchases of US securities by the federal reserve: $10,517.5 Million FR purchases of treasury and agency securities and growth of the monetary base (Billions) Excess reserves in US depository institutions during recessions and non-recessionary periods (Billions) Real yearly changes in the deficit (T – G) and FR Security Purchases (Tr + A) (Billions of 2005 Dollars) Levels of accommodating monetary policy compared to fiscal deficits in recession years during 1959–2017 (Nominal values) Levels of real accommodating monetary policy compared to fiscal deficits in recession years during 1959–2017 Historical data: Nominal treasuries held by FRB, nominal M1 and real GDP (Billions) Unmodified effects of deficits (Crowd Out) consumption and investment Effects of different loanable funds offset models on crowd out in consumption models Results of different investment models of the effects of loanable funds on crowd out Growth in explained variance when adding unmodified crowd out to a standard model Crowd out effects on consumption, with and without offsetting changes in loanable funds Crowd out effects on consumption, with and without offsetting changes in loanable funds (no stand-alone S + FB) Growth in explained variance when adding crowd out to a standard model

113

115 118 119

121

123

125

127 129 145 169 175 182 185

187 192

LIST OF TABLES

Table 10.3

Table 10.4

Table 10.5 Table 10.6 Table 10.7

Table 11.1D Table 11.1

Table 11.2 Table 11.3 Table 11.4 Table 11.5 Table 11.6 Table 11.7 Table 11.8 Table 11.9 Table 11.10A Table 11.10

Effects of crowd out on investment, with and without loanable funds modification of the deficit; stand alone variable included Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases Endogenous and exogenous changes in loanable funds: effects on consumption crowd out Endogenous and exogenous changes in loanable funds: effects on investment crowd out Endogenous and exogenous changes in loanable funds: effects on crowd out (GDP control added to Table 10.6 model) Growth in explained variance when adding crowd out to a standard model Comparing robustness over time of effects on consumption of crowd out, with and without compensating loanable funds (separate stand-alone S + FB variable included) Changes in regression coefficients and t-statistics associated with loanable funds changes Effects of adding “crowd out” and “crowd in” periods Simulated results of combining statistically significant “crowd in” and “crowd out” samples Effects of adding a separate, sand alone loanable funds variable to a crowd out model Crowd out variable coefficients, t-statistics and R 2 in different sample periods Annual growth (+)/decline (−) in deficits 1990–2000 Annual growth (+)/decline (−) in Deficits 1960–2000 Robustness of effects of crowd out on consumption (no stand-alone loanable funds control variable) Growth in explained variance when adding crowd out to a standard model Effects on investment of crowd out, with and without modification by loanable funds (stand-alone (S + FB) and GDP variables included)

xxix

194

197 200 202

203 216

219 222 223 224 224 225 228 229 231 232

233

xxx

LIST OF TABLES

Table 11.1B Table 11.10B Table 11.11

Table 12.1

Table 12.2

Table 12.3

Table 12.4

Table 12.5

Table 13.1

Table 13.2 Table 13.3

Table 14.1

Table 14.2

Base line model with only deficit variables added: estimates of consumption crowd out Base line model with deficit variables added: estimates of investment crowd out Estimates of investment of crowd out, with and without modification by loanable funds (no stand alone (S + FB); GDP variable included) Effects on standard consumption model of an additional separate variable, with and without also adding it as a deficit modifier Robustness over time of effects on consumption of crowd out, with and without offsetting loanable funds (no stand-alone modifying variables were used) Comparing robustness over time of effects on investment of crowd out, with and without accommodating loanable funds modification Comparing robustness over time of effects on investment of crowd out, with and without loanable funds and M1 modification (No stand-alone modifier) Effects on investment of crowd out, with and without loanable funds and M1 modification (no stand-alone modifier, GDP control added) Results of different consumption models of the effects of FR purchases on crowd out (1960–2010 data sample) Results of different consumption models of the effects of loanable funds on crowd out Statistical results for consumption crowd out models using different modifiers β (t-statistic), R 2 (1960–2010 data sample only) Effects of (S + FB) − (Tr + A) on consumption crowd out, with and without deficit modification by FR securities purchases (tr + a) Effects on investment of crowd out, with and without FR securities purchases as deficit offset, with stand alone (S + FB) − (Tr + A)

235 269

271

289

293

299

301

307

325 331

335

343

347

LIST OF TABLES

Table 15.1

Table 15.2

Table 15.3

Table 15.4

Table 16.1

Table 16.2 Table 16.3

Table 16.4

Table 17.1

Table 17.2

Table 17.3

Crowd out effects of deficits on consumption W/ and W/O deficit modification by FR securities purchases; stand-alone (S + FB) − (Tr + A) control for endogenous sources of loanable funds Effects of crowd out on consumption, with and without modification by FR securities purchases (no stand-alone [S + FB] − [Tr + A] control variable) Crowd out effects of deficits on investment W/ and W/O deficit variable modification by FR securities purchases (controlling for endogenous sources of loanable funds (S + FB) − (Tr + A) Effects on investment of crowd out, with and without accommodating FR securities purchases (no separate [ST otal −SG ] control variable, but control for GDP included) Comparing robustness over time of effects on consumption of crowd out, with and without deficit modification by accommodating FR securities purchases Yearly change in deficit and FR open market purchases (billions of 2005 dollars) Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases Real yearly changes in the deficit (T − G) and FR security purchases (Tr + A) (billions of 2005 dollars) Crowd out effects of deficits on consumption with and without deficit modification by FR securities purchases Effects of crowd out on consumption, with and without modification by FR securities purchases (no separate (S + FB) − (T − G) control variable) Effects on investment of crowd out, with and without FR securities purchases modifiers; separate private saving and foreign borrowing control variable included

xxxi

361

363

365

366

381 385

388

395

408

413

415

xxxii

LIST OF TABLES

Table 17.4

Table 18.1 Table 18.2

Table 18.3A Table 18.3

Table 18.4

Table 18.5

Table 20.1

Table 20.2

Table 20.3

Table 20.4

Table 21.1A

Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases (No separate (S T otal −S G ) control variable) Effects of on consumption crowd out W/WO stand-alone endogenous LF variable Effects on consumption of crowd out, with and without compensating FR purchases (no separate (S + FB) − T + A) control variable) A base line estimates of investment crowd out Comparing robustness over time of Effects on investment of crowd out, with and without accommodating loanable funds modification Effects of rowd out on investment, with and without loanable funds accommodation (no separate (S + FB) − (Tr + A) or GDP control variable) Effects of on investment crowd out, with and without loanable funds accommodation (no separate (S + FB) − (Tr + A) control variable, but GDP control variable added) Comparing robustness over time of effects of crowd out on consumption, with and without modification of deficit variables by loanable funds Robustness over time of effects on consumption of crowd out, with and without offsetting loanable funds (no stand-alone (S + FB) or (S + FB – Tr – A) control variable Comparing robustness over time of effects on investment of crowd out, with and without accommodating loanable funds modification, net of FR purchases Comparing robustness over time of effects on investment of crowd out, with and without accommodating loanable funds modification Consistency of coefficient and t-statistic on loanable funds variable in six different time periods, using model given in Eq. 21.1A

417 429

430 435

437

438

444

458

461

467

469

485

LIST OF TABLES

Table 21.1

Table 21.2

Table 21.3

Table 21.4

Table 21.5

Table 21.6

Table 21.7

Table 21.8

Table 21.9

Table 21.9A

Table 21.10

Table 21.11

Consistency of coefficient and t-statistic on total loanable funds variable in six different time periods, using model given in Eq. 21.1 Consistency of coefficient and t-statistic on FR purchases variable in six different time periods, using model given in Eq. 21.2 Consistency of coefficient and t-statistic on combined loanable funds and FR purchases variable in five different time periods, using model given in Eq. 21.3 Consistency of coefficient and t-statistic on total loanable funds and FR purchases variable in six different time periods, using model given in Eq. 21.4 Consistency of coefficient and t-statistic on national savings and FR purchases variable in six different time periods, using model given in Eq. 21.5 Consistency of coefficient and t-statistic on separate loanable funds (net of FR purchases) and FR purchases variables in six different time periods, using model given in Eq. 21.6 Consistency of coefficient and t-statistic on loanable funds variable (S + FB) in six different time periods, using model given in Eq. 21.7 Consistency of coefficient and t-statistic on FR security purchases variable in six different time periods, using model given in Eq. 21.8 (investment) Consistency of coefficient and t-statistic on single loanable funds and FR security purchases variable in six different time periods, using model given in Eq. 21.9 Consistency of coefficient and t-statistic on single loanable funds and FR security purchases variable in six different time periods, using model given in Eq. 21.9 with a GDP control variable added Consistency of coefficient and t-statistic on total loanable funds and FR security purchases variables in six different time periods, using model given in Eq. 21.10 Consistency of coefficient and t-statistic on separate (S) and FR security purchases variables in six different time periods, using model given in Eq. 21.11

xxxiii

486

488

491

492

494

496

499

502

504

506

507

509

xxxiv

LIST OF TABLES

Table 21.12

Table 22.1 Table 24.1

Table 24.2

Table 24.3

Table 24.4

Table 24.5

Table 27.1 Table 27.2 Table 27.3

Coefficients and t-statistics on loanable funds (net of Tr + A) and FR security purchases variables in six different time periods, using model given in Eq. 21.12 Comparisons of Totalloanable Funds to Endogenous Loanable Funds Comparing robustness over time of effects on consumption of crowd out, with and without compensating loanable funds and (Tr + A) modifications Robustness over time of effects on consumption of crowd out, with and without offsetting loanable funds and (Tr + A) modifications. No stand-alone (S + FB) control variable Effects crowd out on investment, with and without compensating loanable funds modifications Robustness over time of effects on investment of crowd out, with and without offsetting loanable funds and (Tr + A) modifications. No stand-alone (S + FB) control variable Robustness over time of effects on investment of crowd out, with and without (S + FB) and (Tr + A) modifications (No stand-alone (S + FB – Tr – A) control variable; GDP control added) U.S. banking system excess reserves (% of total reserves) Explanatory power of models with total loanable funds (LF) variables, compared to baseline Statistical models tested to determine what form of increased liquidity best offset crowd out

511 520

534

537

543

544

548 564 566 572

PART I

Introductory Chapters

CHAPTER 1

Introduction

1.1 The Crowd Out Problem and Accommodative Monetary Policy John Maynard Keynes (1936) created a revolution in macroeconomics. He argued that in periods of economic recession or depression, governments could stimulate the economy and help restore full employment by cutting taxes or increasing government spending. This was a “demand side” argument as to what drove the economy, and seemingly at odds with the “supply side” arguments of classical economists. In 1983 one of Harvard’s greatest economists and macroeconomic modelers, Otto Eckstein, noted with great disappointment that economists, nearly 50 years after Keynes, had failed to reach any general agreement whether these Keynes ian stimulus policies worked. Worse, this author’s own studies, an additional 34 years after Eckstein, indicated the continuing (and embarrassing) lack of consensus on this issue, an issue most central to the question of whether macroeconomics has anything important to say to policy makers. There clearly was a need for a science-based work to resolve the question once and for all. Toward that end, in 2017, a book containing what most observers would argue is probably the most exhaustive scientific study ever done of the effects of Keynesian fiscal stimulus programs, and their effect on the economy (Heim 2017). Its statistical testing of hundreds of models and time periods concluded Keynesian stimulus programs © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_1

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1. could stimulate the economy as Keynes argued, but that unfortunately, 2. these stimulative effects were commonly offset by reduced private spending due to the “crowd out” problem caused by deficits (an issue which Keynes never seriously addressed). Given a constant pool of loanable funds, the need to borrow money to fund Keynesian stimulus programs reduces (“crowds out”) what funds are available for consumers and businesses to borrow, reducing their spending. This reduction has a negative effect on spending that offsets the positive Keynesian stimulus effect, leaving the stimulus ineffective. 3. (1) and (2) left the impression Keynesian stimulus programs didn’t work, when the truth was, they did, but their stimulus effects were offset by a simultaneously occurring separate effect, crowd out. Keynes had failed to address this in his analysis. The study found overwhelming empirical proof, that because of the “crowd out” problem fiscal stimulus programs generally did not seem to lead to any improvement in the economy. Keynesian economists have long argued that the “crowd out” problem is not fatal; that Federal Reserve “accommodative” monetary policy, if undertaken at the same time the Keynesian stimulus programs are undertaken, eliminates the “crowd out” problem and allow stimulus programs to work as Keynes intended. This is done by increasing the loanable funds pool, which increases the funds available for consumers and businesses to borrow. The purpose of this book is to comprehensively and scientifically test the assertion that accommodative monetary policy can eliminate the “crowd out” problem, allowing fiscal stimulus programs (deficit financed tax cuts or increased government spending) to stimulate the economy as intended. The book’s goal is intended to be the largest scale scientific test ever performed on this topic. It includes nearly 1000 separate statistical tests on the US economy testing different parts or all of the period 1960– 2010. These tests focus on whether accommodative monetary policy, which increases the pool of loanable funds, can offset the crowd out problem. This book, employs what we believe to be the best scientific method available to economists for examining this type of problem, 2SLS structural models. It concludes accommodative monetary policy has a systematic enough effect on loanable that it could have offset crowd

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5

out problems, but until the quantitative easing program, Federal Reserve efforts to accommodate fiscal stimulus programs were not large enough to offset more than 23–44% of any one year’s crowd out problem. That provides much the science part of the answer as to why accommodative monetary policy didn’t accommodate; too little of it was tried. In addition, a large part of the book details tests to determine whether accommodative monetary policy by the Fed was more or less effective in stimulating the economy, than was growth in the part of the loanable funds pool that was endogenous, i.e., occurred because of economic growth or other changes in economic conditions. Hundreds of tests were performed, testing different models, and testing each in 6–18 different time periods to determine the answer. The answer was that a dollar increase in the loanable funds pool, created endogenously, had 3–5 times the positive effect on the economy as an increase in loanable reserves due to the Fed’s accommodative monetary policy. There is no theoretical reason why an increase in the pool due to accommodative monetary policy should have less effect than a change due to endogenous growth in the pool. But the administrative mechanics with which the Fed implements accommodative monetary policy appears to provide at least part of the answer. The monetary policy mechanics part that contributed to the Federal Reserve’s failure to accommodate deficits as effectively as endogenous growth involves flaws in the actual methods used by the Federal Reserve as it attempts to increase bank reserves, so as to replace lost borrowing power due to “crowd out,” i.e., enact accommodative monetary policy. 1. Federal Reserve purchases of securities were done from banks, but the wrong type of banks (investment banks rather than commercial and savings banks) and 2. much of the Federal Reserves securities purchases were from foreign banks. In some cases this has increased the loanable funds pool in foreign countries, which helps their economies, but is of little or no use in stimulating the US economy. The Fed mostly buys securities from investment banks and brokerages, who sell the Fed securities mainly so they can buy other securities. Securities purchases by investment bankers do not in any direct way increase the GDP or reduce unemployment (though they do help Wall Street). Fed

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securities purchases would have been much more effective at restoring private borrowing lost to crowd out, if the Fed had restricted its purchases to retail banks, i.e., commercial and savings banks whose main line of business is loaning to those that wished to buy houses, cars, machines, and factories. Such purchases do increase the GDP and lower unemployment, i.e., they help “Main Street.” Worse, many of the Fed’s purchases were from foreign banks, with no guarantee payment by the Fed would be deposited and spent in the United States at all. If not, loanable funds in the United States are not increased, and no offset to the crowd out problem occurs. Hence, the fiscal stimulus does not work. In one period sampled (2014), about 40% of all Fed purchases were from foreign banks and brokerages

1.2

Individual Chapter Contents and Findings

A summary of how these science and policy issues are examined in the remaining chapters of this study is presented below. The findings of each chapter are also summarized. In Chapter 2, we look at previous literature on the subject. We find that the business press nearly unanimously agrees that FR security purchases during the Quantitative Easing period helped Wall Street, the bond and stock markets, by pushing up stock and bond prices, but did not much affect Main Street, i.e., the GDP and unemployment. The academic and professional literature agreed QE had a positive effect on Wall Street stock and bond market prices, but was split on whether there was any positive effect on the GDP and unemployment to go along with it. Chapter 3 discusses the methodology used in this study. The models tested are fairly standard structural models of consumption and investment’s determinants (income, interest rates, profits, etc.), with deficit variables added to measure crowd out effects. They also include either total loanable funds, M1, endogenous, or exogenous loanable funds variables added to measure the effects of each of these liquidity-enhancing variables. Roughly 1000 tests of specific consumption and investment models and time periods were undertaken. Initial findings for any model are tested in multiple time periods to ensure results are replicable. The importance of replication in any economic study (preferably before publication, so as not to waste the reader’s time) is discussed.

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INTRODUCTION

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Techniques used to control for typical time series regression problems are discussed, including stationarity, endogeneity, multicollinearity, serial correlation, and heteroskedasticity. Particular difficulties obtaining significant results when mixing data from “crowd out” and crowd in” periods, or mixing periods in which there is no movement in key deficit variables with periods in which there is, are discussed. Guidelines for acceptable percentages of the data being of one category or the other are suggested. Circumstances under which creating a loanable funds-modified deficit variable is an appropriate way of modeling the effectiveness of changes in loanable funds in reducing crowd out are discussed, as well as circumstances in which a stand-alone variable representing loanable funds should also be used. In short, in consumption models, an increase in loanable funds has two effects: a positive crowd out-reducing effect, and a negative effect stemming from the ceteris paribus (partial derivative) nature of the process of estimating marginal effects using regression, i.e., it measures the effect of an increase in loanable funds on consumption holding income and other variables in the model (taxes, government spending, etc.) constant. That being so, an increase in savings, i.e., loanable funds, i.e., can only occur if there is a reduction in consumption. Two separate effects require two separate variables if one is to see each effect separately. Chapter 4 presents the theory of how crowd out occurs when budget deficits occur, how crowd out negatively affects the GDP, and how changes in M1 or loanable funds can offset it. The basic theory is presented in both literary and mathematical form. Chapter 5 of this study is a policy analysis chapter. It examines the Federal Reserve’s (FR) use of accommodative monetary Policy. It examines whether using investment banks, brokerages, and foreign banks, reduces the effectiveness of accommodative monetary policy (compared to using only US commercial and savings banks), and concludes it does. Test results showing this are presented. This chapter also discusses the quantitative inadequacies of accommodative monetary policy before 2008, noting that only after 2008 was accommodating monetary policy quantitatively large enough to fully offset the crowd out effects of deficits. It also notes the problematic nature of Federal Reserve securities purchases from foreign securities sellers that are not deposited in the US banking system, a factor which reduces the extent to which Fed securities purchases can offset crowd out.

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1.2.1

Estimating Crowd Out’s Actual Effects

Chapter 6 tests to determine if the crowd out problem actually occurs. Chapter 7 extends the initial tests in Chapter 6 tests to different time periods to ensure initial results portray underlying deeply scientific relationship, not just spurious results. In short, it tests whether initial results were worthy of publishing, i.e., could be shown to be replicable in other time periods and models. The goal of this study was to use this procedure to create results so persuasive that analysts would see no need for further studies in this area. We feel we have succeeded at this. 1.2.2

Total Loanable Funds as a Crowd Out Modifier

Several chapters statistically test to demonstrate how effectively growth in the total pool of loanable funds can offset crowd out (Chapters 8– 11). Chapter 8 develops the methodology to test the extent to which the negative effects of crowd out can be offset by changes in the size of the loanable funds pool. It concludes that if the increase in loanable funds is large enough, it can completely offset crowd out. Chapter 9 test different ways of modeling the combined effects of deficits and loanable funds offsets, either as one “modified” deficit variable, or as separate deficit and loanable funds variables. As was noted earlier in discussing methodology, for consumption models, modifying the deficit variable and including a stand-alone modifier variable is the best way to model. For investment, just the deficit modifier may be enough. Chapters 10 and 11 verify that the initial Chapter 8 results can be (and were) replicated in multiple time periods and models. Chapter 12 determines whether M1 or loanable funds best explains how effectively crowd out is offset, and concludes total loanable funds is the better measure. The next two groups of chapters in this study examine whether just the exogenous part of total loanable funds (i.e., the part generated by FR security purchases) or just the endogenous part resulting from changing economic conditions is more important, and whether either part is as impactful when used alone, as the two parts combined into one total loanable funds variable.

1

1.2.3

INTRODUCTION

9

Exogenous Loanable Funds Modifiers (FR Securities Purchases)

How well does only the FR purchases part of the pool of loanable funds work to offset crowd out is examined in (Chapters 13–19). Chapter 13 just controls for FR purchases. Chapters 14 and 15 test the effects of adding FR purchases as a deficit modifier controlling for all other sources of variation in loanable funds. Generally, both chapters’ models explain as much variance as the total loanable funds models of Chapters 10 and 11, the models we generally found to be the best. Since we are controlling for both parts of the total in each of these models, as we did in chapters 10 and 11—just differently, we should not be surprised. Chapters 16 and 17 test for the effect of FR purchases separately controlling for the level of only private savings (rather than total loanable funds net of FR purchases as in Chapters 14 and 15). These models did not explain variation in consumption and investment as well as the total loanable funds models of Chapters 10 and 11. Chapter 18 tests for crowd out effects using FR purchases as a deficit modifier, while controlling for any endogenous changes to the loanable funds pool that may occur at the same time. Here again, the total loanable funds modifier was found to better explain how much crowd out is actually reduced when liquidity in the system increases. 1.2.4

Endogenous Loanable Funds Modifiers

In the next set of tests, we examine how effectively growth in just the endogenous part of the pool of loanable funds can offset crowd out (Chapters 20–24). Chapter 20 examines using endogenous loanable funds growth to reduce deficits, while also using both endogenous and exogenous loanable funds as control variables. These models are compared with models that use total loanable funds (LF) as a deficit modifier and a standalone variable. The chapter concludes that total loanable funds modifiers provide a more accurate definition of how much loanable funds reduce crowd out. Chapter 21 compares models that use only stand-alone variables as modifiers. The models compared include a total LF model, an exogenous modifier model, an exogenous and total LF models, and a model with separate endogenous and exogenous, stand-alone variables in same model. For both consumption and investment, it finds the total loanable funds model is generally the best (explains the most variance).

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Chapter 22 compares stand-alone endogenous LF models to total LF models and finds total LF models explain more variation in consumption and investment. Chapter 23 summarizes some previous chapters’ test results. Chapter 24 compares endogenous and total LF models. Total loanable funds models explained the most variance in most cases, and hence, when subtracted from the deficit, provides the better measure of actual crowd out effects. 1.2.5

Summary Chapters

Chapters 25–30 summarize the results of all earlier chapters. Chapter 25 summarizes the introductory, literature and methodology Chapters (1– 3). Chapter 26 summarizes the theory Chapter (4), and Chapter (5) analyzes the mechanics of implementing accommodative monetary policy, and how successful it has been. Chapter 27 summarizes the tests undertaken to determine if crowd out exists, and if so, how best to scientifically measure the extent to which changes in loanable funds, or reasonable variants of them, can offset it and which appear to work best (Chapters 6–24). Chapter 28 presents some overall conclusions. Chapter 29 provides definitions of acronyms used in equations to represent variables. Chapter 30 is an engineering manual-type of presentation of the book’s key result, generally defining an “engineering” quality result found as the average regression coefficient and t-statistic results for six different, though overlapping, time periods tested for our best models.

1.3

Summary of Key Findings

To conclude this introduction, we offer an advanced look at the book’s major findings. They may be summarized as follows: 1. Fiscal stimulus programs definitely can stimulate the economy, but in doing so, they create crowd out problems which usually leaves fiscal stimulus programs ineffective. 2. If the pool of loanable funds grows sufficiently, it can offset crowd out completely, leaving fiscal stimulus programs fully effective. There is evidence that a complete offsetting of crowd out by increases in the loanable funds pool occurred during the Quantitative Easing

1

INTRODUCTION

11

(QE) period due to Federal Reserve actions, but not before. The size of the pool is policy controllable by the Federal Reserve. 3. Total loanable funds is a better measure of the actual crowd out modifying effect than either its endogenous part or its exogenous part (FR security purchases) alone, though endogenous explains almost of the variation that total does. Total loanable funds also explains more variance than M1. 4. While the level of loanable funds is policy controllable by the Federal Reserve, it is not likely that its current methods of exercising this control have much positive effect on the GDP or lowering unemployment; perhaps only a fifth to a third as much as a same dollar increase in the endogenous loanable funds pool, which is mostly determined by economic growth. This is because the Federal Reserve historically, has relied on purchasing securities from investment banks and brokerages. These institutions typically only sell securities to the Fed (or anybody else) to obtain funds to buy other securities. Securities trading is what they do for a living. This helps inflate bond market prices, helping Wall Street The Federal Reserve, historically, has relied on purchasing securities from investment banks and brokerages. Such institutions most typically only sell securities to the Fed (or anybody else) to obtain funds to buy other securities. After all, securities trading is what they do for a living. This helps inflate bond market prices, helping Wall Street, but does little to increase the demand for real goods and services necessary to raise GDP and lower unemployment, which is what is needed if Federal Reserve actions are to help Main Street. If this hypothesis is correct, the results should indicate a smaller marginal effect on consumption and investment of a dollar’s increase in loanable funds due to FR security purchases than by a dollar’s increase due to growth in the endogenous portion of the loanable funds pool. And this is exactly what we see. For consumption, in 6 of 6 periods tested, the estimated marginal effect is lower for increases in FR purchases than for increases in the endogenous part of the loanable funds pool. For investment the marginal effect of an increase in loanable funds is lower for FR purchases compared to endogenous growth in 5 of 6 periods tested (Chapter 17, Tables 17.5 and 17.6).

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The Federal Reserve’s purchases of securities would more likely stimulate the GDP and reduce unemployment if its purchases of securities were restricted to purchases from US commercial and savings banks. It is these banks, not investment banks and brokerages, that are in the business of directly lending money to consumers and businesses that want to buy, cars, houses, machinery, and other goods and services, the very actions which will raise GDP and reduce unemployment. 5. In addition, many are foreign banks with less incentive to invest Federal Reserve money in the United States than US banks would have. 6. To deficit, or not to deficit, is a policy choice which has huge implications as to whether growth in the future is skewed toward growth in private or public goods. With no deficit, growth in loanable funds increases the GDP by increasing private investment and spending. With a deficit created by a fiscal stimulus program, the increase in loanable funds go to offset crowd out effects (i.e., keep private spending at old levels so the stimulus program works, which also raises GDP. The increase in GDP due to the fiscal stimulus is likely to be more oriented toward production of public goods than the nodeficit increase in private spending characterizing that leads to that increase in GDP. Hence doing deficits amounts to policy decision about private vs public goods.

References Eckstein, O. (1983). The DRI Model of the U.S. Economy. New York: McGrawHill Book Company. Heim, J. J. (2017). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan. Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. London: Macmillan.

CHAPTER 2

Literature Review

This literature review is based on an exhaustive survey of recent literature on the effect of accommodative monetary policy on 1. the stock and bond markets, 2. the GDP, and 3. inequality.

2.1

Summary of Findings

The business press concludes the main beneficiaries of the Quantitative Easing (QE) program have been the owners of stocks and bonds, who have seen the prices of those assets rise dramatically due to QE, and that this has increased inequality (see, for example, Warsh, K., former FR Board member, WSJ 8/24/2016). The business press was also virtually unanimous in assessing the Fed’s attempts to raise GDP and lower unemployment) using QE to stimulate the economy, were a failure. Professional and academic press studies tend to find monetary policy has had a positive effect on both the stock and bond markets, and on GDP. This is particularly true since the beginning of the QE period in 2008.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_2

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2.1.1

Stocks and Bonds

All studies of the effects of the huge increases in FR security purchases during the QE program, without exception, in the business press and academic/professional papers reviewed, found that bond interest rates were lowered (bond market prices increased). A one trillion USD purchase of long-term bonds reduced 10-year US Treasury yields and low-grade corporates by about 30–50 basis points while MBS yields declined by 66 basis points and mortgage rates fell further still…. (Krishnamurthy and Vissing-Jorgensen 2011). 1 Trillion in bond purchases by Fed reduced treasury and corporate bond rates 0.3–0.5%; MBS rates declined by 0.66% Krishnamurthy and Vissing-Jorgensen (2011). Bond purchases equal to 10% of GDP lowered interest rates an average of 0.68% in 28 studies reviewed (Gagnon 2016). Mortgage rate dropped 1.3% (Caixa Bank Research 2018). Klein and Evans (1968), Eckstein (1983), Fair (2004), and Heim (2017) found the same result for bond and mortgage markets, but did not test for stock market effects. Federal Reserve security purchases effectively funded 55% of treasury debt issued during the Obama presidency, compared to 10% during World War II (Gramm and Saving 2017). Bank reserves have grown as a result of quantitative easing to 13.07 for every dollar they are required to hold and have not expanded bank lending (Gramm and Saving 2017), indicating a “pushing on a string” effect of FR purchases increases during the QE period. 2.1.2

GDP

Most professional/academic papers reviewed found stimulative monetary policy have positive effects on GDP or in reducing unemployment. Some papers also found positive effects on inflation. Only 3 found no effect on GDP of QE or earlier efforts by the Fed to increase asset purchases through open market operations. (Business Press articles consistently concluded just the opposite: massive FR security purchases during the QE period had no effect on the GDP or unemployment.) A summary of professional literature findings indicates: QE: 0% effect on inflation or economic growth (Williamson, S., St. Louis FRB 2017). QE lowered unemployment rate 1% … (Wu and Xia 2016). $40 billion in asset purchases increases output 0.4% Bhattarai et al. (2015). Asset purchase equal to 1% of GDP raises GDP 0.58% Weale and

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LITERATURE REVIEW

15

Wieladek (2016). A$600 billion increase in asset purchases increases GDP 0.13% (Chen et al. 2012). Doubling the size of FR balance sheet increases GDP by 0.45% for QE2 and 0.12% for QE3 (Bhattarai et al. 2015). QE1 was estimated to raise GDP 1.0%. Accommodating monetary policy had a positive effect on GDP, but of negligible size: only 0.4% of the size of the combined fiscal and monetary stimulus itself. (Heim 2017), Klein and Evans (1968), Eckstein (1983), and Fair (2004) also found the same result for effect of monetary policy on GDP. Long-term multiplier effects of monetary policy have been small (0.1– 0.4) (Leeper et al. 2017). Multipliers 1.5 when monetary policy is at the zero lower bound (ZLB); less above it (Wataru et al. 2018). The output multiplier is 0.5–1.9, depending on the shadow interest rate (Wataru et al. 2018). Conclude: The professional/academic literature concludes Federal Reserve asset purchases between $40 billion and roughly $1 trillion increased GDP from near 0.00% to 0.58%, with no correlation of study results with purchase size. Multiplier results were similarly mixed, with multiplier effects of monetary stimulus generally varying from 0.5 to 1.9. Business Press articles consistently concluded just the opposite: they found that massive FR security purchases during the QE period had no effect on the GDP. 2.1.3

Inequality

Summary of Effects: All three professional press studies surveyed found changes in monetary policy increased inequality. However, the results of one study indicated contractionary monetary policy changes did it, while the other two said expansionary monetary policy increased inequality. Business press reports found FR security purchase programs (QE) increased inequality.

2.2 2.2.1

Detailed Findings

Assessment of Monetary Policy Effectiveness in the Business Press

It is commonly asserted in the business press that when the FR adopts a stimulative monetary policy, i.e., purchases securities in the open market,

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primarily, it results in a financial markets gain, but not a real economy gain, as noted in the quotes below: 2.2.1.1

Stock Market Effects

…The Federal Reserve’s main ministration for a weak recovery, after all has been stoking a “wealth effect.” By levitating the stock portfolios of the top 1%, jobs and wage growth for the other 99% would be stimulated. “Higher stock prices will boost consumer wealth and help increase confidence” once explained ex-Fed chief Ben Bernanke. It hasn’t worked. The only confidence simulated has been the confidence of hedge funds that stocks might be a good bet in the short term if central banks are printing money… (Jenkins, H., WSJ 11/7/2014)

and …Easy money is driving up the prices of stocks, bonds, houses…central banks are unleashing easy money to fight an imaginary villain, consumer price deflation, at the risk of feeding a real monster, asset price inflation… (Sharma, R., WSJ 5/12/2015)

and …Since the Fed began aggressive monetary easing in 2008,…nearly 60% of stock market gains have come on those days, once every six weeks, that the Federal Open Market Committee announces its decisions…Mr. Trump was basically right in saying that Fed policy has done more to boost the prices of financial assets-including stocks, bonds and housing-than it has done to help the economy overall…Much of the Fed’s easy money has gone into financial engineering, as companies borrow billions of dollars to buy back their own stock…That kind of finance does more to increase asset prices than to help the middle class… (Sharma, R. Chief Global Strategist, Morgan Stanley Investment Management. WSJ 9/29/2016, p. A13) …We were skeptical of the later bouts of QE…Asset prices are up and the wealthy are better off, but the working stiff is still waiting for the economic payoff… (Editorial, WSJ, 5/1/2015a) …the Fed’s great monetary experiment since the recession ended in 2009 looks increasingly like a failure. Recall the Fed’s theory that quantitative easing (bond buying) and near-zero interest rates would lift financial assets,

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which in turn would lift the real economy. But while stocks have soared, as have speculative assets like junk bonds and commercial real estate, the real economy hasn’t. This remains the worst economic recovery by far since World War II… (WSJ editorial, 8/23/2015b)

2.2.1.2

Bond Market Effects; Interest Rate Effects

…Easy money is driving up the prices of stocks, bonds, houses…central banks are unleashing easy money to fight an imaginary villain, consumer price deflation, at the risk of feeding a real monster, asset price inflation… (Sharma, R., WSJ 5/12/2015) …We were skeptical of the later bouts of QE…Asset prices are up and the wealthy are better off, but the working stiff is still waiting for the economic payoff… (Editorial, WSJ, 5/1/2015a) …quantitative easing (QE)…zero to negative interest rates and detailed guidance on future monetary policy amount to…(bond)…market manipulation on a grand scale. (Ip, G. WSJ 7/19/2017)

2.2.1.3

GDP Effects

…We were skeptical of the later bouts of QE…Asset prices are up and the wealthy are better off, but the working stiff is still waiting for the economic payoff… (Editorial, WSJ, 5/1/2015a) …the Fed’s great monetary experiment since the recession ended in 2009 looks increasingly like a failure. Recall the Fed’s theory that quantitative easing (bond buying) and near-zero interest rates would lift financial assets, which in turn would lift the real economy. But while stocks have soared, as have speculative assets like junk bonds and commercial real estate, the real economy hasn’t. This remains the worst economic recovery by far since World War II… (WSJ editorial, 8/23/2015b) …From the beginning of 2008 to the present, more than half the increase in the value of the S&P 500 occurred on the day of Federal Open Market Committee decisions…it appears to make monetary policy with the purpose of managing financial asset prices, …bolstering the share prices of public companies… (Warsh, K., former FR Board member, WSJ 8/24/2016)

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And …So massive were the Fed purchases of treasury debt and mortgagebacked securities that the central bank effectively funded 55% of the treasury debt issued during Mr. Obama’s presidency, as compared with less than 10% during World War II….Recall that the Fed’s bloated balance sheet is the mirror image of bank reserves, which have swollen as a result of the central bank’s various quantitative easing programs…to $13.07 for every dollar they are required to hold…These massive excess reserves have not expanded bank lending or the money supply because the Fed now pays interest on them…in essence converting them to interest-bearing Fed securities… (Gramm, P. and Saving, T, WSJ, 5/18/2017)

And …The 2007–08 financial crisis was also followed by vast monetary expansion…The Fed’s expansion featured a dramatic rise in excess reserves…Remarkably, the strong monetary growth came without inflation. The absence of inflation is surprising but may have occurred because weak opportunities for private investment motivated banks…to hold the Fed’s added obligations…(i.e., reserves)…despite the negative real interest rates paid…the key factor is the flight to quality stimulated by the heightened perceived risk in private investment… (Barro, R. WSJ, 9/20/2016)

2.2.1.4

Inequality Effects

…(The Fed)…expresses grave concern about income inequality while refusing to acknowledge that its policies unfairly increased asset inequality…From the beginning of 2008 to the present, more than half the increase in the value of the S&P 500 occurred on the day of Federal Open Market Committee decisions…it appears to make monetary policy with the purpose of managing financial asset prices, including bolstering the share prices of public companies… (Warsh, K., former FR Board member, WSJ 8/24/2016)

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Assessment of Monetary Policy in the Academic/Professional Literature Stock Market Effects

…we find that fund investors in countries with decreased real interest rates shift their portfolio investment out of the money market and into the riskier equity market. This produces the strongest equity price increase in countries where domestic institutional investors hold a large share of the countries’ stock market capitalization.… (Haur and Lai 2014). Method: Regression of asset fund inflows on short-term interest rates using lagged fund values and lagged market values as controls. …We show that event studies provide very strong evidence that U.S. unconventional policy announcements have strongly influenced international bond yields, exchange rates, and equity prices in the desired manner…. (Krishnamurthy and Vissing-Jorgensen 2011) Method: Event Study. …$1 trillion purchase … raised stock prices by perhaps 1-1.5 percent… (Neely 2015) Method: Event Study; Kiley (2018). …the cumulative financial market impact of the FED’s LSAP program is equivalent to an unanticipated cut in the federal funds target rate that ranges between zero (for three-month yields and 197 basis points with the response of stock prices…within this interval (for ten-year yields)… (Rosa 2012) Method: Event Study. ….This paper investigates the impact of the unconventional policies implemented by the Federal Reserve, the Bank of England, the European Central Bank, and the Bank of Japan on the returns on a broad class of assets…for some economies and periods we also find an impact on …stock prices… (Hosono and Isobe 2014) Method: Event Study. …Monetary policy actions since 2008 have influenced long-term interest rates through forward guidance and quantitative easing. I propose a strategy to identify the comovement between interest rate and equity price movements induced by monetary policy when an observable representing policy changes is not available. A decline in long-term interest rates induced by monetary policy statements has a larger positive effect on equity prices prior to 2009 than in the subsequent period. This change appears to reflect

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the impact of the zero lower bound on short-term interest rates…A decline in long-term interest rates induced by monetary policy statements prior to 2009 is accompanied by a 6- to 9-percent increase in equity prices. This association is substantially attenuated in the period since the zero-lower bound has been binding - with a policy-induced 100 basis-point decline in 10-year Treasury yields associated with a 1½- to 3-percent increase in equity prices. (Kiley 2018) …Unlike other debt, most bank loans have floating rates mechanically tied to monetary policy rates. Hence, monetary policy can directly affect the liquidity and balance sheet strength of firms through existing loans. We show that firms—especially financially constrained firms—with more unhedged loans display a stronger sensitivity of their stock price, cash holdings, inventory, and fixed capital investment to monetary policy. This effect disappears when policy rates are at the zero lower bound, revealing a new limitation of unconventional monetary policy. The floating-rate channel is at least as important as the bank lending channel operating through new loans…. Using market-based monetary policy surprise measures as in Kuttner (2001) and Gurkaynak et al. (2005), we find that while a typical stock price decreases about 4 to 5 percent in response to a 100 basis point (bp) surprise increase in the federal funds rate, the stock price of a firm that has one standard deviation more bank debt relative to assets decreases about 1.6 percent more. (Ippolito et al. 2018) Method: DSGE w/ calibration. …This study examines the impact of unconventional monetary policies on the stock market when the short-term nominal interest rate is stuck at the zero lower bound (ZLB). Unconventional monetary policies appear to have significant effects on stock prices and the effects differ across stocks… (Wu 2018) Method: Vector Autoregression. …The operation of the portfolio balance channel has been emphasized by monetary policymakers as a key channel through which quantitative easing (QE) policies work. We assess whether the investment behavior of insurance companies and pension funds in the United Kingdom during the global financial crisis was consistent with such an effect by analyzing both sectoral and institution-level data. Our results suggest QE led to institutional investors shifting their portfolios away from government bonds toward corporate bonds but did not lead to a shift into equities. (Joyce et al. 2017) Method: Regression of Asset types on central bank securities purchases and control variables for economic conditions.

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Summary of Business Press and Professional Paper Results: All studies surveyed except one found that QE resulted in increased equity market prices. 60% of stock market gains come on days of FOMC meetings (Sharma, R., WSJ 9/29/2016, p. A13). More than 50% of S&P 500 gains came on the day of FOMC decisions (Warsh 2016). …$1 trillion purchase … raised stock prices by perhaps 1–1.5 percent… (Neely 2015) Method: Event Study; Kiley (2018). The impact of the FED’s LSAP program on stocks ranges between zero and 197 basis points (Rosa 2012). A decline in long-term interest rates induced by monetary policy statements prior to 2009 is accompanied by a 6- to 9-percent increase in equity prices. This association is substantially attenuated in the period since the zero-lower bound has been binding—with a policyinduced 100 basis-point decline in 10-year Treasury yields associated with a 1½- to 3-percent increase in equity prices (Kiley 2018). Typical stock price decreases about 4–5% in response to a 100 basis point (bp) surprise increase in the federal funds rate. Worse for firms with much debt (Ippolito et al. 2018). Conclude: Professional/academic literature indicates QE increased stock prices 1–9%; Half the total effect occurred on the day of FOMC announcement of stimulative action. 2.2.2.2

Bond Market Effects; Interest Rate Effects

Event studies imply that a surprise announcement of a one trillion USD purchase of long-term bonds reduced 10-year U.S. Treasury yields and low-grade corporates by about 30 to 50 basis points while MBS yields declined by 66 basis points and mortgage rates fell further still…. (Krishnamurthy and Vissing-Jorgensen 2011). Method: Event Study. …a one standard deviation shock to assets purchases — i.e., 40 billion dollars — reduces 10- year Treasury yields by 10 basis points on impact… (Bhattarai et al. 2015) Method: Bayesian VAR. …This paper examines the impact of large scale asset purchases on U.S. asset prices (nominal and inflation indexed bonds, stocks and the dollar spot exchange rates) using an event study with intraday data…Estimation results show that the LSAP news has economically large and highly significant effects on asset prices…For most U.S. asset prices, the effects of asset purchases are not statistically different from an unanticipated cut in the federal funds rate… (Rosa 2012) Method: Event Study.

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Estimated effects on the 10-year government bond yield of a QE bond purchase equivalent to 10 percent of GDP. These studies unanimously conclude that QE lowers bond yields significantly …. The two most common types of QE studies are event studies and time series studies. The simplest event studies add up movements in bond yields around central bank announcements concerning QE programs. Studies use different sizes of event “windows,” from 30 minutes to 3 days bracketing the announcements. Shorter windows risk missing some of the market reaction; longer windows risk including the effects of other news that is unrelated to QE. By and large, the results are not particularly sensitive to the size of the event window. When QE programs catch markets by surprise, simply adding up the yield movements in the windows is a reasonable way to estimate the total effects of QE on yields… (Gagnon 2016) Method: Literature Review of Past Empirical Studies …This paper investigates the impact of the unconventional policies implemented by the Federal Reserve, the Bank of England, the European Central Bank, and the Bank of Japan on the returns on a broad class of assets in a comprehensive and consistent manner. Controlling for market expectations, we find that for most economies and periods, policies had the effect of lowering long-term government bond yields… (Source: Hosono and Isobe 2014) Method: Event Study. …“For instance, between 2012 and 2016 …the ECB’s accommodative monetary policy helped to reduce mortgage interest rates by 1.3 pp…. However, this low interest rate environment is also pushing up house prices. It encourages investment in property by lowering returns on financial savings and also makes it easier to buy more expensive housing… (Source: Caixa Bank Research: “The Impact of Monetary Policy on Housing Prices.” 10 January 2018. Method: Graphical comparison of housing prices and interest rates. …The operation of the portfolio balance channel has been emphasized by monetary policy makers as a key channel through which quantitative easing (QE) policies work. We assess whether the investment behavior of insurance companies and pension funds in the United Kingdom during the global financial crisis was consistent with such an effect by analyzing both sectoral and institution-level data. Our results suggest QE led to institutional investors shifting their portfolios away from government bonds toward corporate bonds but did not lead to a shift into equities… (Joyce

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et al. 2017). Method: Regression of Asset types on central bank securities purchases and control variables for economic conditions.

(Klein and Evans [1968], Eckstein [1983], Fair [2004], and Heim [2017] also found positive correlations between monetary policy and credit market assets prices; detailed descriptions of those works are given later in this chapter.) 2.2.2.3

GDP Effects

This paper studies the effects of FOMC forward guidance. We begin by using high frequency identification and direct measures of FOMC private information to show that puzzling responses of private sector forecasts to movements in federal funds futures rates on FOMC announcement days can be attributed entirely to Delphic forward guidance. (Campbell et al. 2017) Method: Event Study, DSGE. …Simulation results using a large-scale model (FRB/US) suggest that QE does not improve economic performance if the steady-state interest rate is high, confirming that such policies were not advantageous from 1960 to 2007. However, QE can offset a significant portion of the adverse effects of the ZLB when the equilibrium real interest rate is low…. (Kiley 2018) Method: simulation using large scale FRB/US model.

In January 2013, the Bank of Japan (BOJ) announced that it would pursue a 2% inflation target, and in April 2013 it announced the Quantitative and Qualitative Monetary Easing Program, intended to achieve the 2% target within two years. From 2013 to early 2016, the overnight nominal interest rate was close to zero, and it has been negative since early 2016. In Fig. 2.1, note that the monetary base in Japan (a measure of total liabilities of the Bank of Japan) increased by about threefold from the beginning of 2013 to May 2017. If QE is indeed effective in increasing inflation—the BOJ’s ultimate goal—then surely inflation should have increased in response to this massive QE program. But Fig. 2.2 shows that this was not the case, if we look at the consumer price index (CPI) for Japan. CPI indeed increased in 2014, but largely due to an increase of three percentage points in Japan’s consumption tax in April 2014, which fed directly into the CPI measure. But, from mid-2015 to March 2017, average inflation in Japan was roughly zero, obviously far short of the 2% target.

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Fig. 2.1 Japan monetary base and CPI inflation (Note The monetary base has grown by a large amount in Japan since January 2013, with little or no ultimate effect on inflation. The temporary increase in inflation in 2014 was primarily due to an increase in the consumption tax. Sources Organization for Economic Cooperation and Development and Bank of Japan)

Fig. 2.2 U.S. versus Canada real GDP (Note Canada and the U.S. are subject to the same basic macroeconomic forces, but over this period the Fed conducted QE and the Bank of Canada did not. Canada actually had slightly better real GDP performance. Sources Bureau of Economic Analysis/Federal Reserve Economic Data (FRED) and Organization for Economic Cooperation and Development)

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Since the financial crisis, central bank interest rate policy has been little different in Canada and the United States. But, the Bank of Canada did not engage in QE over this period, while the Fed did. As of December 2016, the Bank of Canada’s balance sheet stood at 5.1% of GDP, as compared to 23.6% of GDP for the Fed. Canada and the United States are typically subject to similar economic shocks, given their close proximity and similar level of economic development; so, if QE were effective in stimulating aggregate economic activity, we should see a positive difference in economic performance in the United States relative to Canada since the financial crisis. In Fig. 2.2, we show real GDP in Canada and the United States, scaled to 100 for each country in the first quarter of 2007. The figure shows that there is little difference from 2007 to the fourth quarter of 2016 in real GDP performance in the two countries. Indeed, relative to the first quarter of 2007, real GDP in Canada in the fourth quarter of 2016 was 2% higher than real GDP in the United States, reflecting higher cumulative growth, in spite of supposedly less accommodative monetary policy. Thus, in these two natural experiments, there appears to be no evidence that QE works either to increase inflation, if we look at the Japanese case, or to increase real GDP, if we compare Canada with the United States….(Source: Williamson [2017]. Federal Reserve Bank of St. Louis) Method: Graphical comparisons of US vs. Canada growth trends; inflation vs monetary base growth trends …between 2012 and 2016…this low interest rate environment is also pushing up house prices. It encourages investment in property by lowering returns on financial savings and also makes it easier to buy more expensive housing… (Source: Caixa Bank Research Monthly Report (2018) “The Impact of Monetary Policy on Housing Prices.” Caixa Bank, Spain. 10 January 2018. Method: Graphical comparison of house prices and interest rates). …Our estimates imply that the efforts by the Federal Reserve to stimulate the economy since July 2009 succeeded in making the unemployment rate in December 2013 1% lower, which is 0.13% more compared to the historical behavior of the Fed… (Wu and Xia 2016) Method: Maximum Likelihood Regression.

Neely and Bhattarai (2016) report that …Bhattarai et al. (2015) find that a one standard deviation shock to assets purchases—i.e., 40 billion dollars

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… increases industrial production and consumer prices by 0.4% and 0.1%, respectively, at a horizon of 10 months. Weale and Wieladek (2016) similarly used VAR analysis to determine that an asset purchase of 1% of GDP raises GDP and CPI by 0.58 and 0.62%, respectively. Their conditional forecasting analysis implies that QE1 raised GDP and CPI by about 2 percentage points at its peak, while QE2 raised GDP and the CPI by about 6 percentage points. Method: Literature Review …Fiscal Policy can be an effective countercyclical tool if monetary policy accommodates the fiscal expansion… (Canova and Pappa 2011) Method: Structural VAR. … We find clear evidence of positive associations between the degree of monetary ease in advance of fiscal consolidation programs and … programs’ success … Successful consolidations tend to be preceded, or accompanied …by greater loosening of monetary policy… (Hellebrant et al. 2012) Method: Graphical comparisons of interest rate vs. fiscal consolidation trends.

Neely and Bhattarai (2016, pp. 27–31) report that:…Chen et al. (2012) calibrate their DSGE model that features preferred habitat preferences, and thus a role for the portfolio balance channel, to assess the effects of LSAPs. They find that a $600 billion purchase of long-term government bonds (roughly matched to the announcement of the QE2 program), together with a credible commitment to hold short-term interest rates at zero for four quarters, increases GDP growth by 0.13% and inflation by 3 bp (both annualized). The bulk of the effects however, is due to the credible commitment by the central bank to hold short-term interest rates at zero in future.… Bhattarai et al. (2015) calibrate their DSGE model that features a central bank with balance sheet concerns that conducts policy under discretion…The results from the calibrated model implies that QE2, which doubles the size of the Federal Reserve’s balance sheet in their calibration without changing much the duration mismatch in Treasury holdings, increased output by about 45 bp. Then they estimate that QE3 or MEP/Operation Twist, which increases the average duration of Treasury bond holdings by around 5 quarters without changing the size of the Federal Reserve’s balance sheet, increased output by about 12 bp. The results suggest that QE2 stimulated the economy more effectively than QE3….Gambacorta et al. (2014), in an early study, estimate a panel

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VAR with feasible generalized least squares (FGLS) on monthly output, price, VIX and central bank assets data from 8 countries—Canada, the euro area, Japan, Norway, Switzerland, Sweden, the United Kingdom, and the United States—over the sample January 2008 to June 2011….the authors conclude that an exogenous increase in central bank assets, which they consider to be the monetary policy instrument at the zero lower bound, temporarily increases output and prices. …Walentin (2014) uses a structural VAR (SVAR) to argue that shocks to mortgage spreads—the mortgage rate less the Treasury rate of the same maturity—which he interprets as credit supply (policy) disturbances, have large macroeconomic effects in the United States. Unanticipated increases in this spread reduce house prices, residential investment, consumption, and GDP. Walentin then indirectly estimates the effects of QE1 in a counterfactual exercise that imposes the ZLB on the Fed Funds rates and uses previous empirical estimates of the effects of 30 QE1 on mortgage spreads. The implied effects are economically large: at peak, consumption and GDP increase by 1.18 and 1.02 percentage points, respectively, while residential investment and house prices increase by 6.74 and 3.00 percentage points, respectively…Bhattarai et al. (2015) also estimate the impact of US QE using a structural Bayesian VAR …Unanticipated fluctuations in Federal Reserve assets produce substantial macroeconomic and financial effects on the US economy…Similarly, Baumeister and Benati (2013) employ a timevarying parameter VAR framework to identify a pure term spread shock that leaves the federal funds rate unchanged but affects the 10-year Treasury yield. The authors estimate that reductions in this interest rate spread produce substantial macroeconomic effects during the ZLB period. Then, using the effects of asset purchases on the interest rate spread, the authors infer the effects of LSAPs on the macroeconomy, finding that such policies successfully averted deflation and output collapse.… Weale and Wieladek (2016) employ a hybrid method that merges LSAP announcement effects approach with a monthly Bayesian VAR to assess the macroeconomic effects of these policies. The paper assumes that the QE policy instrument is the cumulated level of LSAP purchases, scaled by GDP. These authors find that an asset purchase of 1% of GDP raises US (UK) GDP by 0.58% (0.25%) and CPI by 0.62% (0.32%), all of which are statistically significant…Method: Literature Review. Klein and Evans (1968) use a large-scale structural macroeconomic model of 76 equations, 47 of which are behavioral, i.e., econometrically estimated. Klein argues that the Federal Reserve controls both the

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discount rate and, the level of free reserves through open market operations, and therefore monetary policy can have macroeconomic effects (p. 50). Simulated changes in both of these monetary variables positively affect the GDP. Fiscal policy changes also positively affect GDP in the model and would have an additive effect to the fiscal policy changes. The crowd out problem is not discussed in the book. Neither is the role of accommodative monetary policy as a factor affecting fiscal policy’s effectiveness. Method: 2SLS Regression of structural IS/LM model equations. The Eckstein (1983) large-scale structural econometric model, the GDP determination sub-model contains 212 equations, 64 of which are econometrically estimated. Eckstein shows Federal Reserve control over interest rate policy has an effect on consumption and investment. In this respect, the model is similar to Klein’s. The “crowd out” problem resulting when stimulative fiscal policy is unaccompanied by monetary stimulus to keep interest rates down is discussed, and empirical results of simulations of the effects of fiscal policy with and without accommodating monetary policy shown (pp. 35–40). Monetary policy designed to keep interest rates down or augment bank loanable funds are found to be effective in addressing the crowd out problem, therefore leaving a net positive effect of monetary policy on GDP. Method: 2SLS Regression of structural IS/LM model equations. (Author’s note: findings of this current study are the same as Eckstein’s). Fair’s (2004) large-scale structural econometric model has 100 equations, of which 30 are econometrically estimated. Though, as was the case with Klein and Eckstein, none of the consumption or investment equations show the money supply as one of the determinants, the consumer services demand model showed services demand to be a determinant of short-term interest rates, and both the durables and nondurable consumer goods equations show demand to be in part a negative function of mortgage interest rates, as is the demand for residential housing. The demand for fixed investment is in part determined (negatively) by the bond interest rate. Since the Fed has some control over interest rates, we conclude Fair’s model shows that monetary policy can positively affect GDP. Fair includes an interest rate determination equation for the 3 month US Treasury bill interest rate, which is a function of percentage changes in the M1 money supply and the two Taylor Rule variables: unemployment and inflation. Expectations theory is used to model longer term bond and

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mortgage rates as functions of current and lagged values of short-term interest rates (the 3 month treasury bill rate). Empirical results indicate a change in the treasury bill rate has a positive impact on the GDP (p. 155). There is no discussion of the extent to which fiscal policy might vary in effectiveness with accommodating monetary policy. Method: 2SLS Regression of structural IS/LM model equations. The Heim (2017) model is a 56 equation structural econometric model of the macroeconomy containing 38 econometrically estimated equations. The current year prime interest rate was found significant in 6 of 7 models of consumption or its individual subcomponent parts, and in 4 of 7 models of investment and its individual subcomponent parts. Current year M1 was found positively related to housing investment, even after controlling for the positive, statistically significant, effects of declining current year interest rates. (This suggests credit rationing by the FR, as well as FR-induced interest rate changes affect housing investment). With investment, typically effects were felt after a one- or two-year lag. In this study there are two models of the determinants of the prime interest rate: a Keynesian demand for money model, and a Taylor rule model. The money supply was systematically related to interest rates in the Keynesian model in all time periods tested, and also in the Taylor rule model, but only for the QE time period tested. Heim’s structural equations allow for indirect effects on interest rates through M1’s effect on inflation. Method: 2SLS Regression of structural IS/LM model equations. For the Heim (2017) model, dynamic simulations using the statistically estimated structural equations showed the positive effects of fiscal stimulus programs (permanent tax cuts and temporary spending stimulus) on GDP were more than fully offset by the crowd out effects. Hence, the net effect was slightly negative, Permanent increases in spending yielded better results, but still only led to essentially no net effect on GDP. However, when accompanied by accommodative monetary policy, the net negative effects of fiscal stimulus programs were fully offset by an accommodating monetary stimulus of the same size as the fiscal stimulus, and the net effect on GDP was positive, but negligibly small, only increasing GDP about (0.4%) of the size of the combined fiscal and monetary stimulus by the time the new equilibrium was reached. The simulation used the Obama fiscal stimulus number ($800 billion), and an equal-sized increase in M1 by the FR in the simulation. The small permanent effect

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is due to the fact that much of the Obama stimulus was a one year only stimulus. …We introduce liquidity frictions into an otherwise standard DSGE model with nominal and real rigidities… We find that the effects of the liquidity shock can be large, and show some numerical examples in which the liquidity facilities of the Federal Reserve prevented a repeat of the Great Depression in the period 2008-2009. (Del Negro et al. 2017) Method: DSGE model simulation. …We quantify government spending multipliers in US data using Bayesian prior and posterior analysis of a monetary model with fiscal details and two distinct monetary-fiscal policy regimes…Short-run output multipliers are comparable across regimes—posterior means around 1.3 on impact—but much larger after 10 years under passive money/active fiscal than under active money/passive fiscal—90 percent credible sets of [1.5, 1.9] versus [0.1, 0.4] in present value, when estimated from 1955 to 2016… (Leeper et al. 2017) Method: Monetary DSGE Model analysis. …Using a rich dataset on government spending forecasts in Japan, we provide new evidence on the effects of unexpected changes in government spending when the nominal interest rate is near the zero lower bound (ZLB). The on-impact output multiplier is 1.5 in the ZLB period and 0.6 outside of it. We estimate that government spending shocks increase both private consumption and investment during the ZLB period, but crowd them out in the normal period… (Wataru et al. 2018) Method: Comparison of DSGE models under different assumptions. …The effects of monetary policy are less powerful in recessions, especially for durables expenditure and business investment… We also find evidence that contractionary policy shocks are more powerful than expansionary shocks, but contractionary shocks have not been more common in booms… (Silvana and Thwaites 2016) Method: Regression of key economic variables on a monetary shock with controls for GDP trends, prior period values of the dependent variable and the federal funds rate. …In our baseline experiment intended to capture the effectiveness of the American Recovery and Reinvestment Act of 2009, the output multiplier at the ZLB is 1.9 when the weight on the lagged shadow rate is zero, and 0.5 when the weight is 0.85. … (Wataru et al. 2018) Method: New Keynesian DSGE analysis.

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…This paper assesses the macroeconomic effects of unconventional monetary policies by estimating a panel vector autoregression (VAR) with monthly data from eight advanced economies over a sample spanning the period since the onset of the global financial crisis. It finds that an exogenous increase in central bank balance sheets at the zero lower bound leads to a temporary rise in economic activity and consumer prices.… Individual country results suggest that there are no major differences in the macroeconomic effects of unconventional monetary policies across countries, despite the heterogeneity of the measures that were taken… (Gambacorta et al. 2014). Method: VAR. …Unlike other debt, most bank loans have floating rates mechanically tied to monetary policy rates. Hence, monetary policy can directly affect the liquidity and balance sheet strength of firms through existing loans. We show that firms—especially financially constrained firms—with more unhedged loans display a stronger sensitivity of their stock price, cash holdings, inventory, and fixed capital investment to monetary policy. This effect disappears when policy rates are at the zero lower bound, revealing a new limitation of unconventional monetary policy. The floating-rate channel is at least as important as the bank lending channel operating through new loans… (Ippolito et al. 2018) Method: DSGE w/ calibration. …The impact of announcements of large-scale purchases of government bonds on real GDP and the CPI in the United Kingdom and the United States is explored with a Bayesian VAR, estimated on monthly data from 2009M3 to 2014M5. Four different identification schemes are used, all leaving the reactions of GDP and CPI unrestricted, and the transmission channels of the policy are examined. An asset purchase announcement of 1% of GDP leads to a statistically significant rise of 0.58% (0.25%) and 0.62% (0.32%) rise in real GDP and CPI for the US (UK). The transmission channels differ in the two countries… (Weale and Wieladek 2016) Method: Bayesian VAR. …The Great Inflation of the 1970s can be understood as the result of equilibrium indeterminacy in which loose monetary policy engendered excess volatility in macroeconomic aggregates and prices. The Federal Reserve inadvertently pursued policies that were not anti-inflationary enough because it did not fully understand the economic environment it was operating in. Specifically, it had imperfect knowledge about the structure of the economy and was subject to data misperceptions. The combination of learning about the economy and the use of mis-measured data resulted in

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policies, which the Federal Reserve believed to be optimal, but when implemented led to equilibrium indeterminacy… (Lubik and Matthes 2016) Method: VAR and components of DSGE.

2.2.2.4 Effects on Inequality • Whenever the main effect of asset purchases occurs initially and primarily in financial markets and induces a pronounced appreciation of financial asset values, adverse distributional effects may result since primarily wealthier households benefit from it. Adverse distributional effects are likely mitigated once the asset purchases unfold their intended impact on real economic activity and inflation. • Since the ECB’s extended asset purchase program started at a time when long-term interest rates were already low and liquidity in the financial system was abundant, major effects are likely to be observed only in financial markets where they lead to an increase in asset prices and therefore valuation gains for the holders of these assets. • This implies that the ECB’s asset purchase program will most likely, at least in the short-run, exacerbate income and wealth inequalities in the euro area… (Bernoth et al. 2015) Method: Graphical analysis of key data; some literature review. …We use data from the Federal Reserve’s Tri-Annual Survey of Consumer Finances (SCF) and look at the evolution of income by quantile between the “Pre-QE period” and the “QE period” analyzing three key impact channels of QE policy on income distribution: 1) the employment channel 2) the asset appreciation and return channel, and 3) the mortgage refinancing channel. … we find that while employment changes and mortgage refinancing were equalizing, these impacts were nonetheless swamped by the large dis-equalizing effects of equity price appreciations. Reductions in returns to short term assets added further to dis-equalizing processes between the periods. Bond price appreciations, surprisingly, had little distributional impact. We cannot know precisely how much of these changes are due to QE as opposed to other influences, but to assess potential causal effects we utilize a counterfactual exercise to assess the quantitative range of impacts of QE on the main channels. We conclude that, most likely, QE was modestly dis-equalizing, despite having some positive impacts on employment and mortgage refinancing. The modestly dis-equalizing impacts were due to both policy choices and deep seated structural problems, such as the long-term deterioration in labor market

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opportunities for many workers due to globalization and legal and political reductions in labor bargaining power that have contributed to long term wage stagnation. Finally, there is no support in our analysis, for the proposition that raising interest rates would be an efficient mechanism for improving income distribution, because of the likely costs in terms of employment and debt refinancing opportunities. ∗(Montecino and Epstein 2015). Method: Recentered Influence Function (RIF) Regressions; Oaxaca- Blinder decomposition technique. …We study the effects of monetary policy shocks on - and their historical contribution to - consumption and income inequality in the United States since 1980 as measured by the Consumer Expenditure Survey. Contractionary monetary policy systematically increases inequality in labor earnings, total income, consumption and total expenditures. Furthermore, monetary policy shocks account for a non-trivial component of the historical cyclical variation in income and consumption inequality. Using detailed micro-level data on income and consumption, we document some of the different channels via which monetary policy shocks affect inequality, as well as how these channels depend on the nature of the change in monetary policy… (Coibion et al. 2017) Method: Time series analysis of variables constructed from Consumer Expenditures Survey (CEX) data.

Summary of Effects: All three studies surveyed found changes in monetary policy increased inequality. However, the results of one study indicated contractionary monetary policy changes did it, while the other two said expansionary monetary policy increased inequality. (Klein and Evans [1968], Eckstein [1983], Fair [2004], and Heim [2017] also found positive correlations between monetary policy and GDP; are also discussed in the next section of this chapter.) 2.2.3

Comparisons of Findings of the Professional and Business Press

1. Like the business press, the professional press consistently finds open market operations by the FR stimulate the bond and stock markets. 2. Unlike the business press, the professional/academic press finds open market operations by the FR Increase the GDP, at least during the QE years. The professional/academic press finds Federal Reserve asset purchases between $40 billion and roughly $1 trillion increased GDP from near 0.0 to 0.58%, with no correlation of study results with purchase size. Multiplier results were similarly mixed, with

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multiplier effects of monetary stimulus generally varying from 0.5 to 1.9 (Note: this study concludes that because Federal Reserve securities purchases increased loanable funds so much during the QE period, they easily offset government deficits during that period, allowing the stimulus effects of government deficits to work, perhaps for the first time since at least 1960) (see Chapters 15–29). 3. All professional studies surveyed indicated stimulative monetary policy affected inequality, but results were mixed as to whether it increased or decreased it. The business press found stimulative monetary policy, at least during the QE years, increased inequality.

2.3 A Comparison of Cowles, DSGE, and VAR Methodologies Used in Literature Review Somehow, in summarizing the findings of past literature on controversial issues, we have to take into consideration the quality of the studies that produced the results. Is does no one any good to say that overall, results were “mixed” if all the best methodological studies point in one direction and all the worst in another. In this book we wish to both determine the underlying science that allows monetary policy to have an effect on the real economy, and evaluate how well accommodative monetary policy has achieved its objective of stimulating the real economy. Methodologically, how should we go about it? John Taylor, the author of the “Taylor Rule” hypothesis, noted that monetary policy can be evaluated by either historical analysis or the right kind of econometric analysis (structural modeling). He has noted that: … Studying monetary history is, of course, not the only way to evaluate monetary policy. Another approach is to build structural models of the economy and then simulate the models stochastically with different monetary policy rules… (Source: Taylor, J. “An Historical Analysis of Monetary Policy Rules”. NBER Working Paper No. 6768, October 1998)

The approach taken in this book is to determine the underlying structural relationships of variables in the economy that determine the effectiveness of monetary policy, i.e., structural modeling: Over 1200 separate structural models are tested, adding to standard models of investment’s and consumption’s determinants, variables including deficit variables and

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a wide variety of bank reserves and loanable funds variables. Initial findings for each model are retested in from 5 to 17 other, though sometimes overlapping time periods to ensure the initial results were replicable, not idiosyncratic. No result can be considered good science unless it is replicable. It is, after all, 400 years since Newton and the scientific revolution. What’s the point, this far into a scientific age, of publishing any nonscientific work? In today’s scientific world, economists need to be able to assure others that their tests of relationships in one model and in one time period are not just spurious, and have been replicated, preferably before publication. When doing scientific testing, using good econometric models is necessary, but not easy, as noted by Neely and Bhattarai: …Studying the effect of unconventional …(monetary)…policy on the macro economy is both more important and more difficult than studying its effects on asset prices and yields. It is more important because the ultimate goals of central banks pertain to output, inflation and, eventually, consumer welfare. It is also more difficult because problems of endogeneity, simultaneity, omitted variables, specification error and measurement errors are much more serious than for financial markets, which are amenable to the use of “event studies” to gauge the effects of policy announcements. To study the effect of unconventional monetary policy on macro variables, one must use low frequency data and control for non-monetary factors… (Neely and Bhattarai 2016, p. 27)

In surveying the literature of the last few decades, virtually all empirical studies of monetary effects were found to use either the DSGE methodology, or some variant of the VAR methodology. Few employed the type of econometrically based structural model referred to above by Taylor (1998). These three methods are very different ways for trying to uncover empirical reality. Choice of method is critically important: more often than economists would like to admit; they provide different answers to the same economic questions using the same data. Heim (2017, pp. 48–114) has a 46-page section comparing 1. the underlying economic theories tested by each, and the strengths and weaknesses of each, and 2. How successfully these three methodologies were when used to develop a model explaining fluctuations in US GDP 1960–2010.

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3. How successfully each of the three methodologies, when used to reestimate their own models using only 1960–2000 data, were at predicting or explaining actual fluctuations of the GDP in the 10 years following the estimation period, i.e., between 2001 and 2010. A structural model of the Cowles Commission type was found to be by far the most successful at explaining the actual data. Cowles models are versions of the IS/LM model, a large-scale demand-driven structural model with equations to explain the determinants of each variable that affects the GDP. In a Cowles model, every structural equation that plays a role in determining GDP (equations expressing the determinants of consumption, investment, determinants of government spending, imports, etc.) is empirically estimated. Results are combined in an IS curve model and used to calculate the GDP. Typically, these models include scores or even hundreds of equations. By comparison, DSGE models, which in some cases are detailed enough to be considered structural models, mainly tend to be largely deductions from first principles: hypotheses considered so self-evident they do not require testing to be considered “true,” e.g., the amount people work is a trade-off between income and leisure, what you have to pay people to get them to work, and the utility of leisure. Another example of these first principles is the rational expectations hypothesis, which in many DSGE models translates into an assumption people today have full and accurate information of their future income, and from this assumption deduce (e.g.) that consumer spending levels will always be constant at today’s levels, regardless of the (assumedly known) course of future income. Why? Because that is the only path consistent with the assumption that consumers always maximize utility. Some people consider DSGE to be good theory, but bad science, since the equations in its models are mostly deductively, not inductively (statistically) derived. Others say it is bad theory as well, and models, when tested, rarely explain actual data very well. VAR models, by comparison, are considered by some to be good science (every relationship is empirically derived), but bad theory, since the tested relationships are often devoid of theoretical content, i.e., they are not accurate expressions of any known economic theory.

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A full examination of the strengths and weaknesses of the DSGE and VAR models used in the accommodating monetary policy literature reviewed above would require many more pages than space here allows, and would just duplicate Heim (2017), readers are referred there for comparisons of how well work relative to one another. A briefer comparison is provided in the methodology section of this paper (Chapter 3). The results presented in this book on the effectiveness of monetary policy, and the exact mechanisms through which it works are based on empirically derived standard theoretical models of consumption and investment given in IS curve “structural” models described above. The four major large-scale econometric models of the macroeconomy of the type underlying this study, referred to Cowles Models, are the Evans and Klein Model (1968), the Eckstein Model (1983), the Fair Model (2004), and the Heim Model (2017). All four were described in detail earlier in Sect. 2.2.2.3 of this chapter. All of these models are basically IS/LM curve, demand-driven, general equilibrium models.

References Barro, R. (2016, September 9). The Reasons Behind the Obama Non-recovery. Wall Street Journal. Available at: http://www.wsj.com/articles/the-reasonsbehind-the-obama-non-recovery. Baumeister, C., & Benati, L. (2013, June). Unconventional Monetary Policy and the Great Recession: Estimating the Macroeconomic Effects of a Spread Compression at the Zero Lower Bound. International Journal of Central Banking, pp. 165–212. Bernoth, K., Konig, P., Beckers, B., & Grazzini, C. (2015). Quantitative Easing—What Are the Side Effects on Income and Wealth Distribution. DIW Berlin: Politikberatung kompakt 99. Bhattarai, S., Chatterjee, A., & Park, W. (2015, November). Effects of US Quantitative Easing on Emerging Market Economies (UNSW Business School Research Paper No. 2015–26), p. 69. Bhattarai, S., Eggertsson, G. B., & Gafarov, B. (2015). Time Consistency and the Duration of Government Debt: A Signalling Theory of Quantitative Easing (NBER Working Paper No. w21336). Caixa Bank Research Monthly Report. (2018, January 10). The Impact of Monetary Policy on Housing Prices. Spain: Caixa Bank.

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Campbell, J., Fisher, J., Justiniano, A., & Melosi, L. (2017). Forward Guidance and Macroeconomic Outcomes Since the Financial Crisis. NBER Macroeconomics Annual 2016 (Vol. 31, pp. 283–357). University of Chicago Press. Canova, F., & Pappa, E. (2011, October). Fiscal Policy, Pricing Frictions and Monetary Accommodation. Economic Policy, 26(68), 555, 557–598. Coibion, O., Gorodnichenko, Y., Kueng, L., & Silvia, J. (2017). Innocent Bystanders? Monetary Policy and Inequality. Journal of Monetary Economics, 88, 70–89. Del Negro, M., Eggertsson, G., Ferrero, A., & Kiyotaki, N. (2017, March). The Great Escape? A Quantitative Evaluation of the Fed’s Liquidity Facilities. American Economic Review, 107 (3), 824–857. Eckstein, O. (1983). The DRI Model of the U.S. Economy. New York: McGrawHill Book Company. Fair, R. (2004). Estimating How the Macroeconomy Works. Cambridge, MA: Harvard University Press. Gagnon, J. (2016, April). Quantitative Easing: An Underappreciated Success (Policy Brief, No. 16–4). The Peterson Institute for International Economics. Gambacorta, L., Hofmann, B., & Peersman, G. (2014, June 1). The Effectiveness of Unconventional Monetary Policy at the Zero Lower Bound: A Cross-Country Analysis. Journal of Money, Credit and Banking, 46(4), pp. 615–642. Gramm, P., & Saving, T. (2017, May 18). The Economic Headwinds Obama Set in Motion. Wall Street Journal, p. A15. Gurkaynak, R. S., Sack, B., & Swanson, E. T. (2005, May). Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements. International Journal of Central Banking, pp. 155–193. Hasono, K., & Isobe, S. (2014). The Financial Market Impact of Unconventional Monetary Policies in the U.S., the U.K., the Eurozone, and Japan. Japan: Policy Research Institute, Ministry of Finance. Haur, H., & Lai, S. (2014). Asset Allocation and Monetary Policy: Evidence from the Eurozone. Paper presented at 2014 annual meeting of the American Economic Association. Available at: https://www.aeaweb.org/conference/ 2014/retrieve.php?pdfid=665. Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Hellebrant, T., Posen, A., & Tolle, M (2012). Does Monetary Cooperation or Confrontation Lead to Successful Fiscal Consolidation? (Policy Brief No. BP1208). Peterson Institute for International Economics.

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Ip, G. (2017, July 19). Markets to Fed: Please Leave Us Alone. Wall Street Journal. Available at: http://www.wsj.com/articles/markets-to-fed-pleaseleave-us-alone. Ippolito, F., Ozdagli, A., & Perez-Orive, A. (2018, May). The Transmission of Monetary Policy Through Bank Lending: The Floating Rate Channel. Journal of Monetary Economics, 95, 49–71. Jenkins, H. (2014, November 7). Does the Fed Read the Election Returns? Wall Street Journal. Joyce, M., Liu, Z., & Tonks, I. (2017, September). Institutional Investors and the QE Portfolio Balance Channel. Journal of Money Credit and Banking, 49(6), 1225–1246. Kiley, M. (2018). Quantitative Easing and the “New Normal” in Monetary Policy (Finance and Economics Discussion Series, 2018-004). Washington, DC: Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board. Klein, L., & Evans, M. (1968). The Wharton Econometric Forecasting Model. Philadelphia: Wharton School of Finance and Commerce, University of Pennsylvania. Krishnamurthy, A., & Vissing-Jorgensen, A. (2011, October). The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy *NBER Working Paper No. 17555). Kuttner, K. (2001). Monetary Policy Surprises and Interest Rates: Evidence from the Fed Funds Futures Market. Journal of Monetary Economics., 47 (3), 523– 544. Leeper, E. M., Traum, N., & Walker, T. B. (2017). Clearing Up the Fiscal Multiplier Morass. American Economic Review, 107 (8), 2409–2454. Lubik, T., & Matthes, C. (2016, September). Indeterminacy and Learning: An Analysis of Monetary Policy in the Great Inflation. Journal of Monetary Economics, 82, 85–106. Montecino, A., & Epstein, G. (2015). Did Quantitative Easing Increase Income Inequality? Available at: https://www.umass.edu/economics/sites/default/ files/Montecino.pdf. Neely, C. (2015). Unconventional Monetary Policy Had Large International Effects. Journal of Banking & Finance, 52(C), 101–111. Neely, C., & Bhattarai, S. (2016). A Survey of the Empirical Literature on U.S. Unconventional Monetary Policy (Working Paper 2016-021A). Federal Reserve Bank of St. Louis, p. 3. Rosa, C. (2012, May). How “Unconventional” Are Large-Scale Asset Purchases? The Impact of Monetary Policy on Asset Prices. Federal Reserve Bank of New York Staff Reports, No. 560. Sharma, R. (2015, May 12). The Federal Reserve Asset Bubble Machine. Wall Street Journal, p. A13.

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Silvana, T., & Thwaites, G. (2016). Pushing on a String: US Monetary Policy Is Less Powerful in Recessions. American Economic Journal: Macroeconomics, 8(4), 43–74. Taylor, J. (1998, October). An Historical Analysis of Monetary Policy Rules (NBER Working Paper No. 6768). Walentin. (2014). Business Cycle Implications of Mortgage Spreads. Journal of Monetary Economics, 67 (C), 62–77. Warsh, K. (2016, August 24). The Federal Reserve Needs New Thinking. Wall Street Journal. Available at: http://wsj.com/articles/the-federal-reserveneeds-new-thinking-1472076212. Wataru, M., Nguyen, T., & Sergeyev, D. (2018). Government Spending Multipliers Under the Zero Lower Bound: Evidence from Japan. American Economic Journal: Macroeconomics, 10(3), 247–277. Weale, M., & Wieladek, T. (2016, May). What Are the Macroeconomic Effects of Asset Purchases? Journal on Monetary Economics, 79, 81–93. Williamson, S. (2017). Quantitative Easing: How Well Does This Tool Work? Regional Economist, 3rd Qtr. 2017. Federal Reserve Bank of St. Louis. Available at: www.stlouisfed.org/publications/regional-economist/third-qua rter-2017/quantitative-easing-how-well-does-this-tool-work. Wu, W. (2018, March–April). The Credit Channel at the Zero Lower Bound through the Lens of Equity Prices. Journal of Money Credit and Banking, 50(3–4). Wu, C., & Xia, D. (2016, March). Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound. Journal of Money, Credit and Banking. Wiley Online Library. Available at: http://onlinelibrarywiley.com/ doi/full/10.111/jmcb.12300.

CHAPTER 3

Methodology

This study has two objectives: 1. Determine if methods used by the Federal Reserve to implement accommodative monetary policy are effective. This is done in Chapter 7 and the methodology for doing it is discussed there, and 2. Econometrically determine if increases in the pool of loanable funds can offset the “crowd out” effects on consumer and business spending that result from government deficits. The methodology for doing that is described in this chapter. Financing government deficits requires borrowing from the pool of loanable funds. It is argued that this reduces what is left for consumers and businesses to borrow, and that reduced access to borrowed money reduces consumer spending, causing (“crowd out”). If so, this would cause a negative effect on GDP that offsets the positive stimulative effect of the deficit. The existence of the crowd out effect has been amply statistically documented by Heim (2017a, b). The econometric portion of this study will further verify the existence of this crowd out effect (Chapters 6 and 7) with the exact models used in this study. It will then test to determine if same-period growth in the pool of loanable funds can offset crowd out effects (Chapters 8–12). Finally, this study will test to determine if any of several alternative possible ways of offsetting crowd out actually seem to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_3

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work as well at reducing crowd out as changes in the total pool of loanable funds (Chapters 13–24). These alternatives include (1) increases in FR reserve security purchases (accommodative monetary policy), (2) endogenous increases in loanable funds caused by fluctuations in the economy. The test method is to take standard, commonly accepted models of the determinants of consumption and investment (baseline models), and add to these models any same-period changes in loanable funds (or one of the alternatives) that might have an effect on crowd out. The new variable would be added either as a modification to the deficit variable that reduces the deficits size, or as a separate variable, or both. If the addition to the baseline model increases the model’s ability to explain variance in consumption and investment, i.e., raise R 2 and adjusted R 2 , we conclude the evidence supports the theory that loanable funds (or one of the alternatives) can offset crowd out effects, i.e., we reject the null hypothesis. If not we reject the hypothesis that loanable funds or one of its alternatives can offset the crowd out effects of deficits. As a secondary test, we also look for changes in the significance level of the deficit (crowd out) variable, before and after modification by loanable funds changes (or changes in one of the alternatives). Typically, before adding any loanable funds modifier, the deficit variable is found negatively related to consumption and investment and statistically significant, indicating deficits do cause a crowd out problem. If a modifier is added to the deficit variable, it will modify (generally, reduce) the magnitude of the hypothesized crowd out effect of any deficit from the size of the deficit itself (T − G), to (T − G) + (S + FB). If it does modify crowd out effects, the modified deficit’s statistical significance should rise compared to that of the deficit alone, and the R 2 will rise, indicates the deficit alone is an imperfect “errors in variables” estimate of crowd out’s actual effect. If the modifier does not actually offset the crowd out effects, as measured by the deficit alone, adding it to the deficit will create an error in variables problem (Johnston 1963) that reduces the statistical significance of the modified deficit variable, compared to the baseline model. Of course, that’s in a world where testing conditions are ideal. But conditions are never ideal: multicollinearity relationships change with the changed crowd out variable used, or the change in loanable funds may not be fully available to offset crowd out (as we show in Chapter 7), so out loanable funds variable itself may have errors in variables problems. These problems and others that can distort regression results are discussed

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in more detail further below. When evaluating any set of results, they have to be taken into account. We found ourselves continually asking whether insignificant t-statistics resulted from a technical problem or were a substantive result telling us to reject the particular hypothesis being tested. This book’s tests build on the consumption and investment equations found in an empirically tested, 56 equation model of how the US economy works (Heim 2017a) whose results were found replicable in several different time periods. These equations will provide the baseline information on how consumption and investment are affected by changes in variables that are commonly thought to affect them. The use of these models is critical to this book’s statistical methodology for testing loanable funds effects. The credibility of a study’s findings that a variable is statistically significant or insignificant, or what its true magnitude is, depend heavily on how well the study controlled for all the other variables that also affect the dependent variable (the “left out variables” problem; see Goldberger 1961). The Heim (2017a) study exhaustively tests, in multiple time periods and multiple models, to determine what variables need to be included as controls in any consumption or investment function when testing for the magnitude or significance of any one variable (like loanable funds effects). The tests used in that study to ensure that controls were adequate are discussed in the next section and are our justification for why we used certain variables and not others as controls in our test of crowd out or loanable funds effects. All the controls used in that baseline study are repeated to test any new variables added to the models in this study. We did not retest the variables Heim (2017a) already tested on the grounds that that would have been redundant, but all the stationarity, endogeneity, time period robustness, etc., tests used there were repeated for any additional variables tested in those models in this study. Then, using the same variables found in Heim (2017a) to be determinants of consumption and investment, and the same 1960–2010 data set, we then retest those “standard” models to determine 1. Whether Government deficits have crowded out consumer and business spending 1960–2010. 2. Whether crowd out is most accurately measured by the deficit’s size, or by the deficit as reduced by any offsetting increases in loanable funds that occurs at the same time.

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3. Whether dividing changes in total loanable funds into its exogenous and endogenous parts indicates that one is more important in offsetting crowd out than the other. The exogenous part is defined as the part generated by FR purchases of government securities, including agency and mortgage-backed bonds. The endogenous part of loanable funds is taken to be the part that moves up and down with the economy, i.e., total loanable funds (national savings plus foreign borrowing, or S + FB), minus federal reserve security purchases. However, we show later in this book (Chapter 7) that evidence suggests not all, in fact very little, of the proceeds received by banks from selling government securities to the Federal Reserve is used by them to lend to those who wish to borrow so they can buy real goods and services, like cars and furniture, which will increase the GDP. Much of the money received from selling securities to the FR may go to buying other securities. After all, most sellers of securities to the Fed are in the business of selling and buying securities, not selling securities and buying real goods and services. In this case, adding the FR purchases modifier may just create an error in variables problem that lower’s the model’s R 2 and the statistical significance of the deficit variable. We could argue the deficit variable, once modified, turns insignificant because crowd out has been eliminated. However, it is shown elsewhere in this study that FR purchases were never big enough to offset most crowd out that occurred. They have only been big enough to offset a small portion of the yearly deficits occurring; about 1/8 as large on average from 1960 to 2000, and about ¼ as large from 2000 to 2007. Hence, generally, FR purchases shouldn’t have turned the crowd out effect variables insignificant because they were not big enough to offset more than a small part of the deficit’s crowd out effects. There are other reasons that can cause the deficit variables to look statistically insignificant which were noted above.

3.1

General Methodological Issues

As noted earlier, the reliability of marginal effect and statistical significance estimates for any variable in a regression is largely determined by how accurately the analyst determines what other variables need to be controlled for in the model to be tested. Below we explain how we deal

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with these issues were treated in the baseline models tested. Since these baseline models are taken from Heim (2017a) we repeat below the methods used there to determine which variables should be in the baseline models, i.e., what variables need to be included as controls in this study’s tests of loanable funds and other possible crowd out modifiers. Methods for treating endogeneity, stationarity, serial correlation, multicollinearity and heteroskedasticity in any new variables added in this study are also the same as were used in the baseline model and are included in the discussion below. Specific results for endogeneity, stationarity, etc., tests for any particular new variable added to the baseline model are discussed at the beginning of the chapter dealing with that alternative, and are only discussed generically here. Parameter estimates for the models tested were developed using 1960– 2010 annual data. All data were obtained from the Economic Report of the President (2002 and 2011) and the Federal Reserve’s; Flow of Funds Accounts (2011). The baseline economic models used were “standard models” in the sense that all variables commonly cited in the literature as determinants of consumption, Investment, etc., were used in the initial hypotheses tested in this study. Variables initially tested for the baseline model were listed in Chapter 1.3, of (Heim 2017a) and again in the appropriate chapter of Heim (2017a) detailing test results for each equation in the model (Chapters 4–16), and in the summary and conclusions chapter, Chapter 19. To this list of variables were added the variables tested in this study. Some preliminary testing was done to weed out variables cited only occasionally in the literature and found to be statistically insignificant in our initial tests. However, when variables commonly theorized to be significant factors were found insignificant (e.g., interest rates and measures of consumer confidence in some consumption and investment functions), they were left in the model even though insignificant. This was done if it was not clear if the insignificance was a substantive finding, or the result of a technical problem such as multicollinearity, small sample size, or some other econometric problem. Here we follow both Otto Eckstein’s (1983) practical advice (see for example, his multi-family housing demand equation), but also that of statistician M. Triola (2011) who notes that in the absence of statistical significance when evaluating the mean of a sample, the best estimate is the sample mean, not zero (if there is a theoretical reason to think the variable’s coefficient is not zero). In addition, it serves as a reminder that the research agenda for the future

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must include further work to determine if the lack of significance is indicating something substantive about the variable, or only some technical problem with the data and how it is used. When dealing with which (if any), lagged values of a variable to use, economic theory typically provides little if any guidance. In the baseline models presented in Heim (2017a), if theory indicated one variable was a determinant of another, numerous lags were tested, and we adopted the lag level of the determinant found most significantly related to the first variable, unless of course, theory specified a specific lag level. This approach follows that of Tinbergen (1939). Generally the 2017a study followed the same process in defining the values to include when calculating aggregates and averages. It did not use “Life Cycle” or “Permanent Income” averages of income over time as the definition of the “right” income variable to use as a determinant of consumption, as many economists do. Prior testing of different sized averages strongly indicated that current income, or something very close to it, explained the most variance. The evidence was overwhelming, and probably sounds the death knell for DSGE economics, which requires that current consumption be based on knowledge of average income over extensive peiods of time. Similarly, exchange rate testing indicated that the average of the current rate and the past three years’ rates was the lag combination most systematically (significantly) related to consumption and investment, so that is the rate used in our consumption and investment models. All baseline models were initially estimated using OLS. However, testing was then done to determine if endogeneity was present among the variables in the model tested. If so, Two Stage Least Squares (2SLS) was used, using instruments to replace the endogenous variable(s). This was done to eliminate simultaneous equations bias caused by identification problems arising from endogeneity. The process used to identify endogeneity, and replace endogenous variables with strong, non-endogenous instruments was as follows, following a process used by Griffiths et al. (2008): • Hausman endogeneity tests were used to determine what needed to be instrumented. • Wald weak instrument tests were used to ensure the instrument was a reasonable proxy for the variable it replaced, i.e., was not a weak instrument.

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• Sargan “Valid Instrument” tests were used to ensure the chosen instrument was free of any endogeneity with the dependent variable. The same process was used to test for and resolve endogeneity issues of any new variables added in this study. In addition, a reasonably objective way of arriving at suitable instruments is needed to ensure instrument components were not picked to ensure the instrument selected would obtain some desired result, (e.g., the right sign on itself or other variables). Here again, the method we have used reflects Griffiths et al. (2008), as well as that of Pindyck and Rubinfeld (1998): all exogenous and lagged variables in the system were used as the initial components of the instrument. If tests indicate it is a weak instrument, additional lagged values of variables already in the instrument are added. If that is not enough, efforts shift to removing instrument components that have very low statistical significance as a way of increasing t-statistics on remaining variables and the instrument’s F statistic until the standard Wald criteria are met (at least one t-statistic greater than 3.3 or an F -statistic greater than 10.0). All variables in this study and the baseline study were tested for stationarity. If found nonstationary, a variable was detrended unless it was found cointegrated with the dependent variable in the model in which it was used. • ADF (Augmented Dickey-Fuller) Unit Root Tests Used to determine Stationarity • DF (Dickey-Fuller) Test Used to Determine if Nonstationary variables were Cointegrated • Detrending Done to Those Not Cointegrated. All models were tested extensively to ensure the replicability (robustness) of the findings. This is particularly important when using nonexperimental techniques like regression analysis where left out variables or even moderate levels of multicollinearity in any one period can severely distort estimates of a variable’s impact. In developing the baseline model, every model result obtained was tested for robustness in two different ways • Robust to Time Period Sampled: Four Different Time Periods tested. • Robust to Model Specification: Test Sensitivity to two Significant Changes in Variables specified in the model tested.

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Generally, the key coefficients in the equations included in this large-scale model were strong enough to be very robust to time period sampled and choice of regression technique (we typically find more difference between weak and strong instrument results than between OLS and 2SLS strong instrument results). There were occasional exceptions, noted in the testing sections for each baseline model. Testing for robustness to model specification is the baseline model was more complicated. In a model (already) well specified, i.e., explaining roughly 85% or more of the dependent variable’s variance with theoretically sound variables and lags, adding or subtracting variables rarely will lead to significant changes in other variables’ parameter estimates, except perhaps for variables making only marginal contributions to the model. In this circumstance, the stability of results occurs because most of the possible effects of direct multicollinearity or left out variables which are collinear with variables in the model has already been accounted for by including the variables in the model. But, respecifying a model by deleting a variable already in it which accounts for much of the variance in the model is to court disaster. The variable dropped is likely to be multicollinear with many other variables in the model, since many variables tend to move together, at least partially. Dropping it will change the estimated effect of other variables in the model on the variable of interest’s coefficient, since each variable’s coefficient is a function of their collinearity levels with other variables in the equation. Similarly, adding variables to a model which explains little or only moderate amounts of variance will often significantly change the estimated effects of variables already in the model, particularly if the variable added adds much to explained variance. This is because the newly added variable is likely somewhat collinear with variables already in the model, and when entered, will be assigned some of their explanatory power. Hence, tests for specification robustness will be taken to be successful if variables making minor contributions to explained variance can be added or subtracted without changing other variables coefficients much. However, given the nature of correlational tools, we will actually expect that removal of major variables in a model, say the income variable in the consumption function, will result in major distortions to coefficients on the remaining variables. Hence, we do not test for specification robustness this way (Put another way, be suspicious of the coefficients in any model with an R 2 below roughly 80%).

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Hence, the key criteria for evaluating what belongs in an equation are the equation’s ability to explain variance (R 2 ), the statistical significance of a variable’s regression coefficient, and in some tests, comparison of an equation’s mean square error with that of another equation. All models in both the current and baseline studies were tested in first differences, not levels: This has many advantages when dealing with time series data. In our case testing in first differences: • Reduced by Almost Half the Number of Variables found Nonstationary • Raised Virtually All Durbin–Watson Serial Correlation Statistics to 1.6–2.2 Range • Reduced Multicollinearity Effects Substantially: Median Correlation Coefficient Fell from ~0.80 to ~0.40. • Regression Coefficients Far More Stable When Model Changes were made. Newey–West Standard Errors were used throughout to address Heteroskedasticity problems. 3.1.1

The Importance of Replicating Results Before Publication

There are investment and consumption models we take as the “standard” models in tests throughout this book. The models are Eqs. 4.4 or 5.4. TR taken from Heim (2017a). We use “standard” as a statement of what other variables need to be controlled for when we test for the effects of accommodative monetary policy, or other changes in the loanable funds pool, on deficit-induced crowd out effects. It may seem that some variables commonly thought to influence consumption, like consumer confidence, have been left out. Many other variables were initially tested to determine if they were determinants of consumption or investment, but were only found significant in one or two periods tested. The criteria used in (Heim 2017a) to determine if a variable was to be included in the standard model was that they had to be found significant 3 of 4 different, though somewhat overlapping, time periods between 1960 and 2010. Once variables met this replicability test, the robustness of regression coefficients in the baseline model were subject to a model modification test. Their coefficient values could

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vary no more than 30% when an additional two variables were added or subtracted from the model. Needless to say, these are difficult standards to meet. Many variables thought (by many economists) to be determinants of consumption or investment could not meet this standard and were excluded. New variables added in this study were tested in 6–18 time periods, and only considered significant if they added variance in ¾ or more of the periods tested. We justify such exclusions on the following grounds: good science absolutely requires the ability to replicate initial results in different time periods and models. To ensure a study’s results are worth reading, replication should be required before publication wherever possible. After all, this is the twenty-first century. The scientific revolution has been with us for 350 years. In the previous section, we have described the replication efforts that were made before baseline model results were published. In this book we add loanable funds and other variables to these models and reestimate the models to determine if changes in loanable funds, or these other variables can offset crowd out.

3.2 Other Methodological Issues Specific to This Study Chapters 6 and 7 test the hypothesis that, financing government deficits causes a “crowd out” problem to occur when deficits arise, ceteris paribus. By crowd out we mean that government borrowing of loanable funds in the United States reduces, or “crowds out” the loanable funds available to private consumers and businesses to borrow, reducing the level of consumer and investment spending. These negative effects on the economy may offset any stimulus effects of (Keynesian) tax cuts or government spending increases designed to stimulate the economy. Prior statistical (Heim 2017a, b) studies have determined that this crowd out effect is real, but this study again retests the hypothesis to further reaffirm its validity. This study also tests for the best way to test deficits for the crowd out effect. Specifically, we test whether the government deficit alone, measured by the one variable (T − G), or as two separate variables, (T ) and (G), provides the best definition of crowd out effects. Either one measures crowd out by assuming there is always a dollar-for-dollar decline in private consumer or investment spending when a deficit occurs. But this is a hypothesis incorporated into our modeling, not a fact. We will

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test it by comparing it with deficits modified by loanable funds or other modifiers. Other factors may reduce the crowd out effect below the size of the deficit itself. If the deficit increases by $100, and during the same period the pool of loanable funds increases by $100 due to business cycle effects or due to FR security purchases increasing bank reserves, the increase in loanable funds may offset the crowd out effect created by the deficit. If so, the net crowd out effect may appear to be zero. To determine if this happens is the second key objective of this book (along with determining if Federal Reserve accommodating monetary policy has been affective in replacing loanable funds lost to consumers and businesses by the need to finance deficits). To see if this is the case, we tested different modifications of the deficit. For example, after testing the one-variable deficit (T − G) alone for crowd out effects, we reran the same model using the modified form (T − G) + (S + FB) to determine how effectively changes in loanable funds reduced crowd out. In the standard consumption and investment models, the (T − G), or (T ) and (G) variable(s) were tested in both unmodified and loanable funds modified forms. The model which had the largest R 2 , and (generally, but not always) significant t-statistic(s) on the crowd out variable(s), i.e., the model which best fits the data, is taken to most accurately describe the size of crowd out effects Loanable funds are defined as national saving plus foreign borrowing. The Economic Report of the President, 2013, Table B32 defines total gross saving, or national savings, whose components are • personal savings (Personal income not spent on taxes or personal consumption expenditures included in the GDP), • corporate saving (undistributed profits), • depreciation allowances, and • government savings (T − G). Gross savings is calculated on a GNP, not a GDP basis, so it is most accurately defined as “national” savings, which we designate as (S). Foreign borrowing will be designated as (FB). Total loanable funds (S + FB) is defined as the total loanable funds pool.

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If increases in loanable funds can offset crowd out, we consider (S + FB) to be the most theoretically justified definition of the variable that may do the offsetting. That said we also tested a number of different possible offsets to the deficit. There is theoretical justification for some of the alternatives, but in other cases, we just tested them just because they were likely to be of interest to others. We desired our tests and results to be sufficiently comprehensive that others will see all the plausible alternative options have been fully explored. In some cases, the endogenous (S + FB – Tr − A) and exogenous (Tr + A) components of the loanable funds pool are also tested separately to determine which of the two actually offsets crowd out the most. We distinguish between exogenous and endogenous changes to the loanable funds pool as: 1. Exogenous component: increases in loanable funds due to deposits in banks of proceeds received from selling the FR treasury, agency and Mortgage-backed securities (Tr + A) to the Federal Reserve (FR). 2. Endogenous component: business cycle fluctuation—based variation in loanable funds borrowed related to variation in the money multiplier from one phase of the business cycle to the next, increases in savings stemming from increases in aggregate income, or changes in mpc. A list of the deficit modifiers tested is included in Table 3.15 at the end of this chapter. A range of other problems arising in some chapters but not all are also examined. Details of the testing procedures used to deal with these problems are discussed in detail in the first chapter where they occur. These issues include: • • • • • •

Mixing Periods of Deficit Increase and Decrease Statistical Insignificance Caused by Lack of Variation in the Data Left-Out Variables Multicollinearity Insufficient Sample Size Spurious Results Indicating Insignificance.

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GDP Deflator Methodological Adjustments

The GDP chain deflator given in the annual Economic Report of the President is used in various parts of this paper to convert nominal values of the GDP and other variables to “real” values. After 2012 the base year was changed from 2005 to 2009. To allow continued estimation of the real GDP in 2005 dollars from 2013 to 1017, we took advantage of the fact that data was available in Table B3 of both the ERP 2013 and ERP 2018 for the GDP chain deflator using both the 2005 and 2009 base year. On average for the last three years the 2005—deflated values were available (2010–2012), the value of the 2005-based deflator was 1.0848 times the value of the 2009-based deflator. Hence the actual 2013–2017 chain deflator values based on the 2009 base year, were adjusted upward by 1.0848 to obtain estimated values of the chain deflator for those years using 2005 as the base year. Table 3.1 shows the relationship: Results of models tested using these techniques are presented in Chapters 10–11. Table 3.1 Calculating 2013–2017 real GDP using estimated values of the base year 2005 chain deflator Year

Nominal GDPa

Real GDP (2005-based chain deflator)

Base 2005 chain deflator

2010 2011 2012 2013 2014 2015 2016 2017

$14,924 billion 15,518 16,155 16,692 17,428 18,121 18,625 19,387

$13,481 billion 13,688 14,002 14,210 14,465 14,623 14,810 15,075

110.00 113.37 115.38 117.46 120.48 123.92 125.76 128.60

actualb actualb actualb Est. Est. Est. Est. Est.

Base 2009 chain deflatora 102.53 104.17 106.49 108.28 111.06 114.24 115.93 118.55

a Economic Report of the President 2018 (ERP 2018), Table B3; b ERP (2012), Table B3

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3.4 Reconciling Differences in Signs, Significance Levels of Tests in Different Time Periods Originally, we intended to use two criteria, R 2 and t-statistics, to determine the success of a model. R 2 —Did the new variable being added to the standard model (i.e., the deficit, or a modifier) increase R 2 ? If not, we rejected the variable as a significant determinant of consumption or investment; if it did increase R 2 , we compared the increase to that obtained in other models using other definitions of the deficit or other modifiers. If the increases were larger than when the other modifiers were tested, we concluded that this way of modifying the deficit best explained the real level of crowd out resulting from the deficit. t-statistic—Did adding a modifier to a deficit variable increase the tstatistic on the crowd out variable? It was initially assumed that if the baseline model contained statistically significant deficit variables modifying them by a loanable funds or M1 variable would reduce or eliminate the modified deficit variable’s statistical significance, since it had offset the crowd out effect of the deficit. This did not turn out to be an appropriate criterion for evaluating the modifier’s effect on crowd out. In many cases, adding one of the loanable funds alternative modifiers to the deficit changed the deficit variable from significant to insignificant, but left R 2 reduced. This result suggested the modifier had no effect on crowd out, and distorted the real effect given by the deficit variable alone. This anomaly occurred because a modifier that had no real effect on crowd out was subtracted from a variable that did (the deficit), creating an “errors in variable’s” problem (Johnston 1963). It just added random errors to the true magnitude of crowd out, which reduces the true variable’s significance. An effective modifier more likely would leave the level of significance of the deficit variable unchanged or increased, since adding the modifier to the deficit made it a much more accurate measure of real crowd out effects. As a result, in evaluating the effects of different modifiers, we rely primarily on whether adding the modifier increases, leaves unchanged, or reduces R 2 . If modifying the deficit only definition of crowd out creates a modified deficit variable that increases R 2 , we conclude it gives a more accurate picture of true magnitude of crowd out effects than just the

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deficit alone. If it leaves R 2 unchanged, we conclude it has no effect on crowd out, even if it reduces the crowd out variable to insignificance. This problem is discussed in more detail as it arises in various chapters of the book. 3.4.1

Mixing Periods of Budget Deficit (Crowd Out) Increase and Decrease

Fundamentally, a regression coefficient (b) represents the average way that changes in (X ) from observation-to-observation are related to changes in (Y ) in a sample of data tested using the model Y = ƒ(X ). The standard formula representing this relationship in a simple regression is typically shown as  (xi yi ) b =  2 (where lower case xi , yi are deviations of observations xi (i) from their means)

(3.1)

Let y = x, and assume our data set has but two observations on each variable. Then  x1 x1 + x2 x2 y (xi yi ) b =  2 = = 1.00 = average x1 x1 + x2 x2 x xi If y = 2x b =

 x1 2x1 + x2 2x2 y (xi yi ) = 2.00 = average  2 = x1 x1 + x2 x2 x xi

Suppose in another sample y = −2x  x3 (−2x3 ) + x4 (−2x4 ) y (xi yi ) = −2average b =  2 = x3 x3 + x4 x4 x xi If you reestimate b combining both data sets into one larger (i = 1–4) data set, adding the last two samples together, the coefficient collapses to zero if the value of (x 3 , x 4 ) = (x 1 , x 2 ). If not precisely equal, a much smaller net effect (regression coefficient) will likely show, carrying the sign of the dominant data.

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A simple example shows this. Suppose we have the following 3 decades of data (Table 3.2). The effect of mixing samples is clear: combine a sample of data with a statistically significant positive effect, with one that has a statistically significant negative effect, and the combined sample will have a smaller, or zero, coefficient, and which will not likely be statistically significant, (though this depends on the how different the magnitudes of the numbers in one subsample versus the other). This was a common result for some periods sampled in Chapter 18. For example, in Table 18.1.A we added data from a statistically significant “crowd in” (i.e., declining deficit) decade of the 1990s, to data from the earlier statistically significant “crowd out” (i.e., increasing deficit) decades. For example, adding the 1990s data to (1960–1989) data tended to eliminate the statistical significance. Though simple on its face, this is an extremely important finding for us. It will help us interpret the sign and lack of statistical significance on our regression coefficients for our deficit variables when testing samples of data that include both crowd out and crowd in periods. In such periods, Table 3.2 Simulated regression data Decade 1: (strong positive correlation) Year 1 2 3 4 5 6 7 8 9 10

Decade 1: (strong negative correlation)

Decade 1: (no correlation)

Y

X

Year

Y

X

Year

Y

X

1 2 3 4 5.5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5.5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5.5 6 7 8 9 10

1 1 2 1 1 1 1 2 1 1

After regressions are calculated for each decade and the Decade 1 Only Regression Coefficient (t-stat.): +0.997 Decade 2 Only Regression Coefficient (t-stat.): −0.997 Decade 3 Only Regression Coefficient (t-stat.): −0.063 Decade 1&2 Combined Regression Coefficient (t-stat.): Decade 2&3 Combined Regression Coefficient (t-stat.): Decade 1&3 Combined Regression Coefficient (t-stat.):

combined decades, (54.1) (−54.1) (−0.0) 0.000 (0.0) −0.466 (−2.3) +0.466 (2.3)ara>

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the lack of a finding that deficit variables had a statistically significant crowd out effect on consumption or investment may not mean there is none; it may mean we were not careful to avoid mixing crowd in and crowd out periods in the same sample. The part of the loanable funds pool available to consumers and businesses, declines in years in which government deficits increase because of the need to finance the deficit, ceteris paribus, causing a “crowd out” problem. Similarly, in years in which government deficits decline, ceteris paribus, the decline increases the portion of the loanable funds pool available to private borrowers. This causes “crowd in.” There is good evidence “crowd in” normally will have a positive effect on consumption and investment. It increases the pool of privately available loanable funds, and that increases consumer and business borrowing. For example, statistical tests indicate increases in consumer borrowing increase consumer spending (Heim 2017a, Eq. 4.4.TR). There is considerable evidence demand for loans since 1960 may have chronically exceeded the supply of loanable funds until 2008, when the QE program hugely increased the pool of loanable funds leaving it far larger than the demand for loans (Chapters 8 and 9). Excess reserves in US banks indicate very small balances of excess reserves; through the whole 1960–2007 period they varied between only 1–5% of total reserves, and averaged only 2.2%. This consistently small size, in good times and bad, suggests any excess funds during that period were kept for precautionary purposes, not because of a lack of borrower demand. This suggests the demand for loanable funds typically was probably greater than the supply. The “quantitative easing” (QE) years starting in 2008 were an exception to this. QE years were years in which the Federal Reserve engaged in a huge securities purchasing program, massively flooding of banks with increased loanable reserves (Chapter 8). Hence, if we sampled only a decade in which deficits were increasing, like the 1980s, we would expect a negative sign on the regression coefficient describing the way increased government spending affected consumption and investment. For the same reason we would expect a positive sign on the coefficient indicating how years in which deficits caused by cuts in taxes (since the cuts are negatively signed) also had a negative effect on consumption and investment due to crowd out. However, there are circumstances when the spending deficit variable will have the wrong sign, i.e., a positive sign.

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A cut in government spending causing deficit reduction would show as a negative change in (G). This negative change in government spending would, when multiplied by the negative signed regression coefficient on government spending, would show a positive effect on consumption or investment. Similarly, if the deficit declines due to positive changes in tax collections (increases), we would expect this positive change, times the positive coefficient on the taxes variable (T ) to increase consumption or investment. Consider a more typical case. Suppose government spending was rising, but the loanable funds pool was also rising. If the deficit-causing rise in government spending was larger than the change in loanable funds, the net “crowd out” effect G − (S + FB) would be greater than zero. If the increase in loanable funds (S + FB) was greater than (G) in the same period, the result is a “crowd in” effect. Not only does the deficit variable (the increase in government spending) not cause a crowd out problem, the growth in G is positively associated with growth in consumption. If this “crowd in” effect continued for several years, a regression of C = ƒ(G) will show a positive relationship, i.e., the sign on the government spending variable may change from negative to positive. For example, using some hypothetical values for G and (S + FB), if the normal way the spending deficit enters into the consumption function is C = . . . . . . − (G − (S + FB)) = −(100 − (150)) = +50

(3.2)

In a regression for this time period only, we would see the deficit variable (G) positively correlated with consumption, giving the regression coefficient a positive sign. Note in Table 3.3 the general (though not always) tendency when growth in loanable funds exceeds the deficit (like the 1970s and 1990s), for the regression coefficient on the deficit variable to be small or positive, and to be statistically insignificant or perhaps even show a positive, statistically significant “crowd in” effect. By comparison, in periods in which there was much larger growth in deficits than in loanable funds, like the 1960–1980 and 2000–2010 periods, we generally have highly statistically significant negative crowd out effects. Hence we conclude that often the coefficients and significance levels on the spending crowd out variable change from negatively significant when crowd out prevails in the sample period, to either negative

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Table 3.3 Changes in regression coefficients and t-statistics associated with loanable funds changes Period

Loanable funds (T − G) deficit growth net of the coef.(t) govt. deficit during the decade

T only deficit coef.(t)

G only deficit coef.(t)

00–10 average:

$−184.7 billion

+0.42 (4.2)

0.45 (2.4)

60–80 average:

$−27.8 billion

+0.45 (3.3)

0.72 (5.3)

80–90 average:

$−17.8 billion

+0.02 (0.1)

0.10 (0.2)

60–70 average:

$0+6.6 billion

+0.53 (2.4)

0.82 (12.0)

70–80 average:

$0+6.9 billion

+0.22 (1.4)

0.22 (0.9)

90–00 average:

$0+132.9 billion

−0.09 (0.5)

1.18 (3.7)

−0.56 (−1.3) −0.28 (−2.8) −0.20 (−0.2) −0.42 (−7.7) −0.20 (−0.8) +0.50 (6.5)

Regression results use standard regression model, including a control for changes in loanable funds. Data taken from Table 18.1A

Table 3.4 Average yearly increases (+)/decreases (−) in deficits by decade

Decade

Average increase(+)/decrease(−)

1960–1970 1970–1980 1980–1990 1990–1900 2000–2010

$+10.3 billion ($2005) +17.3 +32.6 −39 +125.1

and insignificant, or sometimes positive and significant, when crowd in prevails. In addition to growth in loanable funds, decline in deficits is an additional reason the (G) deficit variable can sometimes appear insignificant, or have a positive sign, is the declining deficits of the in the 1990s decade shown in Table 3.4. In our statistical tests, during the 1990s, accompanying the declining deficit shown above, we see “crowd in” as represented by a positive sign on the government spending deficit variable, and higher than usual positive coefficients on the tax variable. During this decade, the United States experienced a third of a trillion dollar decline in the deficit. This decline

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is also shown in Table 3.3 single variable deficit (T − G) coefficient of (−0.09). The negative sign is consistent with our expectation that a decline in the deficit should result in a positive change in consumption. This is because deficit reduction increases the portion of the loanable funds pool available for private borrowing. There was also a positive sign on the government spending variable, indicating that even though government spending increased, the deficit was declining, i.e., (T ) was growing faster than (G). This stimulated consumption at the same time (G) was growing, causing the positive correlation, but not a causal relationship between increased government spending and increased consumer spending. The equivalent effect on the tax variable (T ) is shown in the larger coefficient in that decade than in others. In Chapter 11, Table 11.1.A, we undertake 90 separate tests of the standard consumption model which differ only by slight differences in the length of the time period tested. Results are consistent with the theory that the cause of most statistically insignificant government spending or tax cut crowd out results in regressions is mixing the declining deficits of the 1990s with data for decades characterized by crowd out. In tests (crowd in) where the 1990s data was a large part of the data set tested, the sign on the government spending variable will actually turn positive. In Table 11.1.A, models including the 1970s and 1980s data were found to have significant crowd out effect for both variables. When the 1990s data was added and the model reestimated, the tax variable coefficients fell, as did the spending variable coefficients (in absolute value), as our analysis above indicated should happen because coefficients are just averages of yearly effects in a sample. In addition, results for both variables turned from significant to insignificant. Similarly, when the 2001–2010 data was added to the 1990s data, the 1990s coefficients for taxes fell, and the coefficient for spending returned to negative by the time all 10 years of data for 2001–2010 were added in. Adding the 2001–2010 data to the 1990s data turned the statistically significant deficit effects to statistical insignificance, again, as expected from our previous analysis. The large deficit declines occurring in many years in the 1990s far exceeded the smaller growth in some other years during that decade, leaving a net decline of about $337.3 billion (2005 dollars) during the 1990–2000 period, as shown in Table 3.4. These negative changes, times a negative regression coefficient on the regression for this decade (Table 3.2), show a positive effect of these deficit declines on consumer

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spending during this period. This was because each yearly decline, though not increasing the total pool of loanable funds, added to the portion of the total pool available for consumer and business borrowing. Hence, from the standpoint of the loanable funds available to private borrowers, the (declining) deficits variable is measuring “crowd in,” yielding a change in the coefficient on the government spending variable from negative to positive and increasing the coefficient on the tax deficit variable when the two components of the deficit are modeled as separate variables. Table 3.5 shows individual year’s deficit declines during the 1990s, mostly related to generally good economic conditions except at the beginning of the decade, as well as a tax increase. In the decade by decade samples (Table 3.3), the statistical insignificance of the government spending deficit variable for the 1970s seems principally associated with small sample size and high multicollinearity with another variable. For the 1980s, the insignificance appears mainly associated with lack of variation in the government spending variable, compounded by small sample size. Let us assume the crowd out effects of deficits, i.e., (T − G) < 0 are reduced, on a dollar-for-dollar basis by any growth in the loanable funds pool (S + FB). Assume further that FR open market operations as well as business cycle fluctuation can increase or decrease the loanable funds (LF) pool, by increasing bank excess reserves. Table 3.5 Yearly changes in the deficit in the 1990s

Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Total deficit Decline 1990–1999

Change in deficita $+96.2 billion +68.1 +104.3 −58.4 −115.6 −22 −95.5 −133 −128 −53.3 $−337.3 billion

a Consolidated US, State and Local government Budgets. Billions

of 2005 Dollars. Economic Report of the President 2012

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Then, based on our statistical findings presented later in Chapter 18 of this study, and this chapter, there are several possibilities: 1. No change in loanable funds occurs in the sample period in which the deficit changes (i.e., no FR accommodative policy, or endogenous growth in LF): Then the crowd out variables will have their expected sign: the coefficient on the taxes variable will have a positive sign indicating a cut in taxes will negatively affect consumption or investment; the coefficient on the government spending deficits will have a negative sign, indicating an increase in government spending, ceteris paribus, will have a negative effect on consumption or investment. Both types of deficits typically are found to be statistically significant, though significance levels on government spending deficits tend to be lower, apparently due to less variation in the data in a typical decade than is the cases for variation in government revenues. Less variation of this type is typically associated with lower significance levels, and should not be taken as a sign spending deficits have less crowd out than tax deficits. 2. There is an increase in loanable funds in the years in the period sampled, but it is smaller than the increase in the deficit in those years: If the increase in loanable funds is small relative to the increase in the deficit, the crowd out variables should retain their expected signs, and roughly the same coefficients and statistical significance (if most or all of the increase in LF is used to purchase real goods and services, not other securities). 3. There is an increase in loanable funds, equal in size to the increase in the deficit: If the increase in loanable funds equals or nearly equals the increase in the deficit each year in the years sampled, the crowd out variable coefficients should decline to approximately zero and become statistically insignificant, since the year to year data on changes in T + (S + FB) and G − (S + FB) should equal/nearly equal zero for each year in the sample. If there is no variation in the variable during a period, it cannot be significantly related to a dependent variable. 4. There is an increase in loanable funds in the years sampled, and it is greater than the increase in the deficit in those years: If the increase in loanable funds is only marginally larger than the increase in the deficit, the crowd out variables should have signs opposite their expected signs, but the variables should be statistically insignificant.

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The sign change represents a “crowd in” effect. For the modified tax cut deficit variable, T + (S + LF), if the change in (T ) is negative, and the change in (S + FB) positive, will give a positive data series for this variable for the time sampled, and it will be associated with a positive effect on consumption or investment. Hence, the sign will stay positive. For spending deficits, the regression coefficient on the modified government spending variable G − (S + FB) should change from negative (the expected sign for the effect of G) to positive as (S + FB) exceeds growth in the deficit (G). If the negative values are significantly positively correlated with changes in consumption or investment, the effect should be statistically significant as well. This, of course, is what we see with the 1990s data. Regression Example of Sign Changes on the Spending Deficit Variable A simple example can show how the regression can assign a negative sign to the (G) variable in deficit periods and a positive sign in surplus years. Suppose the true relationship between consumption and the deficit was C = 1.00 T − 1.00 G + 1.00 Y (Income). Then in government deficit years where the G is larger than the T and growing, e.g., G = 8, 9, or 10, we have (Table 3.6). Arithmetic Examples of Sign Changes on the Spending Deficit Variable We can also show the same result arithmetically as well as with regression coefficients, with a simple “partial derivative” example of the effects of (G) and (S + FB) on consumption, showing the effect of changes in consumption that result from changes in the deficit stemming from increased government spending and any same-period change in loanable funds. Let C = −1.00 * (G − (S + FB)) show the effects of crowd out, and crowd out reduced by changes in loanable funds. Then, if G = 1–5 and the (S + FB) = 0, for 5 periods (t )–(t + 4), we have (Table 3.7): which shows a clear crowd out theory-consistent pattern of growing (G) deficits being associated with declining private consumer spending. (Similar results would result using the tax deficit variable, and the real effect on consumption would be the sum of the two effects in any period).

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Table 3.6 Simulation of deficit and surplus effects on sign of government spending coefficients Small government deficit years example

Large government deficit years example Model: C = + 1.00 T − 1.00 G C = + 1.00 T − 1.00 +1.00 Y + e G + 1.00 Y + e Hypothetical data Hypothetical data Period C T G Y e1 C T G Y t (97) (0) (3) 100 0 (90) (0) (10) 100 t +1 (197) (2) (6) 200 +1 (190) (2) (13) 200 t +2 (296) (3) (7) 300 0 (288) (3) (15) 300 Regression results Regression results C = + 1.50 T – 0.25 G +0.98 C = + 2.67 T – 0.67 Y G +0.97 Y And examples in government budget surplus years using the same model, the results are: Small surplus years example Large surplus years example Model: C = + 1.00 T – 1.00 G + C = + 1.00 T – 1.00 1.00 Y + e G + 1.00 Y + e Hypothetical data Hypothetical data Period C T G Y e1 C T G Y t (99) (0) (1) 100 (109) (10) (1) 100 t +1 (200) (2) (1) 200 −1 (211) (13) (1) 200 t +2 (301) (3) (2) 300 (313) (15) (2) 300 Regression results Regression results C = + 2.00 T +2.00 G +0.97 C = + 0.88 T +0.88 Y G +0.99 Y

e1 0 +1 0

e1 −1

1 Size of error term tested between (1 and 50); sign of government spending variable stayed as shown above, but magnitude changed with error size. The method shown is heuristic, and not a complete solution to the positive sign problem; results are sensitive to sign of error term

Table 3.7 Effects of spending deficit growth on consumption

Period t t t t t

+ + + +

1 2 3 4

(C) = (−1) (−2) (−3) (−4) (−5)

−1.00 (G) −1.00 −1.00 −1.00 −1.00 −1.00

(1) (2) (3) (4) (5)

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Smaller increases in loanable funds, which do not completely offset crowd out (the spending deficit) show a negative relationship between changes in (C ) and changes in (G − (S + FB)), as shown in Table 3.8. Next, again let C = −1.00 (G − (S + FB) show the effects of spending deficit crowd out on consumption. Let the spending deficit’s crowd out effect be reduced by changes in loanable funds. Let G = 5, and let (S + FB) take on different, but larger values than the deficit, for the 5 periods (t = 0–4). Then “crowd in” will result from the net growth in growth in loanable funds relative to (G) (Table 3.9): which shows a clear positive relationship between (C ) and a change in (G) accompanied by an even bigger change in (S + FB). Here, crowd out effects are eliminated by increasing loanable funds through either accommodative monetary policy or some endogenous change in the economy until the growth in loanable funds exceed the size of the government spending deficit (G) during the same period. Finally, we can show that a decline in the spending deficit that leaves it lower than the level of loanable funds also results in a Table 3.8 Effects on consumption of loanable funds growth less than spending deficit

Table 3.9 Effects on consumption of loanable funds growth greater than spending deficit

Period t t t t t

+ + + +

1 2 3 4

Period t t t t t

+ + + +

1 2 3 4

(C) = (−1) (−2) (−3) (−4) (−5)

(C) = (+1) (+2) (+3) (+4) (+5)

−1.00 (G − ( S + FB))

= −1.00(G + ( S + FB))

−1.00 −1.00 −1.00 −1.00 −1.00

= = = = =

(5 (5 (5 (5 (5

− − − − −

4) 3) 2) 1) 0)

−1.00 −1.00 −1.00 −1.00 −1.00

(1) (2) (3) (4) (5)

−1.00 (G − (S + FB))

= (−G) + (S + FB)

−1.00 −1.00 −1.00 −1.00 −1.00

= = = = =

(5 (5 (5 (4 (5

− − − − −

6) 7) 8) 9) 10)

(−5) (−5) (−5) (−5) (−5)

+ + + + +

(6) (7) (8) (9) (10)

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Table 3.10 Effects on consumption of declining spending deficit

Period t t t t t

+ + + +

1 2 3 4

(C) = (+0) (+1) (+2) (+3) (+4)

−1.00 (G − (S + FB))

= −G ± (S ± FB)

−1.00 −1.00 −1.00 −1.00 −1.00

= = = = =

(5 (4 (3 (2 (1

− − − − −

5) 5) 5) 5) 5)

(−5) (−4) (−3) (−2) (−1)

+ + + + +

(5) (5) (5) (5) (5)

positive relationship between changes in (C ) and changes in the loanable funds modified deficit variable (G − (S + FB)). This is a simulation of our “1990s” case discussed earlier (Table 3.10). Clearly declining deficits are associated with growing private spending (consumption) as crowd out theory predicts. In the same fashion, we can show tax cut deficits (T < 0) result in positive changes in consumption if they more than offset the change in the deficit, and negative changes in consumption if they are too small to fully offset the tax cut’s negative effects on consumption. Conclusions: the sign on the spending deficit variable switches from negative to positive when the size of the deficit falls below the same-period change in the level of loanable funds (the 1990s case), or when the change in level of loanable funds is greater than the growth in the spending deficit (the Quantitative Easing period case). Similar effects hold for tax cut deficits when the growth in loanable funds is less or more than the tax cut deficit, but the sign on the coefficient stays positive. 5. Finally, for samples including periods in which decades of deficit growth were much larger than savings growth (like the 1980s or 2000s), that also include periods in which the opposite occurred (like the 1990s—see Table 21.1.B), the sign on the modified deficit variables will depend on which period dominates the sample. Regression coefficients conceptually are, (after all), nothing but averages of yearly changes in the data in time series models. Standard errors, and therefore t-statistics, are conceptually nothing more than a measure of the average way in which individual year data observations vary from that average, (e.g., yearly modified deficits).

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If large parts of the sample have the expected crowd out effects, and large parts have crowd in effects, regressions combining periods of both crowd out and crowd in typically will show the spending deficit variable’s coefficient as statistically insignificant. The coefficient (~the average effect of yearly changes) for the whole sample will likely be small, because it averages a lot of pluses and minuses. The standard error will likely be large, because half the data shows positive and half negative yearly effects. Hence, whatever the sign on the coefficient, it is likely to be statistically insignificant, indicating what large standard deviations always do: that the average (the coefficient) is not at all indicative of the individual values of the underlying data that got averaged to make it. 3.4.2

Statistical Insignificance Caused by Lack of Variation in the Data

Regressions associated with the simulated data in Table 3.2 clearly show that mixing data for a time period which shows a significant positive relationship between two variables with data for the same variables, but a period when there was no change in one of them, reduces the coefficient and statistical significance of the explanatory variable. In Table 3.3, where we look at actual data we see the same thing. t-statistics on the spending deficit variable (G) are smaller in absolute value than that on the tax deficit variable (T ) in four of the six decades surveyed. 1990–2000 was also the only period in which the variation in the spending deficit variable over the decade was larger than the variation in the tax deficit variable. Variation was measured as the ratio of the variable’s average yearly change for the decade, relative to its standard deviation. This clearly shows the importance of variation in a data series. Without variation, a variable may appear to have a statistically insignificant relationship with another variable, when in fact the insignificance may be due only to lack of movement in the variable during the sample period. This is a common problem with policy controllable variables like tax cuts or spending increases, where cuts may occur in one period, but not another because of policy decisions. Hence, samples from one period may show a specific explanatory variable having a significant relationship to a dependent variable, but not samples from another period. Lack of variation in an explanatory variable can cause it to be found insignificantly related to the dependent variable (the correlation between

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a constant and a variable is 0). Lack of variation in the spending deficit appears to be what happened in the 1980–1990 decade that caused the spending deficit to typically have lower significance levels in that decade, the average yearly variation in government spending growth from its decade average growth, given by its standard deviation for the decade, was only a third of average yearly growth. Variation of government spending from its decade average for every other decade during the 1960–2010 period was twice as large or more, as shown in Table 3.11 (and less than the variation for all other variables in the consumption function, except population growth). Table 3.11 Trends in crowd out significance, and movement in other variables Period

60–70 average: 70–80 average: 80–90 average: 90–00 average:

Loanable funds growth net of the govt. deficit during the decade

$+6.6 billion $+6.9 billion $−17.8 billion $+ 132.9 billion 00–10 $− average: 184.7 billion 60–80 $−27.8 average: billion

(T − M1 velocity M2 Money Money GSD /GAv G)c velocity multipa multipb deficit coef.(t)

+0.51 (2.7) +0.24 (3.6) +0.09 (0.7) −0.10 (0.6)

TSD /TAv

4.2

1.6

1.8

4.2

0.67

0.64

5.6

1.6

−1.6

3.2

0.8

2.73

6.7

1.7

1.8

3.3

0.32

0.98

7.0

2

0.6

2.9

0.69

0.59

+0.27 (3.5)

8.9

1.8

0.2

1.9

0.61

12.33

+0.42 (3.1)

5.0

1.6

0.5

3.7

1.05

1.35

a Taken from Table 10.3 in Chapter 10. (M1 multiplier), which used the coefficients in the Table 10.2

model b Calculated as M1/(Tr + A) c Standard consumption model using 1-variable definition of unmodified deficit, without a loanable

funds control variable. Data on total government spending and total revenues used in calculating the deficit are taken from the Economic Report of the President 2012, and 2006, as described elsewhere in this study

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Further, as noted earlier, four of the six t-statistics on the spending deficit variable are smaller in absolute value than that on the tax deficit variable. Only one is larger, (1990–2000 decade). This is also the only decade in which the standard deviation in yearly change in government spending during the decade was larger (relative to the average yearly change in government spending for the decade) than variation in the tax deficit variable. This clearly shows the importance of variation in data used in analyses. Without variation, a variable may appear insignificant (implying not related to the dependent variable) when in fact the insignificance is due to lack of movement in the variable during the sample period. In virtually all tests in this study, the statistical significance of the government spending crowd out variable is less than it is for tax cut crowd out variable, sometimes reducing it to statistical insignificance. The lower level of year by year variation may account for this. This can be illustrated using the formula for the standard error of the regression coefficient in a simple regression y = ƒ(x) given in Nau (2018):  √  s/ n SEb (slope) = Standard Deviation X    e2 , (where s = (1/n − 2) ∗ e2 is error variance and n is sample size) The larger the standard deviation of the explanatory variable (X ) data, ceteris paribus, the smaller the standard error, and therefore the larger the coefficient’s t-statistic. Put another way, even where the underlying economic relationship between a dependent and an explanatory variable is real, you must have sufficient variation in the explanatory variable to show it had a statistically significant effect on the dependent variable. An alternative formulation can be derived from this equation. It more commonly used in economics texts, e.g., Hill et al. (2011), to define the standard error of the explanatory variable in simple regressions: ¯ 2 SEbslope = σˆ 2 / Σ(x − x) In Table 3.12 we show levels of variation each decade in each of our consumption model’s explanatory variables. In looking at the decade

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Table 3.12 Ratio of standard deviation/average yearly change in standard consumption function variables Variable C (Y − T ) (T − G) T G (S + FB) PR DJAV POPYOUNG/OLD POPTOTAL M2AV-2TO-4 CONBOR

1960–1970

1970–1980

1980–1990

1990–1900

2000–2010

0.4 0.6 −6.1 1.3 0.7 2.3 5.3 1.1 0.9 0.1 0.5 −2.5

0.6 0.6 −5.9 3.1 0.8 4.1 24.8 26.1 57 0.1 1 −32.4

0.5 0.8 −2.3 1 0.3 8.2 −256.5 1.5 −0.5 0.1 1.2 329.9

0.5 0.5 2.3 0.6 0.7 1.2 42.1 1 −1.43 0.1 2.1 2.9

0.5 0.5 −1.9 −7.7 0.6 −11.8 −4.5 3.2 15.5 0.2 0.4 −3.5

by decade averages, the low level of variation in the (G) data probably accounts for the lower statistical significance levels routinely found compared to those on (T ). 3.4.3

Left-Out Variables

Some explanatory variables that do affect the dependent variable may not have been included in the model being tested. But the not-included variable that does affect the dependent variable may be correlated with an explanatory variable that is included. If the omitted variable is negatively related to the dependent variable, and positively correlated with an included variable in the model that has a positive effect on the dependent variable, the coefficient will reflect only the small net effect of the two contradictory influences, and be more likely to be insignificant. If the omitted variable is then added to the model, its negative effect is more likely to be captured by its own coefficient, not that of the explanatory variable already in the model with which it is correlated. Several potentially “left out” variables were tested that might possibly have affected the accuracy of crowd out estimates in some models tested. These included the M1 and M2 velocities of money, and the extent to which M1 grew when FR open market operations increased FR purchases of treasuries and agency securities. As shown in Table 3.11, there was

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no correlation found between variation in these variables (by decade), and the deficit when included in the standard consumption equation. Hence, there was no reason to think the coefficient on the deficit variable was either over or understated because of a failure to control for these variables in the model. 3.4.4

Multicollinearity

Levels of multicollinearity vary between explanatory variables from period to period. For this reason alone, period to period results may differ. The more highly intercorrelated two explanatory variables are, the lower their levels of statistical significance tend to be (Fox 1965; Pyndyck and Rubinfeld 1998). A complication with regression estimates from the standard model using only 1980–1990 data is that though the model explained 99% of the variance in consumption during that period, not a single variable was found statistically significant at the 5% level or higher. This suggests that the lack of a statistically significant crowd out effect during this period was due to some larger problem with the model, not lack of crowd out effects. In the 1980–1990 decade, the multicollinearity problem was substantial. There were 8 intercorrelations among the explanatory variables that were equal to or exceeded (0.59). This is extremely high compared to typical correlations in other periods in this paper’s models. High levels of multicollinearity occur in other decades as well. For either the 1970–1980 or 1980–1990 decades, there were seven intercorrelations among the explanatory variables equal to or above (0.60). This is likely to be a contributing source (or the only source) of the low t-statistic on the crowd out variable in Table 3.3 for the 1970–1980 decade (t = 1.4). Also insignificant was the t-statistic for the crowd out variable for the subsequent 1980–1990 decade (t = 0.1). Though multicollinearity is likely a significant factor here, other evidence discussed earlier suggests the lack of significance in the 1980–1990 decade stems principally from the low ratio of variation of (G) to average decade growth (33% for government spending).

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3.4.5

Insufficient Sample Size

There are nine explanatory variables in the standard consumption model and in some Table 3.3 tests, only ten years of data were used to estimate coefficients. Many variables, including the deficit variable, appear insignificant when testing a model with a 10 observation sample, but become significant when the same model is tested on 20 or 30 observation samples. For example, small sample size, can account for some of the insignificance found in the decade-sized samples used in Table 3.13 Increasing sample size to 20 or 30 years shows significant crowd out effects in one of the three samples. This problem is resolved in this study by requiring samples of data to include at least twenty observations. The other two samples contained the 1980s and 1990s decades data. The 1980s was characterized by lack of substantial fluctuation in the government spending variable. the 1990s by the “crowd in” effect resulting from deficit reduction during the decade. As explained earlier, either of these can cause crowd out effects to appear statistically insignificant when that decade alone is tested. But if one of those decades data is combined with enough additional data from other decades, the insignificance may disappear simply because of the increased degrees of freedom. In some cases we address this problem by ignoring findings from samples dominated by data when determining the percent of samples with significant crowd out results from these decades. Table 3.13 Single variable deficit significance in standard consumption model (multi-decade samples)

Period

60–80 70–90 80–00 90–10 60–90 70–00 80–10

average: average average average average: average average

Deficit (T − G) coef.(t-statistic)a

Deficit (T − G) coef.(t-statistic)b

+0.42 +0.16 +0.02 +0.25 +0.22 +0.09 +0.28

+0.45 +0.23 +0.01 +0.39 +0.29 +0.13 +0.37

(3.1) (2.9) (0.2) (3.2) (3.6) (1.5) (4.8)

(3.4) (2.4) (0.1) (3.0) (3.4) (0.1) (4.7)

a Standard Consumption Model w/o LF as stand-alone variable or

deficit modifier b Standard Consumption Model with LF as stand-alone variable

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Spurious Results Indicating Insignificance

Finally, we note that it is possible that findings of crowd out insignificance are spurious. We have attempted to eliminate this problem by testing all models in six to eighteen different, though often overlapping time periods. Initial findings which could not be replicated in most other periods tested were rejected as spurious.

3.5 How Should a Change in Loanable Funds Be Distributed to Tax and Spending Deficits As we show in Chapters 13–14, there is strong statistical evidence that “crowd out” undermines the stimulus effects of Keynesian-type tax cut and government spending deficits, and was found to have done so in most periods sampled, going back to 1960. There is also evidence to show that growth in the loanable funds pool during periods when deficits occur can offset some or all of the impact of the crowd out (Chapters 16–20). The loanable funds pool may grow endogenously due to changing economic conditions and their effect on saving or if there are changes in the level of foreign borrowing. Loanable funds may also grow for exogenous reasons as a result of FR open market efforts to buy bonds and thereby increase excess reserves in banks. This section describes how these increases in loanable funds are modeled and added to consumption and investment equations. Shown below is a model of how changes in loanable funds (S + FB), could be combined with tax cut deficits (T ) and spending cut deficits (G) to show the reduction in crowd out effects that occurs when the total pool of loanable funds increases. Before modification by changes in loanable funds, we define the magnitude of crowd out as equal to deficit size, i.e., (T ) or (G). Also shown is the revised magnitude of crowd out expected after modification of these deficit variables by changes in loanable funds. Let β 1 and β 2 show how the increase in loanable funds might be distributed between tax and spending deficits. Then the current period change in the deficit (T − G), as modified by a current period change in loanable funds (S + LF) may be shown as: (T − G) + (S + LF) = (T − G) + β1 (S + LF) + β2 (S + LF)

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Table 3.14 Coefficients of modified T , G variables and stand alone (S + LF) when (S + LF) distribution varies Test #

Modified T coef. (t-statistic)

Modified G coef. (t-statistic)

(S + LF) coef. (t-statistic)

Distribution to (T), (G)

1.

1.18 (3.7)

0.50 (6.5)

−0.46 (−1.4)*

12.

1.18 (3.7)

0.50 (6.5)

−1.13 (−1.4)*

13.

1.18 (3.7)

0.50 (6.5)

−0.80 (−1.4)*

14.

1.18 (3.7)

0.50 (6.5)

−2.05 (−1.4)*

15.

1.18 (3.7)

0.50 (6.5)

−1.23 (−1.4)*

0 * (S + FB), 0 * (S + FB) 1.0 * (S + FB), 1.0 * (S + FB) 0.5 * (S + FB), 0.5 * (S + FB) 0.33 * (S + FB), 0.33 * (S + FB) 0.2 * (S + FB), 0.4 * (S + FB)

*Results indicate crowd out effect coefficients on deficit variables modified by (S + FB) do not change with changes in how changes in loanable funds are allocated to the deficit variables when used to offset crowd out effects. As a matter of convenience, throughout this book we define β 1 = β 2 = 1.00

= (T + β1 (S + LF)) − (G − β2 (S + LF))

(3.3)

It is impossible from the models used in this study to tell empirically estimate how any increase in loanable funds is divided between these two deficits, but this does not appear to matter. In Table 3.14, we estimate the consumption model given in Eq. 18.1, except that it is only estimated using 1990–2000 data. The model was then estimated five times, each using a different division of the increase in (S + FB). Results are shown in Table 3.14.

3.6 Other Model Specification Issues: Different Deficit Modifiers Tested Probably the most important model specification issues addressing this study were addressed earlier in this chapter: (1) whether to use structural or nonstructural models like VAR, (2) why to use Cowles rather than DSGE structural models, and (3) exactly which control variables to use in structural models. But, there are others: exactly which form of modifier variable to use has to be determined. In Chapters 8 to 24, a variety of different crowd out modifiers are tested to determine which (if any) modifier seems to contribute the most

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to improving the accuracy with which we model actual crowd out effects. Some options are examined despite the fact they have only a tenuous relationship at best with any commonly understood theory of how changes in loanable funds may come about and affect crowd out. The definition of loanable funds (US national saving + foreign borrowing), used in the ERP 2013 Table 32, is the most theory consistent definition of loanable funds. By theory consistent we mean that this definition recognizes that both endogenous changes to total loanable funds, caused by changes in the economy, or exogenous changes due to FR open market operations may result in changes in total loanable funds. These changes may replace losses in loanable funds available to private borrowing due to the need to fund government deficits. However, it could be argued that this is misleading; that part of the (new level of the) loanable funds pool available to private borrowers is still less than it would be if there were no deficit. With no deficit, the whole increase in loanable funds would be available for new and expanded private consumer and business borrowing. There always appears to be unfulfilled private demand for loans. As noted earlier, the evidence for the 1960–2010 period examined indicate that in all years except the quantitative easing years (2008–2010), end-of-year excess reserve balances of banks were very small, about 2% of total reserves, (probably a precautionary balance rather than an indication of inadequate loan demand, since the loanable funds balance stays very small every year, in good times or bad). The fact that in most years, in addition to domestic lending, borrowers have also seen a need to borrow from foreign sources supports this argument. Hence it may be misleading to argue that increases in loanable funds “offsets” crowd out, as though in some sense it was preventing crowd out from occurring. It doesn’t; the increase just provides replacement private funds. But without the deficit, all the growth in loanable funds would be available to finance new private borrowing, not just ensure lower old levels are maintained. That is, it would be used to directly increase the GDP. However, since public spending enabled by the deficit is increasing, the GDP should increase because of that new spending too, even if the growth in loanable funds is diverted to restoring past levels of consumption investment and GDP. Which path to chose is fundamentally a public policy preference, not one that can be determined purely by analytics. Do we want future GDP growth to stem from increased production of private goods, or increased

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production of public goods? If private, no deficits at all, or tax cut only deficits, are called for. If public goods are preferred, spending deficits are called for. That said, there is an analytic aspect to the decision as well. If one path leads to a higher level of economic growth the future than the other, then we have a cost-benefit issue to resolve as well as a public preference issue. There may also be distributional differences in public vs. private spendinggenerated economic growth that affect the choice of paths selected by policy makers. Others may argue there are more accurate ways to show true crowd out effects, than by using (S + FB) to modify the deficit. Their arguments are that 1. Crowd out effects are best measured if the deficit is modified by changes in the money supply that occur. It is argued that increased M1 is a better measure of what is actually spent out of loanable funds increases than the total itself. But the two are closely related. The historically low level of excess reserves in banks at year’s end (see Chapter 15) suggests that by increasing the pool of loanable funds (S + FB), to some extent, increased M1 will also occur. 2. Actual crowd out effects may be best measured if the deficit is modified only by exogenous changes in the pool of loanable funds caused by Federal Reserve’s purchases of treasury and agency securities. (But it is not clear why exogenous changes would work as an offset, but not endogenous changes driven by changes in the economy like economic growth.) 3. Net crowd out effects may be best measured if the deficit is reduced by increases in just the privately available part of the pool of loanable funds; i.e., the total minus the part needed to fund the government deficit, (S + FB) − (T − G). All of these alternative modifiers, and others, were tested to determine empirically which modifier of the deficit best measured the actual crowd out effect of deficits during the 1960–2010 period. All were tested in what otherwise are the same standard consumption and investment models to ensure comparability of results. Results are given in Table 3.15. Definitions of acronyms used in Table 3.15 are included in the table.

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Table 3.15 Modifiers tested and test location by chapter Chapter #:

Deficit modifier relationship tested

9

Effect of Deficits modified by LF, with National Savings (S), and Foreign Borrowing (FB) Stand-Alone Variables on Crowd Out Effects Of Single Variable Deficit (T − G) Modified By LF, Using LF also as a Stand-Alone Variable Effects of Two Variable Deficit (T ) and (G) Modified by LF, Using LF as a Stand-Alone Variable Effects of LF and M1 as Modifiers Compared Effects of Deficits Modified by FR, or (FR and LF), with (S) and (FB) Stand-Alone Variables on Crowd Out Effects of Single Variable Deficit (T − G) modified by Only FR, with a Separate (LF − FR) Variable to Control for Other Factors Affecting LF Effects of Two Variable Deficit (T ) and (G) modified by Only FR, with a Separate (LF − FR) Variable to Control for Other Factors Affecting LF Effects of Single Variable Deficit (T − G) modified by FR, with a Separate LF − (T − G) Variable to Control for Private Saving and FB Effects of 2 Variable Deficits (T ) and (G) modified by FR or M1 on Crowd Out Using Private Saving and Foreign Borrowing (FB) to Control for Other LF Effects Effects of Two Variable Deficit (T ) and (G) modified by FR, Using (LF − FR) to Control for Other Parts of the Loanable Funds Pool Untestable Hypotheses Effects of Deficits Modified by Endogenous LF Compared to Total LF Modifiers Effect of (S + FB), (Tr + A), (S), and (S + FB) + (Tr + A) Used as Stand-Alone Variables Only Effects of Exogenous LF (FR), Endogenous LF (LF − FR) or LF Stand-Alone Variables Compared Difficulties Comparing Total and Endogenous Loanable Funds Separately in Same Model Effects of Two Variable Deficit (T ) and (G) Modified by LF or endogenous LF (LF − FR) Compared

10 11 12 13 14

15

16

17

18 19 20 21 22 23 24

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References Eckstein, O. (1983). The DRI Model of the U.S. Economy. New York: McGrawHill Book Company. Economic Report of the President. (2012, 2018). Washington, DC: Government Publications Office. Fox, Carl. (1965). Intermediate Economic Statistics. New York: Wiley. Griffiths, W., Hill, R., & Lim, G. (2008). Principles of Econometrics. Hoboken: Palgrave Macmillan Publishing. Goldberger, A. S. (1961, December). Stepwise Least Squares: Residual Analysis and Specification Error. Journal of the American Statistical Association, LVI, 998–1000. Hill, R., Griffiths, W., & Lim, G. (2011). Principles of Econometrics. Hoboken: Wiley. Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan. Johnston, D. (1963). Econometric Methods. New York: McGraw-Hill. Nau, R. (2018). Statistical Forecasting: Notes on Regression and Time Series Analysis. Duke University, Fuqua School of Business. Available at: https://people. duke.edu/~rnau/411home.htm. Pindyck, R., & Rubinfeld, D. (1998). Econometric Models and Econometric Forecasts (4th ed.). Boston: Irwin McGraw-Hill. Tinbergen, J. (1939). Statistical Testing of Business Cycle Theories, Volume 2. Business Cycles in the United States of America 1919–1932. Geneva: League of Nations. Triola, M. (2011). Elementary Statistics. New York: Pearson.

PART II

Theory of Crowd Out and Accommodative Monetary Policy

CHAPTER 4

Theory of Crowd Out and Accommodative Monetary Policy

Section 4.1 presents, in nonmathematical form, a theory of how, and under what conditions, an increase in Federal Reserve purchases of government securities can work to stimulate the economy. Section 4.2 provides a more mathematical exposition of how government fiscal policy can be used to stimulate the economy, how they can create a crowd out problem, and how increases in the pool of loanable funds, including FR security purchases, can offset the crowd out effects of government deficits, allowing the fiscal stimulus to work.

4.1 Under What Conditions, Federal Reserve Purchases of Government Securities Can Work to Stimulate the Economy 4.1.1

Overview

When the government attempts to stimulate the economy by increasing government spending or by cutting taxes, it creates or increases the budget deficit, which increases aggregate demand. If the deficit is avoided by offsetting changes in the other component of the budget (T or G), it creates offsetting decreases in aggregate demand, causing the stimulus to be ineffective. Hence, the fiscal actions must create a deficit (or reduce a surplus) if anything more than (at best) a marginally small balanced-budget multiplier stimulus effect is to occur. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_4

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To finance these deficits, governments borrow money from the pool of personal, business and public savings constituting national savings, and/or borrow from foreign countries (from their national savings). This pool of savings and borrowings is the “loanable funds” pool. When government borrows from this pool to finance a deficit, it reduces how much of the pool is available to consumers and businesses to borrow to finance part of their purchases of goods and services. This is a real problem, since in good times or bad, consumers and businesses always borrow money to finance some of their spending. This is why, historically, unborrowed loanable funds (excess reserves) in banks has only been about 2% of total reserves at each year’s end (see Chapter 5), an amount more likely explained as a precautionary savings action by banks than as an indicator that demand for loans is chronically less than supply. For decades, it has been argued that this “crowding out” of private borrowers by government borrowing can cancel out the stimulus effects of government spending and tax cut programs, but that this crowding out effect could be avoided if monetary policy by the Federal Reserve (FR) is “accommodative,” i.e., if the FR increases the pool of loanable funds available to private borrowers enough to replace the loss of pool funds to private borrowers caused by government borrowing. This can be done by having the FR purchases outstanding government securities held by banks, thereby increasing their loanable reserves to levels previously available before the government borrowing began. This solution has been part of standard economic theory for decades. In examining crowd out and accommodative monetary policy, this book has two objectives, one scientific and one institutional and policyoriented in nature. Scientifically, we want to (again) determine if the “crowd out” problem really exists. To do this, we will add a variable (the deficit) to widely accepted (“standard”) models of what variables drive consumption and investment spending. If adding the deficit variable increases the model’s accuracy in explaining consumer or investment spending, and shows, through the sign on the coefficient on the deficit variable that declining spending is associated with deficits, we will conclude deficits, cause crowd out. Then, if the deficit (crowd out) is found associated with reduced consumer and business spending, further tests will be undertaken to determine if increasing the pool of loanable funds, via “accommodating” monetary policy, can provide consumers and businesses with funds to

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offset lost borrowing opportunities due to crowd out. From a modeling perspective, if redefining the “crowd out” variable as the deficit reduced by any FR securities purchases creates a modified deficit variable that is even better at explaining variation in consumption and investment than the deficit alone, we will conclude accommodate policy works. This is done in Chapters 8–24. This study also looks, at the actual Institutional and managerial processes the FR uses to implement “accommodative” policy. We examine exactly from whom the FR purchases government securities in response to new or increases in old deficits, and to what extent. We determine if the amount purchased was large enough to create enough additional loanable funds to offset the deficit Also examined is whether it was an effective process, i.e., one likely, by increasing loanable reserves, to result in increased borrowing by those who wish to purchase real goods and services that raise the GDP and lower unemployment. If the sellers of securities to the Fed are investment banks and brokerage houses, which is the norm, this study looks at whether the proceeds received by such sellers are typically lent out to increase purchases of real goods and services like houses and cars that raise the GDP and lower unemployment, or just used by the sellers to purchase other securities, raising the securities markets. This is done in Chapter 5. 4.1.2

Detailed Analysis of the Crowd Out and Accommodative Monetary Policy Processes

4.1.2.1

Accommodative Federal Reserve Purchases from Depository Institutions When the US Federal Reserve (FR) wishes to “accommodate” stimulative fiscal policy, i.e., help ensure it will be effective, it increases the pool of loanable funds (excess, or non-required bank reserves). It uses open market purchases of US Treasury, Agency, or mortgage-backed bonds from banks to do this. If the bonds are bought from depository banks, the security sellers would be paid by increasing the banks reserves with the Federal Reserve. 1. banks, like commercial and savings banks, would be selling bonds to the FR because the demand for bank loans is greater than their supply of loanable funds. They sell bonds from their loan portfolios to get more money to lend for mortgage, car, furniture, etc. Such

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loans are used to increase demand for real goods and services, which stimulates economic growth. 2. Such banks might also sell bonds to the Fed in times of economic decline for precautionary reasons, to provide themselves with additional liquidity in the event that loan repayment failures reach a high enough level to leave the daily inflow of loan repayments lower than what’s needed help pay daily withdrawals by depositors. 3. It could also be that having sold bonds to the Fed, the bank decides economic conditions warrant increased prudence in lending, so the revenue received from selling the bonds just sits as excess reserves in the bank’s account. However, this would seem unusual: why would the bank have sold the interest-paying bonds in the first place if it thought prospects for lending the resultant reserves were dismal? 4.1.2.2

Federal Reserve Purchases from Non-Depository Institutions By comparison, when the Fed purchases bonds from non-depository (i.e., investment) banks and nonbank bond sellers, like brokerage houses, the sellers are paid (electronically by Fed Wire) from the Federal Reserve’s own accounts, unless the seller has a bank account at the Fed, in which case the Fed could pay by increasing its reserves. Most purchases of such bonds by the FR are from the FR’s primary dealers, which are mostly investment banks and securities dealers and brokerage houses. Until the 1999 repeal of Glass–Steagall, they were not allowed to undertake the type of wholesale and retail banking that commercial and savings banks do that stimulates the real economy, e.g., make car and house loans. Even today the amount of retail loaning they do is miniscule compared to their traditional business of selling securities to get money to buy other securities. If investment banks are selling bonds to the Fed from their own portfolio, principally it would be for portfolio balancing; i.e., to obtain money to buy alternative securities that currently appear to be a more profitable investment than government securities. Their sales of securities to the Fed do not affect the GDP in any direct way, if at all. If they were selling bonds to the Fed for a client (in their capacity as bond brokers/traders/portfolio managers), often it would have been because the client saw alternative securities that appears to be a more profitable investment, i.e., because the client was portfolio balancing. This does not affect the GDP directly, if at all.

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For example, the investment bank may be asked to liquidate bonds owned by a mutual fund client. The client most likely is liquidating the bonds to obtain funds to buy other bonds, stocks, or mutual funds, with no real impact on the GDP. The mutual fund might also be liquidating to obtain funds to redeem shares the mutual funds own clients wish to cash in so they can buy a new car or house, but fund trading activity for this purpose is far less common. When the investment bank or securities dealer is paid by the Fed, it deposits the money in its own bank, generating bank reserves, but typically, will draw them down quickly to buy the desired replacement security. The seller of the replacement security, most likely another security dealer, then deposits the payment in their bank. More likely than not, this dealer also sold the security to raise funds to buy yet another security that looks more profitable. This buying and selling by one dealer to and from another continues in a somewhat endless loop. There is a chain reaction of many financial transactions that follow the Fed’s sale, keeping the financial markets active, but few if any transactions that affect the real economy, so GDP and unemployment are not much affected. Payment for the initial purchase of treasury or agency bonds by the Fed was deposited in the dealer’s bank, creating new reserves. From then on, these reserves just move from bank to bank each day as dealers buy securities from one another. Money multiplier effects of fractional reserve banking could expand the amount of reserves created and lent out. Some portion of what’s lent out may affect the real GDP. But if the turnover of funds from trader to trader is rapid, which we would expect in normal times (generally, the only reason a trader is selling a security is to get funds to buy another), there is little opportunity for this money expansion effect lending to substantially affect the real economy. The rapid movement from trader to trader is likely to mean the reserves are little more than overnight reserves allowing for little more than overnight lending. The increase in reserves stemming from FR security purchases, may increase demand deposits, increasing (M1). But the additional M1 in investment bank’s bank accounts may mainly increase demand for stocks & bonds, increasing demand in those markets (we test for this in Chapter 12). It also raises security prices, since there is a change in money demand for those securities in what is typically an auction market, but no change in supply (we show in Chapter 12 that this happened with the increase in reserves generated by the QE program). Yet, for the most part, demand for real goods and services (i.e., those counted in the GDP) are

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not likely to be much affected. If demand for real GDP does not change, there is no incentive to change supply, hence the unemployment rate is not likely to change either. The attempt to use monetary expansion to stimulate the real economy will have failed if the Fed’s purchases of securities from investment bankers and brokerages just increases demand for securities, not real goods and services. There may be some subsequent positive effects on the real GDP because of rising stock and bond markets, but they are likely to have only a more marginal effect on total aggregate demand: 1. More brokers and traders may be hired, or their salaries increase due to the stock and bond market boom. This increases value added in the finance industry, a component of GDP. 2. The rising stock and bond market may also increase GDP by creating a Wealth effect, which stimulates consumer spending. Traditional estimates are the effect is about 2.5% of the growth in stock and bond market value, and it may be subject to a lag (Heim 2017a). 3. There may also be some increase in business investment due to a “Tobin’s q” effect from rising bond prices. Based on the analysis above, it may be more accurate to say that attempts to stimulate the economy through open market operations principally stimulate financial markets, but may also have a positive, though modest effect on the real economy. If bond market conditions are declining, broker/dealers may rush to sell treasuries (and other securities) to the FR before the markets drop further. Sellers may keep the proceeds in liquid form, perhaps in their own commercial bank checking accounts, not spending it in anticipation of market prices falling further and presenting even better buying opportunities in the future. The excess reserves portion could, of course, be lent out by the commercial bank to borrowers desiring to buy autos, houses, machinery etc., raising the GDP. This could raise the GDP without significantly changing the securities markets. But if the economy is bad enough for securities markets to be in decline, it is likely the decline is large enough to markedly decrease overall demand for commercial and personal loans to buy things in the real GDP. When market conditions are bad, even if payments to security dealers for selling securities to the FR are deposited in the dealers’ demand deposit accounts, creating lendable reserves, and it is lent out to “real

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goods and services” borrowers, the positive effects on demand for real goods and services may not be sustainable once the securities market decline ends. When a consensus is reached that the market has bottomed out, traders instincts will be to buy additional securities “at the bottom,” paying by drawing down demand deposits. Any loans to goods and services buyers made from the reserves created by dealer deposits into their accounts will have to be recalled, or new money flowing into the bank at that time that would normally be used to make additional loans, will have to be used to fund withdrawals from investment bank/trader accounts to buy new securities. If so, these withdrawals will increase demand for securities, raising security prices, but the real economy’s growth will be slowed or remain flat. Theoretically, it could even decline.

A Formal Model of the Effects of Fiscal Stimulus Programs, Their Crowd Out Effects, and How Accommodative Monetary Policy Can Offset Crowd Out Effects, Allowing the Fiscal Stimulus to Work

4.2

In typical models of GDP determination, the determinants of consumption, investment, government spending, and the trade balance are hypothesized, and the four equations expressing these determinants, additively combined into one GDP determination model. A simplified version of such a model, might look like this: C = c0 + c1 (Y − T ) − c2 (I nt)

(4.1)

I = i 0 − i 1 (I nt)

(4.2)

G, (X−M), = assumed exogenously determined In such a model, GDP determination is given as G D P = C + I + G + (X − M) = c0 + c1 (Y − T ) − (C2 + I1 ) + I0 + G + (X − M)

(4.3)

Or, consolidating (Y = GDP) terms, in more policy-usable form, G D P = (1/1 − c1 ) [c0 + i 0 − c1 (T ) + G − (c2 + i 1 ) (I nt) + (X − M)] (4.4)

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In such models, negative changes in (T ) or positive changes in (G), ceteris paribus, stimulate the economy (GDP). But to be stimulative, cutting taxes or raising government spending has to be done holding the other constant, i.e., By incurring a deficit, increasing an existing deficit, or reducing an existing surplus. But how exactly does one finance a deficit? There are three choices; 1. borrow funds from the pool of loanable funds (national savings + foreign borrowing) that would otherwise be borrowed and spent by consumers and businesses, thereby reducing how much they can borrow and spend. This is called crowd out of private spending. 2. print more money to finance the increased government spending or tax cut. That way, the deficit does not have to be financed by reducing the pool of loanable funds available for private borrowing. This is commonly referred to as Modern Monetary Policy (MMP). Think of this, conceptually, as one way in which accommodative monetary policy could theoretically work. There is a second, and more traditional, form of accommodative monetary policy. It is not intended to finance a deficit but to compensate for the negative offsetting effects on the economy that occur when deficits occur. This is done by Federal Reserve (FR) actions to replenish the loanable funds pool for losses in funds available for private borrowing due to the deficit, i.e., crowd out. This type of accommodative monetary policy (or at least the theory of it) has been around as part of monetary theory, since at least the 1930s. 1. The actual process for implementing the second type of accommodative policy is complicated. The FR purchases securities from banks that will use the proceeds to make loans to consumers and businesses who wish to buy real goods and services (or so the theory assumes). Some security purchases might be from individuals (the FR also assumes) will use the proceeds to buy real goods and services. 2. If the proceeds received from such security sales to the FR are deposited into the seller bank’s demand deposit account, or the selling individual’s’ demand deposit accounts, the M1 money supply increases. The sale of securities to the FR may also increase the seller’s income, depending on the capital gains realized. Any income not spent (definitionally) increases the pool of national savings.

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3. The FR may pay for such security purchases from banks by simply crediting the selling banks’ reserves with the FR. Such funds would then be drawn down as the banks lend these reserves out to those wishing to borrow funds to purchase goods and services. Typically, such loans are deposited in the borrower’s demand deposit account, increasing the money supply. Payment in the form of currency has the same effect, as does payment by check from the bank’s own demand deposit account. Should the FR purchase securities? Traditional monetary theory, e.g., Friedman (1963) argues the FR reserve should grow the money supply at the expected rate of growth of the economy; more would be inflationary, less deflationary. Crowd out theory is a slight extension of this; it argues the expected rate of growth will be higher with fiscal stimulus than without, but only if monetary policy is accommodative, i.e., grows enough to cover reduction in private borrowing possible because of the deficit. Absent this, we get a “Volcker Effect”; failure of the money supply to grow at the economy’s expected growth rate stifles growth, creating deflationary (or reducing inflationary) effects. 4.2.1

Crowd Out Effects of Deficit Financing

We can show the negative effects of the crowd out problem on private borrowing by modifying the stimulus model shown in Eqs. 4.1–4.4 by adding a variable to both the consumption and investment equations to show the effects of the deficit on consumer and investment spending. In the equations below, deficit values of total government revenue minus total government spending (T − G) have a negative sign, surpluses a positive sign. The marginal effect on consumption of an increase in (T − G), (a decrease in the deficit), c3 , is assumed positive. C = c0 + c1 (Y − T ) − c2 (I nt) + c3 (T − G)

(4.5)

I = i 0 − i 1 (Int) + i 2 (T − G)

(4.6)

G, (X − M ), = assumed exogenously determined

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In such a model, GDP determination is given as the sum of the determinants of production of consumer and investment goods, plus goods produced for government use and for export (net of imports). G D P = C + I + G + (X − M) = c0 + c1 (Y − T ) − (c2 + i 1 ) (I nt) + i 0 + G + (X − M) + (c3 + i 2 )(T − G) = c0 + c1 (Y ) + (−c1 + c3 + i 2 ) (T ) − (c2 + i 1 ) (I nt) + i 0 + (1 − c3 − i 2 )(G) + (X − M)

(4.7)

Or in more policy-usable form, G D P = (1/1 − c1 ) [c0 + i 0 + (−c1 + c3 + i 2 ) (T ) + (1 − c3 − i 2 ) (G) − (c2 + i 1 ) (I nt) + (X − M)]

(4.8)

Comparing Eqs. 33.4 and 33.8, we see that the pre-multiplier stimulative effect of tax cuts (−c 1 T ) and spending deficits (1.0)(G) are reduced by the marginal effect on consumption and investment (c 3 + i 2 ) of reduced funds available for private borrowing. The reduced stimulus is +(−c 1 + c 3 + i 2) (T ) for tax cut deficits and (1 − c 3 − i 2 )(G) for deficits caused by spending increases. 4.2.2

How Accommodating Monetary Policy Offsets Crowd Out Effects

If we modify Eqs. 4.5–4.8 slightly, we can show how implementation of traditional accommodative monetary policy can offset crowd out. Traditional accommodative monetary policy involves expanding the pool of loanable funds available to private borrowers to the level previously available to them, before government borrowing to finance the deficit. The modification to our simple model above involves adding a variable, namely consumer of business borrowing (Borc , or BorI ), to the variables already in those models determining the level of consumer or business demand for goods and services. There is extensive evidence, showing that consumer borrowing and business borrowing account for variation in consumer and investment spending that would otherwise be unexplained (for example, Heim (2017a), eq. 4.4.TR, 5.4.TR). Further, US bank excess loanable reserves at year’s end have only been 1–5% of total reserves during the nearly

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50 year period 1960–2007. This near-zero level of excess reserves was found in recessions as well as normal times (see Chapter 8). Only with the advent of Quantitative Easing (QE) was that pattern broken, and excess reserves jumped to 96% of total reserves. This suggests that during 1960–2007, the demand for loans chronically has nearly equal to the supply of loanable funds. In reality, the small level of excess reserves suggests it was probably kept for precautionary reasons, not because banks had run out of customers to lend to. This suggests that increasing the pool of loanable funds will increase borrowing, which in turn, will increase consumer and investment spending, thereby stimulating the economy. Chapter 31 shows extensive statistical evidence indicating that increases in the loanable funds pool very consistently increases business borrowing, and also consumer borrowing, though not as consistently. Repeating the crowd out model given in Eqs. 4.5–4.8 with this modification for borrowing, we have: C = c0 + c1 (Y − T ) − c2 (I nt) + c3 (T − G) + c4 (Borc ) I = i 0 − i 1 (Int) + i 2 (T − G) + i 3 (BorI )

(4.9) (4.10)

G, (X –M ), = assumed exogenously determined In such a model, GDP determination is given as GDP = C + I + G + (X − M) = c0 + c1 (Y − T ) − (c2 + i 1 )(Int) + i 0 + G + (X − M) + (c3 + i 2 ) (T − G) + c4 (Borc ) + i 3 (BorI ) = c0 + c1 (Y ) + (−c1 + c3 + i 2 )(T ) − (c2 + i 1 )(Int) + i 0 + (1 − c3 − i 2 )G + (X − M) + c4 (Borc ) + i 3 (BorI ) (4.11) Or in more policy-usable form, GDP = (1/1 − c1 ) [ c0 + i 0 + (−c1 + c3 + i 2 )(T ) + (1 − c3 − i 2 )G − (c2 + i 1 )(Int) + (X − M)] + c4 (Borc ) + i 3 (BorI )

(4.12)

The model suggests that both fiscal and monetary policy can expand the economy.

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For fiscal policy the expansion is due to the increased demand resulting from tax cuts and increased government spending. But only if crowd out effects are offset by increases in the loanable funds pool. For monetary policy, expansion of the economy can occur through open market operations that expand the loanable funds pool when deficits occur, allowing private borrowing and spending to remain at previous levels. The model also implies that even if there is no deficit, monetary stimulus, through open market purchases of securities by the FR, can have a positive effect on the economy. While monetary policy can offset a deficit’s crowd out effects, in the theory presented above, it does not require a deficit to have a positive effect on the economy. That said, the demand for loanable funds is not insatiable, as we learned with QE, when excess reserves which had varied only from 1–5% of total reserves in the 47 years preceding QE’s start in 2008, rose to 93–95% in the 2008–2010 period. So there is some upper limit to the effectiveness of monetary policy, and it depends and it is set at the maximum amount people are willing to borrow. Increasing the loanable funds pool beyond this just leads to the “pushing on a string” problem. Determining just where that limit is an empirical question beyond the scope of this book, although data in Chapter 15 can give us an idea. However, where there is evidence that where prior levels of private borrowing were once higher, but are now crowded out by a deficit, increasing the loanable funds pool by enough to restore the old borrowing level, should offset the negative effect of crowd out, e.g., Chapters 21, 22. The loanable funds pool can increase due to endogenous factors fluctuations in the economy as well as the FR’s exogenous actions. A booming economy, via increased borrowing, will increase the money multiplier and therefore total lendable reserves. Via this channel, as well as by any increases in savings due to increasing incomes, the pool of loanable funds can be increased. Absent a deficit, any increase in the pool of loanable funds can be applied to additional borrowing and spending, growing the economy (provided the economy is not already at full capacity). With a deficit, part or all of any increase in the pool is drained off just to maintain the same amount of private borrowing and spending as in prior periods. The diversion of part of the growth in loanable fund to restoring private borrowing to its old levels would leave less (or none) available to finance new economic growth. While true, diversion of this year’s loanable funds growth to offsetting crowd out allows the government’s fiscal stimulus

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program to work. This too will increase economic growth. Hence, both deficits and non-deficit uses of increases in the loanable funds pool can stimulate economic growth, and it is beyond the scope of this book to try to determine which is better. The net effect on the growth rate of one choice versus another will depend on the relative stimulus effect of diverting part of the loanable funds growth from private borrowing (and spending) to public borrowing (and spending). The increase in government demand for goods and services financed by the deficit will provide new stimulus to the economy. If it provides as much stimulus as the same growth in loanable funds would provide if left available for private borrowing, there may be no net effect on the overall long-term growth rate. One may have a larger effect on growth than the other, but that is a difficult question to answer theoretically to everyone’s satisfaction. It is more a question for empirical testing to resolve. And the type of deficit can make a difference. If all tax cuts were saved, there would be no decline in the part of the loanable funds pool available for borrowing (but no net stimulus effect from the tax cut either). The choice of whether to use increases in the loanable funds pool to finance increased public versus private sector demand will change the composition of the economic growth. If allocated to public demand, i.e., used to finance deficits, there will be less private borrowing to buy cars, houses, and furniture in the long run, and more borrowing to finance public health, transfer programs, and infrastructure building. Hence, we conclude that using a fairly standard theoretical model of GDP determination shows that: 1. government deficit spending programs can stimulate the economy 2. crowd out effects of deficit financing are real and can reduce or eliminate the stimulus effects of deficits. 3. To offset any crowd out effects, open market operations by the FR accommodative monetary policy) can increase the pool of loanable funds available to private borrowers to the extent needed to offset crowd out. This allows the full stimulus effects of deficit-financed fiscal policy to be felt in the economy, raising the GDP and lowering unemployment. 4. Whether there is a deficit or not, when consumer and business borrowing is constrained by inadequate supplies of loanable funds, monetarily expanding the loanable funds pool policy can stimulate

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the economy. However, there are limits; the demand for loanable funds is not insatiable. Using monetary policy to expand the pool beyond the limits of what people want to borrow, largely determined by the general level of the economy, is just “pushing on a string,” and will not bring the desired benefit. Endogenous (growing economy) increases in the loanable funds pool due to an improving economy can also offset deficit’s crowd out effects. But without the deficit, it would increase total private borrowing (i.e., spending), stimulating the economy. The question is, if used to offset a deficit’s crowd out effects on private borrowing instead of increasing private borrowing, what will happen? Will the lost stimulus effect to the economy that would have been received by increased private borrowing be offset by the deficit’s own positive effect on economic growth? This is largely an empirical question. The multiplier effect of families buying more cars or houses may be greater (or less) than the multiplier effect of government spending on roads and bridges or transfer payments. We take no position on it here. 4.2.2.1

Differing Crowd Out Effects of Tax Cut and Spending Deficits The crowd out effects of government spending and tax cut deficits may be different. Our empirical tests often showed differing crowd out effects for tax cut and spending deficits (e.g., part of tax cuts is likely to be saved, reducing crowd out effects), so most crowd out tests in this book test separately for the crowd out effects of tax and spending deficits. There is past evidence of other kinds of differential effects as well. In Heim (2017a and b), crowd out effects of tax cut deficits reduced consumption more than increased spending deficits, and vice versa for investment spending deficits reduced investment more than tax deficits. Distributional effects seemed to explain the different effects of tax and spending deficits. Tax cuts tend to be skewed toward the upper end of the income distribution, and recipients have higher marginal propensities to save. Hence, they consume less per dollar of tax cut and return more to the loanable funds pool than do the typical recipients of spending deficits, who are skewed further down the income distribution and spend more on consumption and are less able to save.

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In addition, as we show in Chapter 24, increases in the loanable funds pool tend to be channeled to business borrowers, not consumer borrowers. Hence, consumer borrowing and spending is likely to increase little just because the pool of loanable funds has increased. increases in loanable funds. However, business borrowing and spending are likely to increase more, since if saving from the tax cut is large, it offsets crowd out, and leave much or all of the increase in loanable funds available to finance increases in investment spending. To capture these different effects, we can make an additional modification to the crowd out variables in our consumption and investment equations. To do so we replace c 3 (T − G) in our consumption equation with c 3a (T ) − c 3b (G). We also replace i 2 (T − G) in our investment equation with i 2a (T ) − i 2b (G). Repeating the crowd out model given in Eqs. 33.9–33.12 with this modification for differential crowd out effects of spending and tax cut deficits, we have: C = c0 + c1 (Y − T ) − c2 (Int) + c3a (T ) − c3b (G) + c4 (Borc ) (4.13) I = i 0 − i 1 (Int) + i 2a (T ) − i 2b (G) + i 3 (BorI )

(4.14)

G, (X − M ), = assumed exogenously determined In such a model, GDP determination is given as G D P = C + I + G + (X − M) = c0 + c1 (Y − T ) − (c2 + i 1 ) (Int) + i 0 + G + (X − M) + (c3a + i 2a )(T ) − (c3b + i 2b ) (G) + c4 (Borc ) + i 3 (BorI ) = c0 + c1 (Y ) + (−c1 + c3a + i 2a ) (T ) − (c2 + i 1 ) (Int) + i 0 + (1 − c3b − i 2b ) (G) + (X − M) + c4 (Borc ) + i 3 (BorI ) (4.15) Or in more policy-usable form, showing the multiplier: GDP = (1/1 − c1 ) [c0 + i 0 + (−c1 + c3a + i 2a ) (T ) + (1 − c3b − i 2b )(G) − (c2 + i 1 )(Int) + (X − M)] + c4 (Borc ) + i 3 (BorI ) (4.16)

Equation 33.16 shows clearly the negative effect of crowd out on consumption and investment, but allows for the coefficients expressing

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the crowd out effects of tax cut and spending deficits to be different. With crowd out, the pre-multiplier stimulative effect on GDP per dollar of tax cut is reduced from −c 1 to +(−c 1 +c 3a + i 2a) , and the stimulative effect per dollar of spending increase is reduced from (1) to (1 − c 3b − i 2b ). 4.2.2.2 Alternative Ways of Modeling Crowd Out Effects In Chapter 31 extensive statistical evidence is presented indicating that increases in the loanable funds pool (LF) are associated very consistently with increases business borrowing, but only associated with increases in consumer borrowing as well in some time periods sampled, not in others. This may be because priority in channeling loanable funds pool funds goes to business lending. Depending on business needs, this leaves differing parts of any increase in loanable funds available for consumer borrowing in some periods, but not in others. Hence, the finding of significant relationships between increases in loanable funds and consumer borrowing in some periods, but not in others. This hypothesis is consistent with our findings in other chapters that a given sample period’s change in loanable funds is more likely to reduce investment crowd out than consumer crowd out. In the Chapter 21 data, changes in loanable funds eliminates investment crowd out in virtually all periods sampled, but for consumption, only in about half the same periods, most often time periods that included QE program years, when increases in loanable funds were far greater than businesses wished to borrow. Increases in the loanable funds pool (S + FB), if large enough, should allow increases in private borrowing and spending that fully offset the negative effects of crowd out. That is, should prevent deficit-induced declines in consumption or investment. Then we can model the effects of changes in the pool of loanable funds on consumption in two ways. First, in the manner shown in Eqs. 4.13–4.16 where consumer borrowing (Borc ) is shown as a determinant of consumption. As discussed earlier, the chronically small level of excess reserves in banks during the years since 1960 (QE period excepted) suggests demand for loans typically exceeds supply. Therefore, to a degree of approximation, increases in the pool can normally be expected to increase borrowing. And because people borrow mostly to allow additional spending, increases in the pool increase spending.

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The model of crowd out and its effects shown below assumes that the level of consumer borrowing is directly influenced by a change in loanable funds available. Empirical evidence in Chapter 31 supports this. The effect of a change in loanable funds (LF) is shown as a separate standalone variable; this amounts to the assumption that we are showing its effect on borrowing separately, and leaving the consumer borrowing variable in the model to account for the other factors that influence consumer borrowing. The coefficient on this LF variable represents its marginal effect on consumption. In consumption models, a change in the LF pool may have two separate, and contradictory effects: 1. it may have the positive effect of offsetting crowd out 2. it may also have a negative effect since at any given income level (and our statistical models, when tested, hold disposable income constant when estimating crowd out and loanable funds effects), any increase in savings out of personal income must (definitionally) come at the expense of consumption, i.e., income = consumption + savings in which case, the coefficient on the stand-alone LF variable, where LF = (S + FB), will represent the net of the two effects. The coefficient may be positive or negative, depending on which of the two influences is the larger. It may be zero if they are the same. Assume they are the same. Then we might rewrite Eq. 4.13 as 4.17, where for ease of exposition we are assuming no other factor affects consumer borrowing except changes in LF C = c0 + c1 (Y − T ) − c2 (Int) + c3a (T ) − c3b (G) + c4 (LF) (assume for now c4 = 0)

(4.17)

Alternatively, we may show the positive and negative effects separately, by including (LF) directly as a variable modifying the deficit variables, as well as include it as a stand alone. In this case, the coefficient on the stand alone will pick up the negative effect on consumption of the decline in mpc necessary to allow an increase in saving (i.e., LF). The coefficients on the now-modified deficit variables will show the positive effects on consumption of crowd out reduction, as shown below.

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1. We can show the positive effect by adding any rise in (LF), a positive number, to the tax cut’s gross crowd out effect, i.e., the cut in (T ), which is a negative number, since ceteris paribus, a decline in (T ) is a deficit-creating or increasing change. The whole change in loanable funds can be used to offset whichever type of deficit occurs: the tax cut deficit or the spending deficit (we showed earlier in this chapter that doing this or dividing it into two parts yields the same statistical results). For tax cut induced deficits, this gives a modified crowd out effect of (T + LF), e.g., (−100 + 50 = − 50). For deficits due to increased spending, we can subtract any increase in loanable funds (LF) from the spending deficit’s gross crowd out effect (G) to get (G–LF). Since spending increases are measured as a positive number, subtraction of LF is an appropriate way to reduce the gross effect for any increase in available loanable funds. For years in which both tax cuts and spending increases occur, the offsetting effects of LF would be prorated, but as notes, statistical tests earlier in this chapter indicated this is not necessary. 2. We also continue to include the same variable (LF) as a separate, stand-alone variable to capture the negative effects on consumption. Then for consistency with Eq. 4.17, our alternative model must be

C = c0 + c1 (Y − T ) − c2 (Int) + c3a (T + LF) − c3b (G − LF) + (?)(LF) = c0 + c1 (Y − T ) − c2 (Int) + c3a (T ) − c3b (G) + ( c3a + c3b )(LF) − (c3a + c3b )(LF)

(4.18)

The only way for this alternative model to achieve consistency with Eq. 4.17 assumed net LF effect of zero and maintain the same coefficients on all the other variables in the 4.17 model is for the coefficient on the stand alone to equal the sum of coefficients on the LF modifiers of (T ) and (G), but with the opposite sign. Consistently, throughout this book, our tests show this result for the coefficient on the stand-alone variable, when the deficit variables are also modified. However, we find that negative effect on consumption is larger than the positive effect, and as a result, the coefficient on the stand-alone LF variable has a net negative sign. That is, increases in (LF) helps reduce crowd out effects, but the decline in the mpc necessary to generate the increased (LF) is even larger, leaving a net negative effect of changes in the (LF) pool on consumption (ceteris paribus).

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In both model alternatives, (1) the model with both a stand-alone (LF) variable, and modified deficit variables (T + LF) and (G − LF), and (2) the model with unmodified (T ) and (G), but including a standalone (LF) variable, are both estimated and used in almost all tests throughout this book. This allows for comparison of estimates of the model showing separate positive and negative effects of changes in the loanable funds pool on crowd out (model 1 above) with estimates of just the net effect for the crowd out variables (model 2). In all actual testing, the consumption function tested includes many more variables than the simple expository model above. See Chapter 21 for the regression results for each variable used in the more sophisticated models. Regression results for variables in the more detailed version of the 4.17 model given in 4.18 (deficit variables modified) are identical to those used in 4.17, with one exception. The exception is the coefficient on the LF variable. In the 4.17 model, the single LF variable coefficient has a net value equal to that shown by adding the positive and negative effects coefficients on the (LF) variable shown in model 4.18. The parameter estimates for the (LF modified) deficit variables remain the same in both models because by modifying (T ) and (G) we are not changing the linear way in which these crowd out variables affects consumption. Only the values of the variables multiplied against these parameter estimates changes when they are modified: (T ) becomes (T + LF), and (G) becomes (G − LF). However, there is a non-acceptable way of modeling the effects of changes in loanable funds on consumption. It would be to just add or subtract LF changes to deficit variables, i.e., (T + LF) and (G − LF), but not include a stand-alone (LF) variable in the model. Suppose the net effect of the two separate loanable funds effects on consumption was zero. If we add a variable which has no net effect on consumption (LF) to two variables (T ) and (G) which do have precise crowd out effects, we have changed the values of these quantitative measures of crowd out. We now have imprecisely defined measures of crowd out, and are asking the regression to tell us whether these imprecise measures of crowd out effects have the same effect as the more precise measures. Generally, in hundreds of

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statistical tests in this book, the result is the estimated effect of the crowd out variables declines markedly, and often become statistically insignificant. This is exactly the result econometricians expect when confronting the “errors in variables” problem, where only a partially inaccurate data set is available for estimation (Johnston 1963). Though illustrated using consumption Eqs. 4.17 and 4.18 we can repeat the same two separate, but equivalent tests of loanable funds effects on investment, using the standard investment model, and obtain the same results: When moving from just using a stand-alone variable to represent loanable funds to using the stand-alone plus loanable funds modified deficit variables, all coefficients in the two models stay the same except for the coefficient on the stand-alone LF variable. See for example Chapter 21, Eqs. 21.3 and 21.4. Consumption Models With and Without a Stand-Alone (LF) Variable With consumption, a change in LF has two separate effects on consumption, a separate positive effect in reducing crowd out, and negative reduced mpc effect from shifting income from spending to saving. Combining the two effects by just using (LF) as a modifier of the deficit variables, and dropping the stand-alone (LF) variable from the model, just distorts the real effect of (LF) on crowd out alone. Let LF effects on consumption be given as C = c1 (T + LF) − c2 (G − LF) − c3 (LF)

(4.19)

The combined effect of two (LF) forces on consumption, a crowd out force and an mpc-changing force, when combined in a model showing only crowd out variables, but no stand-alone LF variable, gives what appears to be crowd out effects defined as c 1 (T + (1 − c 3 )LF) for tax deficits and −c 2 (G − (1 − c 3 )LF) for spending deficits. In a consumption model with deficit variables modified this way, and without the stand alone, we would expect a priori that empirical tests will show reduced coefficients (and significance levels) on the crowd out effects variables compared to consumption models using the LF variable as both a deficit offset and separately, as a stand-alone variable to capture mpc effects. For example, assume the real crowd out effect of a tax cut is c1 (T + LF), e.g., c 1 (−100 + 50) = c 1 (−50), and the larger absolute value of the variable (T + (1 − c 3 )LF), (e.g., −100 + (1 − .5)*50) = − 75 is used to estimate c 1 . Because the effect of LF on the crowd out crowd out variables is now misstated, we would expect lower levels of statistical

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significance, and lower R 2 s as well. This is exactly what we get when testing this type of consumption model (see Chapter 21, Tables 21.1 and 21.2). 4.2.2.3

Investment Models with and Without Stand-Alone (LF) Variables However, with investment models, any increase in loanable funds has just one effect, and it is positive: it increases investment. Therefore, increases do offset declines in investment due to crowd out. Unlike consumption, they do not have a second, negative effect on investment of (in some sense) lowering the marginal propensity to invest. Hence, we do not need a model showing two separate effects. Consider the investment model given in Eq. 4.14, repeated here (assuming LF = borrowing): I = i 0 − i 1 (Int) + i 2a (T ) − i 2b (G) + i 3 (LF)

(4.20)

If there is no increase in (LF) when deficits occur, financing the deficit from the LF pool reduces the money available from the pool for private investment (I); the magnitude of the drop is the amount of the deficit. If there is an increase in the pool, every dollar can be used to offset the deficit-caused reduction in pool funds available for investment. And this can be done without causing a decline in investment for other reasons; while the marginal propensity to consume may decline when increased savings increases the LF pool, but the marginal propensity to invest does not. Given that, we can also reasonably hypothesize our theory of how crowd out and changes in the loanable funds pool affect investment as one without a stand-alone (LF) variable: I = i 0 − i 1 (Int) + i 2a (T + LF) − i 2b (G − LF) + i 3 (0 ∗ LF)

(4.21)

If we left the stand-alone LF variable in the investment model when estimating its parameters, we would be, in effect, dividing one positive influence into two parts, and assigning part of the influence to the modified deficit variables and the rest to the stand-alone (LF) variable. This would likely understate the stand-alone variable’s effect. This is exactly what we find in testing. See Chapter 21, Tables 21.4 and 21.5. With investment there is no a priori reason for preference of one model over the other:

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Using the model that includes the stand-alone LF variable plus the LF-modified deficit variables I = i 1 (T + LF) − i 2 (G − LF) + i 3 (LF)

(4.22)

The available loanable funds offset effect is equals (1 + i3 )(LF) for tax deficit years and -(1 + i3 )(LF) for spending deficit years. For a year in which deficits are partially (βi ) caused by tax cuts and partially (βj ) by spending increases, the modified crowd out expressions become i 1 (T + F) for tax deficit part and i 2 (G − (1 + i 3 βi )LF) for the spending deficit part, where (βi + βj ) = 1.00. Since the only effect a change in loanable funds has on investment is to offset crowd out effects (even to the point of creating what appears to be “crowd in” effects if large enough), so an alternative statement of how effective changes in (LF) are in offsetting deficits is I = i 1 (T + (1 + i 3 βi )LF) − i 2 (G − (1 + i 3 β j )LF)

(4.23)

The crowd out variable in 4.23 more clearly shows the magnitudes of true crowd out effects of deficits, net of any change in LF, on investment. Findings for both types of models are shown in Chapter 21, Tables 3. 4.2.2.4 Declining Deficits Cause “Crowd in” Effects When we experience periods of (LF) growth and declining deficits during the same period, the signs on our crowd out variables (T + LF) or (G − LF) may change, indicating a net “crowd in” effect on consumption or investment, i.e., a net positive effect. A slight rewriting of model 4.17 will illustrate the “crowd in” effect. Assume the value of government spending deficits have been larger than changes in LF levels in the past, leaving a net negative effect on consumption. But suppose this year, the spending deficit falls to zero (G = 0). Then C = c0 + c1 (Y − T ) − c2 (Int) + c3a (T + LF) − c3b (G − LF) − c4 (LF) (4.24) Or in first differences of the data, (where G = 0) C = c1 (Y − T ) − c2 (Int) + c3a (T + L F) − c3b (G − LF) − c4 (LF)

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C = c1 (Y − T ) − c2 (Int) + c3a (T + L F) − c3b (LF) − c4 (LF)

(4.25)

The value of the loanable funds modified government deficit variable −c 3b (0 − LF) = + c 3b (LF) becomes positive. The regression also no longer finds a negative relationship between this variable and consumption, but a positive one, and gives it a coefficient with a positive sign. We find this result later in this study when empirically estimating crowd out effects for decades like the 1990s. The 1990s were characterized by falling deficits. With a constant (LF) pool, a falling government deficit definitionally means more money becomes available for private borrowing and spending. Hence the positive “crowd in” relationship between consumption and (G − LF) we find in the 1990s data (Cptr. 21). A decline in deficits due to an increase in government revenue (T > 0) will also have a positive effect on consumption. If (LF) increase in the same period, the growth in C will be even larger. Typically, in empirical testing, we see this in the data as a larger than usual positive coefficient on the tax variable. If crowd out effects for both types of deficit are the same, the coefficient on (T − G) is the same as on the separate deficit variables. Using this single-variable formulation of the deficit, we can see even more clearly, the effect that results if the deficit has been larger than the level of loanable funds, but now falls to less than that level, C = c0 + c1 (Y − T ) − c2 (Int) + c3 [(T − G) + L F] − (c3 )(LF) (4.26) Or in first differences of the data, C = c1 (Y − T ) − c2 (Int) + c3 [(T − G) + LF] − (c3 )(LF) (4.27) And where  (T − G) = 0 C = c1 (Y − T ) − c2 (Int) + c3 [LF] − (c3 )(LF)

(4.28)

The same periods of “crowd in” effects were also found when testing the investment model.

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Should We Use Accommodate Monetary Policy to Offset Crowd Out?

The empirical findings of this study presented further support the theory crowd out effects can be offset by same-period increases in loanable funds. To say we “can” is science, but just because it is possible to do something (offset crowd out) doesn’t mean we should. That is a public policy question. This section deals with the question: “should we?”. Are there negative effects that offset the positive effects? Assume there is an increase in loanable funds. Without deficits, growth in the loanable funds pool increases the total amount of funds available to finance new private consumer and investment spending, which increases the GDP. The availability of loanable funds is important; The close to zero (2% average) as to banks’ remaining loanable funds at year’s end suggests that typically, demand for loanable funds may exceed supply, as it did consistently from 1960–2007. If deficits occur, financing them requires the government to borrow money from the pool of loanable funds they hadn’t needed before. That reduces funds traditionally available for private borrowing and spending, which lowers the consumption and investment parts of GDP compared to prior periods. Using any same-period growth in loanable funds to offset this decline in the part of the pool available for private borrowing, restores some or all of the old level of private spending out of borrowed funds, leaving GDP unchanged. However, using it to preserve prior levels of private spending, means it is not used to finance increased levels of private spending means (as it would be if there were no deficit), so no growth in private sector spending results. Hence, no increase in GDP due to increased private spending. But, using these funds to offset the deficit, eliminates the crowd out problem, allowing the deficit-financed increase in government spending or tax cut to stimulate the economy, increasing the GDP. While growth in GDP due to increased private spending may not occur if the government spending option is selected, growth in public spending will increase the GDP. For tax cuts, the “public” stimulus does come through the tax cut’s effect on private spending. The increase in loanable funds may offset the deficit, but the increased cash in consumer and business hands from the tax cut increase private spending increasing the GDP. Hence, in periods when the loanable funds pool grows, if no deficits occur in the same period, increased private borrowing and spending

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create growth in GDP. In periods when the loanable funds pool grows, but deficits occur in the same period, the increased public borrowing (to finance the deficit), and resultant government spending out of the borrowing, create growth in GDP. If the deficit is a result of tax cuts, the growth results from increased private spending. To summarize, when the loanable funds pool grows, or are anticipated to grow, three public policy options are available: 1. Choose to not deficit, and leave any increase in the pool of loanable funds to private parties to borrower and spend. Private borrowers will use it to buy more private goods (e.g.) cars, housing, machinery and factories 2. Deficit and channel the increase in loanable funds to public borrowers for use in cutting taxes, The cut in taxes will also increase private spending 3. Deficit, and leave the increase to government borrowers to finance more spending on public goods (e.g.), more policemen, social workers, schools, roads, and bridges. Public preferences depend on the type of growth people wish to see: would they rather have growth in public goods and services, or private goods and services? Public preferences would also be shaped by relative growth rates of all parts of the GDP ultimately resulting from choosing one of the three choices above. Those decisions are larger, global policy decisions, and beyond the scope of this study. In this study, our objective is to undertake further scientific analysis of crowd out, and the extent to which loanable funds (“accommodative monetary theory”) offsets it.

References Friedman, M., & Swartz, A. (1963). A Monetary History of the United States, 1867-1960. Princeton: Princeton University Press. Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan. Johnston, J. (1963). Econometric Methods. New York: McGraw-Hill.

PART III

The Effectiveness of Accommodating Monetary Policy Mechanics

CHAPTER 5

The Role of Primary Dealers, Investment Banks and Foreign Banks in Federal Reserve Efforts to Change Bank Reserves and the Money Supply

The role of primary dealers in the Federal Reserve (FR) efforts to stimulate the economy through open market securities purchases, is described below by the Treasury and the FR: …Primary dealers are banks and securities broker-dealers that trade in U.S. government securities with the Federal Reserve Bank of New York (FRBNY)…the FRBNY Open Market Desk engages in trades in order to implement monetary policy. The purchase of Government securities in the secondary market by the Open Market Desk adds to reserves in the banking system… The primary dealer system was established by the FRBNY in 1960 and began with 18 primary dealers. In 1988, the number of dealers grew to a peak of 46. As of November 2010 there were 22 primary dealers…. (U.S. Treasury 2018) Primary dealers - banks and broker-dealers that trade in U.S. Treasuries with the New York Fed—are the largest group of buyers at auction. These financial institutions are active in buying and selling U.S. government securities. Other auction participants include investment funds, pensions and retirement funds, insurance companies, foreign accounts, non-profit organizations, and others. Only the designated primary dealers are required to bid a specified amount in every Treasury auction. … Competitive bids © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_5

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are usually submitted by large financial institutions for their own accounts or on behalf of customers…. The detailed list of accepted and rejected competitive bids is not released to the public, but the total amount of bids received and total amounts accepted are made available. (NY Federal Reserve 2018) (Notice the absence of commercial and savings banks, on the list of primary dealers. Unlike many of the institutions cited above, these are the institutions whose main business it is to lend money to those who want to buy new goods and services, thereby stimulating the economy. Increasing their reserves is the fastest, most direct way of offsetting the crowd out problem that results from financing government deficits.)

5.1

Primary Dealers Dominate Auctions

For decades, the FR has relied heavily on primary dealers to serve as counterparties when it buys and sells government securities, as noted by the FR itself in the quote below: …Auction market participants submit bids through a communications system called TAAPSLink® . Institutions other than primary dealers15 (including depository institutions, other dealers, and institutional investors) use an Internet version called TAAPSLink v1. Primary dealers—which submit the largest volume of bids in almost every auction—use an alternative version called TAAPSLink v2. Retail investors with TreasuryDirect accounts submit bids by mail, telephone, and Internet applications that ultimately reach TAAPS through TAAPSLink v1. (NY Federal Reserve 2005)

Domination of Federal Reserve trading in the open market with primary dealers, rather than the general market, is not a recent phenomenon. SOMA (System Open Market Account) Records for 2006 indicate a similar dominance: During 2006, the value of permanent holdings…(of treasury securities)… in the SOMA portfolio increased by $34.2 billion…The expansion was achieved by $44.7 billion of outright purchases, mostly in the secondary market from primary dealers… (NY Federal Reserve 2007)

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What Type of Bank Does the Federal Reserve Purchase Securities from: Investment or Depository?

There are various monetary policy instruments that can be used to stimulate the economy. The most important, and most commonly used, of these instruments are 1. increasing bank reserves, which commonly leads to increases in the money supply, though not necessarily to the same extent (depending on money multiplier effects and proportions of new reserves in nonmonetary instruments) and 2. decreasing the short-term interest rate over which the Fed has direct control: the Federal Funds rate. Since doing the first is commonly thought to be required to do the second, both instruments are likely to be adopted simultaneously. This is not always the case, however. It is not impossible that some changes in the Federal funds rate (without changes in reserves) just reflect ex post facto action by the Fed to ensure Fed target rates for the rate remain in synchronized with the actual federal funds rates being negotiated between banks at a given time. Attempts to raise the money supply and cut rates are undertaken by buying up government securities or government agency securities in the open market. To reduce the money supply and increase the federal funds rate, the Open Market Desk at the New York reverses this process, selling securities and thereby reducing bank reserves and thereby, the money supply. The Federal Reserve does make public a complete list of approved “primary dealers” to whom it sells securities to and from whom it buys securities. The total number of dealers involved has varied from 20 to 46 in recent decades. Since the start of the dealer system in 1960 until recently, the dealers have included varying mixes of commercial and savings banks as well as investment banks and securities brokerage houses. Historically, the Federal Reserve has not revealed the names of the firms from whom it has bought or sold bonds (counterparties) in a particular period. In 2010, the Dodd–Frank Act required that the Fed, for the first time, publish the names of its counterparties in these security purchases and sales, and also the amounts purchased or sold by each firm.

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The Fed now publishes this data, starting with the third and fourth quarters of 2010, and extending through the first quarter of 2016 (as of this writing). The quarterly data is published after approximately a two-year lag. Presented below is a sample of the data from 2010–2016 to provide a comprehensive picture of the type of firms the Fed most commonly deals with, and the dozen or so most commonly used dealers. The sample includes the results for the first quarter of 2016, the full years 2014 and 2012, and the last two quarters of 2010. The transactions described were permanent purchases of US government securities. Other transactions, involving temporary purchases (“repos”), and purchases of US government agency bonds were also undertaken, but are not included in these lists. These purchases were all part of the “quantitative easing” program started in 2008 designed to stimulate the economy. They were part of the Bush administration/Federal Reserve efforts to rescue the nation’s big banks and investment houses from the threat of collapse. After 2008, QE was also a response to an economy which was responding sluggishly at best, to the $800 billion Obama stimulus program of 2009, particularly the unemployment rate. These FR purchases were intended to stimulate the real economy, that is, raise GDP and lower unemployment, by providing banks with additional reserves (“loanable funds” to lend out (strengthening financial institutions was another objective). Yet surprisingly, none of the purchases were made from depository banks. Depository banks are the commercial and savings banks whose lending is largely restricted to making loans that can be used to grow the GDP, and in the process reduce unemployment: e.g., loans to build houses, factories or office buildings, or loans to purchase machinery, cars or furniture. Instead, based on the data sampled, it seems the quantitative easing purchases were all made from investment banks or securities brokerage houses, institutions which typically sell securities for the purpose of raising funds to purchase other securities. After all, buying and selling securities is the business they are in. Such purchases are not counted in the GDP. The list of dealers from whom securities were actually bought in the period sampled (Q1: 2016, Q1–4: 2014, 2012, and Q3–4: 2010) is relatively small. The complete list is given in Table 5.1. Though not all of these firms sold treasuries to the Fed in all periods surveyed, many did.

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Table 5.1 Firms from which permanent treasury security purchases were made as part of the quantitative easing program (Q1: 2016; Q1–4: 2014, 2012; and Q3–4: 2010) Seller/Seller’s agent

Type of firm

Barclays Capital o BMO Capital Markets BNP Paribus Securities o Dawia Capital Markets o Deutsche Bank Securities USA o Goldman Sachs & Co. o

Brokerage Services Investment Bank Brokerage Services Investment Bank Investment Bank Investment bank; No commercial banking until 2018 Investment Bank Securities Brokerage Services Securities Brokerage Services

HSBC Securities (USA) J.P. Morgan Securities o Merrill Lynch, Pierce, Fenner & Smith Incorporated o Morgan Stanley & Co. LLC o RBC Capital Markets o RBS Securities

SG Americas Securities, LLC TD Securities (USA) LLC UBS Securities Bank of Nova Scotia, N.Y. Agency Cantor Fitzgerald & Co. Citigroup Global Markets Inc. o Nomura Securities Inter- national, Inc

Jefferies LLC o Society Generale, N.Y. Branch .Credit Suisse Securities (USA) .Mizuho Securities USA Inc. Cabrera Securities S G Americas Securities, LLC

Investment Banking Firm Investment Banking Firm Security Brokerage Firm. The company provides asset-backed loans including mortgage, auto, andmanufactured housing loans. It also offers trading andinvestment banking services Investment Banking Investment Banking and Brokerage Services Securities Brokerage and Trading Services Investment, Corporate Banking, Trade Related Capital Market Services Investment Banking, Real Estate Investing Institutional Brokerage, Portfolio Management, Capital Raising Securities Brokerage Services. It trades mortgaged-backed securities, structured financial securities, and equities. Investment Banking, Sales and Trading of Equities Investment Banking Investment Banking Investment Bank Securities broker Investment Bank

(continued)

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Table 5.1 (continued) Seller/Seller’s agent

Type of firm

G.X. Clarke Loop Capital Markets Mischler Group RBC Capital Services Banc of America Securities

Securities Broker Investment Bank Investment Bank/Brokerage Investment Bank Investment Bank

Sources Federal Reserve Bank of New York. Open Market Operations: Transaction Data. Available at www.newyorkfed.org/markets/omo_transaction_data.html; Firm description from Bloomberg Company Overview Reports. www.bloomberg.com/research/stocks/private or other internet sources of public information, usually the firm’s homepage

Note that there is not a single commercial or savings bank on this list. Table 5.2 lists the total amount of treasury securities permanently purchased by the Federal Reserve from the dealers noted above as part of the Quantitative Easing program during the periods surveyed between Q3: 2010—Q1: 2016. A survey of primary dealers in 1960, 1966 and 1978, 1988, 1998, and 2010 shows the proportion of Primary Dealers which were commercial or savings banks was markedly lower in recent decades than in 1960. Even in 1960, commercial or other depository banks were still a minority of all primary dealers, but at least were some of the institutions used. In 1988 the number of commercial or savings banks included tapered off, even as the total number of primary dealers rose, and in the 1990s plummeted to two, and in 2010 had dropped to zero. Results for the years surveyed were as follows: 2010 1998 1988 1978 1966 1960

0 2 6 7 8 4

of of of of of of

22 35 45 36 20 18

were were were were were were

commercial commercial commercial commercial commercial commercial

or or or or or or

savings savings savings savings savings savings

banks banks banks banks banks banks

Buying from depository institutions would seem preferred if GDP savings banksstimulus was the goal of the QE program. However, this assumes the depository institutions were holding as many government

5

THE ROLE OF PRIMARY DEALERS, INVESTMENT BANKS …

Table 5.2 Permanent treasury security purchases as part of the quantitative easing program (Selected periods Q3: 2010–Q1: 2016)

1/1/16–3/31/16 10/1/14–12/31/14 7/1/14–9/30/14 4/1/14–6/30/14 1/1/14–3/31/14 10/1/12–12/31/12 7/1/12–9/30/12 4/1/12–6/30/12 1/1/12–3/31/12 10/1/10–12/31/10 7/1/10–9/30/10

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$0.319 Billion in US Treasury Bonds Purchased by FR $10.578 Billion in US Treasury Bonds Purchased by FR $52.046 Billion in US Treasury Bonds Purchased by FR $81.287 Billion in US Treasury Bonds Purchased by FR $108.373 Billion in US Treasury Bonds Purchased by FR $272.151 Billion in US Treasury Bonds Purchased by FR $275.037 Billion in US Treasury Bonds Purchased by FR $292.859 Billion in US Treasury Bonds Purchased by FR $294.968 Billion in US Treasury Bonds Purchased by FR $226.003 Billion in US Treasury Bonds Purchased by FR $40.781 Billion in US Treasury Bonds Purchased by FR

securities as the Fed would have liked to purchase during QE. Unfortunately, that was not the case, as shown further below. Still, to the extent possible, it would seem that giving priority to purchases from commercial and savings banks would have better stimulated the economy. As we showed in the literature review section of this book, the business press was virtually unanimous in stating the main beneficiary of purchases under the QE program was the stock and bond markets, not the real economy (Chapter 2). This sounds much like saying the main beneficiary of FR purchases were investment banks and brokerages, not commercial and savings banks.

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5.2 Loss of Efficiency When Using Investment Banks and Brokerages to Implement Accommodative Monetary Policy As shown in the list of primary dealers above, the Federal Reserve, historically, has relied on purchasing securities from investment banks and brokerages. Such institutions sell securities to the Fed (or anybody else) mainly to obtain funds to buy other securities. After all, securities trading, not buying goods and services, is what they do for a living. This helps inflate bond market prices, helping Wall Street, but does little to increase the demand for real goods and services necessary to raise GDP and lower unemployment, which is what is needed if Federal Reserve actions are to help Main Street. That said, some small portion of their sales to the FR may be on behalf of customers who need cash to buy cars and houses, etc. Those purchases by the FR would raise the GDP, stimulating the economy. Because of this, testing should show an increase in loanable funds resulting from an increase in FR security purchases will have a smaller marginal effect on consumption and investment than an increase in loanable funds due to growth in the economic conditions driven (endogenous) portion of the loanable funds pool. And this is exactly what we see in Chapter 10. For consumption, in 6 of 6 periods tested, the estimated marginal effect on consumption of an increase in loanable funds is 94% lower for FR securities purchases than for increases in the endogenous part of the loanable funds pool (.33 vs. 02). For investment the marginal effect of an increase in loanable funds is 80% lower for FR purchases compared to endogenous growth in 5 of 6 periods tested (.20 vs .04). See Chapter 10 text accompanying Tables 10.5 and 10.6 for more details. The Federal Reserve’s purchases of securities would more likely stimulate the GDP and reduce unemployment if its purchases of securities were restricted to purchases from US commercial and savings banks. It is these banks, not investment banks and brokerages, that are in the business of directly lending money to consumers and businesses that want to buy, cars, houses, machinery, and other goods and services, the very actions which will raise GDP and reduce unemployment. FR open market operations to accommodate fiscal stimulus programs, both because they have typically only been a small fraction of the size they need to be, and because of the reliance on investment banks and brokerages, have not reduced the “crowd out” associated with stimulative fiscal policy much at all.

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The failure of accommodative monetary policy to fully accommodate appears responsible for the failure of fiscal stimulus programs to stimulate the economy. This failure has often been viewed as being an indication Keynesian fiscal policy doesn’t work; but the evidence strongly suggests any failures to stimulate were mainly caused by a failure of FR accommodative monetary policy to fully accommodate.

5.3 Primary Dealers Who Are Domestic Vs. Foreign Corporations Foreign banks and brokerages, or those with close connections to them, constitute a substantial portion of those who sell securities to the Fed. Table 5.3 shows the proportion of open market purchases of securities by the Fed were from foreign and US investment banks and brokerages during the 4th quarter of 2014 (37.4%). While we can’t be sure from this evidence what proportion of foreign sellers deposit their FR checks in banks in foreign countries (where it is likely to be used for foreign purposes), evidence presented below indicates some banks do. This provides one explanation of the discrepancy between the increase in Fed holdings of US Treasury, agency and GSEs during the QE years and the smaller increase in total reserves and currency in circulation in banks under its supervision in the United States. Evidence that much of the FR’s security purchases were from foreign bank branches outside the US Confirmation of FR financial transactions with foreign banks is provided by Tooze (2018), who notes In 2006, European banks generated a third of America’s riskiest privately issued mortgage-backed securities. By 2007, two-thirds of commercial paper issued was sponsored by a European financial entity… The Fed acted aggressively and also in highly ingenious ways, becoming a guarantor of last resort to the battered balance sheets of American but also European banks. About half the liquidity support the Fed provided during the crisis went to European banks… Tooze (2018), cited by Zakaria (2018). (emphasis added)

And

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Table 5.3 Q4: 2014 purchases of US securities by the federal reserve: $10,517.5 Million Fed Payment For Securities Bought (Millions)

Counterparty (Payee)

Headquartered: Domestic (D) or Foreign (F)a

$259.9

Bank Of Nova Scotia, NY D Agency 137.1 Cantor Fitzgerald & Co. D 745.6 Citigroup Global Markets D Inc. 2614.20 Goldman, Sachs & Co. D 542.9 HSBC Securities (USA) Inc. D 218.6 Jefferies LLC D 55.4 J.P. Morgan Securities LLC D 1116.60 Merrill Lynch, Pierce, D Fenner & Smith 892.2 Morgan Stanley & Co. LLC D $6582.5 US Treasury Securities Purchased from Domestic Firms 363.8 Barclays Capital Inc. F 473.7 BMO Capital Markets F Corp. 236.2 BNP Paribas Securities F Corp. 295.6 Credit Suisse Securities F (USA) LLC 57.4 Daiwa Capital Markets F America Inc. 285 Deutsche Bank Securities F Inc. 546.2 Nomura Securities F International 867.9 RBC Capital Markets, LLC F 388 RBS Securities Inc. F 197.2 SG Americas Securities, F LLC 106.1 TD Securities (USA) LLC F 117.9 UBS Securities F $3935.0—Purchased from Firms Foreign Owned or Closely Related to Foreign-Owned Firms a Firms were defined as “foreign” if they self-identified as being a non-US firm, were wholly owned

subsidiaries of foreign firms, or were closely related to foreign firms

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…(The crash of the financial system) had spectacular practical consequences in the crisis of 2008. A system characterized by massive corporate interlock faced meltdown. But it lacked an equivalent transnational stabilizing agency. De facto it was therefore the central bank of the United States, the Fed that emerged as the lender of last resort for the entire global banking system… Tooze (2018)

And ….the European financial system would not have survived the crisis had it not been for massive lender of last resort activity by the Fed. Between 2008 and 2009, more than half of the trillions of dollars in liquidity it provided to large banks went to banks that were not American…..Tooze (2018)

Buying bonds from (or lending money to) foreign banks did mean that a sizeable part of the loanable funds increase resulting from FR actions occurred in foreign countries, not in the United States. This diminishes the impact any given level of FR security purchases on the US economy compared to what would prevail if security purchases were only from domestic security sellers. Table 5.4 shows FR purchases of treasury and agency securities in the 1960s to be almost identical to growth in the monetary base. In the 1970s, 80s, and 90s the monetary base increased more than FR securities purchases, suggesting a net inflow of foreign purchasers of US securities, the proceeds from which were deposited in US depository institutions. In the 2001–2010 and 2011–2017 periods, FR purchases noticeably exceed growth in the monetary base, suggesting substantial Table 5.4 FR purchases of treasury and agency securities and growth of the monetary base (Billions)

Period

Growth in FR securities purchases

Growth in monetary base

1961–1970 1971–1980 1981–1990 1991–2000 2001–2010 2011–2017

$33.4 58.5 104.6 239.3 1618.7 1615.5

$32.2 84.2 155.7 279.8 1384.4 1250.8

Source See Table 7.9

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portions of the Feds purchases of treasuries and agency bonds were from foreign banks and brokerages, with deposits accruing in the foreign countries, not the United States. In the 2001–2010 period FR purchases were $234.7 billion greater than the growth in the US monetary base, and in 2011–2017, FR purchases were $364.7 greater than the increase in the US monetary base. It is of course possible that some funds initially deposited in foreign banks would ultimately be lent out to borrowers in the United States, but unlikely that 100% would be; exactly how much was is an empirical question difficult to answer due to fungibility issues. Hence, we conclude Fed purchases from foreign sellers would probably not increase the pool of loanable funds available to US citizens as much as restricting FR purchases to US sellers. This may be part of the reason why accommodating monetary policy does not seem to accommodate.

5.4 The Failure of Accommodative Monetary Policy before Quantitative Easing (QE) and Its Success After; The “Pushing on a String Problem” Excess reserves are a measure of how adequately the available supply of loanable funds is meeting the demand for loans by consumers and businesses. The excess reserves US depository institutions in recessions and non-recession periods is shown in Table 5.5. Levels of excess reserves in recessions and non-recession periods are compared before and after the “Great Recession” era which we define as starting with the financial system’s troubles in 2008. 5.4.1

Effectiveness of Accommodative Monetary Policy 1960–2007

Limitations in the supply of loanable funds, not a lack of demand for them, seems to determine the level of business and consumer borrowing. Table 5.5 indicates that prior to the great recession, whether in recessions or non-recession periods, excess reserves were very small, averaging only 2.1–2.2% of total reserves. This strongly suggests that in recessions as well as non-recession periods, there is no shortage of credit worthy borrowers (relative to the available pool of loanable funds, which of course declines in recessions). Therefore, reduction of the pool of loanable funds available for private use by consumers and businesses due to government

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Table 5.5 Excess reserves in US depository institutions during recessions and non-recessionary periods (Billions) Before the great recession era: Recession years between 1959–2007

Before the great recession era: Non-recession years between 1959–2007 (average)

Recession Years 1960 1961

Excess Total Reserves Reserves $0.89 Billion $41.08 Billion (Av.) (Av.) 2.2% = (Excess / Total)

Excess Reserves $0.74 Billion 0.58

Total Reserves $19.26 Billion 20.13

1974 1980 1981 1982 1990 2001

0.26 36.86 0.51 40.66 0.32 41.93 0.50 41.86 1.67 59.12 1.64 41.05 $0.77 Billion $37.61 Billion (Av.) (Av.) 2.1% = (Excess / Total) Great Recession Era Recession Years Between 2008–2017 Years

2008 2009

Excess Reserves $767.32 Billion

Total Reserves $820.86 Billion

$1075.20 1140.45 $921.26 Billion $980.65 Billion (Av.) (Av.) 93.9% = Excess /Total

Great Recession Era Non-Recession Years Between 2008–2017 Excess Total Reserves Reserves $1910.47 Billion $2042.54 Billion (Av.) (Av.) 93.5% = Excess \ Total (Av.)

Data Taken from Table 5.9

borrowing from the same pool to finance deficits is likely to cause a crowd out problem in recessions as well as non-recession periods. A more extensive study of crowd out effects in recessions and non-recession periods (Heim 2016) also concluded the same thing. This is a key finding for public policy to reduce the crowd out problem. This finding suggests the same policies are needed in recessions to combat crowd out as are needed in normal economic times. In the past, some economists have argued crowd out can’t be a problem in recessions, because private demand for loanable funds falls off, leaving funds to finance government deficits without reducing the

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amounts private consumers and businesses wish to borrow. Hence the stimulus effects of deficits will not be offset by crowd out. In recessions, it is argued, crowd out should not be considered as a reason why deficit finance won’t stimulate the economy. This study shows that while borrowing may drop off, the supply of loans falls off as fast or faster. This leaves any additional borrowing by government during recessions to finance deficits as likely to crowd out private borrowing as in normal times. Bank holdings of securities during recessions was also virtually unchanged from non-recession periods. Banks can only hold reserves, loan them out in traditional fashion to consumers and businesses, or loan them to the government, i.e., buy government securities with them. Excess reserves as a percent of total reserves could stay the same in recessions, even if the bank is unable to find credit worthy customers, if the bank buys government securities with the excess reserves. The constancy of securities holdings in recession and non-recession periods suggests the demand for loans relative to the supply is about the same in both. Hence the argument that excess reserves were low during even recession years in the 1960–2007 period was because banks used excess reserves to increase their holdings of treasury and agency securities, because they could not or would not loan out to their usual customers, does not seem to be supported by the facts. The better explanation seems to be that the demand for loans from credit worthy borrowers equaled or exceeded the loanable funds available 1960–2007, including the additional funds made available by the FR’s purchase of Treasury and agency securities. This comports with (Heim 2007, 2016), which found that crowd out is a problem even during recessions because the pool of loanable funds tends to fall as fast or faster than the fall in loan demand in the United States. During the same period, FR real holdings of Treasury and Agency securities during non-recession years averaged 5.3% of real GDP, but only averaged 4.8% in recession years. One would think that had the FR been trying to implement an accommodative monetary policy, the FR’s holdings of government and agency securities would have been larger in recession periods. Clearly, the main answer, at least for recession years through 2007, to the question: “Why doesn’t FR “Accommodative” monetary policy actually Accommodate?”

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is that the FR didn’t try to accommodate fiscal deficits. to anywhere near the level of accommodation needed. And there is substantial additional evidence to support this conclusion. Table 5.6 shows the size of the deficit in every year between 1960 and 2010, and the extent to which the Federal Reserve purchased enough Table 5.6 Real yearly changes in the deficit (T – G) and FR Security Purchases (Tr + A) (Billions of 2005 Dollars) Year

 (T − G)

(Tr + A)

Year

 (T − G)

(Tr + A)

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

46.9 −56.5 −28.4 26.3 −27.8 15.8 −17.7 −89.2 57.1 80.6 −120.4 −37.8 78.5 55.3 −53.4 −221.5 90.2 62.2 58.3 14.4 −116.1 15.7 −170.4 −66.6 43.3 −34.2 −45.8 62.3 39.8 10.0 −96.2

−0.3 7.8 6.0 14.4 12.2 16.7 10.0 18.7 8.3 7.3 7.7 16.8 −5.2 19.1 −9.4 −0.1 5.6 6.4 2.1 −6.1 −16.5 −6.3 −1.1 15.6 4.0 21.6 24.2 23.7 10.5 −24.6 −1.3

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

−68.1 −104.3 58.4 115.6 22.0 95.5 133.0 128.0 53.3 91.6 −255.2 −395.4 −102.0 47.4 155.9 99.3 −75.5 −379 −539.5 −23.6

30.2 28.0 37.8 30.6 6.2 6.1 37.1 18.9 22.1 26.2 31.2 74.7 25.2 33.3 2.4 10.1 −57.6 −239.1 1226.4 277.3

*Deficit growth is denoted with a negative sign

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securities to offset the deficit’s crowd out effects. Note than with the exception of the 1990s, a declining deficit period, the Fed only bought securities equal to 44% of the average deficit between 1960 and 1990, and only 23% between 2001 and 2007. The 1990s are an exception, there was no crowd out problem for the Fed to accommodate; in all but two of the 10 years 1991–2000 the deficit was declining, Hence, no accommodating Fed securities purchases were needed to offset crowd out. Purchases must have been for some reason other than accommodating the crowd out effects of deficits. Is there any evidence there was a “pushing on a string” problem during this period that might have made it pointless for the FR to do more? From 1960–2007, the data indicate FR expansion of the monetary base (and money supply) during recession years, to the extent it occurred at all, certainly did not result in a “pushing on a string” problem. Table 5.5 shows that up until the great recession era, slightly less excess reserves were to be found in depository institutions in recession years than during years without recessions. In recessions, the loanable funds pool appears to have declined slightly faster than consumer, business, and government’s desire to borrow. Given the constancy of bank security holdings, if loan demand had been falling faster than supply, we would see a build up of excess reserves in recessions. These results suggest that in throughout the 1960–2007 period, the level of borrowing was constrained by limitations on the supply of loanable funds, not by loan demand. Increases in both the monetary base and money supply, could have been substantially greater than they were without running into the “pushing on a string” problem. In short, it appears FR monetary policy could have been more stimulative to the economy than it was during recessions occurring in the 1959–2007 era, and probably during non-recessions as well since there were deficits then, too, that we not matched by increases in FR security purchases designed to increase the loanable funds pool by the same amount. We conclude that a crowd out problem will occur unless FR monetary policy is at least as expansive as the fiscal policy (i.e., the deficit) during the same period. Below, we will compare the size of monetary stimulus during recession years with the size of deficit-financed fiscal stimuli occurring at the same time. We will find that the attempts to accommodate fiscal policy were painfully inadequate throughout the 1960–2007 period. Many economists have argued that historically, they have seen little or no evidence that the fiscal stimulus programs worked. For the 1960–2007

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period, any failures of stimulative fiscal policy appear to be due more to the inadequacy of accommodate monetary policy than to any flaw in fiscal stimulus theory itself. Statistical tests introduced in Chapters 10 and 11 of this study show that tax cuts and government spending increases would positively affect consumption and investment were it not for the crowd out problem. In Table 5.7, we look at key statistics for 1959–2017 relating to monetary and fiscal policy during years in which recessions took place in at least two quarters of the year. We examine deficit growth and FR success in accommodating these deficits by making its securities purchases and the money supply grow in amounts equal to the deficit. We will also look at monetary base growth in those recession years. Clearly, FR purchases of treasury and agency securities increased in highly inadequate amounts (and sometimes actually decreased) compared to annual increases in the deficit in most recession years prior to the great recession era. Table 5.7 Levels of accommodating monetary policy compared to fiscal deficits in recession years during 1959–2017 (Nominal values) Accommodation In Deficit Years Year

1960 1961 1974 1980 1981 1982 1990 2001 2008 2009

Yearly Change in Government Deficit*

Change in FR Holdings of Securities

$8.5B −10.7 −16.7 −56.0 7.6 −95.1 −70.3 −232.4 −412.8 −592.6

$0.4B 0.7 4.4 3.5 8.8 7.7 8.1 40.1 −243.7 1349.00

Increase in M1

Increase in Monetary Base

Billions

% Growth (%)

Billions

% Growth (%)

$0.7B 4.5 11.3 26.7 28.2 38.1 31.8 94.6 228.7 90.6

0.5 3.2 4.3 7.0 6.9 8.7 4.0 8.7 16.6 5.7

$0.5B 1.8 9.0 8.7 9.6 11.0 22.5 50.7 833.4 365.7

1.0 3.4 8.4 5.2 5.4 5.9 7.0 8.1 96.3 21.5

* Deficit = total government revenues-total government spending on goods, services and transfers.

Years of deficit increases have negative signs; deficit reductions have positive signs

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In recession year 2009 the level of FR purchases was positive. It was more than twice as great in volume than what was needed to cover the bank liquidity problem caused by crowd out. Recall from Table 5.5 that excess reserves were very small before 2008, even during recession years. In the pre-great recession years, banks earned nothing on reserves from the FR, so they had little incentive to keep them. This suggests that if banks had more reserves to lend out, they would have lent them out, simply to maximize profits by earning interest. Hence the failure of FR monetary policy to be significantly accommodative during this period probably stifled much of the economic recovery that would have naturally stemmed from the deficit-financed fiscal stimulus programs that were undertaken. In fact it would seem that, intentionally or not, monetary policy fought attempts by fiscal policy to be stimulative during 1959–2007. This failure to adopt a more accommodative monetary policy may explain the limited M1 growth occurring in these recession years. In 8 of the 10 recession years (excepting 1981 and 1960) increases in M1 were not large enough to fully accommodate the growth in the nominal deficit, i.e., solve the crowd out problem. The gap between the increase in M1 needed and what actually occurred was large. For growth in the monetary base, the story is much the same. Fed action was inadequate to offset the nominal deficit in 7 of the 10 recession years (all except 1960, 1981, and 2008). The actual anti-stimulative sale of securities by the FR during 2008 seems incredulous to an outside observer, given that we were many signs we were approaching a recession year. But there is evidence the FR was trying desperately to keep the federal funds rate from completely collapsing during this period, which would have indicated the FR had lost control of interest rates. The FR may have sold the bonds in an effort to push the rate on the street back up to the FOMC target. Note the following report by the FR on open market operations during 2008: …After September 15, the magnitude of liquidity added to the system through various programs exceeded the Federal Reserve’s ability to offset with draining operations. And from the point shortly afterwards when it began to pay interest on reserves up to the December FOMC meeting, the Federal Reserve adopted an entirely different framework and set of operating procedures to implement monetary policy. Under this new

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framework, it relied primarily on the level of interest paid on excess reserves to influence market rates, while largely accepting a generally very high and variable level of excess reserves. But despite the efforts described above to improve its control over rates by successively narrowing the spread between the rate paid on excess reserves and the fed funds target, the fed funds rate traded at levels significantly below-target. (NY Federal Reserve, January 2009, p. 6, emphasis added) Note also that there is some indication here that the FR also understood the policy of paying interest rates on reserves, started in October 2008, was one factor causing unprecedented growth in excess reserves in the system in 2008.

Table 5.8 presents results for the same variables as in Table 5.7, but in real, not nominal, terms. In Table 5.8, we see that in 9 of the 10 recession years, the fiscal deficit was growing. In eight of the nine, accommodating monetary policy, as measured by FR purchases of securities in the open market, was either Table 5.8 Levels of real accommodating monetary policy compared to fiscal deficits in recession years during 1959–2017 Accommodation In Deficit Years Year

1960 1961 1974 1980 1981 1982 1990 2001 (Great 2008 2009

Change in Government Deficit (Real)*

Change in FR Holdings of Securities

$45.8B $0.07B −57.6 0.13 −54.54 1.35 −117.23 1.67 14.47 4.6 −171.50 4.27 −97.33 5.86 −256.33 36.37 Recession Era Starts 2008) −389.14 −364.66 −540.61 1477.16

Real Increase in M1

Real Increase in Monetary Base

Billions

% Growth

Billions

% Growth

NA 15.8B −40.7 −17.2 −19.7 20.7 1.5 77.1

NA (%) 2.0 −4.6 −2.0 −2.4 2.4 0.1 5.9

$NA −0.2B 1.5 −2.6 −13.7 −2.0 −0.8 −36.8

NA (%) 0.1 0.4 −0.7 −4.1 −0.6 −0.2 −5.4

182.8 69.7

12.4 4.5

−6.9 753.8

−0.9 48.6

Deficit = total government revenues-total government spending *Years of deficit increases have negative signs; deficit reductions have positive signs. GDP Chain Deflator Used (2005 = 100). ERP (2018 [2010]): T.B3

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smaller than the deficit (the amount needed to offset crowd out), or negative. For recessions before the great recession, the low level of securities purchases strongly suggests there was no, or virtually no attempt by the FR to implement a monetary policy to accommodate stimulative fiscal deficits during those years. Only in one of the two recession years of the “great recession” era (2009) do we see clear evidence of efforts to use monetary policy to accommodate the crowd out effects of government deficits. 5.4.2

Effectiveness of Accommodative Monetary Policy 2008–Present

During the great recession era (2008–2017) we have a different story. Total depository institution reserves grew hugely during this period. The growth was from $43.46 billion in 2007, to $820.88 billion in 2008 alone (18.9 times the 2007 value), and to $1140.45 billion in 2009. By 2017, they had grown to $2665.94 billion. Clearly the FR had enacted a very stimulative monetary policy, one which more than offset government deficits. But over 93% of the increased reserves remained unlent, i.e., remained in depository banks or at the FR as excess reserves. Clearly, during the 2008–2017 period, FR attempts to stimulate the economy through securities purchases ran into a “pushing on a string” problem of the type Keynesians have argued make it a poor policy choice for stimulating the economy during recessions (at least in amounts greater than needed to accommodate stimulative fiscal policy undertaken at the same time).

5.5 Historical Data on FR Purchases of Government Securities, Reserves, M1 and the Monetary Base As we see in Table 5.9, there is a significant correlation between Federal Reserve purchases of Treasury bonds in the open market and the growth of M1, but not much correlation between growth of the M1 money supply and growth of the GDP.

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Table 5.9 Historical data: Nominal treasuries held by FRB, nominal M1 and real GDP (Billions) Year

Table S.61.a or H.4.1Nominal Value: Securities Held by FR U.S. Treasuries

Table S.61.a or H.4.1 U.S. Agency

Total, Treasury and Agency securities held by FR

ERP 2010, Real GDP 2012 ;FRED for 2013–2016 Nominal M1

Release H.3, T.2 Reserves Of Depository Inst., Total Reserves

Release H.3, T.2 Reserves of Depository Inst., Required Reserves

1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

24.4 24.6 23.7 26.3 26.6 27 28.7 30.5 33.6 36.5 40.5 43.7 49 52.9 57.2 62.1 69 69.8 78.5 80.1 86.7 93.3 100.9 109.5 116.3 119.3 127.7 135.6 150.6 159.2 177.8

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5 1.3 1.9 4.7 6.1 6.8 8 7.9 8.2 8.7 9.1 8.9 8.6 8.4 8.2

24.4 24.6 23.7 26.3 26.6 27 28.7 30.5 33.6 36.5 40.5 43.7 49 52.9 57.2 62.1 69.5 71.1 80.4 84.8 92.8 100.1 108.9 117.4 124.5 128 136.8 144.5 159.2 167.6 186

133.3 134.6 133.5 138.8 140. 140.7 145.2 147.8 153.3 160.3 167.8 172 183.3 197.4 203.9 214.4 228.3 249.2 262.9 274.2 287.1 306.2 330.9 357.3 381.8 408.5 436.7 474.8 521.4 551.6 619.8

NA NA NA NA 18.956 19.262 20.131 20.054 20.702 21.596 22.694 23.785 25.291 27.192 28.053 29.246 31.345 31.415 35.108 36.861 34.99 35.237 36.486 41.678 44.02 40.66 41.925 41.855 38.894 40.693 48.122

NA NA NA NA 18.5 18.5 19.5 19.5 20.2 21.2 22.3 23.4 24.9 26.8 27.8 29 31.2 31.1 34.8 36.6 34.7 35 36.3 41.4 43.6 40.1 41.6 41.4 38.3 39.9 47.1

2549.2 2596.3 2633.6 2603.3 2763.51 2832.27 2898.17 3072.4 3206.7 3392.3 3610.1 3845.3 3942.5 4133.4 4261.8 4269.9 4413.3 4647.7 4917 4889.9 4879.5 5141.3 5377.7 5677.6 5855 5839 5987.2 5870.9 6136.2 6577.1 6849.3

(continued)

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Table 5.9 (continued) Year

Table S.61.a or H.4.1Nominal Value: Securities Held by FR U.S. Treasuries

Table S.61.a or H.4.1 U.S. Agency

Total, Treasury and Agency securities held by FR

ERP 2010, Real 2012 GDP ;FRED for 2013–2016 Nominal M1

Release H.3, T.2 Reserves Of Depository Inst., Total Reserves

Release H.3, T.2 Reserves of Depository Inst., Required Reserves

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

197.6 218.9 233.7 226.8 235.1 266.5 295 332 364.5 378.2 390.9 430.7 452.1 478 511.7 551.7 629.4 666.7 717.8 744.2 778.9 740.6 476 776.6 1021.5 1663.4 1666.1 2208.8 2461.4 2461.6 2463.6

7.8 7.6 7.6 6.5 6.3 6 5.4 4.6 3.6 2.6 2.2 0.7 0.3 0.2 0.1 0 0 0 0 0 0 0 20.9 1069.3 1148.9 952.2 1018.1 1554.3 1788.4 1786.3 1769.8

205.4 226.5 241.3 233.3 241.4 272.5 300.4 336.6 368.1 380.8 393.1 431.4 452.4 478.2 511.8 551.7 629.4 666.7 717.8 744.2 778.9 740.6 496.9 1845.9 2170.4 2615.6 2684.2 3763.1 4249.8 4247.9 4233.4

724.7 750.2 786.7 792.9 824.7 897.0 1024.90 1129.60 1150.70 1127.50 1081.30 1072.30 1095.00 1122.20 1088.60 1183.20 1220.20 1306.30 1376.30 1375.00 1367.60 1374.80 1603.50 1694.10 1837.50 2164.60 2461.10 2663.80 2940.10 3094.50 3341.90

59.369 62.129 63.678 62.732 59.122 55.545 56.578 62.847 61.359 57.896 51.176 47.921 45.208 41.651 38.371 41.051 40.271 42.953 46.847 45.383 43.282 43.463 820.876 1140.45 1078.001 1598.716 1570.384 2541.019 2665.937 2481.187 2095.286

58.2 61.1 62.6 61.8 57.5 54.6 55.4 61.8 60.2 56.6 49.8 46.2 43.7 40.4 37.0 39.4 38.3 41.9 44.9 43.5 41.4 41.7 53.6 65.3 71.4 96.5 111.6 124.8 142.0 150.7 170.2

7086.5 7313.3 7613.9 7885.9 8033.9 8015.1 8287.1 8523.4 8870.7 9093.7 9433.9 9854.3 10283.5 10779.8 11226 11347.2 11553 11840.7 12263.8 12638.4 12976.2 13228.9 13228.8 12880.6 13481.4 13687.8 14001.8 14210.4 14465.1 14622.9 14809.6

(continued)

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Table 5.9 (continued) Year

Table S.61.a or H.4.1Nominal Value: Securities Held by FR U.S. Treasuries

2017 2454.20 Year

1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976

Table S.61.a or H.4.1 U.S. Agency

Total, Treasury and Agency securities held by FR

1776.9 4231.1

ERP 2010, Real 2012 GDP ;FRED for 2013–2016 Nominal M1

3600.40

Release H.3, T.2 Reserves Of Depository Inst., Total Reserves

15075.3 2309.823

Release H.3, T.2 Reserves of Depository Inst., Required Reserves 189.3

Excess Reserves (=Total-Req’d)

Release H.3, T.2 Monetary Base, Currency in Circulation In Circul.

(M1-Cur in Circ) = Demand Dep+trav. ck =D

Col. G&J = Monetary Base (MB)

Soph. M Multiplier: M= ( (1+C/D) / (Rd+ER/D + C/D))*MB

NA NA NA NA 0.5 0.7 0.6 0.6 0.5 0.4 0.4 0.3 0.4 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3

NA NA NA NA 32.8 33.1 34.0 35.3 37.7 39.8 42.3 44.6 47.0 50.7 53.7 57.1 61.1 66.1 71.7 79.0 85.9 93.6

NA NA NA NA 107.2 107.6 111.2 112.5 115.6 120.5 125.5 127.4 136.3 146.7 150.2 157.3 167.2 183.1 191.2 195.2 201.2 212.6

NA NA NA NA 51.8 52.3 54.1 55.4 58.4 61.4 65.0 68.4 72.3 77.9 81.7 86.3 92.5 97.5 106.8 115.8 120.9 128.9

NA NA NA NA 140. 140.7 145.2 147.8 153.3 160.3 167.8 172 183.3 197.4 203.9 214.4 228.3 249.2 262.9 274.2 287.1 306.2

(continued)

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Table 5.9 (continued) Year

1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Excess Reserves (=Total-Req’d)

Release H.3, T.2 Monetary Base, Currency in Circulation In Circul.

(M1-Cur in Circ) = Demand Dep+trav. ck =D

Col. G&J = Monetary Base (MB)

Soph. M Multiplier: M= ( (1+C/D) / (Rd+ER/D + C/D))*MB

0.2 0.2 0.4 0.5 0.3 0.5 0.6 0.8 1.1 1.2 1.0 1.1 0.9 1.7 1.0 1.2 1.1 1.2 1.3 1.4 1.7 1.5 1.3 1.3 1.6 2.0 1.0 1.9 1.9 1.9 1.8

102.8 113.4 124.0 136.0 144.4 155.5 170.2 181.8 195.2 209.1 227.2 244.4 256.8 282.9 304.5 330.5 362.4 399.0 419.7 444.3 475.4 510.5 599.9 584.3 632.3 678.3 716.4 753.5 784.7 811.1 822.3

228.1 243.9 257.8 272.5 292.3 319.3 351.2 369.8 424.6 515.6 523.0 542.3 536.1 541.8 592.5 694.4 767.2 751.7 707.8 637.0 597.0 584.5 522.3 504.3 550.9 541.9 589.9 622.8 590.3 556.5 552.5

139.3 155.1 168.0 176.7 186.3 197.3 209.1 222.4 243.4 268.5 289.4 308.1 319.5 342.0 360.0 387.1 425.3 460.4 477.6 495.5 523.3 555.7 641.5 622.6 673.3 718.6 759.3 800.3 830.1 854.4 865.8

330.9 357.3 381.8 408.5 436.7 474.8 521.4 551.6 619.8 724.7 750.2 786.7 792.9 824.7 897 1024.9 1129.6 1150.7 1127.5 1081.3 1072.3 1095 1122.2 1088.6 1183.2 1220.2 1306.3 1376.3 1375 1367.6 1374.8

(continued)

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Table 5.9 (continued) Year

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Excess Reserves (=Total-Req’d)

Release H.3, T.2 Monetary Base, Currency in Circulation In Circul.

(M1-Cur in Circ) = Demand Dep+trav. ck =D

Col. G&J = Monetary Base (MB)

Soph. M Multiplier: M= ( (1+C/D) / (Rd+ER/D + C/D))*MB

767.3 1075.2 1006.6 1502.2 1458.8 2416.2 2523.9 2330.5 1925.1 2120.6

878.3 924.4 979.7 1067.0 1158.5 1232.2 1327.8 1416.0 1500.6 1606.7

725.2 769.7 857.8 1097.6 1302.6 1431.6 1612.3 1678.5 1841.3 1993.7

1699.2 2064.9 2057.7 2665.7 2728.9 3773.2 3993.7 3897.2 3595.8 3916.5

1603.5 1694.1 1837.5 2164.6 2461.1 2663.8 2940.1 3094.5 3341.9 3600.4

Source ERP 2010 and 2012 for 1960–2012 data; FRED 10/17/17 for 2013–2016 data. Real GDP is in chained 2005 dollars. Source: Federal Reserve Holdings of Treasury Securities (Table S.61.a or Table H.4.1) (Source Z.1 Financial Accounts of the United States. Historical Annual Tables 1955– 1964, 1964–1974 and 1974–1984. Washington: Federal Reserve Board. Available at https://www. federalreserve.gov/releases/z1/current/annuals/a1955-1964.pdf (use same address with 1965–1975 or 1975–1985) Total and Required Reserves, and Curency in Circulation taken from FRB Release H.3, Historic Data; M1 Money Supply (Billions of Nominal $) taken from Economic Report of the Presidient 2018 [2010], T. B26; 2012, T.B70

References Economic Report of the President. (2018 [2010]). Washington, DC: Government Publications Office. Heim, J. J. (2007). How Much Does the Prime Interest Rate Affect U.S. Investment? Journal of the Academy of Business and Economics, VII (1). Heim, J. J. (2016). Do Government Stimulus Programs Have Different Effects in Recessions, or by Type of Tax or Spending Program? Empirical Economics, 51(4). NY Federal Reserve. (2005, Feburary). The Treasury Auction Process: Objectives, Structure, and Recent Adaptations. Current Issues In Economics And Finance, 11(2). Authors: Garbade, K. and Ingber, J. NY Federal Reserve. (2007). Domestic Open Market Operations During 2006. A Report Prepared for the Federal Open Market Committee by the Markets Group of the Federal Reserve Bank of New York. February 2007, p. 21. Available at www.newyorkfed.org/medialibrary/media/markets/omo/omo2006. pdf.

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NY Federal Reserve. (2009). Domestic Open Market Operations During 2008. A Report Prepared for the Federal Open Market Committee by the Markets Group of the Federal Reserve Bank of New York. January 2009, p. 6. Available at https://www.newyorkfed.org/medialibrary/media/mar kets/omo/omo2008.pdf. NY Federal Reserve. (2018). Treasury Auctions New York: Federal Reserve Bank of New York. Auctions by U.S. Treasury, not FR to sell bonds to finance deficits. Available at www.newyorkfed.org/aboutthefed/fedpoint/fed41.html. Tooze, A. (2018, May 22). Framing Crashed (3): Trans-Atlantic Power, Money and Politics. Available at https://adamtooze.com/2018/07/22/framing-cra shed-3-trans-atlantic-power-money-and-politics/. U.S. Treasury. (2018). Who/What are Primary Dealers? U. S Department of the Treasury Resource Center. 2018. Available at https://www.treasury.gov/res ource-center/data-chart-center/quarterly-refunding/Pages/primary-dealers. aspx. Zakaria, F. (2018, December 12). Looking Back at the Economic Crash of 2008. New York Times. Available at https://www.nytimes.com/2018/08/ 10/books/review/adam-tooze-crashed.html?rref=collection%2Fsectioncollec tion%2Fbooks&action=click&contentCollection=books®ion=rank&mod ule=package&version=highlights&contentPlacement=6&pgtype=sectionfront.

PART IV

Does Crowd Out Really Occur?

CHAPTER 6

Does Crowd Out Really Occur? Initial Empirical Evidence—One Time Period

Heim (2017a) contains examples of “standard” economic models, based on an extensive survey of the last 50 years consumption and investment literature. “Standard” models are comprised of variables commonly held by many economists to be determinants of consumption or investment, based on the findings of these past studies. They are the models used as a starting point in this book’s analysis of “crowd out’s” effects on consumption and investment, and to what extent changes in loanable funds can offset these effects. Heim (2017a), found that many of the variables that were significant in earlier studies were tested in models of dubious plausibility. Therefore, variables found significant in this prior review of previous studies were retested before inclusion in Heim (2017a). The first step in this process was retesting in preliminary, or “skeleton,” models controlling for only two other variables commonly considered by economists to be the most important determinants of consumption or investment. For consumption, the two other variables were a variant of disposable income and interest rates. For investment models, the two other variables were a Samuelson accelerator variable and an interest rate variable. All variables found significant when tested in these simple models were then included in one comprehensive consumption or investment model and tested as a group to see which continued to be found statistically © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_6

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significant, controlling for the other variables in the model. Variables that survived this initial statistical testing, i.e., were statistically significant, were taken to constitute the “initial” model findings of what variables constituted determinants of consumption and investment. These initial models were included in Heim (2017a), but only to indicate initial, not final results. Good science requires replication. Therefore, variables found to be statistically significant in the initial models were then subjected to a rigorous process of verification. That process included retesting initial results in 3 additional time periods. Only variables also found statistically significant in at least two of the three additional tests, as well as the initial model, were kept in the model. These time period robust models were then retested to see if specific variable results remained statistically significant when other variables included in the model were varied. The time period robust models were retested with two additional variables added, and then retested again with two of the variables in the initial model subtracted. Only so long as their estimated marginal effects in the initial test stayed within 30% of their initial test values, and the variable remained statistically significant were the initial results considered sufficiently scientifically replicable to be acceptable as the “standard” model in Heim (2017a). Many variables, significant in initial models, could not meet these replication standards and were excluded from the final, “standard” model. Good science requires the ability to replicate initial results in different time periods and in different (but reasonable) models. It also requires the fortitude to throw away variables that don’t, no matter how attractive they otherwise may seem. Other branches of science would not accept less. Why, 350 years after Newton and the scientific revolution, should economists? One variable entering the standard models of consumption and investment is the government deficit. In demand-driven theories of GDP determination, including Keynesian theory, government budget deficits are commonly expected to stimulate the economy by increasing demand. However, some studies have found these deficits have “crowd out” effects which, whatever the deficit’s stimulus effect, simultaneously force a reduction in consumer and investment spending. This “crowd out” is thought to occur because financing the deficit involves borrowing funds from

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banks. That borrowing reduces the banks’ loanable funds available to private consumers and businesses, cause a decline in private spending (which in part depends on borrowing) offsetting the government stimulus. Two of the studies that found this crowd out effect was a pervasive and offsetting effect of incurring deficits were (Heim 2017a, b). Those studies involved hundreds of empirical tests of US consumption and investment spanning the 1960–2010 period, or subsamples thereof. In those studies, the deficit variable(s) used, i.e., the single variable (T − G) or separately (T ) and (G), were added to “standard” consumption and investment models of the type described above. When these “standard” models were retested, it was found the deficit variables had a negative and statistically significant impact on consumption and investment, and their addition markedly increased the amount of variance the model explained. In consumption it was 26% and in investment 28%, as shown below. Hence we conclude the crowd out problem associated with deficits is a real problem negatively affecting consumption and investment tests in Heim (Heim 2017a, b) show completely offset the stimulus effects of deficits. In other words, the statistical studies say Keynesian-type fiscal stimulus programs don’t work unless the crowd out effect can somehow be offset.

6.1

Consumption

This study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included. (estimated using 1960–2010 data) (2SLS—strong instrument For (Y −T ) CD = .54(Y − TT ) + 2.70PR + 27DJ−2 − .714.38POP16/65 (t=)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

R = 60.3% 2

(−0.1)

Ad j. R = 56.5% 2

(2.0)

D.W. = 1.7

MSE = 43.98

(Eq. 6.1A, Same as Eq. 11.1AA) In Eq. 6.1B, the deficit variable (T − G), divided into two separate variables (T ) and (G) to pick up any differences in effects on consumption of tax cut deficits vs. increased spending deficits) is added to the model, and yields adds an astounding 43.6% (26.3 percentage points) to the

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amount of variation in consumption explained by the model. Adding the deficit variables also improves parameter estimates of other variables in the model: it changes the sign on the interest rate variable to the theoretically expected negative sign, and strengthens the statistical significance of all but one variable in the model. In estimating crowd out effects, the consumption function tested controls for the state of the economy by controlling for after-tax income, defined as GDP net of taxes. Results are shown in Eq. 13.2A, which is identical to Eq. 13.1A except for the addition of the deficit variables: CD = .31(Y −TT ) + .32(TT ) − .16(G T&I ) − 7.14PR + .49DJ−2 (t=)

(6.6)

(6.5)

(−1.9)

(−3.1)

(4.5)

− .459.68POP16/65 + .017POP + 36.27M2AV + .09CB2 (4.0)

(2.4)

R = 86.6% 2

Ad j. R = 83.9% 2

D.W. = 2.1

(3.8)

(3.9)

MSE = 26.17 (6.1B)

Rerunning the model using only the one-variable form of the deficit (T − G) yields a coefficient of +.28 (t = 6.2) on the deficit variable and the R 2 and the coefficients and t-statistics on the other variables remain essentially the same as in Eq. 13.2A. Why do deficits account for this much variance, i.e., explain so much of the variation in consumption that no other variable in the model can explain? There are two theories: 1. One theory is that deficits have crowd out effects as described above. Money borrowed from banks to fund government deficits reduces the amount of money banks have left to lend to private consumers and businesses. And the historically low level of excess reserves in banks 1960–2007, about 2%, suggests that historically, private borrowing (and spending out of it) has been constrained by the limited supply available (and foreign borrowing often is called upon to fill the gap. Reducing what’s available for private borrowing forces a reduction in consumption and investment spending, some of which is done with borrowed money each year. 2. If this theory is true, attempts to stimulate the economy by deficitfinanced increases in government spending, or tax cuts may fail. They will fail completely if the reductions in private spending (“crowd out”) caused by the deficits equals or exceeds the stimulus effects to consumer and business spending expected from the

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deficits. Evidence shown in Heim (2017b) indicates crowd out effects of deficits historically have been slightly larger than stimulus effects, leading these stimulus programs to have a slight negative effect on the economy. (This book introduces evidence that this was not the case after 2007, thanks to the large offsetting increase in loanable funds banks had due to Federal Reserve Chair Bernanke’s quantitative easing (QE) program). 3. Another theory is that declining economic conditions automatically cause deficits to increase. It is argued that simultaneously, but not causally, the same declining economic conditions that cause deficits to rise cause consumption and investment to decrease. Hence, the simultaneous rise in deficits and decline in private spending are highly correlated, but not causally related as implied by crowd out theory. The alternative theory argues it is correlational, not causal, and that it is the underlying decline in the economy that causes both. 4. But Heim (2017b) exhaustively controlled for the state of the economy to ensure state-of-the-economy effects did not affect estimates of crowd out’s effects. In over 200 tests of different consumption and investment models, even controlling for the state of the economy, that study still found pervasive evidence of crowd out, and that its effects on consumption and investment are large enough to fully offset the stimulus effects of Keynesian deficits.

6.2

Investment

The crowd out effect of deficits is also related to investment spending. Equation 6.1 presents the “standard” investment model used later in Chapters 10 and 11, except the deficit variables and the loanable funds modifier variable (S + FB) have been removed. The full 1960–2010 data sample is tested in the investment equations below. Below is a standard investment model without crowd out variables and without a loanable funds variable: (2SLS strong instrument for the accelerator variable is used). No variable controlling for economic conditions (GDP) is included. (In Chapter 20, one is included as Eq. 20.3B.) ID = + .41(ACC) + .007POP − 1.25PR−2 (t=)

(7.4)

(2.1)

+ 6.95XRAV + 11.00CAP−1 (2.12)

(2.8)

(−0.3)

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R 2 = 69.4%

Ad j. R 2 = 66.7%

D.W. = 1.4

MSE = 47.38

(6.1)

(Same as Eq. 10.3C) Adding the deficit variables to the model provides a way to estimate any negative effect on investment deficits may have (Eq. 6.2). Adding the deficit variables increases the amount of variance explained by 19.6 percentage points (28%), and increases the statistical significance of several other variables. Adding crowd out variables markedly increases our ability to explain what drives the level of investment. As was the case with consumption, the existence of a crowd out effect of deficits on investment seems undeniable. Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010) ID = + .27(ACC) + .33TT − 33G T&I + .012POP (t=)

(2.6)

(6.4)

(2.8)

(−3.9)

− 4.95PR−2 + 6.68XRAV + 2.43CAP−1 − .02GDP (3.5)

(−2.5)

R 2 = 89.0%

Ad j. R 2 = 85.9%

(1.8)

D.W. = 1.9

(−0.2)

MSE = 29.87

(6.2)

(Same as Eq. 11.4A)

6.3

Conclusion

A major determinant of both consumption and investment is the crowd out of private spending caused by financing government deficits, which completely eliminates the stimulus effects of deficit-financed fiscal stimulus programs.

References Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan.

CHAPTER 7

Does Crowd Out Really Occur? Empirical Evidence—Replication in Many Time Periods

In the last chapter, we mentioned two recent major statistical studies seem to show beyond any reasonable doubt that government financing of fiscal stimulus programs by borrowing from the pool of loanable funds (deficit financing), is associated with reductions in consumer and investment spending. The assumed reason is that this is because in good times and bad, consumers and businesses wish to borrow money, and loaning to the government to finance the deficit leaves less available for them to borrow. This reduces consumer and investment spending.

7.1

The Heim (2017b) Study

In the first of these studies, Heim (2017b) undertook 228 tests of consumption, investment and the GDP. These were full structural models of the determinants of consumption and investment. Each model included variables testing for the effects of government deficits, controlling for other variables commonly thought to be determinants of them. Heim (2017b, Table 5.7), found the following average effects of deficits (T − G) on 16 of the best consumption models: C = .45av (T − G) (t=)

(6.2av )

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_7

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To ensure the results of the initial sample were not spurious, four of the key models from Table 5.7 were tested in four different, though somewhat overlapping time periods. Statistically significant negative relationships of crowd out to consumption or investment were found in fourteen of sixteen tests (Table 5.8). The relationship of deficits to investment, was also found to be negative and statistically significant. Averages for different subsets of 23 tests are given in (Table 6.8). I = .(30 − 35)av (T − G)

(t=)

(3.4−5.6)av

Four of the initial models were each tested in four different time periods and all sixteen tests showed deficits had a statistically significant negative relationship with investment (Table 6.10). Heim (2017b) also tested the effects of deficits tax cut caused by tax cuts, and deficits caused by spending increases separately. Both types of deficits were found negatively related to consumer and investment spending. Results for their effects on consumer spending are shown below and are taken from Table 7.1. C = .59av (T ) − .28av (G) (t=)

(12.0av )

(−3.8)

  average, 5 models

C = .59av (T ) − .28av (G) (t=)

(12.0av )

(−3.8)

  average, 17 models

Clearly, this study showed overwhelming evidence of deficits having “crowd out” effects on private spending. The models tested were nearly identical to what we describe in this book as “standard” consumption, investment, and GDP models.

7.2

The Heim (2017a) Study

In Heim (2017b), only total investment and total consumption were tested. In a later study (Heim 2017a), the effect of government deficits on the three components of consumption (durables, nondurables, and services) as well as consumer imports and domestically produced consumer goods were also studied. Similarly, the three components

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Table 7.1 Unmodified effects of deficits (Crowd Out) consumption and investment

Time period 1960–1980 1960–1990 1960–2000 1960–2007 1960–2008 1960–2010 1970–1990 1970–2000 1970–2007 1970–2010 1980–2000 1980–2010 1975–2004 1980–2004 1985–2004 1985–2005 1996–2010 2000–2010

(Table 10.1)a Consumption Deficit ( T − G) Coef., (t-stat.)

(Table 10.3)a Investment

.48 .31 .22 .37 .36 .38 .23 .13 .36 .37 .01 .37 .27 .29 .28 .29 .69 .42

.01 .14 .21 .15 .23 .23 .13 .22 .16 .24 .20 .22 .12 .06 .18 .18 .25 .24

(1.8) (4.4) (2.6) (5.9) (5.6) (6.3) (2.4) (1.1) (4.3) (5.2) (0.1) (4.8) (2.7) (2.7) (1.2) (1.0) (3.7) (4.4)

Deficit ( T − G) Coef., (t-stat.) (0.1) (1.8) (2.1) (2.1) (2.6) (2.7) (1.1) (1.8) (1.9) (2.6) (1.2) (2.0) (1.2) (0.6) (1.6) (1.5) (1.7) (1.1)

a Models shown include a variable controlling for the size of the loanable funds pool when measuring

crowd out. When not controlled for, 16 of 18 consumption tests showstatistically significant crowd out; for investment 17 of 18. show significant crowd out

of investment (plant and equipment, housing, and inventories) as well as total investment imports and total domestically produced investment goods were also separately studied. All models were tested for a range of econometric problems including stationarity, endogeneity, and heteroskedasticity, and corrected for these problems if found (as was also the case in the 2017b study). Results for the 1960–2010 sample period are reported below only if initial test results were found replicable in at least two of three additional, but overlapping time periods tested. Equation Numbers cited are the equations in Heim (2017a) from which the results were taken. (NS = not significant). Total Consumption

CT = .57(T ) − .38(G) (t=)

(11.0)

(−7.9)

(4.1T.TR)

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Domestic Consumption

(4.4.TR)

CM = .25(T ) − .18(G)

(4.2.TR)

(t=)

Imports Consumption Durables

CT = .34(T ) − .23(G) (6.5)

(t=)

(−4.5)

(7.4)

(−5.4)

CDur = .24(T ) − .14(G) (t=)

(−5.4)

CND = .18(T ) − .12(G)

Nondurables Services

(5.9)

(t=)

(7.2)

(−4.7)

CSer = .45(T ) − .25(G) (t=)

(8.5)

(−5.4)

IT = .30(T ) − .32(G)

Total Investment

(t=)

(2.7)

(−4.4)

(4.9.TR) (4.11.TR) (5.2.TR) (5.2.TR)

ID = .27(T ) − .30(G)

(5.4.TR)

Imports Investment

IM = .05(T ) − .(NS)(G)

(5.6.TR)

Plant and Equipment

IP&E = .14(T ) − .14(G)

(5.10.TR)

Domestic Investment

(t=)

(t=)

(2.9)

(−3.8)

(2.0)

(t=)

(NS)

(NS)

(−2.0)

.. Inventory

(5.11.TR)

IInv = .NS(T ) − .NS(G) (t=)

(NS)

(NS)

(5.13.TR)

Clearly, this study, like (2017b), shows that government deficits negatively affect almost all of the components of consumption and investment.

7.3

Crowd Out Findings in This Study

The key models in this book are given in Chapters 10 and 11. They exhaustively test models of (domestically produced) consumption and (domestically produced) investment goods to determine if crowd out is a problem affecting them. Results are shown below. Later in the same chapters, the question of whether increases in total loanable funds (Chapters 10, 11) or changes in just the portion of loanable funds increases caused by Federal Reserve (FR) purchases of

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securities (Chapter 18) can offset crowd out is examined. The relative suitability of total loanable funds compared to only the endogenous or exogenous parts of it is the main topic dealt with in much of the rest of this study. But that’s for later chapters. In Chapter 6 and this chapter’s tests, we just deal with whether crowd out, is a problem affecting consumption or investment. The large majority of these tests show a significant negative effect on consumption and investment of crowd out. Some do not lack of significance can occur for a variety of reasons: the nonsignificant finding can be spurious, or the period measured may have shown no growth in the deficit. Alternatively, the deficit may have been growing but not consumption or investment (or they may have been growing half the period and declining in the other half). In Chapter 11 the same 18 periods are retested using the same models, except this time using separate variables to account for the effects of deficits caused by tax cuts and deficits caused by increases in government spending. For consumption, 16 of 18 periods sampled showed tax cut deficits having a significant negative effect on consumption, but only 9 of 18 spending deficits (Table 11.2). The mixed spending deficit results appear to be the result of econometric, not substantive problems and will be discussed in detail in the paragraph below. For investment, 11 of 18 tax cut deficits had a significant negative effect, as did 17 of 18 government spending deficits. When testing the deficit as two separate variables, one of the major reasons one or the other sometimes show as insignificant (even when generally they are found significant) has to do with the fact that in such models, the spending variable can be increasing, even though the deficit is declining, so there is no or negative crowd out. We refer to such periods as “crowd in” periods. For consumption, for example, this occurs in 6 of the 9 time periods where we found the crowd out effects of spending deficits to be statistically insignificant. These six time periods were periods in which from 1/3 to ½ of all the data observations included were for the 1990s “crowd in” period, the rest from “crowd out” periods. Both the “crowd in” and “crowd out” periods, when tested separately were statistically significant (but with opposite signs), but when combined, offset each other’s effects, leaving generally very small magnitude “net” coefficients and statistical insignificance. This is discussed in detail in Chapter 11, where some of the samples’ results were heavily influenced by the “crowd

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in” of the 1990s that occurred because deficits during that decade were declining. If crowd out theory is correct, this “crowd in” should have led to positive increases in consumption, and it did.

References Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan.

PART V

Increases in Total Loanable Funds—Do They Reduce Crowd Out?

CHAPTER 8

Initial Tests of Whether Crowd Out Can Be Offset by Increases in Loanable Funds

The evidence in Chapters 6 and 7, taken from Heim (2017a, b) and some from Chapters 10 and 11 below convincingly suggests deficits “crowd out” private spending by reducing the pool of loanable funds available for private borrowing, thereby eliminating, the stimulus effects of deficitfinanced government fiscal policy initiatives. But, the overall size of the pool of loanable funds is policy controllable. Policy actions could be taken to accommodate the fiscal stimulus program by increasing the pool of loanable funds exogenously. This would offset the loss in loanable funds in the existing pool available to private borrowers. Allowing more Keynesian methods of stimulating the economy to work without creating offsetting losses in private spending. The loanable funds pool can also grow endogenously. This occurs mainly in response to growth in the economy which increases incomes. The increased incomes result in increased savings, the largest component in the pool of loanable funds. Unfortunately, this comes during upswings in the economy, but the need to implement fiscal stimulus programs is needed most in economic downswings when the pool if anything, is declining. The question is not whether accommodative monetary policy exogenously, or improvements in the economy endogenously, can increase the pool of loanable funds. For investment, anyway, and possibly consumption, that is shown possible in Chapters 10–11. The real question is, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_8

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have increases in the past occurred and if so have they occurred in large enough quantities to offset the negative effects of crowd out, and done so consistently across multiple time periods? Much of the rest of this book is devoted to establishing the science necessary to provide reliable information as to whether they have or haven’t. If increases in loanable funds do offset crowd out, we can get more accurate estimates of actual crowd out effects by modeling the crowd out effect as the deficit minus the effect of any same-period growth in the pool of loanable funds. One way to test this is to simply add a variable to consumption and investment equations below to pick up and additional variance in those equations that adding the change in the loanable funds pool accounts for. A change in the pool is defined as: Loanable Funds Pool =(S + FB)=    National Savings + Foreign Borrowing .

8.1 Methodology for Testing Increases in Loanable Funds as an Offset to Consumption Crowd Out This is done below for consumption by adding a total loanable funds variable (S + FB) to the consumption standard model in Chapter 11, Eq. 11.1A. All consumption and investment models in this section are taken from Chapter 11, and have been adjusted, as necessary for stationarity, endogeneity, and heteroskedasticity issues. The model below was estimated using one sample: the full 1960–2010 data set. See Chapter 11 for more details. First, we present the same model except that no loanable funds variable is included: CD = .31(Y −TT ) + .32(TT ) − .16(G T&I ) − 7.14PR + 49DJ−2 (t=)

(6.4)

(6.6)

(−1.9)

(−3.1)

(4.5)

− .459.68POP16/65 + 017POP .+ 36.27M2AV + 09CB2 (2.4)

R = 86.6% 2

D.W.= 2.1

(4.0)

MSE = 26.17

(3.8)

(3.9)

(11.1A)

8

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Then we add the stand-alone loanable funds variable (S + FB) to the model: CD = .38(Y −TT ) + .43(TT ) − .24(G T&I ) − .14(ST + FB) (t=)

(6.7)

(8.0)

(−2.8)

(−4.1)

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.0)

(−1.9)

(3.7)

+ 33.67M2AV + .10CB2 (3.5)

R = 88.3% 2

D.W.= 1.9

(4.5)

MSE = 24.68

(11.2)

Adding the stand-alone loanable funds variable strengthens the explanatory power of the model, adding 1.7% to explained variance, and strengthening the estimated magnitude and statistical significance of the deficit variables. The small increase suggests that past increases in loanable funds have offset some, but not much, crowd out. Most likely this is because the increases in loanable funds were too small, or because large parts of the increases were used to buy securities, or used to buy foreign goods and services, neither of which raises US consumption or GDP, as discussed in other sections of this study. The model results indicate there is a net negative effect of a growth in the pool of loanable funds on consumption. This is because of the necessity of lowering the marginal propensity to consume (mpc) if the marginal propensity to save (mps) is increased to increase savings (loanable funds). This occurs in ceteris paribus models, like regression models, that hold disposable income and other variables in the model constant when estimating loanable funds effects. Regression methods use the methods of multivariate calculus used to estimate regression coefficients, i.e., partial derivatives that calculate effects of one variable on another holding all other variables constant. Because of this second effect in consumption models, the coefficient on the loanable funds variable above represents the net effect of a positive effect in reducing crowd out, and this negative effect. We find this to be an issue in estimating consumption effects, but not investment effects. An increase in investment due to an increase in loanable funds does not require a decrease in other investment to fund it. Results indicate there is a net negative effect on consumption. The negative coefficient (−.14) on the loanable funds variable in Eq. 11.2 is the net marginal effect of increasing savings (and therefore the pool of loanable funds) on consumption.

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8.1.1

Separating the Positive and Negative Effects of an Increase in Loanable Funds on Consumption

To separate the negative and positive effects on consumption of an increase in loanable funds, we redefine the crowd out effect. In initial models with no loanable funds variable, it was just the value of the deficit. Now the crowd out effect will be the value of the deficit reduced by any same-period growth in the pool of loanable funds. This is done by 1. adding the change in loanable funds to any changes in taxes. Tax cuts, ceteris paribus, create deficits since government spending is held constant in a ceteris paribus model when estimating their marginal effect. Reductions in taxes (the tax cut deficit) have a negative sign in the data used and are therefore offset by an increase in loanable funds. Hence, the loanable funds modified crowd out effect of a tax cut deficit will be given by Tax Cut Crowd Out = T + (S + FB), and 2. subtracting the change in loanable funds from any increases in spending (which have a positive sign). Increases in spending, ceteris paribus, create a spending deficit. Hence, the loanable funds modified crowd out effect of a government spending increase deficit will be given by Spending Increase Crowd Out = G − (S + FB). These loanable funds modified deficit variables will represent the positive effect on consumption of a change in loanable funds. They are modeled to have the same marginal effect on consumption as does an increase in the deficit (except with the opposite sign), and hence, share the same coefficient. This reflects the assumption that a dollar’s worth of crowd out is caused by a dollar’s worth of deficit, and can be offset by a dollar’s increase in loanable funds. The new consumption model also continues to include a separate, stand-alone (S + FB) variable to measure the negative effect of savings growth on consumption. If the modeling is correct, the sum of the positive effects on the modified deficit variables minus the negative effects shown on the alone variable should precisely equal the net effects shown on the stand-alone (S + FB) variable in Eq. 11.2 above (−.14). They do. Results are presented in Eq. 11.1A taken from Chapter 11 below.   CD = .38(Y −TT ) + .43(T + LFm ) − .24 G - LFT&I(m) (t=)

(8.0)

(6.7)

(−2.8)

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− .81(ST + FB) − 6.09PR + .40DJ−2 − 398.48POP16/65 (−2.8)

(−4.1)

(5.0)

(−1.9)

+ .016POP + 33.67M2AV + .10CB2 (3.7)

R = 83.3% 2

(3.5)

D.W.= 1.9

(4.5)

MSE = 24.68 (11.1A)

Note the positive effects of the modification are now given by reducing the magnitude of the estimated crowd out effect from their premodification level given in Eq. 18.2: .43(T ) − .24(G) (from Eq. 11.2 above) to their now lower modified levels given in Eq. 11.1A. .43(T + (S + FB)) − .24(G − (S + FB)) (from Eq. 11.1A) Hence, a negative change in (T ), a tax cut, is reduced in magnitude by a positive change in (S + FB), and a positive change in (G), an increase in government spending) is reduced by a negative change in (S + FB). Assuming the underlying relationship between deficits and consumption is linear over the range of the change, coefficients should remain unchanged in testing, and they do, as shown above. Notice the magnitude in absolute terms of the negative stand-alone (S + FB) effect increases markedly from −.14 (S + FB) to −.81(S + FB). This is the only variable that changes its Eq. 11.2 values and statistical significance levels when adding the modifiers to (T ) and (G) in Eq. 11.1A. The sizable change in the stand–alone (S + FB) variable’s coefficient occurs because Eq. 11.1A separates the two effects that are netted out in Eq. 18.2. Combine the separate loanable funds effects into one standalone variable, as shown in Eq. 18.2, and they precisely equal the net effect shown in that equation, i.e., .43(T + (S + FB))and − .24(G − (S + FB)) − .81(S + FB) (from Eq. 11.1A) = .43(T ) − .24(G) + (+.43 + .24 − .81) (S + FB)

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=.43(T )−.24(G)−.14(S + FB) (from Eq. 11.2) Hence, when adding a modifier to a model that has both positive and negative effects, it is important to model the two effects separately to clearly understand the underlying economic structure, and properly understand the net effect. Both individual effects may be statistically significant, but their net effect insignificant if the separate effects are close enough in value, except for the value’s sign, to almost cancel each other out. Separating the effects by using (S + FB) twice in the same equation does not change the regression coefficients or statistical significance of the measured crowd out effect. It just means the (previously determined) marginal effect of crowd out on consumption, is now, typically, multiplied by a smaller magnitude variable estimating crowd out effect than before. The modified definitions of the crowd out variable are now measured as T + (S + FB) or G − (S + FB). And the higher R 2 (when the loanable funds variable is added to the model in either gross or net fashion) show that this is a more correct way of estimating crowd out effects than using the deficit variables alone. In theory, we generally expect significance levels of the deficit variables stays the same or increase since the modified crowd out variables are more accurately representing the magnitude of crowd out’s effect on consumption, but there are a number of conditions, discussed elsewhere (Chapter 11) where this might not hold, e.g., if we mix “crowd out” and “crowd in” periods together in one sample.

8.2 Taxes: Another Variable that Has Both Positive and Negative Effects on Consumption The loanable funds variable is not the only one in economic theory to have offsetting positive and negative effects. The government receipts variable (shorthanded as “taxes” in this study) is another variable that has both positive and negative effects on consumption. Using gross income (Y ), and not disposable income (Y − T ), in a consumption function, while also including deficit variables (T ) and (G) to measure crowd out, leads to only net effects of tax changes being measured in a regression model. Failure to separate the positive Keynesian stimulus effects of tax

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cuts, given when using disposable income (Y − T ) as an explanatory variable, and the negative effects of tax cuts on consumption due to crowd out, when (T ) is used as a stand-alone tax variable, can lead to regression coefficients on that variable that reflect the net effect of both effects, thereby obfuscating the separate influences of both effects. To see this, reestimate Eq. 11.2 making one change: instead of disposable income (Y − T ), use gross income (Y ) as the income variable. Then the coefficient on the tax variable becomes the sum of the two effects given on Eq. 11.2: The positive effect on consumption of tax cuts given by .38 (Y − T ), plus the negative effect of a tax cut given by the stand–alone crowd out variable +.43(T ), i.e., −.38(T ) + .43(T ) = +.05T These results are shown in Eq. 8.1 below. Notice absolutely nothing else in the equation changes, except the coefficient and statistical significance of the stand-alone variable (T ) CD = .38(Y ) + .05(TT ) − .24(G T&I ) − .14(ST + FB) − 6.09PR (t=)

(8.0)

(0.7)

(−2.8)

(−4.1)

(−2.8)

+ .40DJ−2 − 398.48POP16/65 + .016POP (5.0)

(−1.9)

(3.7)

+ 33.67M2AV + .10CB2 (3.5)

R = 88.3% 2

D.W.= 1.9

(4.5)

MSE = 24.68

(8.1)

Clearly the estimates of the effect of a change in taxes is misleading in Eq. 8.1. It obscures the two separate effects of a tax cut: the (Keynesian) stimulus effect given by -.38 (T T ) in the disposable income variable, and the Keynesian deficit’s crowd out effect given by the separate variable +.43 (T T ). This error was made by Gale and Orszag (2004) in their consumption model. They used net national product as the income variable. When this was used alone, accompanied by a stand-alone tax variable, the sign on the stand-alone tax variable in their model was negative, suggesting that a cut in taxes would have a positive effect on consumption. To retest this model, Heim (2017a) replaced NNP with disposable NNP = (NNP-T) and the sign on the stand-alone tax variable turned positive (since it now only represents crowd out effects). Combine the coefficients on the two (T ) components, and you get a small net negative value, as obtained in

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Gale and Orszag’s model. This is the same result shown found using this study’s data above, differing only in its estimate of the net effect, which may be accounted for by the difference in sample periods used in the two studies. This is not a unique outcome. For any stand-alone variable in a model, if you also modify other variables in the model by adding or subtracting the stand-alone variable from them, the sum of the effects on these adjusted-value variables, plus the stand alone, will be exactly the same as the net value obtained when a model containing only the stand-alone version of the variable is tested. The reader may wish to test this with their own models.

8.3 Methodology for Testing Increases in Loanable Funds as an Offset to Investment Crowd Out The standard investment model with deficit (crowd out) variables (T , G) but without any (S + FB) loanable funds variable is given in Eq. 8.2 below: I D = + .23(ACC) + .33T T - 36G T&I + .010P O P (t=)

(3.9)

(6.1)

− 4.22P R ( - 2.1)

2

R = 88.5%

- 2

(2.9)

( - 4.7)

+ 6.77X R AV + 1.59C A P (8.8)

(0.9)

(8.2)

D.W. = 1.8 MSE = 29.63

Equation 8.3 below shows the standard investment model with two crowd out (deficit) variables (T ) and (G), and also a stand-alone loanable funds variable (S + FB). It does not include any modification of the deficit variables by changes in loanable funds. The estimation performed used the full 1960–2010 data set): ID = + .18(ACC) + .21TT − 23G T&I + .16( (S + FB)) (t=)

(5.6)

(1.8)

(−2.6)

(2.1)

+ .007POP − 3.24PR−2 + 5.54XRAV + 1.00CAP−1 (2.7)

R = 90.4% 2

(−1.6)

D.W.= 1.9

(2.8)

MSE = 27.49

(0.7)

(8.3)

Adding a stand-alone variable (S + FB) to measure the effect of changes in the loanable funds pool (which can offset crowd out) increases

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explained variance by (1.9) percentage points and the added variable is statistically significant. As was the case with consumption, the small increase in explanatory power suggests increases in loanable funds have helped reduce the effects of crowd out, but only to a relatively minor extent. This was probably because the increase was too small to fully offset crowd out, or a sizeable part of the increase was spent of existing securities or used to buy foreign goods and services. It also shows that the net effect of any increase in loanable funds on investment is positive, unlike the effect on consumption. This is to be expected. Increases in savings and foreign borrowing (loanable funds) both theoretically and empirically (see ERP 2013, Table 32) are associated with identical increases in investment in the standard (S + FB = I ) formulation of the national income accounts. In the empirical data presented in the Flow of Funds accounts, or the annual Economic Report of the President, they are also equal, (except for statistical discrepancy in both cases), Below is the standard investment model with 2 variable Crowd out (T ) and (G), with stand-alone loanable funds variable, and modification of the deficit variables by changes in loanable funds to give loanable funds—modified definitions of the real crowd out effects of deficits: T + (S + FB) and G − (S + FB). (estimated using 1960–2010 data). ID = + .18(ACC) + .21TT(m) − 23GT&I(m) − .28((S + FB) (t=)

(5.6)

(1.8)

(−2.6)

(1.1)

+ .007POP − 3.24PR−2 + 5.54XRAV + 1.00CAP−1 (2.7)

R = 90.4% 2

(−1.6)

(2.7)

D.W.= 1.9 MSE = 27.50

(0.7)

(8.4)

Here, the two deficit variables (T ), (G), are modified to show reductions in deficits by any same-period growth of loanable funds (LF), where (LF) = (S + FB). The coefficients on the modified deficit and stand-alone variables give the sum of the (S − FB) offset effects. When these are added to the coefficient on the stand-alone (S + FB) variable, the net effect is seen to be .16 (S + FB), exactly the result obtained in Eq. 8.3 when (S + FB) is only used as a stand-alone variable in the model. As was the case with consumption, the values of all other variables except the stand alone (S + FB) remained unchanged, as does R 2 .

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Note however, that when loanable funds are also included as modifiers to the deficit variables, the stand-alone loanable funds variable becomes statistically insignificant. This means that unlike consumption, it has no separate, contradictory second effect on investment; its only effect is its effect on crowd out. Hence, unlike consumption, we can use an investment model that only includes (S + FB) as a modifier of the deficit. (This reduction adequately describes how the crowd out effect of deficits is reduced by same-period growth in loanable funds. In investment models, we can delete the stand-alone (S + FB) variable as unnecessary. Also, our general rule is to drop statistically insignificant variables from the model, unless there are compelling theoretical arguments for keeping it. Dropping the variable gives the following model, shown as Eq. 8.5 below: ID = + .17(ACC) + .14TT − 11G T&I + .004POP (t=)

(4.3)

(1.8)

(1.2)

(2.6)

− 2.68PR−2 + 4.92XRAV + 1.30CAP−1 (−1.4)

R = 89.7% 2

(2.7)

D.W.= 2.0

(1.0)

MSE = 28.05

(8.5)

In this model, the net effect on investment of adding a dollar to the loanable funds pool is (.14 + .11)/2 = + .125, compared to the +.16 estimate in Eq. 8.3. Some difference is to be expected. Because regression coefficients and standard errors are in part determined by the level of multicollinearity between all the explanatory variables, dropping or adding a variable to a model usually has some effect on these statistics, A decline in R 2 also occurs, but it is not large (90.4% vs. 89.7%). Though insignificant in Eq. 8.4, the loanable funds variable’s t-statistic (1.1) is still high enough to result in some loss of R 2 , and reduce the explanatory power of some variables a bit. Hence it should probably be left in. More generally, if the stand alone is statistically significant, it means the increase in loanable funds is more than large enough to eliminate all crowd out effects; the left over part is actually creating a crowd in effect. And should be included in the investment model. As we will discuss later in the text, comparing models without deficit modification to models with it allows comparison of the gross crowd out effects of deficits to their crowd out effects net of any offsetting effects of loanable funds growth. For investment, this often can be done with models that do not include a stand-alone loanable funds variable.

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8.4

161

Conclusions

The conclusion of this chapter is that there is a solid scientific basis for believing increases in loanable funds can be used to offset crowd out; we see the science when we see that adding them increases the explanatory power of the model. However, historically, increases in loanable funds, particularly FR increases, have not been large enough to offset crowd out effects as we noted in Chapter 5; the QE period after 2007 is an exception. Other reasons why increases in loanable funds by the FR may not have offset crowd out’s effects on the real economy are that they may have been used to purchase existing securities or foreign goods and services, neither of which increases the US GDP in any direct way in anything like the magnitude needed to fully offset crowd out. That said, crowd out can also be offset be endogenous increases in the loanable funds pool, which are discussed later in Chapters 20–24.

References Economic Report of the President. (2013). Washington DC: Government Publications Office. Gale, W. G., & Orszag, P. R. (2004). Deficits, National Saving, and Interest Rates. Brookings Papers on Economic Activity, 2004(2), 101–187. Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan.

CHAPTER 9

Which Models Best Explain How Changes in Loanable Funds Offset Crowd Out?

As we established in Chapters 6 and 7, to evaluate the stimulus effects of a government deficit, we must include any crowd out effects that occur from financing the deficit. Financing the deficit reduces the portion of the pool of loanable funds available for borrowing by consumers and businesses, thereby reducing their spending which counters the deficit’s stimulus effects, eliminating them. We also showed in Chapter 8 that Deficit-sized estimates of the crowd out effect may overstate its negative effects. Growth in the pool of loanable funds during the same period would increase the funds available to private borrowers that could offset the losses to private borrowers due to crowd out. Hence, at least theoretically, any deficit-sized estimate of the crowd out effect could be offset by any same-period change in the size of the loanable funds pool. This of course assumes the growth is made available for borrowing by the same consumers and business adversely affected by crowd out, or to other private borrowers. To be clear, the evidence presented in earlier studies (Heim 2017a, b) and elsewhere in this study clearly indicates crowd out does occur when deficits occur, regardless of what’s happening with the loanable funds pool. Growth in the loanable funds pool does not prevent it from happening; it just offsets part or all of its negative effects. In this chapter we further empirically test this hypothesis to determine if growth in the pool in deficit years really is associated with reduced crowd out effects in a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_9

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wider range of sample periods than the single periods tested in Chapters 6 and 8 above. The definition of the pool of loanable funds (LF) used in this study is taken from Economic Report of the President, 2013, Table B32. The pool is defined as the combination of national savings (S) available and borrowings from foreign sources (FB) used in any period to finance investment in any year. It is the definition used in the Federal Reserve’s Flow of Funds Accounts in defining the savings/investment identity, and in the annual Economic Report of the President. Growth in loanable funds can occur several ways: (1) FR open market operations can increase bank reserves (“loanable funds”) when deficits occur. This is monetary policy designed to “accommodate” fiscal policy actions to stimulate the economy by increasing the privately available portion of the loanable funds pool to pre-deficit levels. This will restore private borrowing to predeficit levels, unless economic conditions have declined since then. This would be an exogenous increase in the pool of loanable funds. However, if FR open market purchases of securities is done for another reason, e.g., the desire to stimulate the economy beyond previous levels by lowering interest rates, this requires lowering rates enough to attract additional borrowing, not just restore old levels. If the increase in bank reserves is only equal to the crowd out problem, it will only guarantee that current levels of borrowing will continue. It will not provide any additional net stimulus to the economy by allowing private borrowing to increase. However, many economists would argue that the deficit’s stimulus effects, now unfettered by crowd out side effects, should. This is the key point to be empirically tested in this chapter. (With no deficit, any increase in the pool resulting from FR open market operations could, if demand for loans were sufficiently large, finance new private borrowing and spending, also resulting economic growth.) In short, FR open market operations can be used to accommodate fiscal policy stimulus programs, or to directly stimulate the economy as a monetary policy stimulus program. (2) Endogenous growth in the savings portion of the loanable funds pool can occur when the economy is growing, which means incomes are growing, and people and businesses are saving part of their increased income. This increase in saving can also offset the

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165

loss of privately available loanable funds due to crowd out, allowing the stimulus effects of deficits to be felt unfettered. But using the new loanable funds to offset crowd out effects of a deficit implies there is a public policy choice to be made regarding deficits: A. If there were no deficit, the growth in loanable funds could finance growth in new private borrowing to buy new cars, houses or machinery, not just restore its old levels, bringing about growth in the economy. B. If there is a decision to deficit, ensure that the stimulus effects of deficits are not wiped out by crowd out. This allows the direction of growth in the economy to be set by public policy (tax cuts to increase private spending) spending increases on transfer payments, environmental or health programs or infrastructure spending to increase public goods and services. (3) Growth in the loanable funds pool due to increased foreign borrowing. Effects are the same as for growth in the national savings component: it could finance additional new loans over current levels to private citizens or companies. Or it could finance additional loans to the government to finance deficits. In the United States, we do both. It becomes largely the province of public policy decision-making to decide which choice is most appropriate at a particular time. However, there is the question of whether deficit-financed stimulus, with enough loanable funds growth to offset crowd out, or no deficit private stimulus of the same growth in loanable funds leads to the most growth. That is a choice that should be informed by empirical estimation of the effects of both choices, as well as public preferences, but is beyond the scope of this study. This chapter looks at the more limited issue of whether increasing the loanable funds pool can reduce the crowd out problem, allowing the stimulus effects of fiscal policy to work, and to what extent. In examining this question, will also examine whether growth in the loanable funds pool, when there are no deficits, does result in additional economic growth.

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9.1

Effects on the Consumption Function

Consider the effects of changes in the loanable funds pool on sales of consumer goods produced in the US (C D ). As noted in earlier chapters, the accuracy of estimates depends heavily on testing full structural models, i.e., there cannot be any possible “left out variables” problem. Models used in this study depend heavily on decisions made in Heim (2017a) as to what variables needed to be include in consumption and investment models to avoid the crowd out variables problem Heim (2017a) surveyed a large number of past studies to see which variables were commonly hypothesized to be determinants of consumption. All determinants identified were included as controls in preliminary regression testing the effects of crowd out, modified by changes in loanable funds on consumption. Those controls found significant in the initial test were then tested in three additional different, but overlapping time periods. They were discarded if they were not statistically significant in at least three of the total of four periods sampled, since this indicated that they were probably only spuriously, not systematically, related to consumption. Those that proved time period robust were then tested for model specification robustness. This was done by adding to, and in subsequent tests, subtracting two variables from the time period robust model. Any variable in the time period robust model whose regression coefficient (marginal effect) varied by more than 30% from its values in the time series robust model was also deleted from the model, on the grounds estimated effects of the variable were unreliable, i.e., the multicollinearity between explanatory variables was so bad that coefficient values could not be taken as reasonable approximation of true marginal effects. The variables that survived these time period and model specification robustness tests were included in this study in the following model referred to as the “standard” consumption model. In that model, current period values have no time period subscript; where subscripts are used, they indicate the number of year’s lags with which the variable is used. Sources are from the statistical appendix B of the Economic Report of the President, 2012 (ERP 2012), as indicated below. To ensure the data set included data back to 1960, earlier ERP year comparable tables were also used.

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Dependent Variable: Consumption Model C D = Total consumption—Total imports − Capital goods, Industrial supplies and materials) (Tables B2, 104) Explanatory Variables: Consumption Model (Y − T ) = Disposable income (B2, B83) (T − G) = the consolidated deficit for all U.S. governmental entities taken collectively (B83) T = Deficits generated by tax or other revenue cuts (our initial measure of crowd out caused by tax cuts) (B83) G = Deficits generated by total government spending on goods, services and transfers (our initial measure of crowd out caused by spending deficits) (B83) S = Gross U.S. saving = personal + corporate + depreciation + government) (B32) FB = Foreign Borrowing (B32) PR = the Prime interest rate (B73) DJ−2 = Wealth measure; NYSE composite average lagged two years (B95) POP20/65 = Ratio of those 20–24 to those 65 or older in the population (B34) POP = U.S. population (B34) M2−2−4 = M2 money supply (or M2 − M1 component): a measure of recent year (liquid) saving history (B69) C B = Consumer borrowing (FR Flow of Funds Accounts:  Consumer Debt) All these variables were found statistically significant and robust to different time periods tested and robust to addition or subtraction of certain other variables in the equation. A “modified” crowd out effect variable was calculated, representing the initial tax cut or spending deficit (T ) or (G), and any growth in loanable funds (S + FB) used to reduce it. This model was then tested for its effects on consumption. The modified crowd out variables i.e., either (T + (S + LF)) or G − (S + LF), used were derived as follows: (The Deficit)+ (Loanable funds) =(T − G) + (S + FB) = T + β1 (S + LF) or G − β2 (S + LF)

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Precise allocations of part of (S + FB) were not available, so we tested different allocations to see which fit the data best. Tests indicated weights assigned to β1 and β2 (unexpectedly) did not affect the results, so typically in testing below, both weights were each taken to be 1.00, since that was the easiest formulation to use, and any other choice would have been equally arbitrary and not changed the results. Let us call the model above, with deficit variables but exclusive of the loanable funds variable (S + FB), the standard consumption model. The standard model in Eq. 9.1 below, was estimated using 1960–2010 data. Just prior to Eq. 9.1, we also include the standard model (Eq. 11.1AA) before adding the crowd out variables (T ) and (G) to measure crowd out effects. Adding the crowd out variable hugely increases explanatory power, clearly indicating that crowd out, unless offset, is clearly a major problem causing reductions in consumer and investment spending. CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38 POP16/65 (t =)

(0.6)

(7.2)

(3.0)

(3.2)

+ .013POP − 1.58 M2AV + .13 CB2 (3.2)

(2.0)

(−0.1)

R = 60.3% 2

D.W. = 1.7

MSE = 43.98

(11.1AA)

CD = .32(Y − TT ) + .31(TT ) − .16(G T&I ) − 7.17PR (t =)

(6.6)

(6.6)

(−3.2)

(−2.0)

+ .50DJ−2 − .462.21POP16/65 + .016POP (4.5)

(−2.5)

(3.7)

+ 35.87M2AV + .09CB2 (3.8)

R = 86.7% 2

3.9

2 RAdj

= 84.1%

D.W. = 2.1

MSE = 26.04 (9.1)

Notice that we use changes in total taxes (T T ) to represent tax deficits . This is because, as explained in Chapter 8, the effect of a change in taxes on consumption is estimated holding government spending (G T&I ), and the other variables in Eq. 9.1 constant, i.e., ceteris paribus, Since the coefficient measures the marginal effect on consumption of a tax change holding government spending constant, it is a measure of the effect of a tax-induced change in the government deficit on consumption The same is true for government spending. The effect of a change in government spending on consumption is estimated holding taxes and other variables in Eq. 9.1 constant.

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Table 9.1 Effects of different loanable funds offset models on crowd out in consumption models Variable Model 1 T Def : G Def : Sav: FB: CB :

Model 2

Model 3

.32(6.1) .14(2.2) .44(6.8) −.16(−3.4) −.04(−0.4) −.25(−3.3) −.87(6.7) −.73(4.0) .09(3.9) .08(2.6) .10(4.3) R 2 = .81 R 2 = .89 R 2 = .87 2 = .84 R 2 = .77 R 2 = .86 RAdj Adj Adj

Model 4

Model 5

Model 6

.44(6.8) −.25(−3.3) −.19(−4.1) −.04(−0.4) 10(4.3) R 2 = .89 2 = .86 RAdj

.30(5.3) −.12(1.5)

43(6.8) −.25(−3.3) −.28(−6.2) −.14(−1.2) 10(4.3) R 2 = .89 2 = .86 RAdj

.05(1.9) R 2 = .85 2 = RAdj .82

All variables in the model tested in Eq. 9.1 and in models tested in Table 9.1 models below were found stationary or cointegrated their dependent variable. All models except model #2 in Table 9.1 were tested using OLS since no explanatory variables were found endogenously related to the dependent variable. In model #2, both modified crowd out variables were found endogenously related to consumption, the dependent variable. They were replaced by a Wald-strong instrument, were not found endogenously related to the dependent variable (Sargan test), and were estimated using 2SLS. Newey–West standard errors were used to avoid heteroskedasticity problems. The models were estimated in first differences in the data to help reduce multicollinearity and stationarity problems. All models used in the rest of this book were required to pass the same tests before use, unless noted otherwise. In Table 9.1, we will we will also show results of testing variations of this standard model to see which produced the best estimates of crowd out effects of deficits and loanable funds: (1) Using the deficit to measure crowd out, unmodified by offsetting effects of changes in loanable funds. Testing indicates that both tax (T ) and spending (G) deficits create highly statistically significant crowd out problems, with t-statistics of (6.1) and (−3.4), respectively. (2) The model is then modified by subtracting any growth in loanable funds (S + FB) from initial measures of tax cut deficit crowd

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out (T ) and spending deficit crowd out (G). The new “modified” crowd out measures become T + (S + FB) and G − (S + FB). With this model, R 2 does drop noticeably from 86 to 81%. It also eliminates the statistical significance of the hypothesized modified crowd out effect associated with spending deficits, and lowers the significance level of tax cut deficits, though leaving them highly significant. The lowered R 2 suggests we have modified a reasonably accurate definition of crowd out effects by a modifier whose growth just not affects consumer crowd out. Modifying known crowd out relationships given by (T ) and (G) alone, by a variable which has no effect on them, introduces an “error in variables” problem into our variables measuring crowd out, explaining the notable drop in the model’s ability to explain variation in consumption. There was some evidence that growth in loanable funds tends to be channeled toward financing business borrowing, not consumer borrowing, which would be consistent with the observed effect. Alternatively, it may just mean changes in loanable funds have two, contradictory effect on consumption, leaving the net effect at or near zero. This also would reduce the statistical significance levels of the deficit variables and R 2 . Model (3) below attempts to correct for this possible problem. (3) Repeating step (2), but adding two separate stand-alone variables for savings (S) and foreign borrowing (FB). The theoretical basis for doing this is that, given constant income, increased saving, whatever its crowd out benefits, can only occur by reducing the marginal propensity to consume (mpc). Therefore, this mpc effect should be tested separately from our modification of the deficit variables, which is designed to capture just the positive effect of increases in loanable funds in reducing crowd out. Allowing for separately testing the two competing effects will avoid conflating them with test results obtained when testing for the net effect of these two influences by including only as separate stand-alone (S) and (FB) variables, as we do in Model 4. If our theory in Model 3 is correct, we should get a negative sign on the coefficient for the stand-alone (S) variable. Test results for Model 3 indicate that the modified tax and spending crowd out effect variables retain the same coefficients and significance levels as before. The separate savings variable (S) is found to have the expected, negatively significant effect, the FB variable was also negatively significant.

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(4) The standard model with only the stand-alone separate variables (S) and (FB) included to represent the effects of (S, FB), in a “black box”/St. Louis equation sort of way. No modifications of the deficit variables (T ) and (G) were included. These crowd out variables (T ) and (G) remained fully statistically significant, as did the stand-alone national savings variable (negatively), but the FB variable became insignificant. This suggests the FB variable has no significant “net” effect on consumption. (5) We then changed the hypothesized channel through which increases in loanable funds mitigate the crowd out problem: (a) from modification of the tax and spending deficit variables T + (S + FB), and G − (S + FB), to (b) modifying the size of the consumer borrowing variable (C B ) to (C B ) + (S + FB), but no separately entered stand-alone loanable funds variables. In tests, this reduces the R 2 , magnitude, and statistical significance of the consumer borrowing variable, suggesting this is either not the channel through which loanable funds offsets crowd out, or more likely, that the level of borrowing already incorporates the effects of changes in loanable funds that occurred during the year, and we again are just introducing “errors in variables.” Finally, (6) We redo step (5), except we add (S) and (FB) as stand-alone variables as well as include them in the consumer borrowing variable. Here the coefficient and significance of the consumer borrowing variable increase, as does the model’s R 2 to the levels found in models 3 and 4, where the modifier was used as a stand alone only, or coupled with modified deficit variable effects. This indicates we can model the way the effect of loanable funds is felt in reducing crowd out in three different ways (modifying the deficit variables and adding a stand alone, only adding a stand alone, or modifying the consumer borrowing variable while including a stand alone. All three raise the R 2 by 2 percentage points over unmodified deficit baseline model, and all three have the same deficit variable and loanable funds coefficients. The estimates of crowd out marginal effects are actually larger when national saving and foreign borrowing are controlled for by inclusion as a separate variable. One possible explanation is that reducing the crowd out

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variables (T ) and (G) magnitude by the amount of (S + FB), does not change the basic relationship between crowd out and consumption, given by the crowd out variable’s coefficient. It just increases the magnitude of the coefficient on the crowd out variables to reflect the fact that the magnitude of the variables themselves has been reduced by the modifier. Foreign borrowing is probably related to the business cycle; the worse the economy, the less is available in the domestic part of the loanable funds pool, and the more foreign borrowing is relied on, which may be why the sign on the stand-alone foreign borrowing variable is negative. As we noted in Chapter 8, relative to the pool of loanable funds, borrowing in the United States remains strong even in recessions, as indicated by the small historic levels of excess bank reserves in recessions. Heim (2017b) noted that during the early 1980s recession period, the domestic part of the pool of loanable funds dropped far faster than did the demand for loans, and was accompanied by an increase in foreign borrowing was used to accommodate some of this borrowing need. Only when the loanable funds variables are included as stand-alone variables does the standard model’s explanatory power increase. Since there are two separate effects, one positive, one negative, that accompany a change in the loanable funds pool, either both ways have to be shown separately as we do in the model (#3) by including both deficit modifiers and stand-alone (S) and (FB) variables, or only as a stand-alone variable (model #4), whose regression coefficient registers the net effect of the two forces. By comparing our findings, for models 3 and 4, we can compare the two separate effects and their net effect. From doing so it is clear that changes in loanable funds can mitigate the negative crowd out effects of deficits on consumption (if they couldn’t, the coefficients on the stand-alone variables in models #3 and #4 would be the same). However, if the increase in loanable funds results from reduced consumption (rather than income growth, or foreign borrowing growth that is not a substitute for declining domestic savings), the net effect on consumption is to reduce it. It may increase investment, as we show below.

9.2

Effects on the Investment Function

US sales of domestically produced investment goods (I D ), are defined as total US investment minus investment in imported machinery, industrial supplies, and materials. Demand for these products is also affected by

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changes in crowd out and any changes in the loanable funds pool that offsets crowd out. To obtain the most accurate possible estimates of their effects on investment, we must control the effects of the other variables that affect investment. As noted earlier, Heim (2017a) reviewed a large number of past studies to see which variables were most commonly hypothesized to be determinants of investment and determined which of those were found to be consistent determinants of investment in different models and time periods. In this study we include all of those variables as control variable to ensure, as best is possible, that we do not have a “left out variables” problem that could be improperly skewing our estimates of “left in” variables effects. The variables that survived this robustness testing were included in the following model, which we define as the “standard” investment model. In the model. Current period values have no time period subscript; where subscripts are used, they indicate the number of year’s lags with which the variable is used: Data were taken from Tables in statistical appendix B in The Economic Report of the President 2012 (ERP 2012). Dependent Variable: Investment I D = Total investment – imported capital goods and imported industrial supplies and materials (B2, B104) Explanatory Variables: Investment (Y ) = The change in current year GDP (the accelerator) (B2) (T − G) = the consolidated deficit for all U.S. governmental entities taken collectively (B83) T = Deficits generated by tax cuts (our measure of crowd out caused by tax cuts) (B83) G = Deficits generated by government spending (our measure of crowd out caused by spending deficits) (B83) S = Gross U.S. saving = personal + corporate + depreciation + government) (B32) FB = Foreign Borrowing (B32) PR−2 = the Prime interest rate, lagged two periods (B73) CapUtil = Level of capacity utilization (B54) Prof = Level of Profits (B28)

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All these variables were found statistically significant and robust to different time periods tested and robust to addition or subtraction of certain other variables in the equation. A loanable funds modified crowd out variable, i.e., either T + (S + LF) or G − (S + LF), is obtained by adding loanable funds as an offset to the tax variable or subtracting it from the spending deficit, just as was done earlier when testing consumption models. The modified crowd out variables used were derived as follows: (T − G) + (Loanable funds) = (T − G) + (S + FB) =T + β1 (S + LF) or G − β2 (S + LF) Precise data were not available to show how much of each increase in the loanable funds pool was channeled into consumer versus investment borrowing. To find the combination that best explained investment, several weighting schemes were tested. Tests indicated weights assigned to β1 and β2 (unexpectedly) did not affect the results, so typically in testing below, both weights were each taken to be 1.00, since that was the easiest formulation to use. Let us call the model above (exclusive of the national saving and foreign borrowing variables) the standard investment model. Estimates of the model’s parameters are given in Eq. 16.2 below, estimated from 1960 to 2010 annual data. The model is slightly different from that in Heim (2017a) in that no loanable funds modification to the (T ) and (G) variables has yet been made. Variables in this and similar models tested in Table 16.3 were found stationary or cointegrated. No variables in the models tested were found endogenously related to the dependent variable, so OLS was used for model estimation. Newey–West standard errors were used to avoid heteroskedasticity problems. The models were estimated in first differences in the data to help reduce multicollinearity and stationarity problems We will, in this chapter, examine and test the question of whether deficits have related crowd out effects, and whether changes in loanable funds can offset these crowd out effects. In Table 9.2, we will examine crowd out effects in the standard model several ways: (1) Using only the deficit variables (T ) and (G) to measure crowd out, unmodified by loanable funds variables which may lessen the crowd out effects of deficits. Tests of this model indicate that both tax and

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Table 9.2 Results of different investment models of the effects of loanable funds on crowd out Variable

Model 1

Model 2

Model 3

Model 4

T Def : G Def : Sav: FB:

.32(3.8) −.36(−4.6)

.14(2.2) −.11(−1.5)

R 2 = .89 2 = .87 RAdj

R 2 = .90 2 = .88 RAdj

.22(1.9) −.23(−2.9) −.32(−1.4) −.24(−0.9) R 2 = .90 2 = .89 RAdj

.22(1.9) −.23(−2.9) .13(1.4) .21(1.8) R 2 = .90 2 = .89 RAdj

spending deficits create highly statistically significant investment crowd out problems. (2) The deficit model in test 1 is changed by directly modifying the deficit variables (T ) and (G) by adding same period changes in loanable funds (S + FB) directly to (T ) and subtracting it from spending deficit crowd out, i.e., the crowd out variables now become T + (S + FB) and G − (S + FB). In the consumption section above it was explained why the different signs on the loanable fund variable in the modified deficit variables were appropriate With model #2, the modified tax cut deficit variable remains statistically significant, but significance levels decline. The spending deficits crowd out variable becomes statistically insignificant. R 2 increases marginally from 89 to 90%. More explanatory power and reduced statistical significance of crowd out variables suggests that increases in loanable funds do help offset crowd out effects, but the declining significance levels of the deficit variables suggests total loanable funds is at best an imperfect proxy for however much of the total goes into increased investment lending. (3) Repeating test #2, but adding two separate stand-alone variables (S) and (FB) to the model. As was the case with consumption, this effect should be tested separately to determine if there are two separate, and possibly conflicting, effects of a change in saving on investment. That said, a strong a priori argument can also be made that unlike consumption, a separate stand-alone variable is

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not needed. This is because increases in the savings pool definitionally result in increased investment, due to the savings = investment equality thought to hold in macroeconomics. (4) For model #3, testing indicated that the (S + FB) modified crowd out effect variables remain statistically significant for both deficit variables, but the magnitude of their crowd out effect declines, though is still substantial. Both the separate savings variable (S) and the separate (FB) variable are statistically insignificant, indicating any second effect of these variables is not significantly different from zero. This suggests no stand-alone variables are needed. R 2 was the same as in model #2, so no explanatory power is lost by eliminating them. 5. For model #4, (S) and (FB) only included in the standard model as separate, stand-alone variables. The deficit variables (T ) and (G) were not modified by (S + FB). As stand-alone variables only, they would show the net effect of any two or more separate influences (S) and (FB) might have. The magnitude and statistical significance of the tax and spending crowd out variables, i.e., (T ) and (G), without the modifier remained exactly the same as in (3) where they were modified. The sign on both the stand-alone saving variable and the (FB) variable changed to positive, but only the (FB) variable was statistically significant. R 2 was the same as in model #2, so no explanatory power is lost by eliminating them, but with equal R 2 s, it is hard to say one model expresses the data better than the other (except on an “Occam’s Razor” basis). Above Eq. 9.2, we first show how well investment is explained by the standard model without crowd out variables (Eq. 17.3C). Note that it explains noticeably less variance than does Eq. 9.2 which includes the crowd out variables. Clearly investment crowd out, unless somehow offset, is also a real problem likely to reduce investment spending. ID = + .48(ACC) + .008POP + .76PR−2 + 7.37XRAV (t=)

(10.6)

(2.5)

(0.2)

(2.2)

+ 14.08CAP−1 ( 4.3)

R 2 = 69.4%

D.W. = 1.6

MSE = 47.87

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(Same as Eq. 10.3C) Baseline, No Modification Model: (S + FB) Not Used to Modify Deficit Variables, or as Two Stand Alones, (S) and (FB).     ID = .23(ACC) + 33 TT − .36 G T&I + 1.59CAP−1 − 4.22PR−2 (t=)

(6.19)

(3.8)

(−4.6)

(0.9)

(−2.1)

+ 6.77XRAV + .011POP (3.8)

(2.9)

2 = .87.0 R 2 = 88.6% RAdj

D.W. = 1.8 MSE = 29.62

(9.2)

These models were compared using just one sample; its results should only be taken seriously if they can be replicated in other time periods. In Chapter 11, we shall retest these models in 90 different consumption and 18 different investment time periods, though the periods are partially overlapping. If we can replicate the results in other time periods, it will provide assurance our finding here are not spurious, but rather accurately represent how the US economy responds to government deficits and crowd out and how changes in the pool of loanable funds affect can reduce the negative effects of those reactions. Chapter 7 also tests the (S + FB) variable as a modifier to the deficit variables (T ) and (G), with no stand-alone (S) or (FB) modifiers, using the 1960–2010 sample, and arrived at the same conclusions: the ability to explain variation in consumption went down, the ability to explain variation in investment went up.

References Economic Report of the President. (2012, 2013). Washington, DC: Government Publications Office. Heim, J. J. (2017a). An Econometric Model of the US Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan.

CHAPTER 10

Do Loanable Funds Modify the Crowd Out Effects of the One-Variable Deficit (T − G)?

In this chapter, we test to see if modifying the deficit (T − G), using the one variable formulation of the deficit, by any changes in the total loanable funds pool, i.e., national savings plus foreign borrowing (S + FB), provides a better definition of actual crowd out effects, than the deficit alone. This loanable funds-modified deficit definition of crowd out is given as (T − G) + (S + FB). We also separately add loanable funds (S + FB) to the model as a stand-alone variable. This is done to test the hypothesis that, for consumption anyway, an increase in the loanable funds pool has two separate and contradictory effects: it reduces crowd out, which increases consumption, a positive effect. But if disposable income is held constant, which it is in the standard consumption model tested, increases in saving can only occur by reducing consumption, a negative effect; ceteris paribus, an increase in savings definitionally means a reduction in consumption.

10.1 Consumption Results When also Including (S + FB) as a Separate Variable In this section we examine crowd out effects of both loanable funds— modified deficits, and unmodified, deficits. Crowd out is initially defined as the magnitude of the government deficit (T − G). The crowd out variable is then modified by any same-period change (S + FB), and redefined © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_10

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as the modified crowd out variable (T − G) + (S + FB). In Eq. 10.1AA, a baseline standard consumption model without a deficit variable and without any loanable funds modifier is defined. In Eq. 10.1 below, the results are presented for the same consumption model adding the (T − G) deficit variable alone to define crowd out effects. Tests are based on the 1960–2010 data sample. Equation 10.2 presents results for exactly the same model, except the crowd out variable (T − G) is modified by the level of loanable funds (S + FB). In both cases we have added a separate stand-alone control variable to the regression, also equal to the value of total loanable funds (S + FB). This is done to ensure our modified crowd out variable coefficients only pick up the positive effect of crowd out reduction, and not the net of that effect plus the second negative effect resulting from the declining mpc necessary to raise mps and giving us the increase in loanable funds we are testing. The deficit variables, both modified and unmodified, were found to be stationary (ADF test) as were the other variables in the consumption model except the dependent variable, consumption, and the government spending variable, both of which were detrended, No explanatory variables were found endogenous with the dependent variable (Hausman test). Newey West standard errors were used to protect against heteroscedasticity, and variables are tested in first differences to reduce nonstationarity and multicollinearity. For comparison, the standard consumption model for the same time period (1960–2010) taken from (Heim 2017, Eq. 4.4.TR) is also shown. It differs from this study’s Eqs. 10.1 and 10.2, in that the deficit is divided into two variables (T , G), and coefficients for each type of deficit effect are estimated separately. There are two additional ways Heim (2017, Eq. 4.4.TR) is different than the models 10.1 and 10.2 below 1. There is no stand-alone control variable (S + FB) in Heim (2017), and 2. The modifier of T and G for changes in the loanable funds pool is an improved version of the one used in Heim (2017). Standard Consumption Model from Heim (2017):       CD = .29 Y − TT + .34 TT − .23 G T&I (t =)

(6.2)

(6.5)

(−4.5)

− 5.44PR + .48DJ−2 − .515.07POP16/65 (−2.1)

(5.1)

(3.2)

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+ .020POP + 38.00M2AV + .09CB2 (6.0)

(3.7)

(4.9)

R 2 = 87.8% D.W. = 2.2

MSE = 24.88

(4.4.TR)

This study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included (1960–2010 data) (2SLS—strong instrument used for (Y − T ) used to eliminate endogeneity problem):   CD = .54 Y − TT + 2.70PR + .27DJ−2 − .714.38POP16/65 (t =)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

(2.0)

(−0.1)

R 2 = 60.3%

Adj. R 2 = 57.3%(est.)

D.W. = 1.7 MSE = 43.98

(10.1AA)

Standard 1960–2010 Consumption Model with Deficit Variable (T − G), i.e., “Crowd out” Added, But Before Adding Loanable Funds Variable (Otherwise same as Model 20.1 below) (OLS—no endogenous variables):   CD = .29 Y − TT + .28(T − G) − 7.30PR + .49DJ−2 (t=)

(5.9)

(−3.1)

(6.3)

(4.8)

− .579.55POP16/65 + .021POP + 43.55M2AV + .10CB2 (−2.9)

(5.9)

(4.7)

(4.1)

R 2 = 85.9% Adj. R 2 = 83.6% D.W. = 2.1 MSE = 26.47

(10.1A)

The baseline equation before adding the deficit variable explains only 60.3% of the variation in consumption data over the period 1960–2010. When the deficit variable is added to the same model to account for the negative crowd out effects of deficits on consumption, explained variance rises to 85.9%, a 42% increase. To ensure this finding was not just a spurious, abnormal result caused by highly unusual conditions in the initial period sampled, we retested the same models in 17 additional time periods, shown in Table 10.1A. In every case exactly the same result was obtained: adding the crowd out variable increased explained variance markedly, an average of 17.4 percentage points for the 18 samples. Clearly the crowd out effect of deficits has been a consistent problem through out the past 50 years, both in recessions and good times. The question we now wish to ask is: will increases in loanable funds offset the crowd out effects of deficits?

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Table 10.1A Growth in explained variance when adding unmodified crowd out to a standard model Model

From Table#

19 60 – 20 10

19 60 – 20 08

19 60 – 20 07

19 60 – 20 00

19 60 – 19 90

19 60 – 19 80

19 70 – 19 90

19 70 – 20 00

19 70 – 20 07

19 70 – 20 10

19 80 – 20 00

19 80 – 20 10

19 75 – 20 04

19 80 – 20 04

19 85 – 20 04

19 85 – 20 05

19 96 – 20 09

20 Test ratio 00 G – T 20 10

20 Baseline (w/oDef)

Eq.17.1A A

60

72

72

86

43

77

91

91

68

55

86

37

63

74

67

65

83

95

99

NA NA 100 14/18 (T − G)

20 Baseline (w/Def)

T17.1A

(Av. R2 = 71.4%) 86 86 86 90

89

88

93

92

85

88

93

86

86

86

83

83

(Av. R2 = 88.8%) (Av. R2Adj = 82.8%)

NA

9/11

NA

(T − G)

Standard Model from (10.1A) with Stand Alone Loanable Funds Variable (S + FB) Added: CD = .36(Y − TT ) + .38(T − G) − .13(S + FB) − 6.37PR + .40DJ−2 (t =)

(7.3)

(6.3)

(−2.8)

(−6.1)

(5.3)

− .533.54POP16/65 + .021POP + 42.35M2AV + .11CB2 (5.4)

(−2.5)

R = 87.4% Adj. R = 85.0% 2

2

(4.6)

(4.7)

D.W. = 1.8

MSE = 25.29

(10.1)

Standard 1960–2010 Consumption Model from (20.1) with 1 Variable Crowd out, but after the Deficit (T − G) Modified by the Loanable Funds Pool (S + FB) Variable Added:   CD = .36 Y − TT + .38(T − G)m − .51(S + FB) (t=)

(6.3)

(7.3)

(−4.3)

− 6.37PR + .40DJ−2 − .533.54POP16/65 (−2.8)

(5.3)

(−2.5)

+ .021POP + 42.35M2AV + .11CB2 (5.4)

(4.7)

R 2 = 87.4% Adj. R 2 = 85.0%

(4.6)

D.W. = 1.8 MSE = 25.29

(10.2)

As expected from the modeling theory for consumption models developed in Chapters 8 and 9, increasing the loanable funds pool while holding disposable income constant has two contradictory effects on consumption. Equation 10.2 shows that After Total Loanable Funds (S + FB) Added to the Deficit variable, Showing (+.38) Effect in Reducing the Crowd Out Variable’s impact, But this is More than Offset by a (−.51) Effect of the Stand Alone (S + FB) Variable, Leaving a Net (−.13) Effect. (Using 1961–2010 Data). Equation 10.1 also shows the net of these two effects (−.13). We know the increase in loanable funds is helping

10

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

183

offset crowd out, because our estimate of its positive effect (a one-toone reduction in the deficit’s crowd out effect), is consistent with the net effect obtained in a separate test, but the net effect test leaves R 2 unchanged, again indicating the two tests are saying the same thing. We conclude that any increase in the pool of loanable funds that comes by raising national savings by diverting money from consumption will have a net negative effect on consumption (even though it reduces crowd out) due to this redirecting effect. Note in unmodified model, Eq. 10.1 the coefficient (t-statistic) on the deficit (crowd out) variable is = .38 (t = 6.3), signifying a large, highly statistically significant, crowd out effect. When the model is retested in Eq. 10.2 with the crowd out variable modified to show deficit values reduced by any same-period growth in loanable funds, this coefficient and t-statistic remains unchanged. This is also true for the coefficients and t-statistics on all other variables in the model except the stand-alone variable. In Eq. 10.1, the unmodified deficit model, the coefficient on the stand-alone loanable funds variable (S + FB) is. −.13. This proves to be identical to the sum of the coefficient in on the (S + FB) part of the modified deficit (T − G) + (S + FB), which is = .38, and the coefficient on the stand-alone (S + FB) variable, which is −.51. In short, the two models are equivalent, each showing the loanable funds variable to have the same total effect on consumption. In Eq. 10.1, the positive effect of the change in the loanable funds pool on crowd out is real, but was intentionally not used to modify the crowd out variable directly, and hence our crowd out variable did not show it. The stand-alone variable had to show the net of the change in consumption due to shifting spending from consumption to saving (−.51), and the (+.38) effect had in reducing the deficit. This left a net (−.13) net effect on consumption of the change in the loanable funds pool. Hence, if estimates of net effect is desired, it is actually unnecessary to model modify the crowd out variable to account for the change in loanable funds, as long as a stand-alone version of the total loanable funds variable is included in the model. This equivalence, we might add, is only true if exactly the same variable is used as a modifier of the deficit (T − G) as is used as a stand one variable. Also, as we will show with investment further below, if loanable funds only has one effect, or more than one effect, but both in the same direction, the stand-alone variable “competes” with the modified deficit variable to explain the same variance, often leaving both statistically insignificant, when including just one of the two would leave it significant.

184

J. J. HEIM

Coefficients and significance levels of the crowd out variable in both unmodified (T − G) and loanable funds-modified form (T − G) + (S + FB) are presented in Table 10.1 for the time-period 1960–2010. To ensure the results were replicable, and not just spurious, the model was also separately tested in 17 other different time periods, though some of the periods partially overlap. The results, presented in Table 10.1, indicate that in 14 of 18 time periods, the unmodified crowd out variable had a statistically significant negative effect on consumption (+β1 (T − G)). The 4 periods tested for which it was insignificant were periods where 1990s data, which shows “crowd in” due to declining deficits, was a large part of the sample tested and tended to cancel out significant crowd out effects found in other periods included in the sample. After modification, the same 14 of 18 showed significant crowd out effects. For the 18 periods, average R 2 was 89.1%; average adjusted R 2 was 82.8%. In Table 10.1, 14 of the 18 time periods sampled, the crowd out variable (T − G), had a marginally or fully statistically significant negative effect on consumption, both before and after being modified by any change in the size of the loanable funds pool. For 4 of the tests, no crowd out problem was found, even before the (T , G) modifiers were added. As noted in previous chapters, nonsignificant results can occur in an occasional sample even when there is an underlying relationship between variables that is systematic enough to be statistically significant, for two reasons: • if during a certain period, one does not move. You can’t show correlation between two variables when one does not move and the other does. • If statistical problems arise in one sample not found in others, e.g., multicollinearity, or simply the selection of an “outlier” sample from the distribution of possible samples that can be drawn. • When part of the time-period sampled, consumption was rising, but the deficit falling (1990s), and in the other part of the period sampled, both consumption and the deficit were both rising (1980s). Hence, the relationship between the two variables would have been statistically significant in each decade, if each decade was tested alone, with large magnitude coefficients, one with an apparent positive relationship to consumption, one with a negative relationship to consumption. However, when combined, the coefficient (a weighted

w/o

with .48a (1.8) .88 .76

w/o

.48a

(1.8) .88 .76

(4.4) .91 .86

.31a

1960–1990

1960–1980

(4.4) .91 .86

.31a

with .22 (2.6) .90 .87

w/o

1960–2000

.22 (2.6) .90 .87

with .37 (5.9) .87 .84

w/o

1960–2007

.37 (5.9) .87 .84

with .36 (5.1) .87 .84

w/o

1960–2008

.27 (2.7) .85 .80

.27 (2.7) .85 .80

.29 (2.7) .85 .78

w/o

w/o

.13 (1.1) .92 .89 1980–2004

with

.23 (2.4) .94 .90

1975–2004

.23 (2.4) .94 .90

w/o

w/o

with

1970–2000

1970–1990

a AR(1) required b unresolvable autocorrelation in the model

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

.29 (2.7) .85 .78

with

.13 (1.1) .92 .89

with

.28 (1.2) .83 .65 (1.2) .83 .65

with

.28a

.36 (4.3) .87 .83

with

w/o

1985–2004

.36 (4.3) .87 .83

w/o

1970–2007

(1.0) .83 .65

.29a

w/o

1985–2005

.37 (5.2) .88 .85

w/o

1970–2010

.29 (1.0) .83 .65

with

.37 (5.2) .88 .85

with

.69 (3.7) .95 .88

w/o

1996–2010

.01 (0.1) .93 .89

w/o

1980–2000

Robustness over time of crowd out effects on consumption, with and without offsetting changes in loanable funds

Coef: t-stat R2 Adj. R 2 a AR(1) required

Variable ( T − G)

.69 (-1.8) .95 .88

with

.01 (0.1) .93 .89

with

.36 (5.1) .87 .84

with

Table 10.1 Crowd out effects on consumption, with and without offsetting changes in loanable funds

(4.4) .99 .97

.42b

w/o

2000–2010

.37 (4.8) .89 .80

w/o

1980–2010

.38 (6.3) .87 .85

w/o

1960–2010

.42b (4.4) .99 .97

with

.37 (4.8) .89 .80

with

.38 (6.3) .87 .85

with

10 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

185

186

J. J. HEIM

average of adding positive and negative values) is reduced to a net coefficient value near zero and with each observation representing a large magnitude plus or minus from the weighted mean value (the coefficient), the standard error (which like any standard deviation, measures the extent to which individual values are unlike their average value) becomes very large and the result becomes statistically insignificant.

10.2 Consumption Results When Not Including (S + FB) as a Separate Variable Table 10.2 shows result of testing Table 10.1 model, except without a separate stand-alone loanable funds variable. The stand-alone loanable funds variable is deleted to test the hypothesis that increases in the loanable funds pool only have one effect on consumption; they increase it by modifying (reducing) the crowd out effect of deficits on borrowing by private borrowers. Therefore, below we test the hypothesis it may be just duplicative to include (S + FB) in the same equation both as part of the crowd out variables modifying their deficit effects, and then again as a stand-alone variable. With this hypothesis two separate effects on consumption of a change in loanable funds do not need to be separately represented. Conclusions regarding Table 10.2. Before modification, Average R 2 for the 18 samples was 88.1%; Average Adjusted R 2 was 81.2%. After modification, average R 2 fell to 84.8%; average Adjusted R 2 fell to 79.3%. The results suggest the deficit alone is a better estimate of crowd out effects than (just) the deficit reduced by loanable funds growth. By comparison, R 2 results stayed the same when we also added a separate stand-alone loanable funds variable to pick up the negative effect on consumption of increasing the marginal propensity to save in order to obtain the increase in loanable funds, indicating it is the model best fitting the data. In Table 10.2, 16 of 18 tests show statistically significant crowd out when estimated without the modifier (S + FB) being attached to the deficit variable (T − G), indicating a significant crowd out problem was caused by deficits; a large majority of the results, 12 of 18, after modification remain significant (what we expect if loanable funds reduce crowd out (see Theory Chapter 4). This we take as indicating, reasonably conclusively, that there is a crowd out problem associated with government

w/o

.25 (2.4) .84 .76

w/o

.41a (2.8) .88 .77

.21a (2.3) .89 .84

1960–1990 with

1960–1980

.06 (1.1) .86 .79

with .16 (2.4) .90 .87

w/o

1960–2000

.07 (2.2) .89 .86

with .27 (4.9) .86 .83

w/o

1960–2007

.11 (3.1) .81 .78

with .27 (5.0) .86 .84

w/o

1960–2008

.12 (3.2) .81 .78

with

.13 (3.9) .84 .79

.24 (3.0) .86 .78

w/o

.25 (3.6) .86 .79

1980–2004

w/o

.09 (1.3) .92 .90

1975–2004 with

.05 (1.2) .92 .87

w/o

.16 (2.2) .93 .90

1970–2000

w/o

with

1970–1990

.13 (3.0) .84 .77

with

.03 (0.9) .92 .89

with

with 0.14 (2.7) .79 .66

.25a (2.6) .83 .68

.10 (3.5) .81 .76

with

w/o

1985–2004

.25 (4.9) .85 .82

w/o

1970–2007

.28a (3.3) .83 .68

w/o

1985–2005

.27 (6.2) .86 .83

w/o

1970–2010

.15 (2.7) .79 .67

with

.12 (4.4) .81 .77

with

.53a (2.3) .90 .80

w/o

1996–2010

.02 (0.2) .93 .89

w/o

1980–2000

.24a (0.6) .83 .67

with

.01 (0.2) .93 .89

with

.11a (1.8) .99 .96

w/o

2000–2010

.28 (5.3) .85 .81

w/o

1980–2010

.28 (6.3) .86 .84

w/o

1960–2010

.06a (1.2) .97 .89

with

.12 (3.6) .79 .73

with

.12 (4.2) .81 .78

with

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

a AR(1) required b unresolvable autocorrelation in the model

Coef: t-stat R2 Adj. R 2

Variable ( T − G)a

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

Robustness over time of crowd out effects on consumption, with and without offsetting changes in loanable funds (no stand-alone S + FB)

Coef: t-stat R2 Adj. R 2 a AR(1) required

Variable ( T − G)

Table 10.2 Crowd out effects on consumption, with and without offsetting changes in loanable funds (no stand-alone S + FB) 10

187

188

J. J. HEIM

deficits, and that increases in loanable funds in the same period the deficit is incurred can reduce it. With the (S + FB) modifier added to the deficit variable, all 14 had smaller coefficients, significance levels, and R 2 s, meaning the modified crowd out variable explained crowd out’s real relationship with consumption less well than the deficit variable alone. The reduced significance levels are because we are making very large modifications to the deficit, which we know has a highly significant negative relationship to consumption with a variable that has a previously determined near zero net effect (−.13 in Eq. 10.1) on consumption. Hence, we are distorting a highly statistically significant relationship between the deficit alone and consumption by reducing the deficit’s magnitude each year by (S + FB), whose net effect on consumption of near zero leaves it essentially a random variable deduction from the deficit. This is likely to reduce the variable’s statistical significance and the equation’s overall ability to explain variance (R 2 ). That is what did happen. That is why the model that includes the stand-alone variable, in Eq. 10.1 and Table 10.1, is to be preferred; it allows separate estimation of the substantial positive and negative effects on consumption of an increase in loanable funds, ceteris paribus. Conclusions Regarding Consumption: The consumption function with a stand-alone loanable funds variable is the preferred model. It explains more variance 1.0 (1.6 adjusted percentage points on average for 18 periods tested) than the same model without a stand-alone variable. That said, even the model with the stand alone included only explains as much variance, no more, that the deficit model alone, without any loanable funds variable. This strongly suggests growth in the pool of loanable funds does not offset consumer pending crowd out problems caused by deficits.

10.3 Investment Results When also Including (S + FB) as a Separate Variable In Table 10.3, results are presented for 18 tests comparing unmodified (T − G) crowd out and modified (T − G) + (S + FB) crowd out variable coefficients and significance levels. The same model is tested in all 18 tests; only the time-period tested differs between models. The 17 follow up tests are done to ensure initial results are replicable, indicating an enduring underlying economic relationship, not just an idiosyncratic

10

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189

finding peculiar to the initial sample. Test samples generally contain 20 or 30 observations taken from different parts of a 50-year sample of data, 1960–2010. The samples all cover different, but sometimes overlapping, periods of time, e.g., 1970–2000 and 1960–1990. If the underlying relationship is stable over the 50 years, and we are controlling adequately for all the other variables that can affect consumption, we should get the same fit of the model from decade to decade, as was obtained in Heim (2017) for essentially the same consumption and investment models when comparing the model’s fit in different decades of the same 50-year period. (And the author hopes readers will tolerate an author’s opinion offered at this point: this mechanical consistency of underlying economic relations between variable is what makes economics, at least macroeconomics, so much more like real science than the other social sciences. It is also why well designed structural, models with reasonably complete sets of control variable for all variables that affect the dependent variable in any equation, tend to explain the economy’s behavior in decades beyond the same period a well as the do the decades within the sample period. And better that VAR or DSGE models. See out-of-sample comparisons of the three types done in Heim (2017). It is more accurately thought of as an engineering science than as the type of (non)science one typically thinks of when one thinks of “social science”) Now back to this chapter’s analysis of investment functions and their replicability in multiple time periods: Below, we compare this study’s results to the crowd out effect found in a recent study that also used the “standard model.” There a loanable funds modifier to deficit size was used when defining crowd out effects, but no additional, separate, stand-alone loanable funds variable was included (Heim 2017, Eq. 5.4.TR). This model’s results are provided to show continuity with the prior literature when examining this paper’s “standard model” given in Eqs. 10.3 and 10.4. The models used in Eqs. 10.3 and 10.4 use the same time-period robust determinants, modified only by the change from a two-variable definition of the deficit to the one variable definition (T − G) used here. Standard, Time Period Robust, Investment Model, with Modified Deficit Variables from Heim (2017): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(−3.8)

(5.7)

190

J. J. HEIM

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (−2.7)

(2.9)

R = 83.3%

D.W. = 2.0

2

(1.7)

MSE = 28.25

(5.4.TR)

This Study’s Baseline Model, has No Deficit Variables or Loanable Funds Variables Included, but GDP Variable is Included to Control for the State of the Economy: ID = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(4.0)

(0.0)

(−0.3)

+ 5.21XRAV + 10.39CAP−1 + .10GDP (2.0)

R = 76.1% 2

(29)

Adj. R = 73.2% 2

(−1.3)

D.W. = 2.1

MSE = 43.06 (10.3B)

(same as Eq. 11.10C below) Standard investment model without deficit and loanable funds variables: (from Chapter 13; a 2SLS strong instrument for Accelerator used), but no GDP Variable Included: ID = + .48(ACC) + .008POP + .76PR−2 (t=)

(10.6)

(2.5)

(0.2)

+ 7.37XRAV + 14.08CAP−1 (2.2)

R = 69.4% 2

(4.3)

Adj. R = 66.7 2

D.W. = 1.6

MSE = 47.87 (10.3C)

This Study’s Standard “Baseline” Investment Model with 1 Variable Deficit Variable (T − G), before Adding Deficit Modifiers (Using 1961– 2009 data): ID = + .26(ACC) + .32(TT − G T&I ) + .011POP (t=)

(6.5)

(5.5)

(8.3)

− 4.51PR−2 + 8.86XRAV + 2.66CAP−1 (−2.4)

R = 88.7% 2

(3.4)

Adj. R = 87.4 2

(1.6)

D.W. = 1.9

MSE = 29.00 (10.3A)

The baseline equation before adding the deficit variable explains only 69.4% of the variation in consumption data over the period 1960–2010.

10

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

191

When the deficit variable is added to the same model to account for the negative crowd out effects of deficits on consumption, explained variance rises to 88.7%, a 28% increase. To ensure this finding was not an anomaly, the same models were retested in 17 additional time periods, shown in Table 10.1A. In every case exactly the same result was obtained: adding the crowd out variable increased explained variance markedly, an average of 10.4 percentage points for the 18 samples, verifying that the crowd out problem caused by deficits is real (Table 10.1AA). The crowd out effect of deficits has been a consistent problem through out the past 50 years, both in recessions and good times. The question we now wish to ask is: will increases in loanable funds offset the crowd out effects of deficits? Standard Investment Model with 1 Variable Crowd out (T − G), After Adding Separate Accommodating FR purchases Variable) (Using 1961– 2009 data):   ID = + .22(ACC) + .23 TT − G T&I + .13(S + FB) (5.5)

(t=)

(1.7)

(2.7)

+ .008POP − 3.72PR−2 + 7.93XRAV + 2.03CAP−1 (4.0)

R 2 = 90.3%

(2.7)

(−2.0)

Adj. R 2 = 89.0%

(1.2)

D.W. = 1.9 MSE = 27.38

(10.3)

Adding the separate loanable funds variable increases explained variance 1.6 percentage points and indicates increases in the loanable funds pool have a positive ($0.13) effect on investment for every dollar increase in the pool. Hence, we again have proof deficits reduce investment ($0.23 per dollar of deficit) and that same period increases in loanable funds can partially or fully offset that depending on the actual magnitude of the loanable funds increase. Standard Investment Model with 1 Variable Crowd out (T − G), adjusted for accommodating FR purchases) (Using 1961–2009 data): ID = + .22(ACC) + .23(TT − G T&I )m − .10(S + FB) (t=)

(5.5)

(−0.6)

(2.7)

+ .008POP − 3.72PR−2 + 7.93XRAV + 2.03CAP−1 (4.0)

R = 90.3% 2

(−2.0)

Adj. R = 89.0% 2

(2.7)

D.W. = 1.9

(1.2)

MSE = 27.38 (10.4)

From Table#

T10.3C

T10.3B

Eq.10.5

Model

20 Baseline (w/oDef)

20 Baseline (w/Def)

20 Baseline (w/Def)

19 60 – 19 90 65 19 60 – 19 80 72 19 70 – 19 90 – 61 19 70 – 20 00 56 19 70 – 20 07 65 19 70 – 20 10 72 19 80 – 20 00 69 19 80 – 20 10 77 19 75 – 20 04 – 64

(Av. R2 = 87.3%) (Av. R2Adj = 83.8)

88

89

84

19 60 – 20 00 63

80

19 60 – 20 07 66

(includes GDP Control Variable) (Av. R2 = 79.8%) 89 86 83 87 85 92 87 89 83 89

19 60 – 20 08 67

(Does not include GDP Control Variable) (Av. R2 = 68.3%) 76 70 71 80 78 91 82 81 71 76 81 80

19 60 – 20 10 69

82

81

19 80 – 20 04 71

83

75

19 85 – 20 04 63

83

75

19 85 – 20 05 57

96

93

19 96 – 20 09 92

97

95

20 00 – 20 10 91

NA

10/11 (T − G)

NA NA 17/18 (T − G)

NA NA

NA NA NA

G

T

Test ratio

Table 10.1AA Growth in explained variance when adding crowd out to a standard model

192 J. J. HEIM

10

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

193

Note in Eq. 10.3 the coefficient(t-statistic) on the deficit (crowd out) variable is .23 (t = 2.7), signifying a highly significant, large magnitude crowd out effect. In Eq. 10.4, with the loanable funds—modified crowd out variable has the same coefficient and t-statistic results for the crowd out variable (and all other variables except one) are the same, as is R 2 as obtained in the model with only a stand-alone (S + FB) variable (Eq. 10.3). The only difference is the coefficient and t statistic on the stand-alone (S + FB) variable. These have changed for reasons discussed earlier in analysis of the consumption function changes when the (S + FB) variable was added, where we had the same result. In Table 10.3, we repeat the tests undertaken in Eqs. 10.3−10.4, for 18 different, though sometimes overlapping, time periods to show the robustness over time of our results. For the 18 periods, average R 2 was 90.0%; average adjusted R 2 was 86.2%. For the standard model with deficit, but before adding loanable funds variables, R 2 was 87.3%; adjusted R 2 was 83.8%. Adding the loanable funds variable increased the explanatory power of the model by 2.7% (adjusted R 2 by 2.4%). Eleven of the 18 periods sampled, showed crowd out had a statistically significant negative effect on consumption before and after adjusting for hypothesized offsetting changes in the loanable funds pool due to changes in savings and foreign borrowing levels. Recall that for consumption, using the same loanable funds modifier (S + FB), 14 out of 18 tests of the same periods showed statistically significant crowd out effects before and after the crowd out variable was modified. No statistically significant crowd out problem was found in the other seven investment periods tested before or after the (T , G) modifiers were added. As noted earlier, non-significant results can occur in an occasional test even when there is an underlying significant relationship between variables. In this case, there were 7 of the 18 test periods in which “crowd in” data was mixed with “crowd out” period data in amounts between 33 and 50% of the total. As shown in Chapter 18, in this model, crowd in and crowd out effects have different signs and this causes mixed samples to look insignificant even though both parts, when tested, separately, are significant. Deleting these seven samples, we find 9 of the 11 remaining deficits showing statistically significant negative crowd out effects, before and after modification.

.01 (0.1) .96 .91

w/o

1961–1980

.01 (0.1) .96 .91

with .14 (1.8) .91 .88

w/o

1961–1990

.14 (1.8) .91 .88

with .21 (2.1) .91 .89

w/o

1961–2000

.21 (2.1) .91 .89

with .15 (2.1) .87 .85

w/o

1961–2007

.15 (2.1) .87 .85

with .23 (2.7) .88 .86

w/o

1961–2008

.33 (2.7) .88 .86

with

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

.12 (1.2) .88 .84

w/o

1975–2004

.13 (1.1) .90 .85

w/o

1970–1990

.12 (1.2) .88 .84

with

.13 (1.1) .90 .85

with

.07 (0.6) .87 .83

w/o

1980–2004

.22 (1.8) .91 .88

w/o

1970–2000

.07 (0.6) .87 .83

with

.22 (1.8) .91 .88

with

.18 (1.6) .84 .78

w/o

1985–2004

.16 (1.9) .87 .85

w/o

1970–2007

.16 (1.2) .84 .78

with

.16 (1.9) .87 .85

with

.18 (1.5) .87 .78

w/o

1985–2005

.24 (2.6) .91 .88

w/o

1970–2009

.13 (1.1) .87 .78

with

.24 (2.6) .91 .88

with

.25 (1.7) .97 .94

w/o

1996–2009

.20 (1.2) .90 .85

w/o

1980–2000

.25 (1.7) .97 .94

with

.20 (1.2) .90 .85

with

Robustness over time of effects of crowd out on investment, with and without loanable funds modification of the deficit; stand alone variable included

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

.24 (1.1) .96 .88

w/o

with

.24 (1.1) .96 .88

with

.22 (2.0) .90 .88 2000–2009

.22 (2.0) .90 .88

w/o

with .23 (2.7) .90 .89

1980–2009

.23 (2.7) .90 .89

w/o

1961–2009

Table 10.3 Effects of crowd out on investment, with and without loanable funds modification of the deficit; stand alone variable included

194 J. J. HEIM

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10.4 Investment Results When Not Including (S + FB) as a Separate Variable In theory, changes in loanable funds have two possible effects on investment, both positive: 1. the change can offset crowd out or 2. if the change is larger than needed to offset crowd out, may increase total business borrowing and spending on investment. Both effects can be picked up by just modifying the deficit variable. In years in which the growth in loanable funds is less than the growth in the deficit the modified variable still has a remaining negative magnitude, indicating crowd out has a negative effect. In years when the growth is in excess of the growth in the deficit, the coefficient on the modified deficit variable becomes positive indicating “crowd in”), i.e., in a world where S = I showing the change in S in loanable funds had a positive effect on investment. In either case the modification in the deficit is associated with what is really happening to investment. Unlike consumption, It is not clear the separate stand-alone (S + FB) variable is needed; there is no theory suggesting additional effects that have to be measured separately. With our earlier consumption example, modifying the deficit by a number which had little or no net effect on consumption reduced its ability to show its positive deficit’s crowd out effects crowd out. Therefore, a way of separating its two offsetting effects had to be found. Adding a stand alone to pick up the negative effects did that. In Table 10.4, we repeat these tests for 18 different, though sometimes overlapping, time periods to show the robustness over time of our results. Table 10.4 shows that in every period, even with accommodation by growth in loanable funds, there has been a net negative effect on investment that is at least marginally statistically significant. This clearly indicates that the no stand-alone (S + FB) variable model is needed. The results of the model generally show increased R 2 and significance levels for the deficit variable when we define the amount of the deficit that causes a crowd out problem to be the deficit minus any growth in the loanable funds pool. Hence, the crowd out problem can be reduced by policies that increase the size of the privately available portion of the loanable funds pool. Since the pool can grow for endogenous (business cycle related) and exogenous (FR securities purchases related) reasons, These finding mean that, crowd out is a real problem for investment, but that

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there is clear evidence increases in the loanable funds pool can offset it, and, as shown in later chapters, that FR accommodative monetary policy can increase the size of the pool. Below, we compare this study’s results to the crowd out effect found in testing in a recent study using the standard model (Heim 2017), where a total saving and foreign borrowing definition of the loanable funds modifier to deficit size was used, but where no separate control variable loanable funds was used (Heim 2017, Eq. 5.4.TR). The Heim (2017) model results are compared with a version this paper’s “standard model” given below in Eqs. 10.5 and 10.6. It is the same standard model, modified only by a changed definition of how the (S + FB) modifier was used to offset government deficits, Here, unlike Eqs. 10.3 and 10.4, there is no addition of a stand-alone loanable funds variable. Standard Time Period Robust Investment Model from Heim (2017). (Using 1960–2010 data): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) (t=)

(8.7)

(2.9)

(−3.8)

+ .011POP − 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (5.7)

R = 83.3% 2

(2.9)

(−2.7)

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

This Study’s “Baseline” Standard Investment Model, Including 1 Variable Crowd out (T − G), before modification by (S + FB) (Using 1961–2009 data—2SLS Used):   ID = + .26(ACC) + .33 TT − G T&I + .011POP (t=)

(6.5)

(5.5)

(8.3)

− 4.51PR−2 + 8.86XRAV + 2.66CAP−1 (3.4)

(−2.4)

R 2 = 88.7%

Adj. R 2 = 87.4%

(1.6)

D.W. = 1.9 MSE = 29.19

(10.5)

Standard Investment Model with 1 Variable Crowd out (T − G) modified by (S + FB). No Separate Stand Alone (S + FB) Variable Used. (Using 1961–2009 data):   ID = + .22 (ACC) + .18  TT − G T&I m + .007POP (t=)

(6.1)

(7.8)

(5.0)

− 3.39PR−2 + 7.40XRAV + 2.05CAP−1 (1.9)

(2.7)

(1.2)

R 2 = 90.5% Adj. R 2 = 89.3% D.W. = 1.9 MSE = 26.90

(10.6)

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

Coef: t-stat R2 Adj. R 2

Variable ( T − G)

.18 (4.1) .87 .85

.25 (2.4) .82 .78

w/o

w/o

.29 (3.1) .84 .81

1980–2004

.43 (9.5) .89 .86

1975–2004 with

.25 (6.5) .90. .87

w/o

.43 (4.6) .87 .82

1970–2000

w/o

.38 (4.0) .85 .82

1970–1990 with

.23 (6.1) .95 .93

w/o

w/o

.33 (3.7) .92 .90

1961–1990

1961–1980 with

.16 (3.2) .86 .83

with

.23 (10.0) .91 .89

with

.24 (6.7) .90 .88

with

.24 (3.0) .83 .78

w/o

1985–2004

.30 (3.6) .83 .81

w/o

1970–2007

.41 (7.8) .87 .86

w/o

1961–2000

.14 (3.4) .84 .79

with

.17 (5.3) .87 .85

with

.23 (10.1) .90 .89

with

.25 (3.2) .83 .78

w/o

1985–2005

.33 (5.0) .89 .88

w/o

1970–2009

.30 (3.9) .83 .81

w/o

1961–2007

.14 (3.5) .84 .80

with

.18 (6.8) .91 .89

with

.17 (5.8) .87 .86

with

.29 (1.7) .96 .94

w/o

1996–2009

.45 (7.2) .88 .84

w/o

1980–2000

.23 (2.6) .86 .84

w/o

1961–2008

.15 (2.5) .97 .94

with

.22 (7.1) .90 .86

with

.19 (6.0) .88 .87

with

.28 (1.5) .94 .89

w/o

2000–2009

.31 (3.7) .89 .87

w/o

1980–2009

.33 (5.5) .89 .87

w/o

1961–2009

.16 (2.1) .96 .90

with

.17 (5.0) .90 .89

with

.18 (7.8) .91 .88

with

Table 10.4 Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases

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Note in Eq. 10.5 the coefficient (t-statistic) on the deficit (crowd out) variable is .33 (t = 5.5), signifying a highly significant, large magnitude crowd out effect. Adding the modifier in Eq. 10.6 increases R 2 by 1.8% points, reduces the measured magnitude of the crowd out effect downward to (T − G) − (S + FB), and also reduces its estimated marginal effect to ($0.18 per dollar of modified deficit). Statistical significance is improved. The modified version given in Eq. 10.6 appears to be the better model. Before modification, Average R 2 for the 18 samples was 87.2% for the baseline no-loanable funds model; Average Adjusted R 2 was 84.2%. After modification, average R 2 rose to 89.7% (up 2.5%); average Adjusted R 2 rose to 87.1% (up 2.9%). This suggests investment crowd out is better explained by modification of the raw deficit values by any changes in loanable funds that occur in the same period. Seventeen of 18 periods sampled showed crowd out had a statistically significant negative effect on investment before adjusting for offsetting changes in the loanable funds pool; After adjustment, all 18 showed significant crowd out effects. More important, when the deficit variable was modified by the change in loanable funds, the “crowd out effect” became even more statistically significant and explained more of the variance in the data. This supports the notion that the unmodified deficit variable (T − G) is the “errors in variables” version of crowd out’s true effect on investment, and that the modified version (T − G) + (S + FB) more accurately captures the real effect of deficit-induced crowd out on investment. Finally, we note the no stand-alone version of the investment model explains slightly more of the variance in investment than does the version with a stand-alone variable (90.5% vs. 90.3%). The virtually identical R 2 s provide some basis for saying the model with and without the stand-alone variable provide only marginally different results. Conclusions Regarding the Effects of Changes in the Total Loanable Funds Pool on Investment Both model with and the model without a stand-alone (S + FB) variable show that deficits have a statistically significant negative effect on investment, and that the effect can be partially or fully offset by increases in the pool of loanable funds, provided they are large enough. The model that modifies the deficit variable, but does not include the stand-alone variable (S + FB) appears to provide a marginally better description

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of how the deficit and changes in loanable funds affect the crowd out problem. (Adjusted R grows by 0.9% in the model without the stand alone. Though R 2 itself declines 0.3%, adjusted R 2 is considered the better measure of real increases in explanatory power.

10.5 Comparing the Effects of Exogenous (FR Purchases Induced) and Endogenous (Economic Driven Change Induced) Loanable Funds Growth 10.5.1

Effects on Consumption

Previous sections indicate crowd out effects can be modified by growth in loanable funds. In this section we alter slightly the standard model (Eq. 10.2) used earlier in this to see if increases in loanable funds from endogenous sources (changes in the business cycle or mpc) reduce crowd out as much as changes from exogenous sources (FR securities purchases). The model we will test is the same as Eq. 10.2 above except that we are dividing the modified deficit variable used previously (T − G) + (S + FB), into two separate variables, the deficit plus 1. Total loanable funds minus the part of it generated by FR purchases: (T − G) + (S + FB – Tr − A), and 2. The deficit plus only FR purchases: (T − G) + (Tr + A). The new model is shown in Eq. 10.7 below. Note that total (S + FB) is kept as a stand-alone variable.   CD = .31 Y − TT + .19((T − G) + (S + FB) − (Tr + A))

(t=)

(7.3)

(5.1)

+ .17((T − G) + (Tr + A)) − .37(S + FB) (3.8)

(−2.8)

− 4.84PR + .43DJ−2 − .571.32POP16/65 (−2.0)

(5.5)

(3.1)

+ .023POP + 44.96M2AV + .11CB2 (5.6)

R 2 = 88.0%

(5.7)

Adj. R 2 = 85.4%

(3.1)

D.W. = 2.0

MSE = 24.98

(10.7)

New model test results are shown for six different time periods in Table 10.5.

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Table 10.5 Endogenous and exogenous changes in loanable funds: effects on consumption crowd out Variable

1960–1980

1960–1990

1960–2000

Endogenous: (T − G) + (S + FB – Tr − A) .73 .20 .20 (2.1) (1.6) (2.4) Exogenous: (T − G) + (Tr − A) −0.31 .09 .05 (−0.9) (0.7) (0.5) R2 .87 .88 .90 .76 .84 .88 Adj. R 2

1960–2007

1960–2008

1960–2010

.34 (4.9)

.31 (5.6)

.19 (7.3)

.01 (0.1) .88 .85

.09 (1.3) .88 .85

.17 (3.8) .88 .85

Average R 2 for the six samples was 88.2%; average adjusted R 2 was 83.8%. R 2 results were 1 point higher for 4 of the 6 models, 1 the same and 1 lower, compared to Table 10.1, where only total loanable funds was tested, not its two separate parts. The average endogenous marginal effect and t-statistic were .33 (t = 4.0). The average exogenous marginal effect and t-statistic were .02 (t = 1.2); only 2 QE period tests were significant or close to significant, confirming conclusion in earlier chapters that the main reason accommodative monetary policy failed historically (and therefore, sometimes also Keynesian fiscal policy, was that the Fed did not increase loanable funds enough to offset the crowd out effects of deficits. Even in the two QE period tests, the average marginal effect of exogenous growth in loanable funds was less (.13) than the marginal effect of the average endogenous growth in loanable funds (.25), and even larger (.37) when the two recessionary QE samples are excluded. Results indicate endogenous growth in loanable funds positively and significantly related to consumption in all six periods tested, and hence, is a reliable offset to at least some crowd out. However, five of the six tests indicate exogenous growth (FR securities purchases) were not significantly related to consumption spending. For these periods, FR intentional (or unintentional) attempts at accommodative monetary policy appear to have had no significant impact on consumption. The only exception (which provides some proof accommodative policy can work) was during the QE period 2008–2010, when the FR purchased historically unprecedented quantities of securities. Since 2009 was the only year in the study when FR purchases exceeded the year’s deficit, this means that the net

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effect of .17((T − G) − (S + FB) – Tr − A)) was positive as well as statistically significant. When adding only 2008 to the 1960–2007 sample, the significance level of FR purchases increases markedly, by not enough to change the effect to statistically significant. When the whole 2008– 2010 period was added to the 1960–2007 period data, FR purchases becomes a highly significant effect, turning the crowd out variables effect on consumption from negative to positive (i.e., “crowd in”). Hence, on average over the 50 years, Eq. 10.6 above shows the virtual wash between the positive effects on reducing crowd out, given by the coefficients on the modified deficit variables, and the negative effects on the mpc. But, in the QE period, Bernanke’s flooding of the system with liquidity not only offset crowd out effects on consumer borrowing, but increased net loanable funds available to consumers which we see in the form of increased consumer spending associated with the increased liquidity. 10.5.2

Effects on Investment

Similarly, we can test to see if increases in loanable funds from endogenous sources (changes in the business cycle, or the mpc), works better to reduce investment crowd out problems than FR securities purchases (Tr + A). The model we will test is the same that given in Eq. 10.6 above except that in this new model, we are dividing the modified deficit variable used earlier in this chapter (T − G) + (S + FB), into two separate variables, equal to the deficit plus: 1. Total loanable funds minus the part of it generated by FR purchases: (T − G) + (S + FB – Tr − A), and 2. The deficit plus only FR purchases: (T − G) + (Tr + A). The model is shown in Eq. 10.8 below. Note that this model is the investment model without a stand-alone loanable funds variable: ID = + .23(ACC) + .11((TT − G T&I ) + (S + FB − Tr − A)) (t=)

(6.4)

(7.1)

+ .14((TT − G T&I ) + ( Tr + A)) + .008POP (5.8)

(4.2)

− 3.20PR−2 + 7.78XRAV + 2.40CAP−1 (−1.7)

(2.9)

(1.5)

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Table 10.6 Endogenous and exogenous changes in loanable funds: effects on investment crowd out Variable

1961–1980

1961–1990

1961–2000

Endogenous: (T − G) + (S + FB – Tr − A) .27 .33 .24 (1.7) (6.2) (3.3) Exogenous: (T − G) + (Tr − A) .07 −.18 −.03 (0.4) (−1.6) (−0.2) R2 .94 .92 .91 .91 .89 .89 Adj. R 2

1961–2007

1961–2008

1961–2009

.15 (2.3)

.07 (1.5)

.11 (7.1)

.03 (0.3) .86 .84

.20 (4.9) .89 .87

.14 (4.2) .91 .89

a Correlation between endogenous and exogenous components is r = (−0.10)

R 2 = 90.7%

Adj. R 2 = 89.4%

D.W. = 1.8

MSE = 26.85 (10.8)

Test results are shown for six different time periods in Table 10.6: Average R 2 for the six samples was 90.5%; average adjusted R 2 was 87.7%. Average R 2 for the same periods for the baseline standard investment model with deficit variables included, but no-loanable funds variables was 89.0%. The average endogenous marginal effect and tstatistic were .20 (t = 3.7). The average exogenous marginal effect and t-statistic were .04 (t = 1.9; only 2 QE period tests were significant, confirming conclusion in earlier chapters that the main reason accommodative monetary policy failed historically (and therefore, sometimes also Keynesian fiscal policy, was that the Fed did not increase loanable funds enough to offset the crowd out effects of deficits. Even in the two QE period tests, the average marginal effect of exogenous growth in loanable funds was less (.17) than the marginal effect of the average endogenous growth in loanable funds (.20), and even larger (.25) when the two recessionary recessionary QE samples are excluded. Results in five of six cases indicate endogenous growth in the loanable funds pool left the modified crowd out variable negatively and significantly related to increased investment spending. The sixth was almost significant. The findings indicate FR purchases did not offset some or all of the effects of crowd out in 3 of the 4 1960–2007 tests, i.e., in the periods tested prior to QE. (In one, there was marginal significance, but with the

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wrong sign, which we interpret as a spurious result.) They appear to have had no significant impact on investment during those periods (i.e., no effect controlling for the effect of the bulk of (S + FB)—the endogenous part). However, when the years representing the large quantities of FR securities purchases during the QE period are added to the sample, FR purchases did seem related to increases in investment. This suggests that FR accommodative monetary policy, though it didn’t seem to work in most of the period studied (1960–2007) when FR purchases only a small fraction of deficit size, does have a positive effect on investment, as it did on consumption. if implemented in large enough quantities. Declining economic conditions lead to declining tax revenue and also declining investment but such economic conditions are associated with and increased government spending, i.e., taxes are positively correlated to investment trends, spending is negatively correlated. To be sure our significant findings in Table 10.6 truly reflected crowd out effects, and not just economic conditions, the same model was reestimated, with the addition of a variable to clearly control for economic conditions (the GDP). The GDP variable was endogenous with investment, so it was replaced with a Wald-strong instrument, which was not endogenous (Sargan test). The model was retested including current period real GDP as a control for changes in economic conditions. Results are shown in Table 10.7, and were generally the same as with the model without the GDP control. With one exception, where Table 10.6 model showed significant results, so did Table 10.7 model with additional control variable. The same was also true for instances of nonsignificance. However, the model with the GDP Table 10.7 Endogenous and exogenous changes in loanable funds: effects on crowd out (GDP control added to Table 10.6 model) Variable

1961–1980

1961–1990

1961–2000

Endogenous: (T −G) + (S + FB – Tr − A) .27 .34 .26 (1.5) (5.6) (3.2) Exogenous: (T − G) + (Tr − A) −.15 −.17 −.01 (−0.5) (−1.4) (−0.1) R2 .94 .91 .90 Adj. R 2 .91 .88 .88

1961–2007

1961–2008

1961–2009

.17 (2.2)

.11 (1.9)

.14 (7.1)

.06 (0.4) .80 .76

.21 (4.8) .83 .80

.16 (4.1) .86 .84

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explained markedly less of the variance in investment in most periods. Hence we conclude this is a less satisfactory model than Table 10.6 model. Average R 2 for the six samples was 87.3%; average adjusted R 2 was 84.5%.

Conclusions

10.6

Results for effects of deficits and the ability of the total pool of loanable funds to offset crowd out are presented in the two tables below: Cptr. 10 Consumption Summary Table (Total Loanable Funds Deficit Modifier, W/WO Separate (S + FB) Control Variable) Model

From Table#

10 Baseline (w/oDef)

T11.1A A

10 Baseline (w/Def)

T10.2

19 60 – 20 10 60

19 60 – 20 08 72

19 60 – 20 07 72

19 60 – 20 00 86

19 60 – 19 90 43

19 60 – 19 80 77

19 19 70 70 – – 19 20 90 00 91 91

(Av. R2 = 71.4%) 86 86 86 90 89 88 93

19 70 – 20 07 68

19 19 70 80 – – 20 20 10 00 55 86

92 85 88

19 80 – 20 10 37

19 19 75 80 – – 20 20 04 04 63 74

19 85 – 20 04 67

19 19 85 96 – – 20 20 05 09 65 83

20 Test ratio 00 – T G 20 10 95 NA NA

NA NAa 93 86 86 86 83 83 99 100 14/18 (T − G)

(Av. R2 = 87.3%) (Av. R2Adj = 83.8%) 10 Unmodif (w/s-a)

T10.1

87 87 87 90 91 88 94

9/11

92 87 88

93 89 85

85 83 83

95 99 14/18 (T − G)

(Av. R2 = 89.1%) (Av. R2Adj = 82.8%) 10 Modified (w/s-a)

T10.1

87 87 87 90 91 88 94

9/11

92 87 88

T10.2

86 86 86 90 89 88 93

85 83 83

95 99 14/18 (T − G)

93 85

86

86 83 83

99 100 16/18 (T − G)

10 Modified (wo/s-a)

T10.2

81

93

85

86

97

9/11

92 85 88

81

89

85

85

92

(Av. R2 = 84.8) (Av. R2Adj = 79.3%)

92

(T − G)a

11/11 (T − G)a

(Av. R2 = 88.1%) (Av. R2Adj = 81.2%) 81

(T − G)a

93 89 85

(Av. R2 = 89.1%) (Av. R2Adj = 82.8%) 10 Unmodif (wo/s-a)

(T − G)a

81

81

79

82

82

97

14/18 (T − G) 11/11 (T − G)a

a 7 samples containing 1/3-½ of all observations from “Crowd In” years Removed, leaving 11 of 18

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R 2 increases to 88.8%, an increase of 24%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant crowd out effects.

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3. When the stand-alone loanable funds modifier (S + FB) is added to the standard model with deficits, R 2 increases to 89.1% compared to the 88.8% for the standard deficit model, indicating loanable funds is not an important explanatory variable (though not indicating its net effect is negative if the change in loanable funds stems from a declining mpc). When adding a (S + FB) modifier to the deficit, without including the stand-alone (S + FB) variable, explained variation in consumption dropped to 86.1%. For 18 tests, average R 2 dropped the unmodified (i.e., baseline) average of 88.8% to 86.1%, 2.7% points, in the modified model. By comparison, R 2 also dropped from 88.7 to 85.2% in the comparable two deficit variable model in Chapter 18, which also used total loanable funds for a deficit modifier, but not as a stand alone. In short, this chapter models and models in the next chapter, both of which used total loanable funds as a crowd out offset, and were otherwise identical except for the use of one vs. two-variable deficits, had about the same consumption results, as expected.

Cptr. 10 Investment Summary Table (Total Loanable Funds Modifier, W/WO Separate (S + FB) Control Variable)

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J. J. HEIM

R2 (18 time periods)

Model

From Table#

10 Baseline (w/o Def) 10 Baseline (w/o Def) 10 Baseline (w/Def)

Sigif./Total

19 60 – 20 10

19 60 – 20 08

19 60 – 20 07

19 60 – 20 00

19 60 – 19 90

19 60 – 19 80

19 70 – 19 90

19 70 – 20 00

19 70 – 20 07

19 70 – 20 10

19 80 – 20 00

19 80 – 20 10

19 75 – 20 04

19 80 – 20 04

19 85 – 20 04

19 85 – 20 05

19 96 – 20 09

20 Test ratio 00 – T G 20 10

T10.3C

69

67

66

63

65

72 −61

56

65

72

69

77 −64

71

63

57

92

91

NA

NA

T10.3B

(Does not include GDP Control Variable) (Av. R2 = 68.3%) 76 70 71 80 78 91 82 81 71 76 81 80

80

81

75

75

93

95

NA NA

NAa NA

T10.3

(includes GDP Control Variable) (Av. R2 = 79.8%) 89 86 83 87 85 92 87 89 83 89

84

82

83

83

96

97

NA NAa 17/18 (T − G)

88

89

(Av. R2 = 87.3% for 18 samples; 89.0% for first 6)

10 Unmodified (w/s-a)

T10.3

(Av. R2Adj = 83.8% for 18 samples) 90 88 87 91 91 96 90 91

87

91

10/11 (T − G) 90

90

88

87

84

87

97

96

11/18 (T − G)

90

90

88

87

84

87

97

96

11/18 (T − G)

17/18 (T − G)

(Av.R2 = 90.0%) (Av. R2Adj = 86.2% for 18 samples) 10 Modified (w/s-a)

T10.3

10 Unmodif. (wo/s-a)

T10.4

10 Modified (wo/s-a)

T10.4

90

88

87

91

91

96

90

91

87

91

9/11

(Av.R2 = 90.0%) (Av. R2Adj = 86.2% for 18 samples w/o GDP) 89

86

83

87

85

92

87

9/11

89

83

89

88

89

84

82

83

83

96

97

91

87

91

90

90

87

86

84

84

97

96

88

87

90

90

95

90

(Av.R2 = 89.7%) (Av. R2Adj = 87.1%)

(T − G)a

10/11 (T − G)a

(Av.R2 = 87.2) (Av. R2Adj = 84.2%) 91

(T − G)a

18/18 (T − G) 10/11 (T − G)a

a 7 samples containing 1/3-½ of all observations from “Crowd In” years Removed, leaving 10 of 17

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8%. 2. When deficit variables only added to baseline standard model, R 2 increases to 87.3%, an increase of 9.4%, indicating investment cannot be explained without allowing for significant crowd out effects. 3. When the stand-alone loanable funds modifier is added to standard model with deficits, R 2 grows to 90.1% (Adj. R 2 = 83.8) compared to the standard deficit model without a loanable funds modifier (87.3%). This indicates that the adding the total loanable funds gives a model that explains noticeably more of investment’s variation than a model without it. The same total loanable funds model is used in Chapter 18, except with a two-variable deficit, and explains even more (91.2%) of the variance. Clearly crowd out can be offset by growth in the pool of loanable funds. 4. When the total loanable funds modifier is added as a modifier of the deficit only, but not included as a stand-alone variable, R 2 increases on average in the 18 periods tested, from its average of 87.3% before

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adding the endogenous loanable funds deficit modifier to an average of 89.7% after, or 2.4 percentage points higher than before any loanable funds variable was added to the deficit variable in the model. This increase was less than when the loanable funds variable was added as both a stand alone and a deficit modifier (90.1%), though the difference is small enough to be spurious. Hence, the result does not seem large significant enough to imply our general conclusion that stand alone are not needed in investment models is incorrect. Next, the results of consumption testing with total loanable funds endogenous and exogenous components tested separately are summarized. The consumption function with a stand-alone loanable funds variable is the preferred model. It explains more variance (1.6 percentage points on average for 18 periods tested) than the same model without any loanable funds variable. It also explained the data better than the same model with a no standalone (S + FB) variable, but with a deficit -modifying (S + FB) variable. In models without the stand alone, R 2 actually declined even relative to the no (S + FB) base line model by an average of 2.7 percentage points in the 18 periods tested. The poor showing appears to be the result of changes in loanable funds having negative as well as positive effects on consumption which tend to cancel each other out, and which need to be shown separately in the model, i.e., by modifying the deficit variable and by also including it as a separate variable in the consumption model. Results When Testing the Effects of Endogenous and Exogenous Loanable Funds Growth Separately are given in the two tables immediately below: Cptr. 10 Consumption Summary Table (Separate (S + FB – TR − A) an (Tr + A) Deficit Modifiers, With Stand Alone (S + FB) Control Variable)

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J. J. HEIM

Model

From Table#

19 60 – 20 10

19 60 – 20 08

19 60 – 20 07

19 60 – 20 00

19 60 – 19 90

19 60 – 19 80

19 70 – 19 90

19 70 – 20 00

19 70 – 20 07

19 70 – 20 10

19 80 – 20 00

19 80 – 20 10

19 75 – 20 04

19 80 – 20 04

19 85 – 20 04

19 85 – 20 05

19 96 – 20 09

20 Test ratio 00 G – T 20 10

10 Baseline (w/oDef)

Eq.10.1A A

60

72

72

86

43

77

91

91

68

55

86

37

63

74

67

65

83

95

99

NA NAa 100 14/18 (T − G)

10 Baseline (w/Def)

Eq.10.1A

(Av. R2 = 71.4%) 86 86 86 90

89

88

93

92

85

88

93

86

86

86

83

83

(Av. R2 = 88.8%) Total loanable funds 10 Unmodif T10.1 (w/s-a)

87

87

87

90

9/11

91

88

94

92

87

88

93

89

85

85

83

83

95

99

(Av. R2 = 89.1%; Adj. Av. R2 = 82.8%) 2

10 Modified (w/s-a)

T10.1

(Av. R for leftmost 6 = 88.3%; Adj. Av. R = 83.7%) 87 87 87 90 91 88 94 92 87 88 93

87

88

(T − G)

(T − G)a

2

89

85

85

83

83

95

99

90

88

2

88

88

–

–

11/18 (T − G) 9/11

(R2 for leftmost 6 = 88.3%; Adj. Av. R2 = 83.7%) Endogenous (EN) and Exogenous (EX) modifiers model: T.10.5

NA

11/18 (T − G) 9/11

(Av. R2 = 89.1%; Adj. Av. R2 = 82.8%)

10 Modified (w/s-a)

NA

–

(T − G)a

(EN ) (EX) –

–

–

2

(Av. R = 88.2%) (Adj. Av. R = 83.8%)

–

–

–

–

–

–

6/6

1/6b

6/6

1/6

a 7 samples containing 1/3-½ of all observations from “Crowd In” years Removed, leaving

11 of 18 b Significant only in sample including QE years 2008–2010

For the Periods Tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, average R 2 increases to 88.8%, an increase of 24%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects of deficits. 3. When the total loanable funds variable is added as a stand-alone variable, average R 2 increases slightly to 89.1%. 4. When two separate deficit modifiers are used, endogenous and exogenous loanable funds (S + FB – Tr − A) and (Tr + A), while also including the stand-alone total loanable funds variable (S + FB), i.e., added to the standard model with deficits, R 2 decreases from 89.1% using to total loanable funds variable to 88.2% using the two separate components. 5. The endogenous—modified deficit variable was found significant in all six periods tested. However, the exogenous loanable funds modified deficit was only statistically significant during the QE period

10

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

209

when the level of FR security purchases was huge. Prior to 2008, FR purchases were typically small (23–44%) compared to deficit size. Modifying the deficit with them merely created an error in variables problem that reduced the crowd out variable to statistical insignificance. Cptr. 10 Investment Summary Table (Separate (S + FB – TR – A) an (Tr + A) Deficit Modifiers, No Stand Alone (S + FB) Control Variable) R2 (18 time periods)

Model

From Table#

10 Baseline (w/o Def 10 Baseline (w/o Def) 10 Baseline (w/Def)

Sigif./Total

19 60 – 20 10

19 60 – 20 08

19 60 – 20 07

19 60 – 20 00

19 60 – 19 90

19 60 – 19 80

19 70 – 19 90

19 70 – 20 00

19 70 – 20 07

19 70 – 20 10

19 80 – 20 00

19 80 – 20 10

19 75 – 20 04

19 80 – 20 04

19 85 – 20 04

19 85 – 20 05

19 96 – 20 09

20 Test ratio 00 – T G 20 10

T10.3C

69

67

66

63

65

72

61

56

65

72

69

77

– 64 71

63

57

92

91

NA

NA

T10.3B

(Does not include GDP Control Variable) (68.3% Av.) 76 70 71 80 78 91 82 81 71 76 81

80

81

75

75

93

95

NA NA

NAa NA

T10.3

(includes GDP Control Variable) (79.8% Av.) 89 86 83 87 85 92 – 87 89 83

89 –84 82

83

83

96

94

NA NAa 17/18 (T − G)

89

88

80

(18 Sample Av, R2 = 87.3%)

10/11 (T − G)

(Leftmost 6 Sample Av. R2 =87.0%; 6/6 (6/6) Significant) Total loanable funds 10 Unmodif. T10.4 (wo/s-a)

89

86

83

87

85

92

87

89

83

89

88

89

84

82

83

83

96

94

(18 Sample Av, R2 = 87.3%) 10 Modified (wo/s-a)

T10.4

91

88

87

90

90

95

90

91

87

91

90

90

87

86

84

84

97

96

Endogenous (EN) and Exogenous (EX) modifiers model T.10.6

94

92 2

91

86

89

18/18 (T − G) 10/11 (T − G)a

(18 Sample Av, R2 = 89.7%); (Left 6 Sample Av, R2 = 90.2%)

10 Modified (wo/s-a)

17/18 (T − G) 10/11 (T − G)

(EN) EX) 91

–

–

–

–

–

–

–

–

–

–

–

–

2

(Av, R = 90.5%) (Adj. Av, R = 87.7%) Endogenous (EN) and Exogenous (EX) modifiers model (GDP control variable added) 10 Modified T.10.7 94 92 91 86 89 91 – – – – – (wo/s-a) (Av, R2 = 87.3%) (Av, R2 = 84.5%)

–

–

–

–

–

–

–

5/6

3/6b

5/6

3/6a

6/6

2/6b

6/6

2/6a

a 7 samples containing 1/3-½ of all observations from “Crowd In” years Removed, leaving 11 of 18 b 2 of 3 significant periods included 2008 or 2008-2010 QE period years when FR purchases were huge

1. Baseline standard model (no deficit or LF variables or GDP Included): Average R 2 = 68.3%. 2. When a deficit variables were added to baseline standard model, R 2 increases to 87.3%, an increase of 28%, clearly indicating clearly indicating investment cannot be explained without allowing for significant crowd out effects.

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3. When the total loanable funds variable is added as a deficit modifier, but not as a stand-alone variable, average R 2 increases from 87.3 to 90.5%, indicating increases in LF can offset crowd out. 4. When the two separate deficit modifiers, endogenous and exogenous loanable funds (S + FB – Tr − A) and (Tr + A), replace the total LF modifier, with no stand-alone loanable funds variable, R 2 also rises to 90.5% for the 6 samples tested. Like the total loanable funds modifier, it adds to the investment model’s explanatory power a noticeable improvement, and again indicating loanable funds increases can offset crowd out. The finding is consistent with the Chapter 11 model without a stand-alone (S + FB) variable, whose R 2 increased to 90.7% when the deficit modifier (S + FB) was added. Chapter 11 tests the same model except using a two-variable formulation of the deficit. 5. Changes in the endogenous part of total loanable funds appears to have been the main offset to crowd out in the past, being significant in 5 of 6 or 6 of 6 tests, depending on whether the model contained a GDP control variable. Increases in the exogenous part only were significant in 2 of tests, those including data from the early QE years in the sample.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 11

Do Loanable Funds Modify the Crowd Out Effects of the Two-Variable Deficit (T ), (G)?

In Sects. 11.1 and 11.2 below we test the standard consumption and investment models the same way as in Chapter 10, with one change: here we use two separate deficit variables, one for tax deficit effects (T ), and one for government spending deficit effects (G). In Chapter 10, only one variable (T − G) was used to represent the government deficit. The two variable deficit model is used because the multiplier effects of tax cut and spending deficits are known to differ in standard multiplier analysis, raising questions about whether the crowd out effects may also differ. Separating the deficit into its two parts allows us to test whether tax cut and spending deficits have different crowd out effects either before or after modification changes in the loanable funds pool (S + FB).

11.1 Testing the Two: Variable Deficit Consumption Model The “standard” model of consumption’s determinants reflecting the views of many economists on the what variables are determinants of consumption is taken from Heim (2017a, Eq. 4.4.TR). This time period robust,

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_11

211

212

J. J. HEIM

standard consumption model with deficit variables offset by (S + FB) is shown below: CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

−.515.07POP16/65 + .020POP + 38.00 M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

MSE = 24.88

(4.9)

(3.7)

(4.4.TR)

Including this model as a reference model, is a way of showing what variables others have found in the past to be consumption’s determinants, and hence, variables that need to be controlled for in our studies. The accuracy of the coefficients and levels of statistical significance on this study’s crowd out and loanable funds variables, or any other variable, depend greatly on how effectively we control for the fluctuations of other variables that can affect consumption. Any determinant of consumption not controlled for by inclusion in the model can cause findings for the crowd out and loanable funds variables to be distorted if our variables of interest are at all correlated. This is the “left out” variables problem described by Goldberger (1961). With the left out variables problem, coefficients on our variables of interest are likely to reflect not only their own effect on the dependent variable, but the effect of same period changes in some determinant of consumption “left out” of the model when tested. The Heim (2017a) study used an exhaustive process of multiperiod testing to develop a reasonably definitive list of all key variables found related consumption in prior studies. They are included here in all models tested as control variables to avoid the “left out variables” problem. Using this “standard” model in all tests, and just adding crowd out or loanable funds variables to them, also simplifies showing how the models tested in this study are just a logical extension the past findings, and hence consistent with the past canon of consumption function research. The methodology of this study for testing crowd out and loanable funds effects is not likely to look so unusual that it is difficult to know how reliable the models are. Equations 11.1 and 11.2 below, are built on the model above. They show test results for the initial sample tested for models extending consumption theory to better account for the modifying effects on crowd out of changes that occur in loanable funds at the same time. These two

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213

models include all variables in the standard model noted above, but add an additional stand-alone variable measuring the total pool of loanable funds: total U.S. national savings + foreign borrowing, or (S + FB). These models are identical with those tested in Chapter 9, except in Chapter 9, national savings (S) and foreign borrowing (FB) were added to the standard model as two separate variables, not one, as is done here. Chapter 16 also only tested the model in one time period; here we attempt to replicate our initial results in 17 additional time periods. Methodologically, the approach used to test is based on the following: 1. We first establish a baseline model in which the deficit variables are tested without inclusion of any additional variables to account for same-period changes in loanable funds. We then add a single loanable funds variable to control for the effect of fluctuations in the loanable funds pool on consumption. Results of the baseline model without loanable funds are then compared with results from the model with loanable funds added. We evaluate results by noting if adding the loanable funds variable to the model increases the amount of variation in consumption explained. 2. The coefficient on the loanable funds variable will provide an estimate of the marginal effect of a change in loanable funds on consumption. 3. There is reason to believe that the coefficient on this single, standalone loanable funds variable will represent the net of two effects: a positive effect of reducing crowd out and a negative effect because increasing loanable funds by increasing the level of savings in the economy while holding disposable income constant, which requires a reduction in the marginal propensity to consume, a byproduct of the regression’s ceteris paribus method of testing, which holds disposable income constant. The models tested here are ceteris paribus models where disposable income (and all other variables in the model) is held constant when measuring the effects on consumption of an increase in loanable funds. With income constant, growth in loanable funds can only occur by increasing the marginal propensity to save by decreasing the marginal propensity to consume, i.e., consumption must decline. We need some way to account for this in negative effect in the model when testing whether an increase in loanable funds also reduces crowd out, and not get the two effects confused.

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J. J. HEIM

Hence, the first model tested (Eq. 11.1), which only adds one variable to the model, the stand-alone loanable funds variable, must measure both the two separate effects of loanable funds changes on consumption. Since it has to measure two effects, the coefficient on this variable will measure the net impact on consumption of the two effects. In a second model tested (Eq. 11.2), this loanable funds variable is included as a stand alone, and also included a second time as modifier of the deficit variables’ values. The deficit variables, when entered unmodified in the model, indicate an assumption that there is a one-to-one correspondence between the size of deficits and crowd out. If the crowd out effect is modified by changes in loanable funds, subtracting loanable funds changes from the deficit should give us a modified crowd out variable that may better represents the actual crowd out effect that occurs in a period in which a deficit occurs. The second model thereby gives us two way to measure the two contradictory effects of increases in loanable funds separately in the model. 1. The crowd out reducing effect will be given by the coefficient on the modified deficit variable; 2. the mpc—reducing effect, the second effect, will be captured by the coefficient on the stand-alone loanable funds variable, and should have a negative sign if we are correct in our assumption regarding what it measures. If we have designed the 2nd model correctly, the sum of the two effects should be exactly equal to effect found when testing just the net effect of the variables in the 1st model, i.e., including just a stand-alone (S + FB) variable, with no deficit variable modifiers. The sum of the two effects shown in the 1st model does turn out to be identical to the sum of the two effects we see in the second model, as shown below. The unmodified deficit model, Eq. 11.1, defines crowd out as equal to the size of the deficit. That is, it measures crowd out before reducing the deficit by the amount of any same period growth in loanable funds that might offset its effects. This we refer to as the deficit model without modification, or (“w/o”). Equation 11.2 measures crowd out effects after the deficit as reduced by changes in loanable funds that might offset crowd out. This is the deficit model after modification of the deficit by changes in loanable funds. Both models were estimated using the same 1960–2010 data set.

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215

All consumption models tested below have been tested for stationarity and endogeneity problems. All variables are either stationary or cointegrated with their dependent variables. No endogeneity problems were found (Hausman test) with any of the consumption or investment models. Newey–West standard errors were used to avoid heteroskedasticity problems, and the model was estimated in first differences of the data to help reduce nonstationarity and multicollinearity. Equation 11.1AA below presents this study’s baseline (BL) standard consumption model with no deficit variables or loanable funds variables included (1960–2010 data). CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

(2.0)

(−0.1)

R = 60.3% Adj R = 56.5% 2

2

D.W. = 1.7

MSE = 43.98 (11.1AA)

We also include a baseline (BL) standard consumption model with crowd out (deficit) variables (Eq. 11.1A) to provide a measure of the full crowd out effects of deficits that can occur if no offsetting change in loanable funds occurs. C D = .31(Y − TT ) + .32(TT ) − .16(G T&I ) − 7.14PR + .49DJ−2 (t=)

(6.4)

(6.6)

(−3.1)

(−1.9)

(4.5)

−.459.68POP16/65 + .017POP + 36.27M2AV + .09CB2 (4.0)

(2.4)

R = 86.6 Adj. R = 83.9% 2

2

(3.8)

(3.9)

D.W. = 2.1 MSE = 26.17

(11.1A)

Notice the baseline equation before adding the deficit variable explains only 60.3% of the variation in consumption data over the period 1960– 2010. When the deficit variable is added to the same model to account for the negative crowd out effects of deficits, explained variance rises to 86.6%, a 26.3%-point increase. This evidence indicates crowd out is a real problem having negative effects on consumption. To ensure this finding was not an anomaly, we retested the same models in 17 additional time periods, shown in Table 11.1D. In every period tested adding the crowd out variable markedly increased explained variance. The increase averaged 17.4 percentage points for the 18 samples. There seems to have been no sample period from 1960 to 2010 when crowd out was not a problem.

T11.1AA

T11.1A

21 Baseline (wo/Def)

21 Baseline (w/Def)

2

19 60 – 20 08 72 19 60 – 20 07 72 19 60 – 20 00 86

89

19 60 – 19 90 43

91

19 60 – 19 80 77

93

19 70 – 19 90 91

92

19 70 – 20 00 91

86

19 70 – 20 07 68

(Av. R2 = 89.4%); (Adj. R2 Av = 90.6% “w”)

(Av. R = 71.4%) 87 87 87 91

19 60 – 20 10 60

88

19 70 – 20 10 55

94

19 80 – 20 00 86

85

19 80 – 20 10 37

88

19 75 – 20 04 63

88

19 80 – 20 04 74

86

19 85 – 20 04 67

87

19 85 – 20 05 65

92

19 96 – 20 09 83

99

20 00 – 20 10 95

NA

5/5

5/5 b

10/11 5/11a

NA NA 15/18 6/18

NA

Test ratio T G

Signif./Total

effects with periods of statistically significant crowd in effects leaves the effects canceling each other out, leaving a nonsignificant statistic for the effects of deficits, for technical, not substantive reasons (see Chapter 18.1.1 below) b With 7 samples mixing crowd out and crowd in periods data excluded, and 1980s data also excluded because of lack of significant variation in government spending. Lack of variation also leads to insignificant estimates of spending deficit crowd out effects for technical, not substantive reasons: you can’t find a correlation between a variable that is fluctuating and one that is not, even if there is an underlying substantive relationship. (See explanation below)

a With 7 samples mixing large amounts of “crowd out” and “crowd in” periods data excluded. Mixing periods of statistically significant crowd out

From Table#

Model

Table 11.1D Growth in explained variance when adding crowd out to a standard model

216 J. J. HEIM

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217

In Eq. 11.1, a (stand-alone) loanable funds variable is added to the baseline deficit model above to determine if changes in loanable increase the model’s ability to explain consumption behavior. The model was estimated using OLS because no endogeneity issues were uncovered. No stationarity issues were found except those resolved by cointegration. Heteroskedasticity issues were resolved using Newey–West standard errors, and first differencing of the data was used to reduce multicollinearity and serial correlation issues. CD = .38(Y − TT ) + .43(TT ) − .24(G T&I ) − .14(ST + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−4.1)

− 6.09PR + 40DJ−2 − .398.48POP16/65 + .016POP (−2.8)

(5.0)

(−1.9)

(3.7)

+ 33.67M2AV + .10CB2 (4.5)

(3.5)

R = 88.3% Adj. R = 85.8% D.W. = 1.9 2

2

MSE = 24.68 (11.1)

Results indicate changes in loanable funds themselves have a significant effect on consumption which adds 1.7 percentage point to explained variance. Adding the loanable funds control variable strengthened the deficit variables’ statistical significance levels. We interpret the coefficient on the loanable funds variable as indicating the net effect on consumption of two separate effects: the positive effect of reducing crowd out and the negative effect of reducing the marginal propensity to consume (mpc). To obtain separate estimates for these two effects, we reestimate Eq. 11.1 by modifying the deficit variables by any change in loanable funds that may have occurred in the same period as the deficit, while continuing to include the loanable funds variable as a stand-alone variable in the model. Results are presented in Eq. 11.2 below: CD = .38(Y − TT ) + .43(TT )m − .24(G T&I )m − .81(ST + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−5.6)

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.0)

(−1.9)

(3.7)

+ 33.67M2AV + 10CB2 (4.5)

(3.5)

R = 88.3% Adj. R = 85.8% 2

2

D.W. = 1.8

MSE = 24.89 (11.2)

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J. J. HEIM

Note that after modification of the crowd out effect by adding (S + FB) to the tax deficit variable (T ), and subtracting it from the spending deficit variable (G), results for all variables except the stand-alone (S + FB) variable remain the same, as does R 2 . Also note the separate estimates for the three crowd out effects in Eq. 11.2, two of which measure the positive effects of a change in loanable funds on consumption βi (T + (S + FB)) and − βj (G − (S + FB)), and one of which measures the negative effect on the mpc of increasing mps: − βk (S + FB). This equals (+.43) − (−.24) + (−.81) = (−.14) in Eq. 11.2 above, which is precisely equal to the net effect given in Eq. 11.1. All the positive and negative effects in Eq. 11.2 are statistically significant. The identical result in both equations for the net effect is proof there are two separate and contradictory effects on consumption of increasing the loanable funds pool. The fact that the coefficients (marginal effects) of deficits in both models stays the same reflects the fact that changing the magnitude of the estimated crowd out effect does not (and should not) affect the magnitude of the deficit variable’s estimated parameter, if loanable funds offset deficit—caused crowd out on a dollar for dollar basis. The marginal effect of a change in crowd out should stay the same, regardless of whether the change is a dollar change from a large number or smaller number (assuming the relationship is linear). Table 11.1B presents baseline model coefficients (with deficit variables added). Stationarity issues with the consumption and governments spending variables were resolved by detrending; there were no endogeneity issues. Surprisingly, in only 6 of the 18 test periods, spending deficit variables were found statistically significant. Two problems appear to account for this: 1. Samples that contain large portions (1/3 – ½) of their observations from 1990s “crowd in” data with the crowd out data characteristic of other decades typically will have those effects cancel each other out and yield insignificance. This problem is examined in detail in Sect. 11.1.1 of this chapter. Eliminating those samples reduces the number of significant spending crowd out findings from 6 of 18 to 5 of 11 remaining samples.

T Def : NW t stat White t Ordin. t G Def : NW t stat White t Ordin. t ST + FB NW t stat White t Ordin. T R2 Adj.R 2

Variable

.72 (5.3) (4.9) (5.0) −.28 (−2.8) (2.1) (−2.1) −1.46 (−4.2) (−3.7) (−3.7) .94 .88

.36 (2.7) (2.9) (3.9) −.16 (−2.2) (−1.6) (−1.5) −.13 (−1.3) (−1.3) (−1.5) .90 .85

w/o

.72 (5.3) (4.9) (5.0) −.28 (−2.8) (1.5) (2.1) −.47 (−2.6) (2.0) (2.5) .94 .88

1960–1990

w/o

with

1960–1980

.36 (2.7) (2.9) (3.9) −.16 (−2.2) (−1.6) (−1.5) −.65 (−2.5) (−2.3) (−2.8) .90 .85

with .29 (2.6) (2.5) (3.2) −.09 (−0.9) (−0.8) (−0.8) −.10 (−1.2) (−1.4) (−1.2) .91 .88

w/o

1960–2000

.29 (2.6) (2.5) (3.2) −.09 (−0.9) (−0.8) (−0.8) −.48 (−1.8) (−1.7) (−2.1) .91 .88

with .44 (5.7) (5.4) (6.3) −.17 (−2.4) (1.9) (−1.6) −.13 (−3.6) (−2.8) (−2.4) .89 .86

w/o

1960–2007

.44 (5.7) (5.4) (6.3) −.17 (−2.4) (−1.9) (−1.6) −.74 (−4.7) (−4.5) (−4.1) .89 .86

with .42 (5.5) (5.5) (6.5) −.16 (−2.4) (−1.9) (−1.5) −.11 (−3.4) (−2.8) (−2.1) .89 .86

w/o

1960–2008

.42 (5.5) (5.5) (6.5) −.16 (−2.5) (−1.9) (−1.5) −.69 (−4.7) (−4.7) (−4.0) .89 .86

with

.43 (6.7) (6.9) (6.8) −24 (−2.8) (−2.4) (−2.4) −.82 (−5.6) (−5.7) (−4.9) .88 .86

with

(continued)

.43 (6.7) (6.9) (6.8) −.24 (−2.8) (−2.4) (−2.4) −.14 (−4.1) (−3.1) (−2.7) .88 .86

w/o

1960–2010

Table 11.1 Comparing robustness over time of effects on consumption of crowd out, with and without compensating loanable funds (separate stand-alone S + FB variable included) 11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

219

T Def : NW t stat White t Ordin. T G Def : NW t stat White t Ordin. t ST + FBNW t stat White t Ordin. t R2 Adj.R 2

Variable

.43 (1.7) (1.7) (1.7) −.36 (−3.0) (−2.9) (−2.3) −.13 (−1.2) (−1.4) (−1.5) .95 .90

.18 (1.7) (1.7) (1.7) −.36 (−3.0) (−2.9) (−2.3) −1.46 (−2.6) (−2.5) (−2.6) .95 .90

.14 (1.2) (1.0) (1.2) −.11 (−0.8) (−0.7) (−0.8) −.06 (−0.6) (−.06) (−0.8) .92 .89

w/o

w/o

with

1970–2000

1970–1990

.14 (1.2) (1.0) (1.2) −.11 (−0.8) (−0.7) (−0.8) −.32 (−1.0) (−0.9) (−1.2) .92 .89

with .44 (4.2) (4.4) (5.1) −.14 (−1.5) (−1.1) (−1.0) −.14 (−3.0) (−2.5) (2.0) .88 .84

w/o

1970–2007

.44 (4.2) (4.4) (5.1) −.14 (−1.5) (−1.1) (−1.0) −.71 (−4.6) (−3.9) (−3.3) .88 .84

with .41 (4.6) (5.2) (5.5) −.17 (−2.0) (−1.4) (−1.2) −.11 (−2.9) (−2.5) (−1.7) .89 .86

w/o

1970–2009

.41 (4.6) (5.2) (5.5) −.17 (−2.0) (−1.4) (−1.2) −.68 (−5.1) (−2.5) (−3.5) .89 .86

with .07 (0.8) (0.6) (0.5) .11 (0.7) (0.5) (0.6) .01 (0.1) (0.1) (0.1) .94 .88

w/o

1980–2000

.07 (0.8) (0.6) (0.5) .11 (0.7) (0.5) (0.6) .02 (0.2) (0.1) (0.1) .94 .88

with

Comparing robustness over time of effects on consumption of crowd out, with and without loanable funds accommodation

Table 11.1 (continued)

.40 (4.7) (5.1) (4.5) −.28 (−1.8) (−1.8) (−1.8) −.13 (−3.4) (−2.7) (−1.7) .87 .82

w/o

with .40 (4.7) (5.1) (4.5) −.28 (−1.8) (−1.8) (−1.8) −.81 (−3.9) (−4.5) (−3.5) .87 .82

1980–2010

220 J. J. HEIM

T Def : NW t stat White t Ordin. T G Def : NW t stat White t Ordin. t ST + FBNW t stat White t Ordin. t R2 Adj.R 2

Variable

.35 (3.2) (3.0) (3.2) +.02 (0.2) (0.1) (0.1) −.02 (−0.3) (−0.2) (−0.2) .88 .82

.35 (3.2) (3.0) (3.2) +.02 (0.2) (0.1) (0.1) −.36 (−1.7) (−1.4) (−1.1) .88 .82

.38 (3.3) (2.8) (3.0) .02 (0.2) (0.1) (0.1) −.05 (−0.6) (−0.5) (−0.4) .88 .81

w/o

w/o

with

1980–2004

1975–2004

.38 (3.3) (2.8) (3.0) .02 (0.2) (0.1) (0.1) −.42 (−1.6) (−1.3) (−1.1) .88 .81

with .39 (2.4) (2.1) (2.2) .19 (1.0) (0.7) (0.6) −.07 (−0.4) (−0.4) (−0.4) .86 .74

w/o

1985–2004

.39 (2.4) (2.1) (2.2) +.19 (1.0) (0.7) (0.6) −.27 (−0.7) (−0.5) (−0.5) .86 .74

with .40 (2.7) (2.2) (2.3) +.21 (1.1) (0.8) (0.7) −.07 (−0.4) (−0.4) (−0.4) .87 .76

w/o

1985–2005

.40 (2.7) (2.2) (2.3) +.21 (1.1) (0.8) (0.7) −.26 (−0.7) (−0.5) (−0.5) .87 .76

with .66 (3.3) (3.7) (4.0) −1.09 (−2.8) (−2.8) (−3.6) −.19 (−3.1) (−2.8) (−2.6) .97 .90

w/o

1996–2010

.66 (3.3) (3.7) (4.0) −1.09 (−2.8) (−2.8) (−3.6) −1.93 (−3.1) (−3.2) (−4.1) .97 .90

with .45 (2.4) (2.3) (2.2) −.56 (−1.3) (−1.0) (−1.0) −.11 (−1.4) (−1.1) (−1.0) .99 .95

w/o

with .45 (2.4) (2.3) (2.2) −.56 (−1.3) (−1.0) (−1.0) −1.11 (−1.6) (−1.4) (−1.3) .99 .95

2000–2010

11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

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222

J. J. HEIM

Table 11.2 Changes in regression coefficients and t-statistics associated with loanable funds changes Period

00–10 60–80 80–90 60–70 70–80 90–00

Average loanable funds growth net of the govt. deficit during the decade Average: Average: Average: Average: Average: Average:

$ $ $ $ $ $

−184.7 Billion −27.8 Billion −17.8 Billion +6.6 Billion +6.9 Billion +132.9 Billion

(T-G) deficit Coef.(t)

T only deficit Coef.(t)

G only deficit Coef.(t)

+.42(4.2) +.45(3.3) +.02(0.1) +.53(2.4) +.22(1.4) −.09(0.5)

.45(2.4) .72(5.3) .10(0.2) .82(12.0) .22(0.9) 1.18(3.7)

−.56(−1.3)a −.28(−2.8) -.20(−0.2) −.42(−7.7) −.20(−0.8) +.50(6.5)

a Result sensitive to adding or subtracting even one year. Coefficient (t ) = −.69 (−4.3) if 1998–1999

data included with the 2000–2010 decade; −.55 (−1.8) if only 1999 data is added

2. The second problem was the lack of variation in the government spending in the 1980s when the standard deviation on spending during the decade was only 30% of the average level of spending. For the other four decades in our data set, the standard deviation was between 64 and 229%. Without significant variation there can’t be statistically significant correlations. Five of the remaining 11 samples had this problem. Removing them from the 11 remaining samples (after the 1990s samples are deleted), leaves five remaining samples, all 5 showing statistically significant negative spending deficit effects. (No such data variation problem arose for tax deficits, whose decade standard deviations as a percent of decade average values, varied from 61 to 766%. For the seven 1990s problem samples the typical effect was to reduce the average coefficients and significance levels from 31.2(4.1) for the unaffected 11 samples to 26.6(3.4) for the affected seven samples, as calculated from the Table 11.1B data, but in 5 of 7 cases, leave the tax deficit variable still statistically significant. Hence tax deficits showed significant crowd out in almost all of the 18 samples). 3. There is another reason why for consumption, tax deficits are found to have significant crowd out effects more often than spending

.72 (5.3)

−.28 (−2.8)

.72 (5.3)

−.28 (−2.8)

G Def : t stat

−.16 (−2.2)

.36 (2.7) −.16 (−2.2)

.36 (2.7)

with

w/o

w/o

with

1960–1990

1960–1980

T Def : t stat

Variable

−.09 (−0.9)

.29 (2.6)

w/o

−.09 (−0.9)

.29 (2.6)

with

1960–2000

| | | | | |

|

|

−.36 (−3.0)

.43 (1.7)

w/o

−.36 (−3.0)

.18 (1.7)

with

1970–1990

Table 11.3 Effects of adding “crowd out” and “crowd in” periods

−.11 (−0.8)

.14 (1.2)

w/o

−.11 (−0.8)

.14 (1.2)

with

1970–2000

| | | | | |

|

|

+.50 (+6.5)

1.18 (+3.7)

w/o

with

1990–2000

11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

223

224

J. J. HEIM

Table 11.4 Simulated results of combining statistically significant “crowd in” and “crowd out” samples Variable (T ) deficit (t-statistic) (G) deficit (t-statistic) R2

Decade (X) sample

Decade (Y) sample

Decades (X) and (Y) combined sample

.88 (6.0) −.71 (−2.1) .86

.02 (1.6) 1.04 (38.9) .99

.03 (0.4) .05 (0.1) (.01)

Table 11.5 Effects of adding a separate, sand alone loanable funds variable to a crowd out model Variable (T ) deficit t-statistic (G) deficit (t-statistic) R2

Decade (X) sample (without)

Decade (X) sample (with)

Decade (Y) sample (without)

Decade (Y) sample (with)

.88 (6.0) −.71 (−2.1) .86

.93 (10.8) 3.18 (3.1) .96

.02 (1.6) 1.04 (38.9) .995

.03 (1.8) 1.12 (8.4) .996

deficits. In the baseline model for consumption, we found only 6 of 18 samples showed significant crowd out, but that two technical problems accounted for the 12 insignificant findings, namely the 1990s crowd in period problem and the limited amount of variation in the government spending variable in the 1980s. For investment (as we show in Table 11.10), using the same government spending variable we do not see these insignificant findings in most samples. One possible reason why is that government spending is a more important determinant of investment spending than consumer spending. Heim (2017a, Tables 4.4.1 and 5.4.1) shows that with very similar models for the 1960–2010 period, variation in the government spending variable accounts for much more of the variation in investment than does government spending in the consumption model. Depending on whether the “first out” or “first in” method of stepwise regression is used to determine the government spending variable’s contribution to total variance

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

225

Table 11.6 Crowd out variable coefficients, t-statistics and R 2 in different sample periodsa Period sampled

Tax deficit

Spend. deficit

R2 Period sampled

Coef. t-stat Coef. t-stat 1960– 1970 1960– 1971 1960– 1972 1960– 1973 1960– 1974 1960– 1975 1960– 1976 1960– 1977 1960– 1978 1960– 1979 1960– 1980 1960– 1981 1960– 1982 1960– 1983 1960– 1984 1960– 1985 1960– 1986 1960– 1987 1960– 1988

.82

(12.0) −.43 (−7.7)

.76

(6.6) −.38 (−5.3)

.76

(5.3) −.38 (−3.2)

.78

(3.9) −.33 (−3.1)

.71

(4.1) −.32 (−3.0)

.83

(7.1) −.31 (−3.1)

.83

(7.4) −.31 (-3.5)

.75

(5.0) −.25 (−2.2)

.74

(5.2) −.26 (−2.5)

.75

(5.1) −.25 (−2.2)

.71

(5.3) −.28 (−2.8)

.71

(5.5) −.27 (−2.8)

.69

(4.4) −.23 (−1.9)

.63

(3.9) −.26 (−2.1)

.59

(4.5) −.23 (−2.1)

.52

(3.7) −.21 (−2.0)

.50

(3.4) −.19 (−2.1)

.50

(3.4) −.18 (−2.2)

.51

(3.5) −.19 (−2.8)

Tax deficit

Coef. t-stat Coef. .99 1980– 1990 .98 1980– 1991 .95 1980– 1992 .93 1980– 1993 .95 1980– 1994 .94 1980– 1995 .94 1980– 1996 .93 1980– 1997 .93 1980– 1998 .93 1980– 1999 .94 1980– 2000 .94 1980– 2001 .91 1980– 2002 .92 1980– 2003 .93 1980– 2004 .92 1980– 2005 .93 1980– 2006 .93 1980– 2007 .93 1980– 2008

R2

Spend. deficit t-stat

.10

(0.2) −.20

(0.3) .97

.15

(0.5) −.05

(0.1) .97

.12

(0.4)

(0.1) .97

.26

(1.2) −.25 (−1.0) .96

.22

(1.1) −.15 (−0.8) .96

.20

(1.1) −.11 (−0.8) .95

.15

(0.9) −.30 (−0.7) .95

.13

(0.9) −.02 (−0.1) .94

.14

(1.3)

.08

(0.5) .92

.08

(0.7)

.09

(0.6) .93

.08

(0.8)

.11

(0.7) .94

.05

(0.4)

.12

(0.7) .93

.24

(2.6)

.19

(1.1) .91

.35

(2.6)

.02

(0.2) .90

.38

(3.3)

.02

(0.2) .88

.40

(4.1)

.04

(0.2) .89

.43

(4.1) −.01 (−0.1) .88

.47

(4.8) −.04 (−0.3) .88

.39

(4.2) −.05 (−0.5) .88

.07

(continued)

226

J. J. HEIM

Table 11.6 (continued) Period sampled

Tax deficit

Spend. deficit

R2 Period sampled

Coef. t-stat Coef. t-stat 1960– 1989

1970– 1980 1970– 1981 1970– 1982 1970– 1983 1970– 1984 1970– 1985 1970– 1986 1970– 1987 1970– 1988 1970– 1989 1970– 1990 1970– 1991 1970– 1992 1970– 1993 1970– 1994 1970– 1995 1970– 1996 1970– 1997

.37

(2.9) −.14 (−2.0)

.22

(0.9) −.20 (0.8)

.25

(1.3) −.24 (0.8)

.31

(2.4) −.33 (−4.7)

.25

(2.3) −.36 (−2.7)

.50

(8.4) −.58 (−7.1)

.36

(5.2) −.57 (−5.4)

.34

(6.6) −.56 (−5.3)

.33

(4.9) −.44 (−4.0)

.33

(4.7) −.38 (−4.6)

.20

(1.7) −.34 (−3.2)

.18

(1.6) −.36 (−3.0)

.18

(1.3) −.19 (−0.8)

.18

(1.4) −.20 (−1.2)

.18

(1.4) −.23 (−1.8)

.18

(1.5) −.22 (−1.6)

.17

(1.2) −.18 (−1.5)

.16

(1.2) −.18 (−1.5)

.15

(1.1) −.19 (−1.7)

Tax deficit

Coef. t-stat Coef. .91 1980– 2009 1980– 2010 .99 1990– 2000 .99 1990– 2001 .99 1990– 2002 .99 1990– 2003 .99 1990– 2004 .99 1990– 2005 .99 1990– 2006 .98 1990– 2007 .98 1990– 2008 .96 1990– 2009 .95 .91 1987– 1997 .91 1988– 1998 .91 1989– 1999 .92 .90 1990– 2000 .90 1991– 2001 .90 1992– 2002

R2

Spend. deficit t-stat

.42

(4.7) −.13 (−1.2) .89

.40

(4.7) −.28 (−1.8) .87

1.18

(3.7)

.50

(6.5) .99

.78

(1.7)

.38

(7.6) .99

.73

(7.8)

.37

(6.4) .99

.85

(6.5)

.29

(2.2) .98

.57

(3.0)

.34

(1.8) .91

.57

(3.2)

.34

(2.0) .92

.61

(5.9)

.34

(2.0) .92

.57 (10.8)

.37

(2.0) .92

.39

(4.1) .31

(1.7) .90

.44

(4.2)

.08

(0.4) .90

.09

(0.1)

.15

(0.3) .96

1.46.

(2.5)

.52

(2.4) .99

.65

(2.9)

.29

(2.1) .99

1.18

(3.7)

.50

(6.5) .99

1.03

(1.4)

.39

(1.2) .99

−.81

(0.4)

.01

(0.0) .98

(continued)

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

227

Table 11.6 (continued) Period sampled

Tax deficit

Spend. deficit

R2 Period sampled

Coef. t-stat Coef. t-stat 1970– 1998 1970– 1999

.16

(1.3) −.12 (−0.9)

.15

(1.2) −.12 (−0.9)

Tax deficit

Coef. t-stat Coef. .90 1993– 2003 .92 1994– 2004 1995– 2005 1996– 2006 1997– 2007 1998– 2008 1999– 2009 1990– 2010 2000– 2010 1999– 2010 1998– 2010 1996– 2010 1993– 2010

R2

Spend. deficit t-stat

.93

(9.0)

.89

(4.9) .99

.80

(5.6)

.85

(2.7) .99

1.55

(1.3)

2.95

(1.0) .96

1.00

(2.1) −.62 (−0.3) .95

.87

(4.3)

.47

(1.8) −.47 (−0.5) .99

−.14

(0.2)

.35

.10

(0.4) .99

(0.1) .99

.41

(3.2) −.23 (−0.7) .99

.45

(2.4) −.56 (−1.3) .99

.45

(3.3) −.55 (−1.8) .99

.45

(3.3) −.55 (−1.8) .99

.66

(3.2) −1.09 (−2.8) .97

.32

(3.3) −.54 (−2.0) .91

a Same Model used as in Eqs. 11.1 and 11.2 and in Table 11.1

explained by the model, government spending explains 2–11 times as much variation in investment model than in the consumption model. It explains from 11–22% of the total variation in investment compared to 2–5.6% for consumption. This implies that even small fluctuations we found in government spending lead to significant moves in investment and be easier for the regression to distinguish from movement in other variables. This may explain our much more frequent findings of government spending being significantly related

+96.23 +68.10 +104.25 −58.39 −115.58 −22.02 −95.53 −133.03 −127.96 −53.32 −91.60

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Source ERP (2012) for nominal values, then deflated using the GDP deflator

Deficit growth(+)/decline(−)

Year

Table 11.7 Annual growth (+)/decline (−) in deficits 1990–2000

−78.19 −115.52 +8.47 +50.86 +189.14 +108.70 +131.32 +202.18 +216.28 +135.78 +184.10

L oanable funds growth(+)/decline(−)

228 J. J. HEIM

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

229

Table 11.8 Annual growth (+)/decline (−) in Deficits 1960–2000 Year

Deficit growth(+)/decline(−)

Loanable funds growth(+)/gecline(−)

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

−46.93 +56.52 +28.37 −26.34 +27.85 −15.82 +17.67 +89.25 −57.09 −80.55 +120.38 +37.82 −78.48 −55.30 +53.44 +221.50 −90.18 −62.23 −58.34 −14.42 +116.13 −15.67 +170.40 +66.63 −43.29 +34.19 +45.80 −62.27 −39.81 −10.00 +96.23 +68.11 +104.26 −58.39 −115.58 −22.03 −95.54

−6.14 +5.39 +44.33 +30.70 +28.66 +69.89 +40.41 −13.62 +28.59 +31.94 −74.29 +40.48 +87.77 +101.78 −42.83 −139.22 +117.98 +136.09 +130.42 +11.08 −102.71 +111.18 −103.06 −20.71 +304.12 −26.47 −31.19 +93.58 +72.41 −56.11 −78.20 −115.53 +8.48 +50.87 +189.14 +108.71 +131.32

(continued)

230

J. J. HEIM

Table 11.8 (continued) Year

Deficit growth(+)/decline(−)

Loanable funds growth(+)/gecline(−)

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

−133.03 −127.96 −53.32

+202.19 +216.28 +135.78 +184.11 −205.34 −102.92 +13.89 +238.65 +207.19 +255.41 −302.12 −222.40 −571.12 +244.98

−91.60 +255.23 +395.37 +101.98 −47.44 −155.87 −99.28 +75.48 +379.04 +539.51 +23.59

Source ERP, 2013, Nominal Values Tables GDP Deflator Table B3 (2005 = 100)

to investment than we found with consumption, despite the 1990s and variation problems with the data. With the tax deficit variable, the situation is just the opposite. The Tax deficit variable explains 2.4–14 times as much variation in consumption as the government spending variable (12% vs. 5% using “1st out” stepwise regression; 28% vs. 2% using “1st In” stepwise regression. Tax deficits hurt consumption, i.e., cause more variation in consumption, much more than spending deficits, and hence, are more likely to show statistically significant crowd out effects. We theorize that the reason for this is that financing tax cut deficits reduces the money available for consumers to borrow, and the tax cuts for the most part go to those who save and invest the money, not spend it on consumer goods. The increased savings that takes place is shifted our of consumption toward investment. Hence, the strong crowd out effect of tax cut deficits. Financing spending deficits, though they also reduce funds available to consumers to borrow and spend, are more likely to be channeled to those at the lower end of the income spectrum, who are most likely to replace the lost borrowing power with increased

T Def : t-stat G Def : t-stat R2 Adj.R 2

Variable

.50 (3.0) −.19 (−1.3) .90 .82

.24 (2.2) +.06 (0.5) .85 .73

.25 (3.4) −.10 (−1.2) .90 .86

.14 (2.7) .08 (1.3) .87 .82

with

w/o

w/o

with

1960–1990

1960–1980

.23 (2.8) −.03 (−0.5) .90 .88

w/o .11. (1.8) .04 (0.6) .90 .87

with

1960–2000

.32 (5.1) −.13 (−1.1) .87 .84

w/o .16 (2.2) .07 (0.6) .82 .79

with

1960–2007

.31 (5.1) −.13 (−1.2) .87 .84

w/o

.18 (2.5) .19 (0.7) .83 .79

with

1960–2008

.31 (6.3) −21 (−1.9) .88 .85

w/o

.15 (2.3) .02 (0.1) .83 .79

with

1960–2010

Table 11.9 Robustness of effects of crowd out on consumption (no stand-alone loanable funds control variable)

11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

231

From Table#

T10.3C

T10.3B

Eq.11.10A

Model

20 Baseline (w/o Def)

20 Baseline (w/o Def)

21 Baseline (w/Def)

19 60 – 20 08 67 19 60 – 20 07 66 19 60 – 20 00 63 19 60 – 19 90 65 19 19 60 70 – – 19 19 80 90 72 −61 19 70 – 20 00 56 19 70 – 20 07 65 19 70 – 20 10 72 19 80 – 20 00 69

89

76

71

80

78

91

82

81 2

71

76

81

84

89

87

95

90

90

86

(Av. R2 = 89.8% ) (Av. Adj. R2 = 85.9%)

86

90

89

(includes GDP Control Variable) (Av. R = 79.8% )

70

(Does not include GDP Control Variable) (Av. R2 = 68.3% )

19 60 – 20 10 69

90

80

89

80

19 19 80 75 – – 20 20 10 04 77 −64

89

81

19 80 – 20 04 71

89

75

19 85 – 20 04 63

89

75

19 85 – 20 05 57

Table 11.10A Growth in explained variance when adding crowd out to a standard model

98

93

19 96 – 20 09 92

98

95

20 00 – 20 10 91

NAa

NA

NAa

NA

8/11

9/11

11/18 16/18

NA

NA

NA

NA

Test ratio T G

Signif./Total

232 J. J. HEIM

T Def : t-stat G Def : t-stat S + FB t-stat R2 Rev.R 2

Variable w/o

with

−.10 (−1.2) −.12 (−1.3) .56 (2.8) .98 .96

w/o

−.10 (−1.2) −.12 (−1.3) .59 (5.4) .98 .96 .09 (0.9) −.21 (−2.4) .31 (3.1) .92 .88

1960–1990

1960–1980

.09 (0.9) −.21 (−2.4) .00 (0.0) .92 .88

with .20 (1.5) −.19 (−1.8) .27 (2.4) .90 .88

w/o

1960–2000

.20 (1.5) −.19 (−1.8) −.12 (−0.4) .90 .88

with .12 (1.2) −.17 (−1.7) .20 (3.6) .88 .85

w/o

1960–2007

.12 (1.2) −.17 (−1.7) −.08 (−0.4) .88 .85

with

.21 (1.6) −.18 (−1.6) .19 (2.8) .88 .86

w/o

1960–2008

.21 (1.6) −.18 (−1.6) −.21 (−0.8) .88 .86

with

.22 (1.6) −.16 (−1.9) .18 (2.8) .91 .89

w/o

with .22 (1.6) −.16 (−1.9) −.19 (−0.8) .91 .89

1960–2010

Table 11.10 Effects on investment of crowd out, with and without modification by loanable funds (stand-alone (S + FB) and GDP variables included)

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spending out of their new spending-deficit generated income. As a result, in consumption models we find few periods in which tax deficits are insignificant, but many in which spending deficits are insignificant. For investment, just the opposite is true, and most likely for the same reasons. Tax cuts are most often saved and invested offsetting crowd out effects on investment. Spending deficits also cause crowd out, but recipients are more likely to be consumers than businesses, hence they do not provide an offset to investment crowd out, and spending deficits are found to create statistically significant crowd out effects for investment more often than tax cut deficits (see analysis of Table 18.10 results). Table 11.1B presents estimates of R 2 and deficit variables’ statistical significance for 18 time periods for the baseline consumption model with deficits, but before inclusion of any loanable funds variable. These are presented for comparison with the same models including loanable funds variables during the same 18 periods, which are presented in Table 11.1 further below Table 11.1.B. For comparison with the initial sample results, Table 11.1 presents crowd out and loanable funds test results for the loanable funds models used above in Eqs. 11.1. and 11.2. Results are shown for the initial tests using the whole 1960–2010 test period, and also shows results of attempts to replicate these results in 17 shorter time periods between 1960 and 2010.

T β(t)

.53(3.9) .28(3.2) .23(2.8) .33(5.6) .33(5.6) .32(6.6)

Sample Period

1960–1980 1960–1990 1960–2000 1960–2007 1960–1908 1960–2010

R2 .91 .89 .91 .87 .87 .87

G β(t)

−.21(−1.6) −.10(−1.7) −.03(−0.5) −.08(−1.5) −.08(−1.6) −.16(−1.9) 1970–1990 1970–1900 1970–2007 1970–2009 1980–2000 1980–2010

Period .11(1.4) .10(1.3) .32(3.9) .33(4.6) .09(1.3) .31(4.5)

T β(t) −.25(−2.1) −.07(−0.7) −.05(−0.5) −.08(−1.1) .11(0.7) −.20(−1.4)

G β(t) .93 .92 .86 .88 .94 .85

R2

1975–2004 1980–2004 1985–2004 1985–2005 1996–2010 2000–2010

Period

.35 .34 .33 .34 .39 .26

(3.8) (4.0) (4.2) (5.0) (2.2) (4.8)

T β(t)

Table 11.1B Base line model with only deficit variables added: estimates of consumption crowd out

.03(0.3) .06(0.4) .25(1.3) .26(1.4) −.82(−1.7) −.05(−0.2)

G β(t)

.88 .88 .86 .87 .92 .99

R2

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For each time period given in Table 11.1, two sets of statistics are presented. One in which includes the separate, stand-alone loanable funds variable, but no modification of the deficit variables (T , G) by changes in loanable funds “w/o”), and one in which includes the separate loanable funds variable and the deficit variables are modified by same period changes in loanable funds (“with”). The modified deficit crowd out variables are, T + (S + FB), and G − (S + FB). The separate loanable funds variable is defined as (S + FB). Table 18.1 does contain three tstatistics for each deficit variable’s coefficient. Each based on a different type of standard error: Newey–West, White and ordinary least squares errors. In this study, normal practice is to deal with heteroskedasticity by using Newey–West errors; the others are presented for comparison and to show that only rarely does the choice of error affects decisions about whether a variable is statistically significant or not. A summary of Table 11.1 findings is presented below at the end of the table. Effects on R2 : For the 18 periods sampled, for both the modified and unmodified models, average R 2 was 90.6% and average adjusted R 2 was 85.3%. Adding the stand-alone loanable funds variable to the baseline model with deficit increases R 2 in 10 of 18 periods tested, with no change in R 2 for the other 8 periods. The average increase for the 18 periods was small, 1.3 percentage points. This indicates that changes in loanable funds, ceteris paribus, may not have an effect on consumption, or not a huge one. We conclude the R 2 results are theory consistent: changes in loanable funds should affect levels of consumer spending. Other evidence developed later suggests this minimal effect is due to channeling of new loanable funds away from consumption and toward investment. When the deficit variables were replaced by loanable funds modified deficit variables in a model with a stand-alone loanable funds variable, R 2 was unchanged in all 18 test periods, which is as it should be: the modified model just breaks into two parts the net effect shown in the unmodified (“w/o”) model.

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Effects on Crowd Out Variables When the separate loanable funds variable was added to the model, the number of tests showing significant crowd out increased. Tax cut crowd out was significant in 17 of 18 tests, but government spending crowd out increased to only 9 of 18 of tests. This does not mean they have no crowd out effect. Six of the 9 spending deficit tests that showed statistically insignificant crowd out effects were for periods that mix substantial periods of statistically significant “crowd out” due to rising deficits with substantial periods of statistically significant “crowd in”, which had substantially declining deficits (namely, the 1990s). Tests combining the two subperiods combine effects that tend to cancel each other out in the regression, leaving a near zero coefficient on the crowd out variable, and leaving it statistically insignificant. (See theory Chapter 4 for a discussion and examples of this problem). The tests are insignificant because a large portion of the sample shows crowd in, while the rest shows crowd out. Hence no clear, overall trend emerges. For spending deficits, Because the results do not mean that crowd out (or crowd in) are statistically insignificant, these time period samples are best not included in evaluation of the test results. For the remaining 12 samples, the results 9 of 12 show significant crowd out effects of deficits. Tax cut deficits, tend show reduced coefficients and significance levels in the same six periods, though remaining significant in 5 of 6 cases. Removing them leaves 12 of 12 periods showing significant crowd out effects of deficits resulting from tax cuts. Ignoring the samples with this technical problem, we conclude our crowd out effect results overall are theory consistent. The topic is discussed in more detail in Sect. 11.1.1 below. Changes in Loanable Funds Have Positive and Negative Effects on Consumption As noted earlier, changes in loanable funds can both a positive and a separate negative effect on consumption. The positive effect comes from crowd out effect of additional loanable funds, modeled as a reduction in the deficit by any same period increase in loanable funds. The negative effect results because absent changes in income, the increases in loanable funds (saving) can only occur by decreasing consumption. In the models used here, disposable income is held constant when estimating the effects

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of an increase in loanable funds, and for the savings, the main component of (S + FB), to cause (S + FB) to grow, the marginal propensity to consume must decline. Results Generally Invariant to Type of Standard Error Used Results in Table 11.1 are shown using three different 3 types of standard errors: Newey–West, White, and ordinary standard errors. This is done to show the results are generally the same regardless of which is used. Generally in this study, we used Newey–West standard errors because they are useful in addressing both heteroskedasticity and autocorrelation. This choice is discussed in detail in the Sect. 11.1.4 further below. Table 11.1 shows that the type of standard errors used can change tstatistics slightly, but almost never affect the count of how many results were found to be statistically significant. Only in two of 36 tests did one type of standard error produce significant results while the others did not. In 34 of the 36 tests, if one standard error produced a significant t-statistic, they all did; if one produced and insignificant results (which does happen), all three types of standard errors did. Combining Samples with Crowd Out and Crowd In Effects We do need an explanation for why nine of the 18 spending deficit tests in Table 11.1 showed no statistically significant crowd out effect, either before or after modification. Also, tax cut coefficients on all six tax cut deficits, though still significant, were also markedly lower than in other periods. The next section of this chapter (11.1.1) addresses that issue.

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Mixing Crowd Out and Crowd in Periods May Distort Results

There are a number of reasons why crowd out can be found insignificant in some empirical tests: 1. There are periods when crowd out may not exist. 2. During some of periods sampled, there may be no fluctuation of government spending or taxes. You can’t correlate something with a constant or near constant and get a statistically significant correlation. 3. Some sample sizes may be too small to generate significant results. In our sampling, the spending deficit crowd out variable has the expected sign, but was insignificant when only 1970s data was sampled. It also had the expected sign but was insignificant when only 1980s data was sampled, but had the right sign and was significant when the two samples were combined! 4. Samples that mix data from statistically significant periods of “crowd out” with data from data from periods of statistically significant “crowd in” will tend to cancel each other out and leave a nonsignificant result. This is the problem we address in this section. There were some periods, particularly in the 1990s, when loanable funds increased markedly due to a booming economy, which increased funds available for private borrowing. A decline in budget deficits increased privately available loanable funds even further. The increase in privately available loanable funds was so great the United States actually had “crowd in”, not “crowd out.” In the 1990s, the average yearly growth in loanable funds net of government saving (or deficits), was $132.9 billion (2005) dollars. The average yearly decline in the deficit was $33.7 billion (in 2005 dollars). A decline in the deficit means more of a (constant sized) loanable funds pool is available for private borrowing and spending. So, the pool available for private borrowing increased noticeably during the 1990s, as did consumption. Government spending also increased during this period (but less than taxes, so the deficit declined). Statistically the correlation between government spending growth and consumption growth was positive, so testing this decade alone, we find the sign on the

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(G) variable was positive instead of the negative sign we expect because normally government spending growth increases deficits and causes crowd out. Without a deficit, the whole loanable funds pool would be available for increased private borrowing and spending. There is a similar effect during periods when the deficit is growing, but the pool of loanable funds is growing even faster. The growth in the pool replaces the loanable funds lost due to crowd out, and provide some additional new loanable funds to finance new private borrowing. Table 18.2 shows the negative relationship between average annual growth in the loanable funds pool and the statistical significance of crowd out on consumption. The more loanable funds grows the less likely crowd out is found to be a statistically significant problem negatively affecting consumption. Periods of large growth in loanable funds and declining deficits can combine to create big increases in privately available loanable funds not needed to offset deficits. This leads to not just restoration of pre-deficit consumption levels, but net increased consumption. That leaves a net “crowd in” effect. This can occur when both government spending and revenue are both increasing, but revenue is growing faster than spending, reducing the deficit. Just a reduction in the deficit alone can increase loanable funds available to private borrowers, leading to increased private spending. If the pool of loanable funds is also growing, it will further increase funds available for private borrowing and spending. In such periods, for taxes, the correlation between increases in taxes and consumer spending will be positive. For government spending (when deficits are declining) there will also be a positive correlation between government spending and consumer spending, which may show as a positive coefficient on the government spending variable in a sample dominated by this effect, like the 1990s. By comparison, when deficits are rising the correlation is negative; then positive growth in government spending is associated with negative growth in private spending, even if loanable funds are rising, but their growth is less than the spending deficit).

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The 1990s was a decade of declining deficits and large growth in loanable funds. Tests on that decade alone (Table 11.1.A) show positive, statistically significant coefficients on both the tax and spending deficit variables, consistent with our explanation above. This is a perfectly normal statistical finding, given the behavior of the underlying data during this period. It is not telling us there is no negative effect of spending deficits on private consumption spending. A finding of statistical insignificance in one or both of the deficit variables can occur when you combine statistically significant crowd in periods with data from other periods showing statistically significant crowd out, and to be expected. Here is why: Regression coefficients are but weighted averages of the relationship of changes in taxes (or government spending) to consumption in each of the years in a period sampled, ceteris paribus. If you add a series of observations (like the 1960–1980s) showing a negative effect of increased government spending on consumption (due to rising deficits due to the spending) with a period in which the observed relationship between spending and consumption is positive due to declining deficits prevailing, even though government spending is increasing (like the 1990s), the regression coefficient will be the weighted average of the two, and since it is a net effect, generally small in size. The resulting coefficient may be insignificant. The variable’s standard error (like any standard deviation), merely show the average way any individual year’s data on the relationship of a deficit variable to consumption differs from the mean difference for the whole period. Suppose the average effect (regression coefficient) for the positive years was (+.50), and for negative years the coefficient was (−.40). Suppose also for each sample, these coefficients were highly statistically significant, i.e., that the individual observations in each sample closely matched their averages for the whole period. Then, assuming both samples are weighted the same, when combined the coefficient will be (+.10), and all the individual year’s observations will be considerably bigger or smaller than this average, leading to a large standard error and low t-statistic (statistical insignificance).

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To illustrate, in Table 11.3 we repeat findings from Table 11.1 for 1960–1980 and 1960–1990 (all crowd out, no crowd in) and 1960–2000 (part crowd out, part crowd in). Notice that as soon as we add the 1990s data in, crowd out results on the government spending variable go from significant to insignificant. This is also true when we add in 1990s data to a 1970–1990 sample. The net effect of combining the two samples is a smaller coefficient and statistical insignificance even though the 1990s decade data by itself has a highly significant positive government spending coefficient (crowd in years), and the 1960–1980 or 1990, and 1970– 1990 data have a highly significant negative coefficient on the government spending variable (crowd out years). Clearly, the examples above show that simply adding highly significant crowd out and crowd in results from different period samples together can result in sample results indicating deficits appear to have no statistically significant effect on consumption (the null hypothesis), when in fact they do. The alternative hypothesis is that adding the two together caused the insignificance. To show this alternative hypothesis can explain nonsignificant crowd out effects, we construct our own simplified “crowd out” (“Decade X”) and “crowd in” (“Decade Y”) data sets, and separately estimate their regression coefficients and significance levels. Separate hypothetical data sets for crowd out decade (X ) and the crowd in decade (Y ) are created. There are 10 observations for each decade. Equation 11.3 shows a simple model of crowd out effects constructed using the underlying data sets. Then we add the two data sets together and reestimate the model to obtain coefficients and significance levels for the combined model. C = α + β (T − G) + e = α + β T − β G + e

(11.3)

Positive and negative stochastic error terms (e) had to be included in the consumption (C ) variable in order for the model to be stochastic and run properly. To do this, for both the crowd in and crowd out decades, roughly equal valued additions and subtractions from the calculated values for consumption were made. This was done to reflect the usual expectation that their expected value in the population, though not necessarily their actual value in each sample, is zero. Data sets were devised for both decades to show statistically significant crowd out effects in decade (X )

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and statistically significant crowd in effects in decade (Y ), before any loanable funds effect was added. The data for decade (X ) and decade (Y ) were separately estimated using OLS, and then the combined sample of decades (X ) and (Y ) data was estimated, also in OLS. Results are shown in Table 11.4. Using a one-tail test of significance (critical value of t = 1.65), both variables show significant crowd out or crowd in effects when tested in their own decades only. However, when the two samples were combined the deficit variables (T deficit) and (G deficit) both fall to insignificance. They also have smaller coefficients, and R 2 s, as was predicted. Note that while crowd in changes the sign on the spending deficit variable, it just reduces the coefficient on the tax cut deficit variable. Hence, based on the evidence provided above, we conclude we conclude that either statistically significant crowd out (or crowd in) can be observed in periods sampled, as long as the sample periods do not mix periods of crowd in with periods of crowd out. In samples that combine “crowd out” and “crowd in” periods, the crowd out variables are likely to appear statistically insignificant. This does not mean they are. In the Table 11.1 tests, 9 of the 18 tests show (G) to be statistically insignificant, but 8 of the 9 insignificant periods sampled mix the 1990s crowd in decade data with crowd out data from the 1960–1990 period, and in 6 of the 9, crowd in decade data was a full 1/3 to ½ of all the data. In the 9 of 18 tests showing (G) to have a significant crowd out effect, three contained no 1990s data, one contained only four observations from the 1990s decade, and 5 that did contain 1990s data were very large samples of 39–50 observation in which the ten 1990 observations effect was relatively small compared to the preponderance of the data in the sample, which did show crowd out. Hence, in averaging the crowd out coefficients dominated, they were close enough to the weighted average coefficient to leave the deficit variables statistically significant. The 2000–2010 decade shows the deficit variables insignificant for a different reason. At the end of that decade, the Quantitative Easing (QE) period increase in loanable funds that was so much larger than private demand for loanable funds that 94% of it remained unborrowed. We experienced the age-old “pushing on a string problem” which can hamper the effectiveness of monetary policy. Hence in the 2000–2010 period, the government deficit, though it rose, when modified by the change in loanable funds was insignificant related to consumer spending. The large

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loanable funds decutionds from deficit values left a modified deficit variable that more closely resembled the QE loanable funds increase than the deficit, and the QE increase for the most part never left the banks, so it couldn’t affect consumption. Remove the QE period years “outliers” from the sample, and the (G) variable again becomes significant. This difference in reconciling different sample results having (legitimately) different signs is not a common problem in economics. Most variables economists study (like income and consumption) show either a consistent positive or negative relationship, not positive in one period, negative in another over large numbers of periods. And spuriously insignificant results are just that; results that appear in one or a few periods, but not often. 11.1.1.1

Adding a Separate, Stand-Alone Loanable Funds Variable to a Crowd Out Model The models shown in Table 11.4 show crowd out effects. They do not show the effects of any change in the loanable funds pool that may be occurring at the same time. If a separate, stand-alone variable is added to the simulation model above, and the model is reestimated, results change markedly, and in the predicted way: if the increase in loanable funds is larger than the growing deficit (Model X ), it changes the sign on the crowd out effect of government spending from negative to positive, and increases the positive coefficient on the tax variable. For models with growing loanable funds pools, which show the effects of declining deficits, the coefficients on both variables are already positive due to deficit decline alone (Model Y ). Adding the increasing loanable funds variable just increases coefficient value on both the (T ) and (G) variables. See Table 11.5.

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As predicted, when adding the separate loanable funds variable when its value is larger than the deficit increases coefficients and t-statistics on the crowd out variables and raises the model’s R 2 . Section 11.1.1.1 Conclusions: 1. Table 11.1 showed significant tax cut crowd out in virtually all (16 of 18) samples. However, only half the samples (9 of 18) showed statistically significant crowd out related to government spending deficits. This may mean tax cut deficits do cause crowd out problems which can offset some or all of their stimulus effect, but spending deficits do not, at least not predictably. While we cannot rule this explanation out with certainty, points 2–5 below suggest another cause may be more likely, namely, mixing crowd out and crowd in periods in the same sample. There is a theory, and empirical evidence, to support this claim. We could not think of a compelling hypothesis to explain why, if crowd out doesn’t. affect consumer spending, we should get a full 9 of 18 tests saying it does. Further, our tests in Table 11.1 test for the existence of crowd out effects controlling for the level of loanable funds, i.e., holding them constant. In Table 11.2 below, we relax that assumption, and estimate the effect of spending crowd out on consumption without controlling for any offsetting growth in the pool of loanable funds pool. When we do that, the percentage of tests in Table 11.2 showing highly significant crowd out effects (t > 2.0) of spending deficits falls to zero. In Table 11.1, controlling for loanable funds, in the same six tests, all six had highly statistically significant crowd out effects. This is consistent with the hypothesis that spending crowd out exists as a real problem, but that increases in the loanable funds pool can offset it. 2. Even though crowd out exists and has a test-verified negative effect on consumption, the data may show no decline in consumption if loanable funds are growing at or near the rate at which the deficit is growing in a given period. Regression results will indicate no statistically significant relationship between consumption and crowd out, but not because crowd out does not exist, but because it is offset by loanable funds pool increases in the same period.

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3. If the pool of loanable funds is growing at a faster rate than the deficit, the coefficient and significance level of the tax variable will grow, and the sign on the spending variable change from negative to positive (and its statistical significance may grow). 4. If you combine data from periods when there was statistically significant crowd out with data from periods where there was statistically significant crowd in, (i.e., loanable funds growth exceeds deficit growth, as noted in (2)), coefficients on the crowd out variable may be found statistically insignificant. 5. All the major test periods shown: 1960–1980, 1960–1990, 1970– 1990, and 1990–2000 showed statistically significant crowd out or crowd in. The 2000–2010 period did not, but not for a crowd out related reason. There, QE in the 2008–2010 period caused a massive growth in loanable funds far in excess of consumers’ interests in borrowing. Since it was not borrowed, it was not spent. Hence the relationship between loanable funds—modified deficits and consumer spending breaks down and id found statistically insignificant. Replacing the 2008–2010 years in the standard model tests of Table 11.1 with 1987–1989 restores the statistically significant crowd out effect. (Adding the 1987–1989 data was necessary because the standard model has so many variables it won’t run with less than 10 data observations.) 11.1.1.2 Can Table 11.1 Results Be Replicated in Other Samples? Table 11.1 results are illustrative, and test a significant number of time periods. A more comprehensive list of different, but overlapping periods sampled and their crowd out results are given in Table 11.6. In Table 11.6, coefficients and t-statistics for the loanable funds (S + FB) modified deficit variables and unmodified deficit variables (T , G) and R 2 are the same (because models include the stand-alone (S + FB) control); so they are only presented once. In most cases, each new sample shown includes the prior sample years, plus one additional year’s data. This allows careful examination of how the coefficients and significance levels vary as we slowly add crowd in year data to samples initially dominated by crowd out data. As more and more crowd in data is added to a sample that initially represented only a crowd out period, it reduces crowd out coefficients and significance levels because of the offsetting effects of crowd in and crowd out on consumption (as we discussed above).

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90 tests were undertaken. Fifty one of 90 show fully or marginally statistically significant coefficients on the government spending deficit variable. As we noted earlier in connection with Table 11.1, the model is estimated holding the level of loanable funds constant. This is so we do not confound the effects on consumption of changes in the loanable funds pool, as explained earlier, with the crowd out effects of the deficit variables in the same equation. With Table 11.1, of 18 different spending deficit samples, we found half showed statistically significant crowd out effects even after modification of the deficit variables in models including a loanable funds variable. Table 11.6 tests indicated 51 of 90 show significant spending deficit crowd out results. When interpreting Table 11.6, recall that regression coefficients conceptually represent the average way one variable changes when there is variation in another during a given period of time, holding constant all other variables in the model. Add or subtract some periods of time from the sample and you are likely to change this average, especially with policy variables like tax and spending levels which fluctuate with the economy, but in part are policy maker (exogenously) controlled. Recall that data used is yearly change data (1st differences). Insignificant regression coefficients on the deficit variables can result for substantive reasons (no real relationship). Insignificance can also result for technical reasons even if there is a significant underlying relationship between deficits and consumption. Consider a period of time in which the spending deficit is negatively related to consumption (like the 1960– 1980s), with a large negatively signed coefficient found on the spending deficit variable in testing. Suppose 1990s data were added to the sample. The 1990s were a decade where “crowd in” prevailed, and for that decade a positive relationship between spending and consumption would typically be found because of the declining deficit, even if government spending were increasing (but not as much as government receipts). In tests of the 1990s—only data, this would leave the coefficient on the spending deficit variable positive and it might be large for those years. Combine the two periods, one crowd out (1960–1990) and one crowd in (1990s) and you are likely to get a small magnitude net regression coefficient. It is also likely to be statistically insignificant since significance is determined based on how close individual observations are to the net or average vale. Here it means comparing the large effects of the crowd out and crowd in years with the small net coefficient. Standard errors are but a measure of the average way individual data points differ from this small whole-data set

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average. Since the coefficients on the deficit variable for the crowd out and crowd in periods were both large, finding the “average” way they differ from the small combined sample average will yield a large standard error and low levels of statistical significance. To elaborate, recall again that regression standard errors, like all standard deviations, measure the average way that individual year’s data relate that year’s changes in the deficit to same year changes in consumption. Calculating the standard deviation involved finding the average way these individual changes differs from the average way they vary (i.e., the regression coefficient) for the whole data set. The standard errors are likely to be large relative to the combined samples’ small net average (coefficient), so the coefficient is likely to be found statistically insignificant. This would be true even if separately, the two individual samples, the crowd out and crowd in samples, in the composite sample were each strongly statistically significant when tested alone. We see this in Table 11.6. The samples that include only the 1960s, 1970s, and 1980s data have large positive coefficients on the tax cut deficit variable, indicating negative effects on consumption when the change in taxes is negative (tax cut). For spending deficits, samples from these decades are found to have negative coefficients on the government spending variable, indicating increases in government spending deficits are associated with negative changes in consumption, ceteris paribus. As shown below, samples including all 1960s, and 1970s years data, or 1960s through 1980s data provide exactly these deficit variable results: Results indicate that both tax cut deficits and spending deficits cause statistically significant crowd out problems. The same is true for the samples containing just 1970s and 1980s data, as shown below (see Table 11.6). 1960–1979 data: .75 (t = 5.1) tax deficit effect and −.25 (t = − 2.2) spending deficit effect 1960–1989 data: .37 (t = 3.9) tax deficit effect and −.14 (t = − 2.0) spending deficit effect However, during the 1990s, the deficit declined in 7 of 10 years, reducing government’s borrowing from the pool of loanable funds, which increased the part of the loanable funds pool available to for private borrowing (“crowd in”). This leads to increased private borrowing, which leads to increased consumer spending. The increased in consumer

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spending may occur even if government spending is increasing, but increasing less that the increase in government receipts, so that the deficit is declining. If consumption is found to be increasing at the same time, government spending and it can create a statistical finding that increased government spending is related, perhaps significantly, to a positive increase in consumption. In reality, this increase in consumption at the same time government spending is growing is occurring because taxes are growing even faster than government spending, leading to a decline in the deficit. It is the decline in the deficit, not the increase in government spending, that is causing the growth in consumption. Examples of data sets from Table 18.6 dominated by 1990s data shows this apparent positive result. For example, samples from the following years show this result: 1990–2000 data: 1.18 (t = 3.7) tax deficit effect and +.50 (t = 6.5) spending deficit effect 1989–1999 data: .65 (t = 2.9) tax deficit effect and +.29 (t = 2.1) spending deficit effect 1988–1998 data: 1.46 (t = 2.5) tax deficit effect and +.52 (t = 2.4) spending deficit effect Alternatively, we see when we combine crowd out and crowd in samples (e.g., the 1980s and 1990s data samples) the coefficients on the crowd out variables decline in absolute size, and become statistically insignificant, as shown in the following examples from Table 11.6. 1980–1999 data: .08 (t = 0.7) tax deficit effect and +.09 (t = 0.6) spending deficit effect 1980–1997 data: .13 (t = 0.9) tax deficit effect and −.02 (t = − 0.1) spending deficit effect The small coefficients are because the average effect of crowd out on consumption during the 1980s and 1990s is small. This is because there was a large magnitude, statistically significant negative effect of spending increases (deficits) in the 1980s offsetting most of large, statistically significant positive effects in the 1990s. Further, because the large valued positive and negative changes (represented by the coefficients above) in

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both subsamples are so different from the small composite sample coefficient, the joint 1980s and 1990s samples show statistically insignificant net crowd out effects for both tax cut and spending increase deficits. Hence, in evaluating Table 11.1 results, we should discount results obtained from samples combining relatively even numbers of deficit decrease and deficit increase years, and count only the results for samples strongly dominated by one or the other effect. This would mean our first six samples in Table 11.1, which start with the 1960–1980 period, and the following additional samples: 1960–1990, 1960–2000, 1960–2007, 1960–2008 and 1960–2010 samples. This is not a common problem to run into when econometrically testing a variable’s statistical significance. For example, when testing the income–consumption relationship, we never have to worry that we may find a strong positive, statistically significant relationship in one decade, and then retest it on another decade and getting a strongly significant negative relationship. Nor do we expect that by adding two statistically significant samples together, we will find no statistically significant relationship. With the income–consumption relationship, or other expected relationships, we expect to find either a significant positive or negative relationship in different samples, or statistical insignificance (but not significant positive and significant negative relationships in different samples). For most variables, theory doesn’t specify the relationship can be positive in one period and negative in another for good economic reason. But in this study, where both crowd out and crowd in can occur for theory-consistent reasons, statistical insignificance can occur when both crowd out and crowd in periods are tested in the same sample. This technical reason for insignificance should not be taken as a finding that no significant crowd out relationship exists. Table 11.6 also shows that we have a similar problem when looking at individual years in the 2000–2010 decade when combining them with 1990s data. To show what was going on in the 2000–2009 decade alone, below we reproduce 11 year data samples in which the end year was a different year in the 2000–2010 period. (We need at least 10 observations for the regression to calculate results when testing our standard consumption model given in Eqs. 11.1 and 11.2.) Note that 5 of the 11 tax deficit coefficients are statistically insignificant, as are 8 of the 11 spending deficit coefficients:

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1999–2009 data: − .14 ( t = 0.2) tax deficit effect and +.10 (t = 0.1) spending deficit effect 1998–2008 data:

.47 (t = 1.8) tax deficit effect and −.47 (t = −0.5) spending deficit effect

1997–2007 data:

.87 (t = 4.3) tax deficit effect and +.35 (t = 0.4) spending deficit effect

1996–2006 data: 1.00 (t = 2.1) tax deficit effect and −.62 (t = −0.3) spending deficit effect 1995–2005 data: 1.55 (t = 1.3) tax deficit effect and +2.95 (t = 1.0) spending deficit effect ----------------------------------------------------------------------------------------------------------------1994–2004 data:

.80 (t = 5.6) tax deficit effect and +.85 (t = 2.7) spending deficit effect

1993–2003 data:

.93 (t = 9.0) tax deficit effect and +.89 (t = 4.9) spending deficit effect

1992–2002 data: −.81 (t = −0.4) tax deficit effect and +.01 (t = 0.0) spending deficit effect 1991–2001 data: 1.03 (t = 1.4) tax deficit effect and +.39 (t = 1.2) spending deficit effect 1990–2000 data: 1.18 (t = 3.7) tax deficit effect and +.50 (t = 6.5) spending deficit effect

Clearly, as we add a few years from the early 2000s to the 1990s decade data (removing an equal number of early 1990s years to maintain a constant 11 years in the sample), results generally stay significant with the expected “+” sign on the government spending variable we expect in “crowd in” periods. In these sample the 1990s data still constitute half or more of the data set. As we add in additional years’ data from the latter half of the 2000s, increasing to eight of the none-1990s years, government spending becomes insignificant. We are mixing too heavy a dose of crowd out decade data in with the crowd in decade data. The tax variable coefficients also become insignificant in the 1998–2008 and 1999–2009 samples, which are most removed from the 1990s period only data. Overall, when the data used are 1990s data alone, or with only a few observations from another decade, the effects for the 1990s dominate and show large, statistically significant positive coefficients on the spending variable and crowd in. When you mix data from crowd out and crowd in periods together, the effects tend to cancel each other out and you get very small coefficients which are statistically insignificant.

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In addition, during the 1990s, the total pool of loanable funds available for borrowing increased, making even larger amounts of the loanable funds pool available for private borrowing increased consistently in most years, as shown in Table 11.7. Even if deficits had not declined, this would have given us another source of “crowd in” effect beside declining deficits during this decade. Unlike (G), a period of declining deficits does not change the sign on the (T ) variable’s coefficient. A change upward in government revenues (T ) which reduces the deficit also creates a positive change in consumption by increasing the loanable funds pool available for private borrowing. Hence here, the sign on the (T ) variable is already positive, so we observe the added positive effect as an increase in the coefficient on the tax variable. (T ) growing faster than (G) caused the deficit level to decline during the 1990s. This offset the more traditional negative effects of yearly deficits characterizing the 1970s and 1980s data, so no statistically significant impact of crowd out is shown when data for the 1990s is added to data for the 1970s and 1980s. It was not clear why deficits had such a positive effect on consumption in the 2000–2008 period. We disaggregated total government spending into its goods and services component (which enters the GDP), and its transfers spending component (which doesn’t), and retested. The positive sign on the spending deficits in the 2000–2008 period in Table 11.6 is totally associated with changes in transfer spending, which often translates into high levels of consumer spending. The findings suggest there are distributional effects of transfer spending that offset the crowd out problem, namely more spending on consumer goods takes place out of transfer payments than is lost to consumer borrowing through crowd out. The declining deficits of the1990 s were due in part to the 1990s being the decade of welfare reform and the large 1993 tax increase, as well as the booming economy’s effect on tax collections (Table 11.8). This book’s focus is on doing good science. The objective is to determine if the crowd out problem really exists and the extent to which changes in the loanable funds pool can offset it. But doing good science doesn’t necessarily answer important public policy questions related to government deficits.

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• If there were no deficits to offset, the whole of any increase in the loanable funds pool (including increases due to FR open market operations) could be used to finance additional, new private consumption or investment spending, assuming we were below full employment potential). This would grow the private sector of the economy. • But with deficits, there is crowd out, which requires some or all of the increase in loanable funds to just to maintain pre-deficit levels of private consumer and business spending. Not as much, if any, is left to finance new growth in the economy. That said, the fiscal stimulus programs, whose deficit is funded by the money taken from the loanable funds pool would stimulate an alternative form of economic growth. This type growth would not be available without the deficit. • Hence, both deficiting or not deficiting can lead to economic growth, but of different types. How to resolve the public policy issue of whether to deficit or not comes down to two things: 1. social preference for future growth to be more private goods and services (cars, houses, entertainment), or public goods and services (roads, bridges, transfer payments). 2. comparing the economic growth rates likely to result from the deficit and no deficit options. Even small differences in growth rates make significant differences in standards of living over time (Solow 1957), so the right choice is very important. 11.1.1.3

Comparing One-Variable and Two-Variable Deficit Results Chapter 10, examined whether variations in the consolidated government deficit, expressed as one variable (T − G), were related to variation in consumption and investment, controlling for other factors thought to affect consumption. In Table 10.1 we presented results for 18 different, though often overlapping samples of data from the 1960–2010 period. The initial test was on the full 1960–2010 data set and indicated consumption declined $0.38 for every dollar increase in the deficit variable (T − G). The result was highly statistically significant (t = 6.3). In an attempt to see if these results could be replicated, 17 other tests of different parts of the original 50 year test period were tested using the same model. Fourteen of the 17 tests did replicate the original replicate

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the findings in the sense that the regression coefficients had the same sign, had roughly the same magnitudes (with some exceptions), and were statistically significant at the 5% level or better. The four insignificant ones were samples in which 1990s data (with crowd in) were roughly even matched with data from the 1970 and/or eighties or 2000s which showed crowd out effects, as was the case with some of our findings in Table 11.1.A above. Hence, we concluded in Chapter 10 that the government deficit was in fact the systematically associated with crowd out problems. In this first part of this chapter, we tested the exact same models as in Chapter 10 except that we divide the deficit variable (T − G) into the deficit’s two component parts (T ) and (G) and test each, ceteris paribus, i.e., while holding the other deficit variable constant, as well as other determinants of consumption, as was done in Chapter 10. In Table 11.6, the standard consumption model with an added standalone variable representing total loanable funds availability was tested. 90 regressions representing different, by overlapping sample periods were tested. Results, presented in Table 11.6, typically indicated crowd out was a statistically significant problem, whether caused by tax cut deficits (51 tests) or spending increase deficits (39 tests). Tests also indicated the 1990s were a “crowd in” period. In eight of the 11 years 1990– 2000, taxes grew more than spending, a reduction in the deficit, which increased the pool of loanable funds available for consumer or business borrowing causing a statistically significant “crowd in” situation. When testing combined amounts of the 1990s data with crowd out data from the 1970s, 1980s, or 2000s, the two effects canceled each other out; regression coefficients declined in size, measuring just a residual effect, and became statistically insignificant (19 spending cases). But this did not mean deficits don’t induce crowd out; it only means that symmetrically, surpluses induce “crowd in”. Combining the two in one data set tends to create an average effect (regression coefficient) near zero, and statistical insignificance, since both types of periods separately tended to have large coefficients, making the average unrepresentative of the individual data components. This is the type of “statistical insignificance” that large standard errors relative to coefficient size, are intended to convey.

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Overall then, we conclude our larger table of 90 tests in Table 11.6 supports our Table 11.1 results specified earlier. Most samples in both tables showed some form of crowd out. Both tax cut and spending deficit crowd out were generally supported by our statistical findings, as is the symmetric notion of crowd in when there are budget surpluses, at least when tested in models including a stand-alone variable representing loanable funds. In short, the one and two variable deficit models yield consistent results. 11.1.1.4

Heteroskedasticity (or Heteroscedasticity) and Autocorrelations In this study, there were many instances of heteroscedasticity and many of autocorrelation. Much autocorrelation was removed by using first differences, not levels, of the data. In some cases, an autocorrelation control, typically AR(1) was also used. After this, in most cases, the Durbin– Watson statistics met or exceeded minimum standards, indicating we had eliminated any 1st order autocorrelation problems. Hill et al. (2003) recommended using a DW criterion of (−1.3) as a lower limit when determining if autocorrelation was significant. In fact, we typically used (−1.6) as the lowest level of acceptable autocorrelation, and most the regressions in this study did have Durbin–Watson statistics of −1.6 to +2.5. Newey–West standard errors can give an additional margin of safety from the effects of the autocorrelation problem, as well as heteroskedasticity problems, and were generally used in this study. “the estimator is used to try to overcome autocorrelation (also called serial correlation) and heteroskedasticity in the error terms in the models, often for regressions applied to time series data” (Wikipedia, “Newey – West estimator”) Also, from Wooldridge, Introductory Econometrics, 3rd ed. Cptr. 12: Serial correlation and heteroskedasticity in time series regressions “…A very common strategy for considering the possibility of AR(1) errors is the Durbin-Watson test…”…..”…the methodology to compute what are often termed heteroskedasticity and autocorrelation – consistent (HAC) standard errors was developed by Newey and West; thus they are often referred to as Newey – West standard errors…”.

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Newey–West, and perhaps White standard errors sometimes yield higher t-statistics than ordinary standard errors when applied to a given data set, such as the set used in developing Table 11.1. By separately examining significance levels of variables tested in Table 11.1 above using Newey– West, White and ordinary standard errors, we can determine if our general choice of Newey–West errors affected findings on whether or not crowd out was a statistically significant problem affecting consumption. We estimated the Table 11.1 consumption model t-statistics using White and ordinary standard errors on all 108 coefficients on the deficit variables and the stand-alone (S + FB) variable reported in Table 11.1. The results were as follows: 1. 52 of the 108 t-statistics calculated using Newey–West standard errors were equal to or smaller than t-statistics calculated using ordinary standard errors. 2. 67 of the 108 t-statistics calculated using Huber–White standard errors were equal to or smaller than t-statistics calculated using ordinary standard errors. 3. 73 of 108 Newey–West t-statistics were fully (63) or marginally (10) statistically significant. 4. 67 of 108 Huber–White t-statistics were fully (53 or marginally (14) statistically significant. 5. 63 of 108 Ordinary t-statistics were fully (54) or marginally (9) statistically significant. Overall, there was a marginal tendency for Newey–West t-statistics to be found statistically significant more often. This we believe was because they were better at taking autocorrelation and heteroscedasticity issues into consideration. In general in this book, we use Newey–West standard errors t calculate t-statistics because of its usefulness in helping address both serial correlation and heteroscedasticity. Huber–White only treats heteroscedasticity. Ordinary standard errors treat neither. We also reestimated standard errors for the investment model results shown in Table 11.1 further below. t-statistics using Newey–West, Huber–White and ordinary standard errors on all 72 coefficients on the deficit variables and the stand-alone (S + FB) variable reported in Table 11.1. The results were as follows:

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1. 24 of the 72 t-statistics calculated using Newey–West standard errors were equal to or smaller than t-statistics calculated using ordinary standard errors. 2. 31 of the 72 t-statistics calculated using Huber–White standard errors were equal to or smaller than t-statistics calculated using ordinary standard errors. 3. 57 of 72 Newey–West t-statistics were fully (46) or marginally (11) statistically significant. 4. 57 of 72 Huber–White t-statistics were fully (45) or marginally (12) statistically significant. 5. 53 of 72 Ordinary t-statistics were fully (45) or marginally (8) statistically significant. Overall, there was no difference using the Newey–West and White standard errors in the number of tests found at least marginally significant. There was a slight tendency for both to be found only statistically significant more often than occurred using ordinary standard errors. As before, this we believe was because they were better at taking autocorrelation and heteroscedasticity issues into consideration. White t-statistics were also marginally more likely to be found statistically significant than ordinary t-statistics. we typically use Newey–West standard errors to calculate t-statistics because of its usefulness in helping address both serial correlation and heteroscedasticity. Huber–White only treats heteroscedasticity. Ordinary standard errors treat neither.

11.2 Consumption Models Without Stand Alone (S + FB) Results presented in Table 11.1 allowed us to determine the effectiveness of loanable funds in offsetting crowd out problems created by government deficit financing. This was done by comparing the amount of variance explained by the model before and after the loanable funds variable was added to the model. The role of loanable funds in offsetting crowd out was judged significant if adding the variable to the model allowed us to better explain variation in consumption. In the model tested. Loanable funds was included as a stand-alone variable, as well as also used to modify the deficit variables. The evidence suggested that while the deficit modifiers allow us to determine the crowd out offsetting

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effects of increase in the loanable funds pool, there was a second result of increasing loanable funds (i.e., the mps). It lowered mpc, which had a separate negative effect in consumption. To separately estimate the size of that effect, required the model also include a stand-alone loanable funds variable. To determine if this second stand-alone use of the loanable funds variable is really necessary, i.e., whether the second negative effect of increasing loanable funds is real, we would like to see more direct results of how subtracting increases in loanable funds from the deficit variables affect the coefficients and significance levels of these variables, when no separate stand-alone loanable funds variable is also included in the model. Removing the stand alone, only the model’s R 2 , deficit variables’ coefficients and significance levels would change when the model was 1. tested with deficit variables alone measuring crowd out effects, and then 2. retested with deficits reduced by any growth in the loanable funds pool during the same period. Table 11.9 retests the same “with” and “without” models as in Table 11.1, but does not include a separate, stand-alone loanable funds (S + FB) control variable in the otherwise standard model. Testing is to determine if modifying the deficit variables by same period changes in loanable funds provides a better explanation of the of crowd out’s effects on consumption, i.e., improves R 2 —our ability to explain the variation in consumption that occurs from year to year. There were no stationarity problems with either the modified or unmodified variables. The model without the deficit variables being modified had no endogeneity problems, so it was estimated using OLS However, in the modified model, G + (S + FB) was found endogenous with the dependent variable and was replaced by a Wald-strong instrument, which was not endogenous (Sargan test). R2 Effects Before modification, in the six samples tested, R 2 was 88.7%; after modification, 85.0%. Before modification average adjusted R 2 was 84.8%; after modification, 79.8%. R 2 dropped in all six models after the deficit variable used as the initial estimate of crowd out was replaced by the modified deficit. The loanable

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funds modified deficit model did not explain variation in consumption nearly as well as the unmodified deficit model. This implies one of two things: 1. changes in loanable funds do not reduce consumption crowd out, and just distort the values of variables the deficit that do when used to modify them. 2. the modified deficit hypothesis was modeled inappropriately for testing, and gave misleading results. Crowd Out Variable Effects Crowd out effects of tax cut deficits are statistically significant in all six time periods tested, both in the baseline model and after adjustment for changes in loanable funds. Modifying the deficit reduced coefficients and significance levels on the tax cut deficit variable. For government spending deficits, the spending deficit variable before modification, was significant in four of the six periods sampled. After modification, it was insignificant in all six periods tested, Overall, the reduced R 2 accompanying deficit modification suggests that the modifying variable (loanable funds) had a zero or near zero net effect on consumption. Therefore, using it to modify a variable (the deficit) known from baseline model to be significant without modification is something like subtracting a random variable from a significant variable: it reduces the frequency with which it is found significant. Without the stand-alone variable, when we add or subtract (S + FB) from the deficit variables, we are modifying variables we know have a statistically significant crowd out effect on consumption by variables by a large variable that has little or no net effect on consumption because of its competing positive and negative effects. Hence the best interpretation for why adding the modifier to the deficit caused the variables to become insignificant is because it had an “errors in variables” effect: it modified the values of a statistically significant variable with non-significant values, causing the resultant variable to only partially accurately reflect the underlying crowd out effect that was making consumption change. And by distorting the deficit’s values, it reduced the accuracy of a significant relationship, causing the model to explain less variation in consumption, reducing R 2 .

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These results are different than those obtained earlier in Table 11.1 where the model tested also included a stand-alone loanable funds variable, and adding the loanable funds modifiers increased R 2 . There, the same six sample periods showed identical coefficients and highly significant t-statistics for the same number of deficit variables, before and after modification, and that is considered the more theory-consistent model because it allows for separate estimation of both the positive and negative effects on consumption of a change in the pool of loanable funds. In short, results obtained from this form of the consumption model seem to be a result of bad modeling, and the earlier form of modeling, whose results are shown in Table 11.1, which included a stand-alone loanable funds model should be preferred. In the next section, more detailed evidence will be presented showing that the results above were the result of bad modeling, and not indicative that we had proven that increases in loanable funds eliminate spending deficit crowd out problems.

11.3 Crowd Out Effects on Investment Using Stand-Alone Loanable Funds Variable We take Eq. 5.4.TR from Heim (2017a) as a “standard” investment model containing variables most economists would agree are determinants of investment, and variables which should be controlled for to avoid the “left out” variables problem when estimating the separate effects of any one variable on investment. The “standard” model is presented to show that the models developed here are built on previous findings regarding investment’s determinants. It is in this way we attempt to add to past findings regarding investment, while showing our findings leave previous findings intact, not replace them. The model from Heim (2017a) is: Standard Investment Model from Heim (2017a) (Using 1960–2010 data) ID = + .26(ACC) + .27(TT ) − .30(G T&I ) (t=)

(8.7)

(2.9)

(−3.8)

+ .011POP − 4.72PR−2 (5.7)

(−2.7)

+ 6.81XRAV + 2.55 CAP−1 (2.9)

(1.7)

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R 2 = 83.3%

D.W.= 2.0

MSE = 28.25

261

(5.4.TR)

Equations 11.4 and 11.5 below present the same model shown in Heim (2017a), with the addition of a stand-alone loanable funds variable tested using the same 1960–2010 data. Equation 11.4 adds a stand-alone loanable funds variable to the baseline deficit model, but does not include any modification of the deficit variables as a second way to reflect changes in loanable funds (S + FB) in the model. Equation 11.5 includes both. In Heim (2017a) the deficit was also modified by changes in loanable funds during the same period, but not in quite the same way. Nor did it include a stand-alone loanable funds variable. Here, we simply add the change in loanable funds to the effects of any negative change in total taxes resulting from a tax cut (the tax cut deficit) represented by a negative change in (T ). Adding loanable funds thereby reduces the deficit’s estimated crowd out effects. The treatment of spending deficits is different. We subtract the change in loanable funds from any change in the spending deficit (represented by a positive change in (G). This has the effect of reducing the estimated crowd out effect of deficits caused by increased spending. All variables were found Augmented Dickey Fuller (ADF) stationary; No Hausman endogeneity was found between the dependent and explanatory variables except for the GDP variable which was replaced by a Wald-strong, non-endogenous (Sargan test) instrument. Newey–West standard errors were used to avoid heteroskedasticity and help address autocorrelation problems. Below is a Standard investment model with no deficit variables or loanable funds. A 2SLS strong instrument, Sargan tested, was used for the accelerator. No GDP Control Variable Included. ID = + .48(ACC) + .008POP + .76PR−2 (t=)

(2.5)

(10.6)

(0.2)

+ 7.37XRAV + 14.08 CAP−1 (2.2)

R = 69.4% 2

(4.3)

Adj.R = 66.7% 2

DW. = 1.6

MSE = 47.87

(Same as Eq. 10.3C) The model below presents this Study’s Baseline Model, With No Deficit Variables or Loanable Funds Variables Included, but GDP Variable

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Included to Control for the State of the Economy ID = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(0.0)

(4.0)

(−0.3)

+ 5.21XRAV + 10.39CAP−1 + .10GDP (2.0)

R = 76.1% 2

(−1.3)

(2.9)

Adj.R = 73.2% 2

D.W.= 2.1 MSE = 43.06

(Same as Eq. 10.3B; and same as Eq. 11.10C above) To the baseline model, we now add Deficit Variables, but not a loanable funds Variable (1960–2010 Sample) ID = +.27(ACC) + .32TT − .33G T&I (t=)

(6.4)

(2.6)

(−3.9)

+ .012POP − 4.95PR−2 + 6.68XRAV (2.8)

(−2.5)

(3.5)

+ 2.43CAP−1 − .02GDP (−0.2)

(1.8)

R = 89.0% Adj. R = 85.9% 2

2

D.W. = 1.9

MSE = 29.87 (11.4A)

(old Eq. 11.10.A, Table 11.10A) The baseline equation before adding the deficit variable explains only 76.1% of the variation in consumption data over the period 1960–2010. When the deficit variable is added to the same model to account for the negative crowd out effects of deficits on consumption, explained variance rises to 89.0%, a 12.9%-point increase. To ensure this baseline deficit model was not an anomaly, we retested the same models in 17 additional time periods, shown in Table 11.10A. In every case exactly the same result was obtained: adding the crowd out variable increased explained variance markedly in the 18 samples. There can be little question but that crowd out is a problem negatively affecting investment. The crowd out effect of deficits has been a consistent problem through out the past 50 years, both in recessions and good times. The crowd out variable, on average, adds 11.4 percentage points to explained variance in models with a GDP control variable. The next issue to be addressed is whether increases in loanable funds can offset the negative crowd out effects of deficits. To do this, we add a stand-alone loanable funds variable to the deficit model above, but no deficit modifiers are added. This model is given in Eq. 11.4, estimated

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using 1960–2010 data. ID = + .23(ACC) + .22TT − 16G T&I + .19((S + FB)) (t=)

(1.6)

(5.1)

(−1.9)

(2.8)

+ .008POP − 4.25PR−2 + 5.25XRAV (2.0)

(2.3)

(−2.1)

+ 1.48 CAP−1 − 04.GDP (0.6)

(1.2)

R = 90.6%

Adj.R = 88.7%

2

2

D.W.= 2.0

MSE = 27.93

(11.4)

Adding the stand-alone loanable funds variable increases explanatory power of the model 1.6%. Next, while continuing to include the stand-alone variable in the model, the deficit variables are replaced by the modified deficit variables (Eq. 11.5 below, also estimated using 1960–2010 data). ID = + .23(ACC) + .22TT − 16 G T&I (t=)

(1.6)

(5.1)

(−0.8)

− .19((S + FB)) + .008POP − 4.25PR−2 (2.0)

(−2.8)

(−2.1)

+ 5.25XRAV + 1.48 CAP−1 − .04GDP (2.3)

R = 90.6% 2

(1.2)

Adj.R = 88.7% 2

(0.6)

D.W.= 20

MSE = 27.93

(11.5)

As in prior models that include the separate stand-alone loanable funds variable, Eqs. 11.4 and 11.5 are identical except for whether they contain the modified or unmodified form of the deficit variables. For both models, all the coefficients and t-statistics are the same in the two equations except for the stand-alone loanable funds variable (S + FB). There, the (.19) coefficient in Eq. 18.4 exactly equals the sum of the three (S + FB) coefficients in Eq. 18.5: (+.22) − (−.16) + (−.19) = (+.19) as discussed in the earlier consumption sections of this chapter. Definitions of the variables used in these equations are as follows; (in the actual tests, the  sign in the equations above preceding these variables indicates first differences of the data are used, not levels, in estimating the models:

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I D = Domestically produced investment goods (total – imported capital goods + industrial supplies and materials) (ACC) = The accelerator ( U.S. GDP) T T = Total consolidated U.S. federal, state and local government revenues G T&I = Total consolidated U.S. federal, state and local government spending, including transfers (S + FB) = Total U.S. loanable funds: National savings plus foreign borrowing POP = U.S. population PR−2 = U.S. prime interest rate lagged two years XRav = U.S. real exchange rate average for current and past three years) CAP−1 = U.S. Capacity utilization lagged one year GDP = U.S. GDP Table 11.10A shows the baseline deficit model values of the deficit variables, their significance levels, and R 2 s before the addition of any loanable funds variables. Results are shown for the 18 time periods tested using one or the other of the two investment models tested in this chapter. For tax deficits, crowd out effects for 11 of 18 are statistically significant, and of the seven insignificant, four are for samples with the 1990s “crowd in” problem discussed in the consumption sections of this chapter. For spending deficits, 17 of 18 were significant. Recall that in the baseline model for consumption, we found only 6 of 18 samples showed significant crowd out from spending deficits, but that two technical problems accounted for the 12 insignificant findings, namely the 1990s crowd in period problem and the limited amount of variation in the government spending variable in the 1980s. Here, using the same government spending variable we do not see these problems leading to statistical insignificance in most samples. One possible reason why is that government spending is a more important determinant of investment spending than consumer spending. Heim (2017a, Tables 4.4.1 and 5.4.1) shows that with very similar models for the 1960– 2010 period, variation in the government spending variable accounts for much more of the variation in investment explained by the model than does government spending in the consumption model. Depending on whether the “first out” or “first in” method of stepwise regression is

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used to determine the government spending variable’s contribution to total variance explained by the model, government spending explains 2–11 times as much variation in investment model as in the consumption model. It explains from 11–22% of the total variation in investment compared to 2–5.6% for consumption. This implies that even small fluctuations we found in government spending lead to significant moves in investment and be easier for the regression to distinguish from movement in other variables. This may explain our much more frequent findings of government spending being significantly related to investment than we found with consumption, despite the 1990s and variation problems with the data. With the tax deficit variable, the situation is just the opposite. The Tax deficit variable explains 2.4–14 times as much variation in consumption as the government spending variable (12% vs. 5% using “1st out” stepwise regression; 28% vs. 2% using “1st In” stepwise regression. Tax deficits cause more variation in consumption than spending deficits, and hence, are more likely to show statistically significant crowd out effects. We theorize that the reason for this is that financing tax cut deficits reduces the money available for consumers to borrow, but the tax cuts for the most part go to those who save and invest the money, not spend it on consumer goods. Hence, the strong crowd out effect of tax cut deficits. Financing spending deficits, though they also reduce funds available to consumers to borrow and spend are more likely to be channeled to those at the lower end of the income spectrum, who are most likely to replace the lost borrowing power with increased spending out of there new spendingdeficit generated income. As a result, in consumption models we find few periods in which tax deficits are insignificant, but many in which spending deficits are insignificant. For investment, just the opposite is true, and most likely for the same reasons. Tax cuts are most often saved and invested offsetting crowd out effects on investment. Spending deficits also cause crowd out, but recipients are more likely to be consumers than businesses, hence they do not provide an offset to investment crowd out, and spending deficits are found to create statistically significant crowd out effects for investment more often than tax cut deficits (see analysis of Table 11.10 results). Table 11.10 repeats the key crowd out and loanable funds findings in Eqs. 11.4 and 11.5 above, and for 5 other test periods. All results for the 5 other time periods estimated use exactly the same models as Eqs. 11.4 and 11.5 above. Only the length and dates of the test period

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changes, reflecting our desire to see if the initial results can be replicated (the hallmark of good science). In Table 11.10 for each time period, two sets of statistics are presented. In one set, there is a stand-alone loanable funds variable, but no modification of the deficit variables (T ) and (G) by the loanable funds variable. Columns showing these results of these tests are labeled “w/o.” In the other set of results, labeled “with,” the model includes a stand-alone loanable funds variable (S + FB), and deficit variables modified by the same loanable funds variable. We made these tests to test whether, as was the case for consumption, there is a second, negative, effect of changes in loanable funds that offsets their positive effect of reducing crowd out’s effects. R2 Results For the six periods tested, average R 2 was 91.2% and average adjusted 2 R was 88.6%. In all 6 periods sampled, adding a separate stand-alone total loanable funds variable to the model increased the model’s ability to explain variation in investment. The average increase was substantial: 2.3 percentage points. Adding the loanable funds modified deficit variable to the model (with a stand-alone loanable funds variable), and R 2 remains unchanged, suggesting the two ways of modeling the loanable funds effect are equivalent. In five of six cases, the stand-alone loanable funds variable becomes insignificant. The reason for this appears to be that the (S + FB) variable, when used to modify the deficit variables fully explains how the loanable funds effect investment (by reducing crowd out), and that in these samples, there is no additional variance caused by (S + FB) left to explain. Crowd Out and Loanable Funds Effects: For the baseline model with deficit variables, 5 of 6 periods sample showed statistically significant crowd out effects of unmodified tax cut deficits, and 6 of 6 unmodified spending deficits showed crowd out effects. Clearly government deficits are systematically associated with crowding out of private investment spending, a finding consistent other recent studies on this topic (Heim 2017a, b). This again indicates that deficit financed fiscal stimulus programs will reduce private investment spending unless the crowd out effect is offset in some way. Adding the stand-alone loanable funds variable to the baseline deficit model, the number periods that tax cut deficits showing significant crowd out effects fell from 5 of 6 to 1 of 6. The number of significant crowd

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

267

out effects for spending deficits fell slightly from 6 of 6 to 5 of 6. Results were unchanged, when (S + FB) was also added as a deficit modifier. The finding that after adding the loanable funds variable, the number of significant crowd out effects for tax cut deficits dropped from 5 of 6 to 1 of 6 sample periods suggests that most money received from deficit financed tax cuts is saved, and simply offsets any loss of privately available loanable funds loss to finance the deficit, hence no significant crowd out effect. Tax cuts usually favor the upper end of the income stream, where (often) additional disposable income current spending is already at desired levels. Therefore the tax cut, or large parts of it is often just saved and invested. Hence, the lack of significant crowd out effect is not surprising. However, there is a second possible explanation. The taxes and loanable funds variables are highly correlated (.74) compared to other variables in this study, and reduced statistical significance is a common consequence of multicollinearity. Hence the drop may be misleading; it may be for technical, not substantive reasons. Hence, it is not completely clear whether tax cut deficits have no crowd out effects on investment, or whether the test results above are just showing a technical problem. For government spending deficits, 6 of 6 tests showed them associated with statistically significant negative crowd out effects in pre-modification models as well as 5 of 6 post modification models. Recipients of government spending programs, particularly transfer program recipients, tend to need the money to maintain current levels of consumption. Hence, little of the increased income generated is saved and available as an offset to investment borrowing reduced by crowd out. Hence, our finding that spending deficits are systematically associated with statistically significant crowd out effects.

11.4 Crowd Out Effects in Investment Models Without a Stand-Alone Loanable Funds Variable Equations 11.5A and 11.5B rerun the same “with” and “without” deficit modification models as in Table 11.10, but without the separate standalone control variable (S + FB). As before, a GDP variable is added to the standard investment model to control for effects of the business cycle. When modeling consumption, increases in loanable funds were found to have two effects on consumption: (1) increases reduced deficit caused crowd out, increasing consumption, (2) but the same increase in loanable

268

J. J. HEIM

funds, ceteris paribus, also definitionally reduced consumption, because reducing consumption was necessary to increase savings. With investment, increases in loanable funds resulting from increases in savings simply increase the funds available to offset crowd out, or if there are no deficits, for new investment. By dropping the separate loanable funds variable from the model we are testing to see if simply reducing the tax and spending deficit variables by any same period changes in loanable funds adequately shows the effect of loanable funds changes in reducing investment crowd out. (Of course, if the increase in loanable funds is coming out of existing income, it may reduce consumption in the short run—a typical Solow growth model side effect, but one which generally increases long term economic growth, including consumption levels.) Repeated below is the baseline unmodified deficit model from Eq. 11.10.A, and No Stand-Alone (S + FB) Variable is Included (1960– 2010 Sample) ID = + .27(ACC) + .33TT − 33G T&I (t=)

(2.6)

(6.4)

(−3.9)

+ .012POP − 4.95PR−2 + 6.68XRAV (2.8)

(3.5)

(−2.5)

+ 2.43CAP−1 − .02 GDP (−0.2)

(1.8)

R = 89.0% 2

Adj.R = 87.1% 2

D.W.= 1.9

MSE = 29.87

(From Eq. 11.10A) Results for this model in 18 different time periods are given in Table 11.10B. Below, the same model as 21.10A, except the deficit variables are modified by changes in (S + FB), (1960–2010 Sample). ID = + .22(ACC) + .18TT(m) − 06G T&I(m) (t=)

(5.0)

(2.0)

(−0.7)

+ .007POP − 4.12PR−2 (2.1)

(−2.2)

+ 4.77XRAV + 1.51 CAP−1 − .05 GDP (2.4)

R 2 = 90.2%

D.W.= 2.0

(1.2)

MSE = 28.20

(−0.7)

(11.10B)

T β(t)

.13(0.9)

.28(2.2)

.32(2.7)

.26(2.3)

33(2.7)

.33(2.6)

Sample Period

1960–1980

1960–1990

1960–2000

1960–2007

1960–2008

1960–2010

R2 .95 .87 .89 .84 .86 .89

G β(t)

−.35(−3.8)

−.42(−3.2)

−.40(−5.2)

−.36(−3.2)

−.33(−2.8)

−.33(−3.9) 1980–2010

1980–2000

1970–2009

1970–2007

1970–2000

1970–1990

Period

.30(2.0)

.27(1.5)

.32(2.3)

.23(2.0)

.33(2.5)

.25(1.1)

T β(t)

−.31(−2.4)

−.42(−3.3)

−.34(−3.5)

−.37(−3.1)

−.45(−4.5)

−.55(−2.8)

G β(t)

.85

.89

.90

.86

.90

.90

R2

2000–2010

1996–2010

1985–2005

1985–2004

1980–2004

1975–2004

Period

Table 11.10B Base line model with deficit variables added: estimates of investment crowd out

.15 (1.8) .09 (1.1) .09 (1.3) .09 (1.3) .29 (2.6) .01 (0.0)

T β(t)

1.11(1.8)

.52(1.1)

−.42(4.5)

−.41(−4.4)

−.41(−3.7)

−.40(−3.7)

G β(t)

.98

.98

.89

.89

.89

.89

R2

11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

269

270

J. J. HEIM

Notice the loanable funds modified deficit definition of crowd out increases explained variance by 1.2 percentage points, indicating the modified version of the deficit variables better expresses the true magnitude of deficit crowd out effects than just the deficit alone. In this sample, Eqs. 11.10A and 11.10B show that modifying the deficit variables results in a drop in coefficients and significance levels of the deficit variables, which may indicate increases in loanable funds offset crowd out, at least in part. Unlike the comparable consumption model, modifying the deficit variables also increases in the variation in investment explained (R 2 increases 1.2%), though not as much as the (2.9%) of the investment model in the previous section that included a stand-alone variable. Because of the increase in R 2 we can be reasonably certain, the lower coefficient and significance levels (in absolute value) obtained for the deficit variables in this model are indeed better estimates of crowd out effects, i.e., deficits net of loanable funds growth). In this sample, the reason the increase in R 2 is relatively small is probably because there was little or no tax cut crowd out to start with, unlike consumption, where we had both tax cut and spending deficit crowd out. The tax cut crowd out was a factor for consumption because in general, the tax cut money was not spent on consumer goods, so it did not offset consumer crowd out. As we show below, there is also evidence that increases in loanable funds do go to reduce consumer crowd out problems. In Table 11.11, we show the 1960–2010 results shown above and retest the model on 17 additional time periods to determine if the initial results can be duplicated. R2 Effects: Average R 2 for the 18 unmodified samples was 89.8%; average adjusted 2 R for the same samples was 85.9%. Average R 2 for the 18 modified samples was 90.7%; average adjusted R 2 for the same samples was 87.2%. Results indicate R 2 was higher with the modification of the deficit variables in 13 of 18 time periods tested, the same in 3, and lower in two. For the 18 time periods sampled, R 2 rose an average of 0.90 percentage points higher in models where the deficit variables were modified by total loanable funds (S + FB). This is not much (though the adjusted R 2 rose more: 1.3%, suggesting the loanable funds modification did reduce crowd out). The model with a stand alone rose much more: (2.0%). The sign in

T Def : t-stat G Def : NW t-stat R2 Adj.R 2

.25 (1.1) −.55 (−2.8) .90 .84

.05 (0.6) −.24 (−2.5) .92 .88

.33 (2.5) −.45 (−4.5) .90 .87

.15 (1.4) −.15 (−1.7) .90 .88

with

w/o

w/o

with

1970–2000

1970–1990

.10 (1.9) (1.9) (1.1) −.20 (−3.1) (−2.7) (−2.4) .91 .89

Variable

.05 (0.6) (0.7) (0.7) −.27 (−4.1) (−3.8) (−3.9) .97 .95

.13 (0.9) (1.2) (1.0) −.35 (−3.8) (−3.0) (−2.9) .95 .91

.28 (2.2) (2.1) (2.0) −.42 (−3.2) (−3.1) (−2.9) .87 .83

w/o

with

1960–1990

w/o

with

1960–1980

T Def : NW t-stat White t Ordin. T G Def : NW t-stat White t Ordin. t R2 Adj.R 2

Variable

.16 (1.9) (1.9) (1.9) −.14 (−2.2) (−2.4) (−2.2) .90 .88

with

.23 (2.0) −.38 (−3.1) .86 .82

w/o .08 (1.1) −.14 (−1.7) .89 .86

with

1970–2007

.32 (2.6) (2.9) (2.7) −.40 (−5.2) (−4.4) (−4.3) .89 .86

w/o

1960–2000

.10 (1.7) (1.7) (1.7) −.13. (−1.8) (−1.8) (2.0) .88 .85

with

.32 (2.3) −.34 (−3.5) .90 .88

w/o

.18 (1.7) −.05 (−0.5) .91 .89

with

1970–2009

.26 (2.3) (2.4) (3.5) −.34 (−3.2) (−3.1) (−3.2) .84 .81

w/o

1960–2007

.17 (1.9) (2.0) (2.9) −.07 (−0.7) (−0.8) (−1.0) .87 .85

with

.27 (1.5) −.42 (−3.3) .89 .83

w/o

.05 (0.5) −.18 (−2.0) .90 .85

with

1980–2000

.33 (2.7) (3.0) (4.8) −.33 (−2.8) (−2.8) (−2.9) .86 .83

w/o

1960–2008

.18 (2.0) (2.1) (3.1) (−.06) (−0.7) (−0.8) (−1.0) .90 .89

with

.18 (1.5) −.03 (−0.2) .91 .88

with

(continued)

.30 (1.6) −.31 (−2.4) .90 .87

w/o

1980–2009

.33 (2.6) (2.9) (4.9) −.33 (−3.9) (−3.5) (−3.4) .89 .87

w/o

1960–2010

Table 11.11 Estimates of investment of crowd out, with and without modification by loanable funds (no stand alone (S + FB); GDP variable included) 11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

271

T Def : NW t-stat G Def : NW t-stat R2 Adj.R 2

Variable

.15 (1.8) −.41 (−3.7) .89 .86

.06 (0.9) −.17 (−2.1) .90 .87

.09 (1.1) −.41 (−3.7) .89 .84

.00 (0.0) −.20 (−2.5) .90 .86

with

w/o

w/o

with

1980–2004

1975–2004

Table 11.11 (continued)

.09 (1.3) −.42 (−4.5) .89 .83

w/o .01 (0.2) −.18 (−2.1) .86 .78

with

1985–2004

.09 (1.3) −.42 (−4.5) .89 .83

w/o .01 (0.2) −.18 (−2.2) .86 .79

with

1985–2005

.29 (2.6) +.52 (+1.1) .98 .95

w/o .29 (4.6) +.20 (5.0) .98 .96

with

1996–2009

.01 (0.0) +1.11 (+1.8) .98 .93

w/o

.25 (2.5) +.18 (+1.4) .97 .89

with

2000–2009

272 J. J. HEIM

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

273

the stand alone in most cases is negative, suggesting that “forcing” the loanable funds and crowd out effects to share the same coefficient may be overstating the extent to which an increase in loanable funds can offset crowd out. Part of the increase may go into foreign, not US domestic investment, or part may go into investment in stocks and bonds, which generally do not lead in any direct way to an increase in investment. Effects of Choice of Standard Errors: As was the case with consumption, choice of standard errors did not make a difference: what was significant or marginally significant using one type error was significant or marginally significant using all types of errors. The same is true for instances of non-significance. We conclude that, when deficits occur, increases in the loanable funds pool have had a small, effect of reducing the decline in investment associated with the crowd out problem, but the evidence using this no-stand alone model is somewhat ambiguous. The investment model with a stand alone appears to better explain the variation in investment. Crowd Out and Loanable Funds Effects; For the baseline model without deficit modification, results indicated statistically significant levels of tax cut deficit crowd out in 11 of the 18 periods sampled (recall that because of the higher than average propensity of tax cut recipients to save rather than spend, we do not expect as much crowd out as with consumption). After deficit modification this is drops to 8 of 18 in the no-stand alone model. (In the model with a stand alone, it dropped to from 6 of 6 to 1 of 6.) The baseline model showed statistically significant crowd out resulting from spending deficits in 17 of 18 periods tested. After loanable funds modification, these deficits showed significant crowd out effects in 13 of 17 cases. (In the model with a stand alone, modification increased the number significant from 5 of 6 to 6 of 6.) Unlike models with a stand-alone loanable funds variable, we do not necessarily expect that adding the (S + FB) modifier to the deficit will always leave it with the same coefficient and significance levels, and we see that here, but only a few are so affected by modification they cease to show a remaining “net” crowd out effect. However, even those that remain significant typically have reduced coefficients and significance levels, suggesting modification has at least partially offset the crowd out effects of deficits.

274

J. J. HEIM

One hypothesis for why we more often find significant crowd out effects for tax deficits with this model, but not the earlier model containing a separate loanable funds variable, is because of “left out” variable bias. Goldberger (1961) noted, when an explanatory variable that is “left out” of a regression is correlated with a “left in” variable, the left in variable will pick up the variance it explains, and the variance of the left out variable, and to the extent the two variables are correlated. We have that situation here. The loanable funds variable is highly positively correlated (+.79) with the tax growth variable, but loanable funds are not controlled for in the model. Hence, every time taxes increase, the regression assigns to them their own (lack of significant) effect on consumption, and also the positive effect on investment of any growth in loanable funds. Similarly, when taxes decline, loanable funds, being positively correlated, also decline. Though the decline in taxes does not effect investment, the decline in loanable funds does, and is associated with a decline in investment. Hence, the discrepancy with the nonsignificant finding for tax cut crowd out’s effect on consumption in Table 11.10, where the level of loanable funds was controlled for when calculating the marginal effects on investment of tax cut deficits. Effects of Choice of Standard Errors: As was the case with consumption, choice of standard errors did not make a difference: what was significant or marginally significant using one type error was significant or marginally significant using all types of errors. The same is true for instances of nonsignificance.

11.5

Chapter Summary

The two tables below summarize the findings and conclusions for this chapter.

From Table#

T11.1AA

T11.1B

T11.1

T11.1

Model

11 Baseline

11 Baseline (w/Def)

11 Unmodified(w/ s-a)

11 Modified (w/s-a)

2

19 60 – 20 08 72

19 60 – 20 07 72

19 60 – 20 00 86

89

91

93

92

19 70 – 20 00 91

86

19 70 – 20 07 68

88

19 70 – 20 10 55

94

19 80 – 20 00 86

85

19 80 – 20 10 37

88

19 75 – 20 04 63

88

89

89

91

90

94

95

92

(Av. R2 = 90.2%); (Av Adj. R2 = 85.3%) 88

89

94

87

88

88

88

88

19 80 – 20 04 74

86

86

86

19 85 – 20 04 67

87

87

87

19 85 – 20 05 65

97

97

92

19 96 – 20 09 83

99

99

99

20 00 – 20 10 95

NAa

NA

G

15/18 6/18a

NA

NA

T

Test ratio

16/18 9/18

11/11 8/11a

(5/5 5/5b) 16/18 9/18

91

19 70 – 19 90 91

(Leftmost 6 Sample Av. R2 = 88.7%; Significant: T 6/6, G 4/6) 88 89 89 91 90 94 95 92 88 89 94 87 88

87

19 60 – 19 80 77

10/11 5/11a

87

19 60 – 19 90 43

Signif./Total

(18 Sample Av. R2 = 89.4%); (Av. Adj. R2 = 84.3%)

87

(Av. R = 71.4%)

19 60 – 20 10 60

R2 (18 time periods)

Cptr. 11 Consumption Summary Table

11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

275

T11.9

T11.9

11 Unmodif. (wo/s-a)

Modified (wo/s-a)

83

87

83

87

82

87

90

91

87

89

86

91

–

–

–

(Av. R2 = 88.7%; Av. Adj. R2 = 85.0%) (Av. R2 = 85.0%; Av. Adj. R2 =79.8%)

62/90 52/90

(T11.1 a subset of 18 time periods from the 90 periods in T11.6) (R2 average = 94%. For 90 time periods tested)

4/6 4/6a 0/6 0/6a

6/6 6/6 6/6 6/6

46/50 44/50a

11/11 8/11a

(Av. R2 = 90.2%; Av Adj. R2 = 85.3%)

spending deficit w/o modification far overstates actual crowd out effect. Actual effect better shown in the modified models with most spending deficits found significant. The R 2 s clearly indicate that adding the unmodified deficit variables increases explained variance. Also, the 1980s decade show little variation in government spending, a key requirement for showing statistical significance. Eliminate the samples with the 1990s crowd in problem reduces then number of samples but still leaves a lot (6 of 11) with insignificant (G) statistics. But then deleting the 1980s lack of variation problems leaves only five samples, all of which show a significant negative relationship of government spending deficits to consumption. Notice that when the spending deficit variables are modified by changes in loanable funds, there is enough variation in the modified variable so that the lack of variation problem disappears. (See Table 11.1B detailed discussion of the lack of variation issue.) Tax deficits do not have the limited variation problem, so we see fairly consistently in all periods tested a tendency for tax cut deficits to be significant

a 7 samples containing 1/3 – ½ of all observations from “Crowd In” years Removed, leaving 11 of 18 b Unmodified spending deficit shows lower % significant than after modification. Probably an error in variables problem, where the

T11.6

11 Modified (w/s-a)

(continued)

276 J. J. HEIM

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

277

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R 2 increases to 89.4%, an increase of 25%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When loanable funds modifiers are added to standard model with deficits, either as a stand-alone variable, or as a stand alone and also as a deficit modifier, average R 2 increases from 89.4 to 90.8%, indicating adding loanable funds increases explanatory power, but does not have a net positive effect on consumption by eliminating crowd out. This is because there is also a negative mpc effect on consumption of raising the level of loanable funds (controlling for income), that needs to be controlled for. The stand-alone loanable fund variable, when used alone, shows the net effect of the two opposing forces. When also used as a deficit modifier in the same model, the coefficient on the modifier clearly shows it can offset crowd out, but the slightly larger negative coefficient on the stand-alone variable indicates its mpc effect, which is larger than the crowd out effect. 4. When the loanable funds modifier is added to the standard model as a modifier of the deficit, variables, but without also being included as a stand-alone variable, average R 2 drops an average of 2.1% points, indicating the model without a stand-alone loanable funds variables does not explain consumption crowd out as well as the model with it. In all 6 models tested, the model explained less variance after the deficit was modified by the loanable funds variable than before. This is because of the two, separate, competing effects of an increase in loanable funds, the positive loanable funds effect and the negative mpc effect, which are not captured well without a stand-alone variable in the model. 5. In the best consumption model, the model including a stand-alone loanable funds variable, for 90 periods tested, averaged R 2 = 94%. With removal of periods in which “crowd in” characterized 1/3 – ½ of the data, for the remaining 50 periods tested, 46(T) were found significant, and 44 (G). Our theory (Cptr. 4) said that if crowd out could be offset by increases in loanable funds, the crowd out variables (T ) and (G) should remain significant after modification. In almost all cases, they did.

T10.3B

Eq.11.10A 89

10 Baseline (w/o Def)

11 Baseline (w/Def)

19 60 – 20 08 67 19 60 – 20 07 66 19 60 – 20 00 63 19 60 – 19 90 65 19 19 60 70 – – 19 19 80 90 72 −61 19 70 – 20 00 56 19 70 – 20 07 65 19 70 – 20 10 72 19 80 – 20 00 69

70

71

80

78

91

82 2

81

71

76

84

89 2

87

95

90

90

86 2

90

89

81

90

80

89

80

19 19 80 75 – – 20 20 10 04 77 −64

(18 sample period Av. R = 89.8% ) (Adj. R = 86.3%) (Leftmost 6 Sample Av. R2 = 88.3%; Significant T 6/6, G 6/6)

86

(includes GDP Control Variable) (Av. R = 79.8%)

76

(Does not include GDP Control Variable) (Av. R2 = 68.3%)

T10.3C

10 Baseline (w/o Def)

19 60 – 20 10 69

From Table#

Model

R2 (18 time periods)

Cptr. 11 Investment Summary Table

89

81

19 80 – 20 04 71

89

75

19 85 – 20 04 63

89

75

19 85 – 20 05 57

98

93

19 96 – 20 09 92

98

95

20 00 – 20 10 91 G

NAa

NA

NAa

NA

8/11

9/11

11/18 16/18

NA

NA

NA

NA

T

Test ratio

Signif./Total

278 J. J. HEIM

T11.10

T11.11

T11.11

11 Modified (w/s-a)

11 Unmodif.(wo/sa)

11 Modified (wo/s-a)

86

88

88

84

88

88

89

90

90

87

92

92

95

98

98

90

86

90

87

88

90

91

97

92

90

89

91

(Av. R2 = 90.7%; Av. Adj. R2 = 87.2% for 18 samples)

90

90

89

91

90

89

89

89

90

90

86

86

89

–

(91.8% Av.; Adj. R2 = 89.5%)

90

–

(91.8% Av.; Adj. R2 = 89.5%)

(Av. R2 = 89.8%; Adj. Av. R2 = 85.9% for 6 samples)

89

91

91

a 7 samples containing 1/3 – ½ of all observations from “Crowd In” years Removed, leaving 11 of 18

T11.10

11 Unmodif.d(w/sa)

(continued)

98

98

–

–

97

98

–

–

5/6 5/6

1/6 1/6

7/11

8/18

8/11

7/11a

14/18

10/11a

1/6 5/6 11/18 17/18

5/6

1/6

11 DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

279

280

J. J. HEIM

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8%. 2. When deficit variables only added to standard model, R 2 increases to 89.8%, (Adj. R 2 = 86.3) an increase of 13%, clearly indicating clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When loanable funds modifiers are added to standard model with deficits, either as a stand-alone variable, or as a stand alone and also as a deficit modifier, average R 2 increases to 91.8%, indicating increases in deficits net of loanable funds changes do better explain the exact extent to which deficits are related to investment crowd out than just the deficit variables alone. 4. In investment models without a stand-alone loanable funds variable, when the deficit variables are modified by the loanable funds variable, R 2 increases in every one of the 18 periods tested compared to the unmodified model, 89.8–90.7%. Improved ability to explain investment are what we would expect if increases in loanable funds truly do offset part of the crowd out effects of deficits on investment. Our theory (Cptr. 4) said that if crowd out could be offset by increases in loanable funds, the crowd out variables (T ) and (G) should remain significant after modification. In almost all cases, they did, particularly when the mixed crowd out/crowd in period samples were not included. (The model with a stand-alone variable increased R 2 even more, to 91.2%, suggesting the model with the stand alone is the better model. There is no theoretical basis for assuming there is also a “second effect” of a change in loanable, so this is somewhat surprising. The sign on the stand-alone crowd out variable in Table 11.10 is negative for most tests. This indicates that the coefficients on the modified deficit variables overstate their true offset value. They assume a dollar of loanable funds increase offsets a dollar of crowd out. Part of the increase in loanable funds may be spent on foreign investment, or used to buy securities, neither of which directly affect investment. Enough of the increase in loanable funds may be used to increase investment , but not enough to explain the

11

DO LOANABLE FUNDS MODIFY THE CROWD OUT EFFECTS …

281

effect of loanable funds on investment as well as the model with a standalone variable. Therefore the stand-alone model seems to provide the preferred explanation. Either model, however, supports the notion that crowd out is reduced by increases in the loanable funds pool, because both models show R 2 increased when loanable funds are added to the model.) We conclude this chapter strongly indicates deficits cause both consumption and investment crowd out problems which reduce or eliminate their effectiveness, and that increases in the loanable funds pool can help offset these effects for investment, allowing deficit-financed fiscal stimulus programs to have the stimulus effects on the economy they were intended to have. For consumption, the loanable funds increase is obtained by reducing mpc controlling for all other factors, and this would have negative effects. But, as is shown in another chapter, increasing loanable funds by FR open market action avoids this problem and allows for consumer crowd out to be offset.

References Economic Report of the President. (2012, 2013). Washington, DC: Government Publications Office. Goldberger, A. S. (1961, December). Stepwise Least Squares: Residual Analysis and Specification Error. Journal of the American Statistical Association, LVI, 998–1000. Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Heim, J. J. (2017b). Crowding Out Fiscal Stimulus. Hoboken: Palgrave Macmillan. Hill, R., Griffiths, W., & Lim, G. (2011, 2003). Principles of Econometrics. Hoboken: Wiley. Solow, R. (1957, August). Change and the Aggregate Production Function. The Review of Economics and Statistics, 39(3), pp. 312–320. Wooldridge, J. M. (2005). Introductory Econometrics (3rd ed.). Cincinnati: Southwestern Publishers. Cptr. 12: Serial correlation and heteroskedasticity in time series regressions.

PART VI

Comparing M1 and Total Loanable Finds Effects on Crowd Out

CHAPTER 12

Does M1 More Accurately Define the Extent to Which Crowd Out Can Be Modified Than Total Loanable Funds?

In this chapter we test the consumption (Sect. 12.1) and investment model (Sect. 12.2) in the same way we did in Chapter 11 except we test the M1 money supply as a modifier, and compare it with modifiers we have previously tested. The models tested or compared will be: 1. total loanable funds (S + FB), 2. the endogenous portion of loanable funds only (S + FB) − (Tr + A), 3. the money supply (M1), and 4. the money supply combined with the exogenously created part of the loanable funds pool (M1 + Tr + A). M1 is tested with the same models we’ve used in recent chapters. The hypothesis is that M1 may be a better indicator than total loanable funds of how much of any increase in total loanable funds actually gets lent out and used to purchases goods and services. We also test M1 and the loanable funds pool (S + FB) as one combined variable to see if M1 might be an additional source of funds, in excess of (S + FB) which might also modify crowd out effects. Finally, we test M1 with the exogenously determined part of total loanable funds to see if It and M1 might even better explain the magnitude of crowd out effects than just M1 alone.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_12

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Testing the Consumption Model

12.1

Below we again test crowd out effects using the model we take as the “standard” consumption model, taken from Heim (2017), Eq. 4.4.TR, which is included here to present an idea of what, in previous studies, the determinants of consumption have been found to be. The Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07POP16/65 + .020POP + 38.00M2AV + .09CB2 (6.0)

(3.2)

(3.7)

(4.9)

R 2 = 87.8%

D.W. = 2.2

MSE = 24.88 (4.4.TR)

To start, we show This study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included (1960–2010 data). This model is presented to show clearly how much succeeding models, which add in deficit variables and loanable funds variables, actually increase the explanatory power of the model: CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(7.2)

(0.6)

(3.0)

(1.6)

+ .013POP − 1.58 M2 AV + .13CB2 (3.2)

(2.0)

(−0.1)

R = 60.3% 2

D.W. = 1.7

MSE = 43.98 (11.1AA)

Next we show this study’s Baseline (BL) Standard Consumption Model with 2 Variable Crowd Out (T and G) Deficit Effects Estimated Separately. This Model is Estimated Before Deducting Loanable Funds Changes from (T ) or (G), and Before (T + G) is Added as a Stand-Alone Variable: CD = .31(Y − TT ) + .32(TT ) − .16(G T&I ) − 7.14PR + .49DJ−2 (t=)

(6.4)

(6.6)

(−1.9)

(−3.1)

(4.5)

− .459.68POP16/65 + .017POP + 36.27M2AV + .09CB2 (4.0)

(2.4)

R = 86.6% 2

(3.8)

D.W. = 2.1

(3.9)

MSE = 26.17 (11.1A)

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

287

Next we show Eqs. 12.1A, which includes (S + FB) as the stand-alone variable only, Eq. 12.1B which includes it as both a stand alone and as a deficit variable modifier, and Eq. 12.2, which includes M1 with the loanable funds modifier (S + FB + M1) as both a stand alone and as a deficit variable modifier. All consumption and investment models tested below have been tested for stationarity and endogeneity problems. All variables were stationary or cointegrated with their dependent variables. No endogeneity problems were found (Hausman test) with any of the consumption or investment models. The Standard Consumption Model with 2 Variable Crowd out (T , G), with only stand-alone (S + FB) offset changes: CD = .38(Y − TT ) + .43(TT ) − .24(G T&I ) − .14(ST + FB) − 6.09PR (t=)

(8.0)

(6.7)

(−2.8)

(−2.8)

(−4.1)

+ .40DJ−2 − 398.48 POP16/65 + .016POP + 33.67M2AV + 10 CB2 (5.0)

(3.7)

(−1.9)

R = 88.3% 2

Adj. R = 86.5% 2

(4.5)

(3.5)

D.W. = 1.9 MSE = 24.68 (12.1A)

The Standard Consumption Model with 2 Variable Crowd out (T ), (G), after offsetting (S + FB only) changes to (T ) and (G) as well. Standalone (S + FB) variable still included in the model: CD = .38(Y − TT ) + .43(TT )m − .24(G T&I )m − .81(ST + FB) − 6.09PR (t=)

(8.0)

(6.7)

(−2.8)

(−5.6)

(−2.8)

+ .40DJ−2 − 398.48POP16/65 + .016POP + 33.67M2AV + 10CB2 (5.0)

(3.7)

(−1.9)

R = 88.3% 2

Adj. R = 86.5% 2

(4.5)

(3.5)

D.W. = 1.8

MSE = 24.89 (12.1B)

Next we wish to test a second model, the Standard Consumption Model with 2 Variable Crowd out (T ), (G), with only stand alone and deficit modifier (S + FB + M1): CD = .36(Y − TT ) + .38(TT )m − .20(G T&I )m − .68(ST + FB + M1) (t=)

(7.1)

(6.6)

(−2.4)

(−5.4)

− 6.86PR + .41DJ−2 − 459.31POP16/65 + .017POP (−3.3)

(4.1)

+ 37.69M2AV + .10 CB2 (3.59)

(3.6)

(−2.3)

(4.1)

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R 2 = 87.7%

Adj. R 2 = 85.1%

D.W. = 1.9 MSE = 25.28

(12.2)

As you can see, results are similar for all variables using either the (S + FB + M1) modifier, or only the (S + FB) modifier used in Chapter 11. Also, crowd out variable t-statistics are highly significant in both models. However, the model using the (S + FB + M1) modifier has slightly lower variable significance levels, and R 2 than the (S + FB) model. This suggests that total (S + FB) is a better indicator of the extent to which changes in loanable funds affect consumption than (S + FB) and M1 together (the larger difference in adjusted R 2 also suggests total loanable funds gives the better of how much crowd out can be offset than just M1 alone. M1 can vary due to fluctuation in the money multiplier even when (S + FB) is constant. In addition, not every dollar lent out stays in the form of M1; some borrowers may deposit their loans in savings or CD accounts. Note that in Eq. 12.1B after modification of the crowd out effect by adding (S + FB) to the tax deficit variable (T), and subtracting it from the spending deficit variable (G), results for all variables except the stand-alone (S + FB) variable remain the same, as does R 2 . This result has occurred repeatedly in earlier chapters and is explained there. See, for example, Chapters 9 and 11. In Table 2.1, we present results using the standard model with one of four additional variables added. The added variable is either 1. (S + FB) variable (results taken from Chapter 11 and Eqs. 12.1A and 12.1B models). 2. (S + FB + M1) 3. M1 only, or 4. (M1) + (Tr + A). All results cited in Table 12.1 for different time periods were estimated using the same models as in Eqs. 12.1A and 12.1B and 12.2 above except for varying the loanable funds variable used. Only the time periods tested changes. For each time period given in Table 12.1, two sets of statistics are presented.

w/o

with

1960–1990

w/o

with

1960–1980

(S + FB) Modification only Model from Cptr. 11 T Def( : .72 .72 .36 .36 t-stat (5.3) (5.3) (2.7) (2.7) G Def : −.27 −.27 −.16 −.16 t-stat (−2.8) (−2.8) (−2.2) (−2.2) ST + FB −.47 −1.46 −.13 −.65 t-stat (−2.6) (−4.2) (−1.3) (−2.5) R2 .94 .94 .90 .90 .88 .88 .85 .85 Adj. R 2 .91 .89 BL R 2 * (S + FB + M1) Modification Model from Cptr. 12 T Def( : .60 .60 .32 .32 t-stat (5.0) (5.0) (2.6) (2.6) G Def : −.24 −.24 −.12 −.12 t-stat (−2.3) (−2.3) (−1.8) (−1.8) S + FB + M1 −.19 −.79 −.06 −.38 t-stat (−1.3) (−3.7) (−0.7) (−1.9) .92 .92 .89 .89 R2 .85 .85 .84 .84 Adj. R 2 .91 .89 BL R 2 * (M1 Modification only Model from Cptr. 12) T Def( : .53 .53 .29 .29 t-stat (3.6) (3.6) (3.0) (3.0)

Variable

.29 (2.6) −.09 (−0.9) −.48 (−1.8) .91 .88

.28 (3.1) −.07 (−1.0) −.37 (−3.0) .91 .88

.22 (2.6)

.28 (3.1) −.07 (−1.0) −.09 (−1.8) .91 .88 .91 .22 (2.6)

with

.29 (2.6) −.09 (−0.9) −.10 (−1.2) .91 .88 .91

w/o

1960–2000

.33 (5.3)

.42 (5.8) −.14 (−2.2) −.12 (−3.0) .89 .86 .87

.44 (5.7) −.17 (−2.4) −.13 (−3.6) .89 .86 .87

w/o

.33 (5.3)

.42 (5.7) −.14. (−2.4) −.54 (−5.5) .89 .86

.44 (5.7) −.17. (−2.4) −.74 (−4.7) .89 .86

with

1960–2007

.33 (5.2)

.37 (5.6) −12 (−2.2) −.07 (−2.6) .88 .85 .87

.42 (5.5) −16 (−2.4) −.11 (−3.4) .89 .86 .87

w/o

.33 (5.2)

.37 (5.6) −.12 (−2.2) −.45 (−5.5) .88 .85

.42 (5.5) −.16 (−2.4) −.69 (−4.4) .89 .86

with

1960–2008

.32 (6.2)

.38 (6.6) −.20 (−2.4) −.48 (−6.3) .88 .85

.43 (6.7) −.24 (2.8) −.82 (5.6) .88 .86

with

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

(continued)

.32 (6.2)

.38 (6.6) −.20 (−2.4) −.09 (−4.1) .88 .85 .87

.43 (6.7) −.24 (−2.8) −.14 (−4.1) .88 .86 .87

w/o

1960–2010

Table 12.1 Effects on standard consumption model of an additional separate variable, with and without also adding it as a deficit modifier

12

289

−.21 −.21 (−1.5) (−1.5) .05 −.69 (0.2) (−2.5) .91 .91 .84 .84 .84 .84 Modification Model .53 .53 (3.6) (3.6) −.21 −.21 (−1.5) (−1.5) .04 −.70 (0.2) (−2.5) .91 .91 .84 .84 .91

−.11 −.11 (−2.0) (−2.0) .13 −.27 (1.5) (−1.9) .89 .89 .84 .84 .89 .89 from Cptr. 12 .29 .29 (3.0) (3.0) −.11 −.11 (−1.9) (−1.9) .12 −.28 (1.5) (−2.0) .89 .89 .89 .89 .89

with

w/o

w/o

with

1960–1990

1960–1980

*BL R 2 = Baseline Model R 2 taken from Table 11.1A

G Def : t-stat M1 t-stat R2 Adj. R 2 BL R 2 * (M1 + Tr + A) T Def( : t-stat G Def : t-stat M1 + Tr + A t-stat R2 Adj. R 2 BL R 2 *

Variable

Table 12.1 (continued)

−.03 (−0.4) −.31 (−2.8) .91 .88 .91 .22 (2.7) −.03 (−0.5) −.33 (−3.0) .91 .88

.22 (2.7) −.03 (−0.5) −.07 (−1.2) .91 .88 .91

with

−.03 (−0.4) −.06 (−1.0) .91 .88 .91

w/o

1960–2000

.32 (5.3) −.07 (−1.4) −.08 (−1.2) .87 .84 .87

−.08 (−1.4) −.01 (−0.1) .87 .84 .87

w/o

.32 (5.3) −.07 (−1.4) −.47 (−5.5) .87 .84

−.08 (−1.4) −.42 (−4.6) .87 .84 .87

with

1960–2007

.32 (5.1) −07 (−1.4) −.07 (−1.2) .88 .85 .87

−.08 (−1.5) .00 (0.0) .87 .85 .87

w/o

.32 (5.1) −.07 (−1.4) −.47 (−5.5) .88 .85

−.08 (−1.5) −.41 (−4.7) .87 .85 .87

with

1960–2008

.29 (4.4) −.11 (−1.3) −.04 (−1.5) .87 .84 .87

−.16 (−1.9) −.01 (−0.1) .87 .84 .87

w/o

.29 (4.3) −.11 (−1.3) −.44 (−4.1) .87 .84

−.16 (1.9) −.48 (4.7) .87 .84 .87

with

1960–2010

290 J. J. HEIM

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

291

1. One in which there is one of the four variables above added as a stand alone, e.g., (S + FB), but no modification of the deficit variables (T ) and (G) by the same modifier, and 2. one in which the regression model in (1) above is reestimated adding the same variable, e.g., (S + FB) also as a modifier to the deficit variables., e.g., T + (S + FB) and G − (S + FB). We may summarize Table 12.1 results as follows: (S + FB) Model From Cptr. 11: Adding the (S + FB) total loanable funds variable to the baseline deficit model without a loanable funds variable increased R 2 in 5 of the 6 models tested and left it unchanged in one. The average gain was 1.5 percentage points. For tax cut deficits, 6 of 6 (T ) and 5 of 6 spending deficits (G) show significant crowd out, before and after modification. This is very similar to the baseline model which showed 5 of 6 (T ) significant, and 6 of 6 (G) significant. The higher R 2 shows that adding loanable funds improves our ability to explain what variable affect consumption. As explained in Chapter 18, the crowd out variable’s marginal offsetting effect is given by the net of the positive values of the coefficients on the (T ) and (G) variables. (S + FB + M1) Model: Adding the (S + FB + M1) total loanable funds variable to the baseline model increased R 2 in 4 of the 6 models tested but only slightly and left it unchanged in two, The average gain was 0.8 percentage points, less than the 1.5 points average gain obtained using (S + FB) alone. 6 of 6 (T ) and 5 of 6 (G) show significant crowd out, before and after modification. This is very similar to the baseline model which showed 5 of 6 (T ) significant, and 6 of 6 (G) significant. The higher R 2 compared to the baseline deficit (but no loanable funds) model shows that adding loanable funds improves our ability to explain what variable affect consumption, but the fact that it is found lower than that found using (S + FB) alone suggests that M1 does not add to explanatory power, and may reduce it marginally. (M1 Only) Model: Adding the (M1) variable to the baseline model left R2 unchanged in all 6 of the 6 models tested unchanged; adding it to the baseline deficit model without loanable funds variable provided no gain in explanatory power. Six of 6 (T ) were found significant, compared to 5 of 6 in the baseline model but only 2 of 6 (G) show at least marginally significant crowd out before and after modification, compare to 6 of 6 in the baseline model. The M1 model suggests that in 4 of the 6 time periods, there was no crowd out from government spending deficits. This seems

292

J. J. HEIM

to contradict most of our earlier chapter findings on whether spending deficits cause crowd out, and for no clear reason. If M1 had proven to be a significant determinant of consumption, this would be a big issue, but since, unlike the (S + FB) models, it adds nothing to explained variance, it is not a variable worth further examination. The reduced numbers of samples with significant spending deficits probably reflects the errors in variables” problem. It may also reflect the multicollinearity problem, since changes in M1 and government spending are fairly highly correlated. (M1 + Tr + A): Model: Adding the (M1 + TR + A) total loanable funds variable to the baseline model left R2 unchanged in 5 of the 6 models tested; in one it increased one percentage point. Hence, the average gain was 0.2 percentage points, which is better than the M1 only model above, but not enough o indicate that FR action alone has much effect on consumption. 6 of 6 (T ) significant before and after, compared to 5 of 6 in the baseline model. 1 of 6 (G) is marginally significant, and an additional 3 are close to marginally significant (t = 1.4 or 1.5), compared to 6 of 6 in the baseline model. Again, the results for the spending deficit probably reflect the errors in variables or multicollinearity problems. Conclude (for Consumption) Table 12.1 seems to indicate that changes in (S + FB) better explain what how much of changes in the loanable funds variable can offset crowd out than M1, or combinations of M1 and FR purchases. R 2 was higher for (S + FB) models in all but 3 of the 24 models tested. For those three, it was the same. This suggests M1 is not a good proxy for total loanable funds. and that FR purchases have not traditionally been large enough to have much impact on consumption. Table 12.2 retests the same models as in Table 12.1, but without including the separate loanable funds (S + FB), (S + FB + M1, M1, or (M1 + Tr + A) control variables. With these tests, we can see if including them as separate variables, in addition to including them as modifiers to the tax and spending variables makes a difference in our crowd out estimates. There are no stationarity problems with either the modified or unmodified variables. The model without the deficit variables being modified was without endogeneity problems, so it was run in OLS. In the modified model, G − (S + FB) was found endogenous with the dependent variable and was replaced by a Wald-strong instrument, which was not endogenous (Sargan test). We may summarize Table 12.2 results as follows:

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

293

Table 12.2 Robustness over time of effects on consumption of crowd out, with and without offsetting loanable funds (no stand-alone modifying variables were used) Variable1960–1980 w/o

with

1960–1990

1960–2000

1960–2007

1960–2008

1960–2010

w/o

w/o

w/o

w/o

w/o

with

with

with

(S + FB Only) Model from Cptr. 11: .24 .25 .14 .23 .11. .32 .16 T Def : .50 t-stat (3.0) (2.2) (3.4) (2.7) (2.8) (1.8) (5.1) (2.2) −.03 .04 −.13 .07 G Def : −.19 +.06 −.10 .08 t-stat (−1.3)(0.5) (−1.2)(1.3) (−0.5)(0.6) (−1.1)(0.6) .90 .85 .90 .87 .90 .90 .87 .82 R2 .82 .73 .86 .82 .88 .87 .84 .79 Adj. R2 (S + FB + M1) Modification Model from Cptr. 12 .22 .24 .15 .20 .13. .31 .24 T Def( : .51 t-stat (2.9) (2.5) (3.3) (3.0) (2.6) (2.4) (5.1) (3.4) −.04 .09 −.03 .11 −.06 .20. G Def : −.22 .02 t-stat (−1.2)(0.2) (−0.5)(1.2) (−0.2)(1.7) (−0.5)(2.0) .90 .86 .89 .87 .91 .90 .87 .83 R2 .82 .74 .85 .82 .88 .87 .84 .79 Adj. R2 (M1 Modification only Model from Cptr. 12) .37 .24 .22 .21 .16 .32 .29. T Def( : .51 t-stat (2.9) (3.3) (3.3) (3.9) (2.6) (2.6) (5.1) (4.0) −.03 .20 −.06 .22 G Def : −.22 −.07 −.04 .05 t-stat (−1.2)(−0.8)(−0.5)(0.6) (−0.3)(2.3) (−0.5)(2.3) .90 .89 .89 .89 .91 .89 .87 .83 R2 .82 .81 .85 .84 .88 .86 .84 .79 Adj. R2 (M1 + Tr + A) Modification Model from Cptr. 12 .36 .29 .22 .23 .14 .33 .27 T Def( : .53 t-stat (3.9) (3.2) (3.2) (3.0) (2.7) (2.4) (5.6) (3.6) −.08 .19 G Def : −.21 −.01 −.10 −.01 −.03 .12 t-stat (−1.6)(−0.1)(−1.7)(−0.2)(−0.5)(2.3) (−1.6)(2.8) .91 .88 .89 .88 .91 .89 .87 .83 R2 .85 .80 .85 .84 .88 .87 .84 .81 Adj. R2

with

with

.31 .18 (5.1) (2.5) −.13 .19 (−1.2)(0.7) .87 .83 .84 .79

.31 .15 (6.3) (2.3) −21 .02 (−1.9)(0.1) .88 .83 .85 .79

.31 .25 (5.1) (3.8) −.06 .21 (−0.5)(2.2) .87 .83 .84 .79

.32 .23 (6.3) (4.2) −.14 .16 (−1.2)(1.6) .88 .84 .86 .80

.31 .29 (5.6) (5.1) −.06 .22 (−1.6)(0.5) .87 .83 .84 .80

.32 .32 (6.3) (5.5) −.14 .18 (−1.2)(2.1) .88 .84 .86 .81

.33 .27 (5.6) (3.7) −08 .20 (−1.6)(2.9) .87 .83 .85 .81

.32 .21 (6.6) (3.0) −.16 .29 (−1.9)(4.9) .87 .82 .84 .78

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J. J. HEIM

(S + FB) Model From Cptr. 11: Adding the (S + FB) total loanable funds variable to the baseline model as a deficit variable modifier reduced, not increased, the baseline deficit model’s ability to explain variance (R 2 ) in all 6 of the 6 models tested. The average decline was 3.5%. As we noted in Chapter 18, the likely reason for the decline is that increases in loanable funds (S + FB) have two offsetting effects on consumption: they eliminate crowd out, but, ceteris paribus, can only occur (income constant) if there is a cutback in consumption. The net of these two leaves a large number, (S + FB), being subtracted from the deficit variables, which has little if any net significant impact on consumption. Deficits do have a significant relationship, so this creates an error in variables problem reducing R 2 and deficit variables significance levels. Six of 6 (T ) show significant crowd out, before and after modification (but lower significance levels after). 5 of 6 (G) show marginally significant or significant crowd out before modification; but 0 of 6 show significant crowd out effects after. But these declines in significance levels seem more related to expected results of error in variables problems than to success in reducing crowd out. In short, for consumption, the “no-stand alone” loanable funds model seems to be a bad model. Because changes in loanable funds have two, largely offsetting effects on consumption, without modeling them separately distorts the impact of the variables (the deficit) to which they are added. A stand-alone loanable funds variable is also needed to allow both effects to be shown separately. Including the stand alone leaves a theory consistent result for the loanable funds effect (same coefficient as the deficit variable alone, higher R 2 compared to baseline model) and for the stand alone (negative sign on regression coefficient). (S + FB + M1) Model: Adding the (S + FB + M1) variable to the baseline model as a deficit variable modifier reduced, not increased, the baseline model’s ability to explain variance (R 2 ) in all 6 of the 6 models tested. The average decline was 3.3%. The reasons for the decline appear to be the lack of a stand-alone loanable funds variable, and the lack of a significant relationship between changes in consumption and changes in the money supply (see the M1 model discussion below). Six of 6 (T ) show significant crowd out, before to and after modification (but lower significance levels after). By comparison, for spending deficits, 5 of 6 (G) before modification were significant, and 4 of 6 modified (G) were statistically significant, but had positive signs after modification (1960–2000, 2007, 2008 and 2011 samples). This suggests the combined loanable funds and M1 modifier caused net crowd in effects

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

295

to result. We see this effect again further below in the model that uses M1 and only the portion of the changes in loanable funds attributable to FR purchases. Particularly in the last three samples, the economy (including endogenous loanable funds) was in decline, but FR purchases and M1 were increasing. (M1) Model: Adding the (M1)) variable to the baseline model as a deficit variable modifier reduced, not increased, the baseline model’s ability to explain variance (R 2 ) in all 6 of the 6 models tested. The average decline was 2.7%. Six of 6 tax cut deficits (T ) showed statistically significant crowd out effects before and after modification. For spending deficits, 3 of 6 (G) showed significant crowd out effects before modification, but none were significant after. Since R 2 was markedly lower after modification in 6 of 6 tests, it suggests that adding the modification is resulting in lowed deficit significance levels for both (T ) and (G) because it is creating an “error in variables” problem, i.e., is distorting the true crowd out effect, not because it is really causing increases in consumption large enough to offset crowd out. (In addition, In Table 12.1, the sign on M1 as a stand-alone variable is consistently negative, which is difficult to explain theoretically). (M1 + Tr + A) Model: Adding the (Tr + A + M1) variable to the baseline model as a deficit modifier reduced, not increased, the baseline model’s ability to explain variance (R 2 ) in all 6 of the 6 models tested. The average decline was 3.2%. Six of 6 tax cut crowd out variables (T ) were significant before and after modification (though with lower significance levels). For spending deficits, 5 of 6 (G) show marginally significant crowd out before modification, with the expected negative sign, and four of six are significant after modification, but have positive signs! Only the two samples ending with 1980 or 1990 data have negative signs. As we explained earlier, this may stem from the rapidly declining economy of the 2007–2010 period, causing major reductions in the endogenous part of the loanable funds pool. The lower R 2 after modification in all 6 periods tested, suggests that modifying the deficit variables by (Tr + A + M1) is creating an “error in variables” problem. Overall, the markedly lower R 2 s in the models, compared to the comparable Table 12.1 models, suggest that consumption models with stand-alone modifier variables are the better models. R 2 in Table 12.2 after modification drops even further. That said, there is some evidence suggesting that (S + FB + M1) and (Tr + A+M1) can offset at least spending deficit crowd out (if the increase in FR purchases is huge).

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12.2 Testing the Two-Variable Deficit Investment Model The model we take as the “standard” investment model, i.e., the model containing many variables previous researchers have found to be significant determinants of investment, but excluding any such variables for which findings could not be replicated in at least three of four different time periods and in three different models. This standard model taken from Heim (2017), Eq. 5.4.TR. 12.2.1

Investment Models with a Stand-Alone Loanable Funds Modifier

For comparison of representative past findings with this study’s work, we include the Standard Investment Model from Heim (2017) (Estimated using 1960–2010 data): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

(1.7)

R = 83.3% D.W. = 2.0 MSE = 28.25 (5.4.TR) 2

This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, and No GDP Variable Included to Control for the State of the Economy: is estimated as: ID = + .48(ACC) + .008POP + .76PR−2 + 7.37XRAV + 14.08CAP−1 (t=)

(10.6)

(2.5)

(2.2)

(0.2)

R 2 = 69.4%

D.W. = 1.6

(4.3)

MSE = 47.87 (10.3C)

(Same as Eq. 10.3C) This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy is estimated as: ID = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(4.0)

(0.0)

(−0.3)

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297

− 5.21XRAV + 10.39CAP−1 + .10 GDP (2.0)

(−1.3)

(2.9)

R = 76.1% 2

D.W. = 2.1

MSE = 43.06

(10.3B)

(Same as Eq. 10.3B; and same as Eq. 21.10C below) Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010) ID = + .27(ACC) + .33TT − 33G T&I + .012POP (t=)

(6.4)

(2.6)

(2.8)

(−3.9)

− 4.95PR−2 + 6.68XRAV + 2.43CAP−1 − .02GDP (3.5)

(−2.5)

(−0.2)

(1.8)

R = 89.0% 2

D.W. = 1.9

MSE = 29.87 (11.4A)

The same model, with the addition only of a control variable for changes in the pool of loanable funds (S + FB), follows in Eqs. 12.3A, and with both this stand-alone variable and a (S + FB) deficit modifier, in Eq. 12.3B. Here, we simply add the change in loanable funds to the negative -valued sign on any tax cut, reducing the estimated crowd out effect. We subtract it from any change in the deficit caused by changes in government spending, also reducing the estimated crowd out effect. In Eqs. 12.4A and 12.4B, the same equations are repeated, but this time the variable used to modify (T ), (G) and as a stand alone (S + FB + M1). All variables were found Augmented Dickey Fuller (ADF) stationary; No Hausman–endogeneity was found between the dependent and explanatory variables, and Newey–West standard errors were used to avoid heteroskedasticity. The Standard Investment Model with 2 Variable Crowd out (T , G), before ((S + FB)) is used to modify their value, But with (S + FB) StandAlone Variable (Using 1960–2010 data): ID = + .18(ACC) + .21TT − 23G T&I + .16((S + FB)) (t=)

(5.6)

(1.8)

(−2.6)

(2.1)

+ .007POP − 3.24PR−2 + 5.54XRAV + 1.00CAP−1 (2.7)

(−1.6)

R = 90.4% 2

(Equation 12.3A) (same as Eq. 11.3)

(2.8)

D.W. = 1.9

(0.7)

MSE = 27.49 (12.3A)

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J. J. HEIM

The Standard Investment Model with 2 Variable Crowd out (T , G), Includes the Stand Alone and Deficit-Modifying Effects of (S + FB) (Using 1960–2010 data): ID = + .18(ACC) + .21TT(m) − 23G T&I(m) − .28((S + FB)) (t=)

(5.6)

(1.8)

(1.1)

(−2.6)

+ .007POP − 3.24PR−2 + 5.54XRAV + 1.00CAP−1 (2.7)

(2.7)

(−1.6)

R = 90.4% 2

D.W. = 1.9

(0.7)

MSE = 27.50 (12.3B)

(Equation 12.3B) (same as Eq. 11.4) Equations 12.4A and 12.4B repeat models shown immediately above except they use (S + FB + M1) as the variable used to test for loanable funds effects. Standard Investment Model with 2 Variable Crowd out (T , G), before modifying (S + FB + M1) added to them) (Using 1960–2010 data): ID = + .20(ACC) + .29TT − 33G T&I + .08((S + FB + M1)) (t=)

(5.7)

(2.5)

(−4.1)

(1.1)

+ .009POP − 3.14PR−2 + 6.08XRAV + 1.38CAP−1 (2.8)

(3.0)

(−1.4)

R = 89.1% 2

(0.8)

D.W. = 1.8

MSE = 29.22 (12.4A)

Standard Investment Model with 2 Variable Crowd out (T , G), adjusted for accommodating (S + FB + M1) (Using 1960–2010 data) ID = + .20(ACC) + .29TT(m) − 33G T&I(m) − .53((S + FB + M1)) (t=)

(5.7)

(2.5)

(−4.1)

(−2.6)

+ .009POP − 3.14PR−2 + 6.08XRAV + 1.38CAP−1 (2.8)

(−1.4)

R = 89.1% 2

(3.0)

D.W. = 1.8

(0.8)

MSE = 29.22 (12.4B)

Tables 12.3 present results for testing these four models in six different, though overlapping, time periods. Results in the six periods are estimated use exactly the same model. Then, Table 12.4 drops the stand-alone (S + FB + M1) variable, and retests the remaining model in the same six time periods.

w/o

.17 (1.8) −.15 (−1.7) .30 (3.1) .90 .86 .27 (2.2) −.31 (−3.4) .20 (1.6) .88 .86 .86

.19 (1.4) −.17 (−1.9) .17 (0.5) .87 .83

w/o

.27 (2.2) −.31 (−3.4) −.38 (−1.4) .88 .86

.17 (1.8) −.15 (−1.7) −.02 (−0.1) .90

with

1960–2000

.13 (1.6) −.11 (−1.2) .12 (0.6) .90

with

1960–1990

w/o

with

1960–1980

(S + FB only) Model from Cptr. 11: T Def : −.02 −.02 .13 t-stat (−0.4) (−0.4) (1.6) G Def : −.12 −.12 −.11 t-stat (−1.3) (−1.3) (−1.2) S + FB .65 .54 .36 t-stat (9.7) (4.1) (4.2) R2 .97 .97 .90 .90 .83 BL R 2 : (S + FB + M1) Model from Cptr. 12: T Def : .07 .07 .19 t-stat (1.6) (1.6) (1.4) G Def : −.20 −.20 −.21 t-stat (−1.9) (−1.9) (−1.9) S + FB + M1 .41 .14 .23 t-stat (8.7) (1.2) (1.4) R2 .95 .95 .87 .93 .93 .83 Adj. R 2 .90 .83 BL R 2 :

Variable

.15 (1.7) −.24 (−2.3) .19 (2.8) .86 .83 .82

.12 (1.4) −.13 (−1.3) .22 (3.1) .87 .82

w/o

.15 (1.7) −.24 (−2.3) −.20 (−1.2) .86 .83

.12 (1.4) −.13. (−1.3) −.02 (−0.1) .87

with

1960–2007

.28 (2.5) −27 (−2.4) .10 (1.5) .87 .84 .85

.20 (1.8) −.16 (−1.5) .19 (2.4) .88 .85

w/o

.28 (2.5) −27 (−2.4) −.44 (−2.2) .87 .84

.20 (1.8) −.16 (−1.5) −.17 (−0.7) .88

with

1960–2008

.29 (2.5) −.33 (−4.1) −.53 (−2.6) .89 .87

.21 (1.8) −.23 (−2.6) −.28 (−1.1) .90

with

(continued)

.29 (2.5) −.33 (−4.1) .08 (1.1) .89 .87 .89

.21 (1.8) −.23 (−2.6) .16 (2.1) .90 .89

w/o

1960–2010

Table 12.3 Comparing robustness over time of effects on investment of crowd out, with and without accommodating loanable funds modification

12 DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

299

.42 (5.3) −.34 (−3.3) −.08 (−1.1) .86 .84 .86

.40 (3.4) −.27 (−2.2) −.83 (−3.3) .84 .79

.42 (5.3) −.34 (−3.3) −.84 (−7.9) .86 .86

.42 (5.3) −.34 (−3.3) −.84 (−8.2) .86 .83

with

.29 (3.4) −.30. (−2.0) −.00 (−0.0) .82 .78 .82

.29 (3.4) −.25 (−2.0) −.09 (−1.1) .82 .79 .82

w/o

.29 (3.4) −.30. (−2.3) −.58 (−3.8) .82 .82

.29 (3.4) −.25. (−2.0) −.63 (−4.5) .82 .82

with

1960–2007

.34 (4.0) −31 (−2.4) .04 (0.4) .86 .83 .85

.31 (3.8) −23 (−1.7) −.14 (−1.7) .86 .84 .85

w/o

.34 (4.0) −.31 (−2.4) −.61 (−3.7) .86 .86

.31 (3.8) −23 (−1.7) −.68 (−5.3) .86 .86

with

1960–2008

*BL = Baseline model with no (S + FB), (S + FB + M1), (M1) or (M1 +Tr + A) stand-alone or deficit modifying variable

.42 (5.3) −.34 (−3.3) −.08 (−1.0) .86 .83 .86

w/o

1960–2000

.40 (3.4) −.27 (−2.2) −.85 (−3.2) .84 .79

with

w/o

w/o

with

1960–1990

1960–1980

(M1 only) Model from Cptr. 12: T Def : .29 .29 .40 t-stat (3.2) (3.2) (3.4) G Def : −.30 −.30 −.27 t-stat (−2.1) (−2.1) (−2.2) M1 .26 −.33 −.17 t-stat (1.2) (−1.3) (1.4) R2 .91 .91 .84 Adj. R 2 .85 .85 .79 .90 .83 BL R 2 : (M1 +Tr + A) Model from Cptr. 12: T Def : .29 .29 .40 t-stat (3.4) (3.4) (3.4) G Def : −.30 −.33 −.27 t-stat (−2.3) (−2.3) (−2.2) M1 .41 −.22 −.16 t-stat (1.9) (−1.1) (−1.4) R2 .92 .92 .84 .87 .87 .79 Adj. R 2 .90 .83 BL R 2 :

Variable

Table 12.3 (continued)

.33 (3.7) −.36 (−2.8) −.00 (−0.1) .89 .87 .89

.31 (3.8) −.31 (−3.6) −.14 (−1.8) .89 .87 .89

w/o

.33 (3.7) −.36 (−2.8) −.69 (−4.8) .89 .87

.31 (3.8) −.31 (−3.6) −.76 (−7.9) .89 .89

with

1960–2010

300 J. J. HEIM

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DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

301

Table 12.4 Comparing robustness over time of effects on investment of crowd out, with and without loanable funds and M1 modification (No stand-alone modifier) Variable1960–1980 w/o

with

1960–1990

1960–2000

1960–2007

1960–2008

1960–2010

w/o

w/o

w/o

w/o

w/o

with

with

with

with

with

(S + FB only) Model from Cptr. 11: .14 .37 .17 .42 .17 .29 .11 .34 .16 .33 .14 T Def : .31 t-stat (3.0) (2.7) (3.8) (3.6) (5.4) (3.5) (3.4) (2.5) (4.0) (2.6) (3.9) (2.2) G Def : −.29 −.26 −.30 −.16 −.37 −.14 −.29 −.12 −.30 −.07 −.36 −.11 t-stat (−1.9)(−3.1)(−2.3)(−2.2)(−4.2)(−2.6)(−2.7)(−1.9)(−2.6)(−0.9)(−4.7)(−1.5) .90 .96 .83 .90 .86 .90 .82 .87 .85 .88 .89 .90 R2 .86 .94 .79 .88 .83 .89 .79 .85 .83 .87 .87 .88 Adj. R2 (S + FB + M1) Model from Cptr. 12: .12 .37 .12 .42 .13. .29 .09 .34 .18 .33 .15 T Def : .31 t-stat (3.0) (2.5) (3.8) (2.4) (5.4) (2.0) (3.4) (1.8) (4.0) (2.0) (3.9) (1.7) G Def : −.29 −.24 −.30 −.15 −.37 −.20 −.29 −.15. −.30 −.04 −.36 −.08 t-stat (−1.9)(−3.0)(−2.4)(−1.6)(−4.2)(−2.3)(−2.7)(−1.8)(−2.6)(−0.3)(−4.7)(−0.7) R2 .90 .95 .83 .87 .86 .87 .82 .85 .85 .84 .89 .85 .87 .93 .80 .83 .83 .84 .79 .83 .82 .81 .86 .83 Adj. R2 (M1 only) Model from Cptr. 12: .25 .37 .17 .43 .19 .29 .20 .34 .25 .33 .23 T Def : .31 t-stat (3.0) (2.8) (3.8) (2.3) (5.4) (1.8) (3.4) (2.6) (4.0) (2.8) (3.9) (2.2) −.29 .06 −.30 .22 −.36 .05 G Def : −.29 −.25 −.30 −.02 −.37 .04 t-stat (−1.9)(−2.0)(−2.4)(−0.2)(−4.2)(−0.5)(−2.6)(−0.6)(−2.6)(−1.7)(−4.7)(0.4) .90 .90 .83 .77 .86 .69 .82 .71 .85 .75 .89 .74 R2 .87 .86 .80 .71 .83 .64 .79 .67 .82 .71. .86 .71 Adj. R2 (M1 +Tr + A) Model from Cptr. 12: .26 .37 .15 .43 .18 .29 .20 .34 .26 .33 .20 T Def : .31 t-stat (2.9) (3.2) (3.8) (2.1) (5.4) (1.8) (3.4) (2.5) (4.0) (3.1) (3.9) (2.2) G Def : −.29 −.30 −.30 .04 −.37 .07 −.29 .06 −.30 .06 −.36 .28 t-stat (−1.9)(−2.1)(−2.2)(0.4) (−4.2)(0.8) (−2.7)(0.7) (−2.6)(0.6) (−4.7)(3.3) .90 .91 .83 .76 .86 .69 .82 .72 .85 .77 .89 .75 R2 .86 .88 .79 .70 .83 .63 .80 .68 .83 .73 .87 .72 Adj. R2

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Comparing Eqs. 12.4A to 12.4B, we find that all coefficients and tstatistics, except one, are the same before and after modification. The exception is the stand-alone (S + FB) variable, whose value changes from (+.08 (t = 1.1)) to (−.53 (t = −2.6) R 2 also remains the same. This is also true when the modifier is (S + FB + M1). It is the result typically achieved when testing a model with a stand-alone variable only, and then retesting it with both the stand alone and using it to modify (T ) and (G). In Table 12.3 we use the standard investment model with deficit variables, adding an additional variable to test for whether the (S + FB), (S + FB + M1), M1, or (M1 + Tr + A) add to the explanatory power of the standard model. In Table 12.3, for each time period given, two sets of statistics are presented. In one set, there is a stand-alone variable, either (S + FB), (S + FB + M1), M1 or (m1 + Tr + A) added to the model, but no modification of the crowd out variables (T , G) by the same variable, and one in which there is both the stand-alone variable and modification of the deficit variables’ by the same variable. We may summarize Table 12.3 results as follows: (S + FB) Model From Cptr. 11: Adding the (S + FB) total loanable funds variable to the baseline model increased R 2 in 6 of the 6 models tested. The average gain was substantial: 4.5 percentage points. The sign on the added (S + FB) variable was positive and highly significant in all 6 tests, indicating increases in loanable funds are associated with positive changes in investment. Hence, we conclude, increases in loanable funds can effectively offset the negative effects of crowd out caused by deficits. For tax cut deficits, in 6 of 6 periods tested using the baseline deficit model (see Table 12.4), which had no (S + FB) explanatory variables, statistically significant crowd out effects of deficits were found. After adding just the stand-alone (S + FB) variable, this dropped to 4 of 6 (T ) (but at lower significance levels), and stayed at 4 of 6 after the standalone model was modified further by modifying the deficit variables, For spending deficits, 6 of 6 showed statistically significant crowd out in the baseline deficit model, but this dropped to only 2 of 6 (G) show significant crowd out after adding the stand-alone loanable funds variable, and stayed at 2 of 6 after further adding the deficit variable modification. Since adding (S + FB) raises R 2 at the same time it reduces some periods’ crowd out effect to insignificance, it may be that (S + FB) can sometimes eliminate crowd out problems caused by spending deficits, but not as reliably as we would like.

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303

After being added as a modifier of the deficit variables, the stand alone generally becomes statistically insignificant in 5 of 6 test periods, unlike consumption tests, where it typically became more significant. This strongly suggests that unlike consumption, there is only one effect of a change in loanable funds on investment, and using two variables in the same model to represent its effects simply dilutes them, resulting in a showing of lower levels of significance. Theoretically, the investment model including a stand alone is also questionable; the rationale for a separate second effect on investment resulting from adding a stand-alone (S + FB) variable is not as obvious as it is with consumption. (S + FB + M1) Model: Adding the (S + FB + M1) variable to the baseline model increased R 2 in 5 of the 6 models tested and left it unchanged in one. The average gain was 2.8 percentage points, markedly less than the 4.5% gain using only (S + FB), and suggesting M1 changes are not related to investment changes or are already accounted for in the total loanable funds variable (S + FB). For the modifier variable (S + FB + M1), as a stand alone, it was found significant in 3 of 6 tests. After the deficit variables were also modified, only 2 of 6. This provides a little further evidence that changes in loanable funds only have one effect on investment, and that is through their ability to compensate for crowd out effects. For tax cut deficits, 6 of 6 baseline deficit models showed statistically significant crowd out associated with deficits. This fell to 5 of 6 (T ) in both the stand-alone (S + FB + M1) model and the same model with the deficit variables also modified. For spending deficits, the baseline model showed significant crowd out in 6 of 6 periods tested. After adding the stand-alone variable, 6 of 6 (G) still showed significant crowd out, before and after deficit variable modification. This suggests M1 is not effective as an offset to crowd out, at least not in addition to the offset advantages provided by (S + FB) alone. (M1 Only) Model: Adding the (M1) funds variable to the baseline model increased R 2 marginally (1 percentage point) in 3 of the 6 models tested and left it unchanged in three. The average gain was 0.5 percentage points, with the results strongly indicating M1 is not an effective crowd out offset compared to the total loanable funds variable (S + FB). For tax cut deficits, 6 of 6 (T ) significant and 6 of 6 (G) show significant crowd out before and after modification, as was the case with the baseline model. This suggests changes in M1 alone do not help offset

304

J. J. HEIM

crowd out, or do not help enough to eliminate crowd out as a significant problem. (M1 + Tr + A): Model: Adding the (M1 +Tr + A) variable to the baseline model increased R 2 in 3 of the 6 models tested and left it unchanged in three. The average gain was small: 0.7 percentage points, again, noticeably less than the total loanable funds model. For tax cut deficits, 6 of 6 (T ) significant before and after. 6 of 6 (G) also significant, as was the case with the baseline model. Coefficients and t-statistics are nearly identical to those in the (M1 only) model. Results suggest neither M1 or (Tr + A) is effective in eliminating investment crowd out. 12.2.2

Investment Models Without a Stand-Alone Loanable Funds Modifier

Next, the same investment models without a stand-alone modifier variable were examined. There was evidence this model, which allows for only the deficit variables to show the effect of loanable funds or M1 modification on the crowd out problem. The stand alone is dropped because in theory also there is no easy way to explain why two separate representations are needed. All variables were found Augmented Dickey Fuller (ADF) stationary; No Hausman–endogeneity was found between the dependent and explanatory variables, and Newey–West standard errors were used to avoid heteroskedasticity. All results in Table 12.4 use exactly the same investment models tested in Table 12.3, except 12.4 drops the stand-alone variables (S + FB), (S + FB + M1), (M1) and (M1 + Tr + A). Only the dates of the period used to test the models changes. In Table 12.4, for each time period given, two sets of statistics are presented. In one set, there is no direct modification of the crowd out variables (T , G) by the same period change in the modifier used in the model, and one in which there is modification. We may summarize Table 12.4 results as follows: (S + FB) Model From Cptr. 12: Adding the (S + FB) total loanable funds variable to the baseline model with deficit increased R 2 in 6 of the 6 models tested. The average gain was substantial: 4.3 percentage points (about the same as for the model with only a stand-alone (S + FB) variable (4.5%). This strongly indicates changes in total loanable funds have a significant impact on investment by offsetting) crowd out.

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305

For tax cut deficits, the baseline model indicated significant crowd out in 6 of 6 periods tested. After adding the (S + FB) variable, 6 of 6 (T ) were still showing significant crowd out effects after modification, indicating the negative effects of government deficits on the pool of loanable funds could be offset dollar-for-dollar by increases in loanable funds. For spending deficits, the baseline model showed 6 of 6 periods tested had significant crowd out effects, but only 4 of 6 (G) show significant crowd out after modification (the two tests including early QE years, involving large increases in FR purchases, showed insignificant crowd out effects of spending deficits, suggesting “errors in variables” problems stemming from the huge increase in FR purchases unassociated with increased investment). (S + FB + M1) Model: After modification R 2 increased in 4 cases, and declined in two others, The average gain was 1.3 percentage points, suggesting adding M1 to the (S + FB) modifier is reducing the explanatory power of the model compared to just using (S + FB) alone. Put another way, it suggests increasing M1 has no positive impact, and is just distorting the regression’s ability to see clearly the offsetting effects of increases in loanable funds. For tax cut deficits, 6 of 6 showed crowd out before deficit modification, and 6 after, though at lower significance levels. For spending deficits, 6 of 6 showed significant crowd out before modification of the deficit variables, 4 of 6 (G) after modification (the two tests including early QE years, involving large increases in FR purchases, showed insignificant crowd out effects of spending deficits). (M1 Only) Model: R 2 markedly lower after modification in 5 of 6 cases and unchanged in one test. The average decline in R 2 is 9.8%. For tax cut deficits, 6 of 6 (T ) showed significant crowd out effects before and after modification (but with lower significance levels after). For spending deficits, Six of 6 (G) show significant crowd out before, but only 2 of 6 after. The declining R 2 in modified tests indicates that the decline in significance levels of the deficit variables more likely results from an “errors in variables” (or multicollinearity problem) than because M1 has some effect in offsetting crowd out from spending deficits. (M1 + Tr + A): Model: R 2 markedly lower after modification in 5 of 6 cases. The average decline is 9.2%, slightly less than adding M1 alone, indicating there may be a small positive effect of FR purchases in offsetting crowd out, but very small at best

306

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For tax cut deficits, 6 of 6 (T ) showed significant crowd out before and after modification. For spending deficits, 6 of 6 (G) show significant crowd out before, but only 2 of 6 after. Results are nearly identical to those for the M1 test alone. This suggests (TR + A) is not adding to the deficit offsetting capabilities of M1. R 2 s for the (S + FB) model were higher in all six periods tested than in the other three modifier models tested, and hence, appears to be the more accurate way of showing the extent to which investment crowd out is offset than by any one of the three M1 variants tested. 12.2.3

Investment Models Without a Stand-Alone Loanable Funds or M1 Modifier, but with a Business Cycle Control Variable

As we note in a later (Chapter 24), (S + FB) is positively correlated with movements in the economy and with its investment component. That means rising taxes are positively related to investment, and rising government expenditures negatively related to investment. Hence our two crowd out variables (T ) and (G) may be found statistically significant, simply because the economy fluctuates, if we do not estimate their effects holding the level of the economy constant. We can test for whether our hypothesis that this control is needed is correct, by adding a variable (the GDP) to control for the economy’s fluctuations. GDP was endogenous with the dependent variable and replaced by a Wald-strong, non-endogenous instrument. There was no stationarity issued. Newey–West standard errors were used, and the model was estimated in first differences of the data. All results in Table 12.5 use exactly the same investment models tested in Table 12.4, except 12.5 adds a variable (GDP) to control for the state of the economy when estimating crowd out effects. Only the time periods used to test the models changes. In Table 12.5, for each time period given, two sets of statistics are presented. In one set, there is no modification of the crowd out variables (T , G) by the same period change in the modifier used in the model, and one in which there is modification. We may summarize Table 12.5 results as follows: Explained Variance: The total loanable funds modifier explained considerably more variance than any of the three alternatives, whether measured by R 2 or adjusted R 2 . Before adding any loanable funds or M1 modifiers, the standard model with deficit variables had an R 2 of 88.3%

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

307

Table 12.5 Effects on investment of crowd out, with and without loanable funds and M1 modification (no stand-alone modifier, GDP control added) Variable1960–1980 w/o

with

1960–1990

1960–2000

1960–2007

1960–2008

1960–2010

w/o

w/o

w/o

w/o

w/o

with

with

with

with

with

(S + FB only) Model from Cptr. 11: .04 .28 .10 .32 .16 .26 .10 .33 .17 .33 .18 T Def : .13 t-stat (0.9) (0.6) (2.2) (1.9) (2.6) (1.9) (2.3) (1.7) (2.7) (1.9) (2.6) (2.0) G Def : −.35 −.27 −.42 −.20 −.40 −.14 −.34 −.13 −.33 −.07 −.33 −.06 t-stat (−3.8)(−4.1)(−3.2)(−3.1)(−5.2)(−2.2)(−3.2)(−1.8)(−2.8)(−0.7)(−3.9)(−0.7) .95 .97 .87 .91 .89 .90 .84 .88 .86 .87 .89 .90 R2 .91 .95 .83 .89 .86 .88 .81 .85 .83 .85 .87 .89 Adj. R2 Average R 2 = 88.3% unmodified; 90.5% modified Average Adj. R 2 = 85.2% unmodified; 88.7% modified (S + FB + M1) Model from Cptr. 12: .04 .20 .05 −.36 .07 .35 .04 .42 .18 .42 .18 T Def : .12 t-stat (0.7) (0.5) (1.1) (0.5) (−2.5)(0.8) (2.1) (0.7) (3.0) (1.4) (3.1) (1.6) G Def : −.34 −.25 −.45 −.19 −.41 −.22 −.32 −.18 −.31 −.04 −.35 −.03 t-stat (−3.8)(−3.4)(−3.1)(−1.9)(−5.2)(−2.7)(−2.5)(−2.1)(−2.2)(−0.2)(−3.4)(−0.3) R2 .95 .96 .88 .88 .88 .89 .77 .87 .79 .84* .84 .87 .91 .94 .84 .83 .85 .86 .74 .84 .75 .82* .82 .80 Adj. R2 Average R 2 = 85.1% unmodified; 88.5% modified Average Adj. R 2 = 81.8% unmodified; 84.8% modified (M1 only) Model from Cptr. 12: −.08 .20 −.02 .36 .03. .35 .12 .42 .14 .42 .13 T Def : .12 t-stat (0.7) (−0.4)(1.1) (−0.2)(2.4) (0.4) (2.1) (1.4) (3.0) (1.7) (3.1) (1.5) −.45 .12 −.41 .14 −.32 .10. −.31 .15 −.35 .16 G Def : −.34 .09 t-stat (−3.8)(−2.4)(−3.1)(3.1) (−5.2)(1.6) (−2.5)(1.32) (−2.2)(1.8) (−3.4)(1.8) .95 .93 .88 .86 .88 .81 .77 .78 .79 .80 .84 .84 R2 .91 .88 .84 .81 .85 .76 .74 .74 .75 .77 .82 .81 Adj. R2 Average R 2 = 85.1% unmodified; 83.7% modified Average Adj. R 2 = 81.8% unmodified; 79.5% modified (M1 +Cr + A) Model from Cptr. 12: −.06 .20 −.03 .36 .04. .35 .14 .42 .23 .42 .17 T Def : .12 t-stat (0.7) (−0.3)(1.1) (−0.3)(2.4) (0.6) (2.1) (1.5) (3.0) (2.2) (3.1) (2.1) −.45 .12 −.41 .14 −.32 .10 −31 .11 −.35 .16 G Def : −.34 .08 t-stat (−3.8)(2.3) (−3.1)(3.4) (−5.2)(1.5) (−2.5)(1.3) (−2.2)(1.3) (−3.4)(2.6) .95 .93 .88 .87 .88 .81 .77 .79 .79 .79 .84 .84 R2

(continued)

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J. J. HEIM

Table 12.5 (continued) Variable1960–1980 w/o

with

1960–1990

1960–2000

1960–2007

1960–2008

1960–2010

w/o

w/o

w/o

w/o

with

w/o

with

.75

.76

.82

.81

with

with

with

Adj. .91 .88 .84 .82 .85 .77 .74 .75 R2 Average R 2 = 85.1% unmodified; 83.8% modified Average Adj. R 2 = 81.8% unmodified; 79.8% modified d(nom_grosssav/gdpdefb3) + d(nom_forborr2/gdpdefb3) d(fr_treas/gdpdefb3 + fr_agency/gdpdefb3)

+

d(m1_b69/gdpdefb3)

+

(S + FB) Model From Cptr. 11: Adding the (S + FB) total loanable funds variable to the baseline model increased R 2 in 6 of the 6 time periods tested. The average gain was substantial: 2.2 percentage points, indicating changes in total loanable funds had a significant impact on investment. Our presumption is that the investment increase occurred because increases in loanable funds can offset the crowd out effects of deficits. This gain in R 2 was only half the size of the 4.5 point gain observed in the comparable Table 27.4 model, which does not have a variable holding business cycle fluctuations constant when estimating the effects of loanable funds on deficits. The difference indicates that half the crowd out effect of deficits arises from deficit inducing changes in the business cycle rather than exogenously determined increases in spending or tax cuts. For tax cut deficits, 5 of 6 (T ) showed significant crowd out before and after modification (but reduced coefficients and significance levels after). For spending deficits, 6 of 6 (G) show significant crowd out before and 4 of 6 after modification. So we interpret the result as consistent with the theory that increases in loanable funds reduce crowd out effects. (Had the reduction in deficit variable coefficients and significance levels resulted in reduced R 2 , we would have concluded adding a modifier just created an error in variable problem, and that that was the cause of the decline in deficit coefficients and significance levels.) (S + FB + M1) Model: Adding the (S + FB + M1) total loanable funds variable to the baseline model increased R 2 in 6 of the 6 models tested, but less than adding (S + FB) alone. The average gain was 0.2 percentage points. This suggests changes in M1 do not positively affect investment, ceteris paribus, and that just adding it to a variable (S +

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

309

FB) that we do know affects investment just creates an error in variables problem that reduces the observed significance of (S + FB) alone. For tax cut deficits, 4 of 6 (T ) before modification showed significant crowd out, only 1 of 6 (T ) after, For (G), 4 of 6 showed significant crowd out before modification, but only and 4 of 6 (G) after. For spending deficits, results are same as with (S + FB) alone, but with lower coefficients and significance levels. The declines in R 2 and significance levels compared to the (S + FB) only model suggests an error in variables problem, not success in reducing crowd out. (M1 Only) Model: Adding the (M1) variable to the baseline model decreased R 2 in 5 of the 6 models tested, and left it unchanged in one. The average loss was substantial: 4.6%. For tax cut deficits, 4 of 6 (T ) time periods tested showed significant crowd out before modification, but only 1 of 6 after modification. For spending deficits, 6 of 6 (G) tests show significant crowd out before, but 6 of 6 after. Declining significance levels associated with modifying the deficit variables also results in declining R 2 . This suggests the M1 modifier was creating an “errors in variables” problem for the deficit variables, not reducing crowd out, i.e., that M1 does not affect investment, and just distorts the values of variables that do when used to modify them. (M1 + Tr + A): Model: Adding the (M1 + Tr + A) variable to the baseline model decreased R 2 in 5 of the 6 models tested, and left it unchanged in one. The average drop in R 2 was substantial: 4.5%. For tax cut deficits, Model: 4 of 6 (T ) significant before and 2 of 6 (T ) after modification, the same as when using just M1 alone as the modifier. For spending deficits, Six of six (G) show significant crowd out before, but only 3 of 6 after (compared to 6 of 6 using M1 alone), Overall, the results for the M1 only and (M1 + TR + A) model are very similar, indicating adding FR purchases to M1 over the periods studied did not have much of an effect on investment.

12.3

Comparing Model Results with (Table 12.5) and Without (Table 12.4) GDP Control

Adding the business cycle control variable generally increased explained variance, hence its addition helps us better understand the correlates of changes in investment. For example, in the models using total loanable funds as the deficit modifier, adding the GDP control variable increased R 2 in 8 of 12 tests, left it unchanged in 3 others.

310

J. J. HEIM

Overall, two general findings stand out when comparing models with and without a GDP control variable: 1. The total loanable funds deficit modifier (S + FB) seemed by far the best at explaining how growth in a loanable funds-related factor can offset the negative effects of crowd out. R 2 s were higher in all tests than for the other three models. The M1 modifier showed no positive relationship to investment. 2. About half of all deficit-induced crowd out of investment spending is due to endogenous factors related to the business cycle. The other half appear related to exogenous actions undertaken by government to either increase spending or reduce government revenues. Table 12.4 shows the combined effects of both. Table 12.5, by controlling for GDP, shows the exogenous changes only. For tax deficits, models without the GDP control variable showed significant crowd out after modification 22 out of 24 possible times (4 models, 6 time periods). With the GDP control variable for the state of the economy, only 8 of 24 showed significant crowd out remaining, i.e., crowd out caused by policy decisions to deficit. For spending deficits, models without the GDP control variable showed significant crowd out after modification 12 out of 24 possible times (4 models, 6 time periods). With the GDP control variable for the state of the economy, only 11 of 24 showed significant remaining crowd out., i.e., crowd out caused by policy decisions to deficit. Finally, we note that consumption and investment results for the four modifiers, when compared against each other, were about the same when Table 12.1 was compared with 12.4 or 12.5 For consumption using the using the same four models, R 2 s and t-statistics on (S + FB) models remained virtually identical when M1 was added to the (S + FB) modifier and stand-alone, suggesting M1 added nothing to the (S + FB) modifier. When M1 alone was used as modifier, R 2 s and t ’s dropped markedly. When (M1 + Tr + A) as added to the baseline model, R 2 only increased in 1 of 6 cases, and then only by one point, but significance levels increased relative to those on the stand-alone (M1) modifier.

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

311

Summary of Chapter 12 Results

12.4

The 4 tables and notes below summarize our findings for Chapter 12 consumption and investment models: Cptr. 12 Consumption Summary Table 1 (S + FB), (S + FB + M1), M1, and (M1 +FR Purchases) Deficit Modifier and Stand-Alone Models Model

19 60 – 20 08 72

19 60 – 20 07 72

19 60 – 20 00 86

T11.1AA

19 60 – 20 10 60

11 Baseline (w/Def)

Eq. 11.1A

(Av. R2 = 71.4%) 87 87 87 91

11 Modified (w/s-a) (S + FB Modifier)** 12 Modified (w/s-a) (S + FB + M1) Modifier** 12 Modified (w/s-a) (M1) Modifier** 12 Modified (w/s-a) (M1) + (Tr + A) Modifier**

T11.1

11 Baseline (wo/Def

From Table#

19 60 – 19 90 43

89

19 60 – 19 80 77

91

19 70 – 19 90 91

93

19 70 – 20 00 91

92

19 70 – 20 07 68

86

19 70 – 20 10 55

88

19 80 – 20 00 86

94

19 80 – 20 10 37

85

19 75 – 20 04 63

88

19 80 – 20 04 74

88

(Av. R2 = 89.4% for 18 samples; 88.7% for 6 used below)

88

89

89

91

90

94

(Av. R2 = 90.2%; Adj. R2 = 86.5%)

–

19 85 – 20 04 67

86

19 85 – 20 05 65

87

19 96 – 20 09 83

92

19 00 – 20 10 95

99

Test ratio T

G

NA

NA

NA 15/1 8 10/1 1 (5/5

NA* 6/18 * 5/11 * 5/5* *) 5/6

6/6 6/6

5/6* 5/6

T12.1

88

88

89

91

89

92

(Av. R2 = 89.5%) Adj. R2 = 86.5%)

–

6/6 6/6

5/6*

T12.1

91

89

91

87

87

87

(Av. R2 = 88.7%) Adj. R2 = 85.5%)

–

6/6

2/6

6/6

2/6*

T12.1

91

89

91

87

88

87

(Av. R2 = 88.8%) Adj. R2 = 85.6%)

–

6/6

1/6* * 1/6*

6/6

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18 **Results for modified and unmodified models were the same for R 2 , coefficients, and t-statistics on all variables except the “stand alone” variable hypothesized as an offset. Hence only one set of deficit variable and R 2 results for each model are shown above

For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 68.3% 2. Baseline standard model with deficit variables added: average R 2 increases to 88.7%, an increase of 30%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects. 3. When the stand-alone loanable funds modifier (S + FB) is added to the standard model with deficits, R 2 increases from (88.7%) to (90.2%), an increase of (1.5%). As noted in earlier chapters, this suggests the true effect of crowd out is better stated as the deficit

312

J. J. HEIM

net of any changes in total loanable funds that occur in the same period. 4. Only one of the other three modifiers (S + FB + M1) explains noticeably more variance (R 2 = 89.5) than the standard model with deficit variables (88.7%), and that is less of an increase than obtained using the fourth modifier, (S + FB), alone. This suggests that adding M1 to (S + FB) just creates an errors in variables problem. It would appear that the effects of a change in M1 is captured when modeling total loanable funds or that it simply is not a significant determinant of consumption. 5. When using the M1 + FR Purchases modifier (M1 + Tr + A), R 2 increases from (88.7%) to (88.8%) over the standard model with deficit variables but without any crowd out offset variable. Essentially, it does not seem that increases in M1 and FR purchases have been effective in offsetting crowd out in the past. 6. Even less successful was using M1 alone as the offset. Adding this variable left R 2 unchanged at the same level (88.7%) as prevailed in the model before any hypothesized crowd out offsets were added. 7. In addition, both the M1 and M1 plus FR purchases model result in most spending deficits to move from statistically significant (5 of 6 in the (S + FB) and (S + FB + M1) models to statistically insignificant in the M1 and (M1 + TR + A) models, contrary to our theoretical expectations, probably due to multicollinearity or “errors in variables” effects. For this reason also, these models seem inappropriate as explanations of what, if anything, serves to offset the crowd out effects of deficits.

Cptr. 12 Consumption Summary Table 2 (S + FB), (S + FB + M1), M1, and (M1 +FR Purchases) Deficit Modifier (No Stand-Alone Offset) Models

12

Model

19 60 – 20 08 72

19 60 – 20 07 72

19 60 – 20 00 86

T11.1AA

19 60 – 20 10 60

11 Baseline (w/Def)

Eq.11.1A

(Av. R2 = 71.4%) 87 87 87 91

11 Unmodified (wo/s-a) 11 Modified (wo/s-a)

T11.9

87

87

87

T11.9

83

83

T12.2

88

T12.2

84

11 Baseline (wo/Def

12 Unmodified (wo/s-a) 12 Modified (wo/s-a)

From Table#

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

19 60 – 19 90 43

19 60 – 19 80 77

19 70 – 19 90 91

19 70 – 20 00 91 92

19 70 – 20 07 68 86

19 70 – 20 10 55 88

19 80 – 20 00 86 94

19 80 – 20 10 37 85

19 75 – 20 04 63 88

19 80 – 20 04 74 88

19 85 – 20 04 67

92

20 00 – 20 10 95 99

Test ratio T

G

NA

NA

NA 15/1 8 10/1 1 (5/5

NA* 6/18 * 5/11 * 5/5* *)

91

93

91

89

91

(Av. R2 = 88.7%; Adj. = 84.8%)

–

6/6

4/6

82

90

87

86

(Av. R2 = 85.2%; Adj. = 79.8%)

–

6/6

0/6

87

87

91

89

90

(Av. R2 = 89.5%; Adj. = 85.3%)

–

6/6

0/6

83

83

90

87

96

(Av. R2 = 87.2%; Adj. = 80.2%)

–

6/6

4/6

2

87

19 96 – 20 09 83

89

(Av. R2 = 89.4%)

86

19 85 – 20 05 65

313

12 Unmodified (wo/s-a) 12 Modified (wo/s-a)

T12.2

87

87

87

91

89

90

(Av. R = 88.5%; Adj. = 84.8%)

–

6/6

2/6

T12.2

82

84

84

89

88

88

(Av. R2 = 85.8%; Adj. = 81.8%)

–

6/6

1/6

12 Unmodified (wo/s-a) 12 Modified (wo/s-a)

T12.2

91

89

91

87

87

87

(Av. R2 = 88.7%; Adj. = 86.2%)

–

6/6

5/6

T12.2

88

88

89

83

83

82

(Av. R2 = 85.5%; Adj. = 81.8%)

–

6/6

4/6

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18 **No samples containing “crowd in” decade (1990–1999) data were removed, so no separate results shown

For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 68.3% 2. Baseline standard model with deficit variables added: average R 2 increases to 88.7%, an increase of 30%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects. 3. When the loanable funds (S + FB) variable is added as a deficit modifier to the standard model with deficits, R 2 decreases from (88.7%) to (85.2%), a decrease of (3.5%). As noted in earlier chapters, this suggests that the better formulation is the one which also has a stand-alone loanable funds variable of the same type, which resulted in an increase in R 2 to 90.2% when (S + B) was added. 4. When the (S + FB + M1) is added as a deficit modifier to the standard model with deficits, R 2 decreases from (88.7%) to (87.2%), a decrease of (1.5%), again indicating the model with a stand alone,

314

J. J. HEIM

which saw an increase in R 2 to 89.5% is the better consumption model (though not as good as (S + FB) model. 5. When using the M1 + FR Purchases modifier (M1 + Tr + A), R 2 decreases from (88.5%) to (85.8%) unmodified version. Again, when a stand-alone variable of the same type was included, R 2 was higher (88.7%), but still not as high as the comparable (S + FB) model. 6. When using M1 alone as the offset, R 2 slightly increased using the deficit modifier from 85.5% to 85.8%, but still was 3% below the same model including a stand-alone M1 variable as well. 7. In addition, in all four models, adding the deficit modifier without a stand-alone modifier resulted in a noticeable increase in deficit variables that were significant before modification, becoming statistically insignificant. As we have noted before, theoretically, this should not happen in a good modifier model.

Cptr. 12 Investment Summary Table 3 (S + FB), (S + FB + M1), M1, and (M1 +FR Purchases) Deficit Modifier and Stand-Alone Models Sigif./total

R2 (18 Time periods) Model

From Table#

19 60 – 20 10 69

19 60 – 20 08 67

19 60 – 20 07 66

19 60 – 20 00 63

19 60 – 19 90 65

19 60 – 19 80 72

19 70 – 19 90 −6 1

19 70 – 20 00 56

19 70 – 20 07 65

19 70 – 20 09 72

19 80 – 20 00 69

19 80 – 20 10 77

19 75 – 20 04 −6 4

10 Baseline T10.3C (w/o Def) (Does not include GDP Control Variable) (Av. R2 = 68.3%) 10 Baseline T10.3B 76 70 71 80 78 91 82 81 71 76 81 80 80 (w/o Def) (includes GDP Control Variable) (Av. R2 = 79.8%) 11 Baseline Eq.11.10 89 86 84 89 87 95 90 90 86 90 89 90 89 (w/Def) A (Av. R2 = 89.8% for 18 Samples; Adj. Av. R2 = 86.3) (88.3% for 6 used below) 11 Modified T11.10 91 88 88 90 92 98 (Av. R2 = 91.2%; Adj. R2 = 87.5%) (w/s-a) (S + FB Modifier)** 12 Modified (w/s-a) (S + FB + M1) Modifier**

T12.3

12 Modified (w/s-a) (M1) Modifier**

T12.3

12 Modified (w/s-a) (M1) + (Tr + A) Modifier**

T12.3

89

89

89

87

86

86

86

82

82

88

86

86

87

84

84

95

91

92

(Av. R2 = 88.7%; Adj. = 85.8%)

(Av. R2 = 86.3%; Adj. = 86.2%)

(Av. R2 = 88.7%; Adj. = 86.0%)

19 80 – 20 04 71

19 85 – 20 04 63

19 85 – 20 05 57

19 96 – 20 10 92

20 00 – 20 10 91

81

75

75

93

95

89

89

89

98

98

–

–

–

–

Test ratio T

G

NA

NA

NA NA

NA* NA

NA 11/1 8 8/11

NA* 16/1 8 9/11

1/6

5/6

1/6

5/6*

5/6

6/6

5/6

6/6*

6/6

6/6

6/6

6/6*

6/6

6/6

6/6

6/6*

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18

12

DOES M1 MORE ACCURATELY DEFINE THE EXTENT …

315

**Results for modified and unmodified models were the same for R 2 , coefficients, and t-statistics on all variables except the “stand alone” variable hypothesized as an offset. Hence only one set of deficit variable and R 2 results for each model are shown above

For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 77.7% 2. Baseline standard model with deficit variables added: average R 2 increases to 88.3%, an increase of 14%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects. 3. When the stand-alone loanable funds modifier (S + FB) is added to the standard model with deficits, R 2 increases from (88.8%) to (91.2%), an increase of (2.0%). As noted in earlier chapters, this suggests the true effect of crowd out is better stated as the deficit net of any changes in total loanable funds that occur in the same period. 4. Only one of the other three modifiers (S + FB + M1) explains more variance (R 2 = 88.7) than the standard model with deficit variables (88.3%), and that is less of an increase than obtained using. (S + FB) alone, suggesting that adding M1 to (S + FB) detracts from the explanatory power of the (S + FB) model, i.e. mostly, it just creates an errors in variables problem. It would appear that the effects of a change in M1 is captured when modeling total loanable funds variable itself. 5. When using the M1 + FR Purchases modifier (M1 + Tr + A), R 2 decreases from (88.3%) to (86.5%) compared to the standard model with deficit variables (but without any crowd out offset variable). Essentially, adding M1 + (Tr + A) detracts from the explanatory power of the (S + FB) model, or even the deficit model itself. 6. Even less successful was using M1 alone as the offset. Adding this variable caused R 2 to decline to (85.3%), which is markedly lower than prevailed in the deficit model (88.3%) before any hypothesized crowd out offsets were added. 7. These is one problem complicating the interpretation of the results: Deficits, vary with the phase of the business cycle, as do consumption and investment; so growing deficits are negatively correlated to private spending, and sometimes it is just the business cycle

316

J. J. HEIM

driving the relationship, not intentional deficit creation as a stimulus measure.

Cptr. 12 Investment Summary Table 4 (S + FB), (S + FB + M1), M1, and (M1 +FR Purchases) Deficit Modifiers; (No Stand Alone, GDP Added) Models Sigif./total

R2 (18 Time Periods) Model

10 Baseline (w/o Def)

From Table#

T10.3C

19 60 – 20 10 69

19 60 – 20 08 67

19 60 – 20 07 66

19 60 – 20 00 63

19 60 – 19 90 65

19 60 – 19 80 72

19 19 19 19 19 70 70 70 70 80 – – – – – 19 20 20 20 20 90 00 07 09 00 −6 56 65 72 69 1 (Does not include GDP Control Variable) (Av. R2 = 68.3%) 76 70 71 80 78 91 82 81 71 76 81

19 80 – 20 10 77

19 75 – 20 04 −6 4

19 80 – 20 04 71

19 85 – 20 04 63

19 85 – 20 05 57

19 96 – 20 10 92

20 00 – 20 10 91

NA

NA

NA NA

NA* NA

NA 11/1 8 8/11

NA* 16/1 8 9/11

81

75

75

93

95

90

89

89

89

89

98

98

G

T10.3B

11 Baseline (w/Def)

Eq.11.10 A

11 Unmodified (wo/s-a) 11 Modified (wo/s-a)

T11.11

89

86

84

89

87

95

(Av. R2 = 88.3%; Adj. = 82.8%)

–

5/6

6/6

T11.11

90

87

88

90

91

97

(Av. R2 = 90.5%; Adj. = 84.3%)

–

5/6

4/6

12 Unmodified (wo/s-a) 12 Modified (wo/s-a)

T12.4

84

79

77

88

88

95

(Av. R2 = 85.2%; Adj. = 82.8%)

–

4/6

6/6

T12.4

87

84

87

89

88

96

(Av. R2 = 88.5%; Adj. = 84.5%)

–

1/6

4/6

12 Unmodified (wo/s-a) 12 Modified (wo/s-a)

T12.4

84

79

77

88

88

95

(Av. R2 = 85.2%; Adj. = 82.8%)

–

4/6

6/6

T12.4

81

75

77

82

82

94

(Av. R2 = 81.8%; Adj. = 71.6%)

–

1/6

2/6

12 Unmodified (wo/s-a) 12 Modified (wo/s-a)

T12.4

84

79

77

88

88

95

(Av. R2 = 85.2%; Adj. = 82.8%)

–

4/6

6/6

T12.4

80

78

77

82

82

94

(Av. R2 = 82.2%; Adj. = 72.3%)

–

1/6

1/6

89

80

T

10 Baseline (w/o Def)

(includes GDP Control Variable) (Av. R2 = 79.8%) 89 86 84 89 87 95 90 90 86 90

80

Test ratio

(Av. R2 = 91.2% for 18 samples; 88.3% for 6 used below)

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18 **No samples containing “crowd in” decade (1990–1999) data were removed, so no separate results shown

For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 77.7% 2. Baseline standard model with deficit variables added: average R 2 increases to 88.3%, an increase of 14%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects.

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3. When the loanable funds (S + FB) variable is added as a deficit modifier to the standard model with deficits (but no stand-alone variable), R 2 increases from (88.3%) to (90.5%), a decrease of (2.2%). This is a slightly better result than obtained with the same model, but including a stand-alone (S + FB) variable (90.3%). 4. When the (S + FB + M1) is added as a deficit modifier to the standard model with deficits, R 2 increases from (85.2%) to (88.5%), a increase of (3.3%), but still less than the (S + FB) only model. The same model with a stand alone, saw an increase in R 2 to 88.7%, a slightly better result (but including a stand alone without theoretical justification). 5. When using the M1 + FR Purchases modifier (M1 + Tr + A), R 2 decreases from (85.1%) in its unmodified version to (82.3%) in the modified version, both less than the 86.3% achieved when also including a stand-alone modifier of the same type, but worse than obtained in either of the two models above using the (S + FB) modifier. 6. When using M1 alone as the offset, R 2 decreased using the deficit modifier from 85.1 to 82.2%, but still was 3% below the same model including a stand-alone M1 variable as well. 7. Essentially, adding one of the two modifiers including total loanable funds (S + FB), increased the model’s explanatory power, indicating changes in (S + FB) can offset crowd out. For the two models with an M1 component in the modifier, but no (S + FB) component, adding the M1-based modifier to the deficit variables reduced the models’ ability to explain variance, i.e., ceteris paribus, changes in M1 do not affect the level of total investment. 8. In addition, the (S + FB) model had the highest number of significant deficit variable(crowd out) effects after modification in the six-time periods tested, which was the expected finding. As we have noted before, theoretically, this should happen in a good modifier model. The loanable funds variable proved to be a better measure of how much crowd out could be reduced than M1.

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Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

PART VII

Exogenous Increases in Loanable Funds (Fr Security Purchases): Effects on Crowd Out

CHAPTER 13

Alternate Ways of Modeling How Deficit Variables Modified by Accommodative Monetary Policy Reduce Crowd Out (Bernanke, Mankiw Definitions of Accommodative Monetary Policy)

The Federal Reserve (FR) practices “accommodative” monetary policy to offset the crowd out effects of deficits through open market purchases of government securities, or even if there is no deficit, just when it wants to help stimulate the economy, increasing the pool of loanable funds. When deficit-financed government fiscal stimulus programs are undertaken, financing the deficit reduces the portion of the pool of loanable funds available to others, and by doing so, crowds out private borrowing and spending. “Accommodative” monetary policy involves the US Federal Reserve (FR) open market operations designed to increase the loanable funds pool to the amount previously available to private borrowers but now unavailable. Accommodative monetary policy involves purchases of treasury securities, government agency securities, and mortgage backed securities (“Tr + A”). FR purchases of such securities from banks increase the banks’ excess reserves, i.e., their loanable funds, and thereby increases the total pool of loanable funds (LF). These purchases provide banks with the additional reserves allowing them to increase lending for purchases of homes, cars, machinery, or other real goods and services. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_13

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To have the desired effect, the banks the FR buys government securities from must be banks which make loans that stimulate the real economy, i.e., loans to customers intending to use them to buy housing, cars, machinery, factory construction, or other real goods and services included in the GDP. FR purchases from banks that sell one set of securities in order to enable their seller to purchase others, or to finance corporate takeovers do not meet this criterion in any direct way. They may have some later positive impact on the real economy, but that is hard to document and should be considered a hypothesis, not a fact. This implies FR open market purchases of securities should be only be from banks (or non-bank lenders) like commercial and savings banks which loan money in the retail markets. These are the markets that people and businesses use to borrow money to purchase real economic goods and services, items entering the GDP and therefore affecting unemployment levels. Where does fiscal policy fit into all this? One widely held school of thought since Keynes’ time argues that deficit-financed fiscal programs, involving either tax cuts or increased government spending, will increase aggregate demand, thereby stimulating the economy. To determine how much of a fiscal stimulus will result, we must calculate the expected stimulus , and then reduce it by any crowd out effects drawing down the pool of loanable funds to finance the deficit may cause. Empirical testing in Chapters 10 and 11 of this study shows crowd out effects can be offset before they can be felt by offsetting increases in the loanable funds pool during the deficit-incurring period. FR purchases of securities in the open market is one way increases in the pool of loanable funds can be brought about. These increases can restore the loanable funds pool available for private borrowing by consumers and businesses to pre-deficit size, thereby neutralizing the crowd out effect before it can be felt. This is accommodative monetary policy. Former FR Chair Ben Bernanke discussed the effects of such FR security purchases on private sector borrowing this way: …Conventional monetary policy easing works by lowering market expectations for the future path of short-term interest rates, which, in turn, reduces the current level of longer-term interest rates and contributes to an easing in broader financial conditions. These changes, by reducing borrowing costs and raising asset prices, bolster household and business spending and thus increase economic activity…. (Bernanke 2011)

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Bernanke argued the problem was lack of demand for loans, and that one way to increase it is to lower interest rates by buying up securities. But the near non-existence of excess reserves in the banking system every year from 1960 to 2007 suggests the problem was not lack of demand, but lack of supply, i.e., lack of loanable funds. FR securities purchases can solve that by increasing the size of the pool (while at the same time lowering interest rates). But again, the data on how small the pool of excess reserves is each year 1960–2007 suggests the problem is not lack of demand, it is lack of supply, i.e., a shortage of loanable funds). Mankiw (2010) also discusses the effect of FR monetary policy to offset the negative effects of a Keynesian fiscal stimulus on the interest rate: …One assumption about monetary policy is that the Fed keeps the nominal interest rate constant. That is, when fiscal policy shifts the IS curve to the right…the Fed adjusts the money supply to shift the LM curve in the same direction. Because there is no crowding out of investment due to a changing interest rate, the fiscal policy multipliers are similar to those from the Keynesian cross…. (Mankiw 2010, Chapter 11)

Keynesian fiscal stimulus programs traditionally have been deficit financed to ensure they result in an increase in total demand. The need to finance the deficit increases the demand for loanable funds from pre-deficit period levels. This increase in demand relative to supply is seen by the FR (perhaps by observing rising interest rates, further decline in excess reserve levels, etc.). Though the FR can affect the pool exogenously, the largest changes in the loanable funds pool historically have been endogenous changes resulting from the growth or decline of the economy’s effect on national savings. A rising economy increases national savings, much of which gets deposited in banks, increasing banks’ loanable reserves. Increased foreign borrowing in response to economic conditions also increases the pool. Hence, most of the up and down movement in the pool of loanable funds goes on in response to economic conditions, not FR open market actions. Endogenous growth in the pool can provide a second way of offsetting the negative effects of crowd out.

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13.1 Effects of FR Securities Purchases on Consumption To obtain the most accurate possible estimates of the crowd out effects of the deficit, and how any changes in loanable funds affect crowd out, we control for the effects of the other variables that affect consumption to avoid over or underestimating our estimates of crowd out effects. As noted earlier, Heim (2017) exhaustively studied the issue of what variables could be robustly said to be the determinants of consumption. This process is described in the consumption section of Chapter 9 and in the methodology chapter (Chapter 3). The variables found to systematically affect consumption include those in the following list. If lagged values are used in the models tested, subscripts denote the lag level: current year values have no subscript. Data were taken from the tables cited in the Economic Report of the President (ERP) 2012 and for various other years. Dependent Variable—Consumption Model C D = Total consumption—(Total imports—Capital goods, Industrial supplies, and materials) (ERP Tables B2, 104) Explanatory Variables—Consumption Model (Y − T ) = Disposable income (ERP B2, B83) (T − G) = the consolidated deficit for all US governmental entities taken collectively (ERP B83) T = Deficits generated by tax or other revenue cuts (our initial measure of crowd out caused by tax cuts) (ERP B83) G = Deficits generated by total government spending on goods, services, and transfers (our initial measure of crowd out caused by spending deficits) (ERP B83) S = Gross US saving = personal, + corporate + depreciation + government) (ERP B32) FB = Foreign Borrowing (ERP B32) PR = the Prime interest rate (ERP B73) DJ−2 = Wealth measure; NYSE composite average lagged two years (ERP B95) POP20/65 = Ratio of those 20–24 to those 65 or older in the population (ERP B34) POP = US population (ERP B34) M2−2−4 = M2 money supply (or M2 − M1 component): a measure of recent year (liquid) saving history (ERP B69)

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C B = Consumer borrowing (FR Flow of Funds Accounts:  Consumer Debt) (Tr + A) = FR purchases of treasury, agency, or mortgage backed securities (Table 10.6). In previous studies (Heim 2017) all these variables, except (Tr + A), which was not included in the earlier studies, were found statistically significant and robust to different time periods tested and robust to addition or subtraction of certain other variables in the model. The effect of savings and foreign borrowing variables (S + FB), or total loanable funds (LF), was only tested as a modification of the (T ) and (G) variables used to measure crowd out, and not as a stand alone in Heim (2017). The effects of these (S and FB) variables were tested in Cptrs. 16-18 above, and are considered the better way to model the loanable funds pool, since (Tr + A) is only a part of the total pool. In those earlier chapters, we tested whether growth in the total pool of loanable funds (S + FB) could modify the negative effects of the deficit on crowd out. In this chapter, we test the hypothesis that a limited portion of the total loanable funds pool, the exogenous part of the pool, namely, FR open market securities purchases (Tr + A), is the only part of loanable funds pool that actually offsets crowd out effects of (T) and (G) deficits . Results are presented in Table 13.1. We shall also test it as a stand-alone source Table 13.1 Results of different consumption models of the effects of FR purchases on crowd out (1960–2010 data sample) Variable

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

T Def :

.32 (6.6)

.32 (4.5)

.29 (4.8)

.25 (4.2)

.36 (8.9)

G Def :

−.16 (−2.0)

+.39 (7.1)

.10 (2.0)

−.04 (−0.5) −.09 (−2.2) .14 (3.7)

−.18 (−2.2)

.09 (3.9)

−.11 (−1.4) −.45 (−4.3) .12 (3.3)

.03 (3.6)

R 2 = .87

R 2 = .82

R 2 = .87

R 2 = .87

R 2 = .85

2 = RAdj .84

2 = .78 RAdj

2 = RAdj .85

2 = RAdj .84

2 = RAdj .82

.25 (4.6) −.04 (−0.5) −.23 (−3.2) .14 (3.7) R2 = .87 2 = RAdj .84

Tr + A C B:

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of funds for offsetting crowd out. In other words, we test the hypothesis that the total pool of loanable funds (S + FB) is just an oversized proxy for the changes in one component of this total that makes a difference: (Tr + A). We will refer to the model above (exclusive of the FR securities purchases) the standard consumption model because it contains the variables identified by economists most frequently as determinants of consumption. This model’s parameters were estimated in Chapter 11, and parameter estimates were presented in Eq. 11.1 above, and are repeated here: CD = .32(Y − TT ) + .31(TT ) − .16(G T&I ) − 7.17PR + .50DJ−2 (t=)

(6.6)

(6.6)

(−2.0)

(−3.2)

(4.5)

− .462.21POP16/65 + .016POP + 35.87M2AV + .09 CB2 (3.7)

(−2.5)

(3.8)

(3.9)

R = 86.7% D.W. = 2.1 MSE = 26.04 2

(11.1)

The same model, without the deficit (crowd out) variables explains a lot less variance (60.3%), indicating that without some kind of effective offset, consumer crowd out is a significant problem (see Eq. 10.1A.A) This consumption model, with deficit variables, will be used as the base model, to which will be added a variable measuring FR securities purchases: (Tr + A). This allows systematic examination and testing of whether changes in loanable funds due to FR securities purchases (Tr + A) mitigate crowd out effects, and if so, determine the actual mechanism through which this occurs. Inclusion of the other variables as controls helps ensure we do not mistake the effects of other variables on consumption, variables which may in part be correlated with (Tr + A), with the effects of (Tr + A) itself, i.e., no “left out” variables problem of the type discussed by Goldberger (1961) when analyzing the deficiencies of stepwise multiple regression. There are six alternative ways of adding to Eq. 11.1 above to show how crowd out is affected by the amount of FR security purchases in the same period. They include adding it as a stand-alone variable, a deficit variable modifier, a consumer borrowing modifier, or various combinations of those choices. Results of testing these alternatives are shown in Table 13.1. The theory justifying any such modification of the standard model might be that any change in the total loanable funds pool can

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result from the FR’s purchases of securities (exogenous sources), or from endogenous sources (fluctuations in economic conditions). In Table 13.1, we will examine the effect of FR security purchases on consumption without including the stand-alone total loanable funds variable (S + FB) as a control variable. We seek to determine if (S + FB) is just an imperfect proxy for just one of its components: FR open market security purchases, or (Tr + A). If (S + FB) is just an imperfect proxy for (Tr + A), the (Tr + A) model should better explain the data than the full (S + FB) model (Chapter 11). R 2 should be higher than for Chapter 11 models, and increased statistical significance levels should be seen in the (Tr + A)–modified deficit (crowd out) variables compared to Chapter 11, now that the real deficit offsetting effect (Tr + A) is clearly specified, and not simply a somewhat obfuscated part of another variable (S + FB). Using only (Tr + A) should eliminate an “errors in variables” problem of using (S + FB) if it is just an imperfect proxy for (Tr + A)). In Table 13.1, we will test for crowd out and loanable funds effects on the standard model in six different ways: (1) The deficit will be tested unmodified by the effects of changes in loanable funds. This is test #1, Results indicate that both tax and spending deficits create statistically significant crowd out problems, consistent with our findings for the same model in Chapter 18. A dollar’s deficit caused by tax cuts in the standard model yields a 32 cent reduction in consumer spending; the reduction per dollar of spending deficit is 16 cents. Both reductions are statistically significant. (These are only the effects of deficits on consumption. The same deficits will also have additional crowd out effects on investment, as shown further below); (2) Test 2 modifies test 1 by using changes in FR security purchases (Tr + A) directly to modify the measures of tax cut crowd out and spending deficit crowd out we use: they now become T + (Tr + A) and G − (Tr + A). No separate, stand-alone (TR + A) variable is added. The results indicate the marginal effect of tax cut deficits stays unchanged at 32 cent per dollar of (Tr + A modified) tax cut deficit, and highly statistically significant. For government spending deficits, the FR security purchases appears to more than eliminate the crowd out effect leaving a significant net positive stimulus effect

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of 39 cents. Statistical significance for the tax cut deficit variable declines, but increases for the spending deficit variable. R 2 declines markedly from 87 to 82%, suggesting the model #1 formulation of crowd out effects, measured as (T ) and (G) in unmodified form, gives a more accurate picture of the magnitude of true crowd out effects on consumption than does the a crowd out magnitude measured as (T ) or (G) modified by (Tr + A). Results do suggest that FR purchases may more effective reducers of spending crowd out than tax cut crowd out. (3) Same as the test #2 model, except a separate stand-alone FR purchases variable is added to the model, and the FR securities purchase modifier from the Tax (T ) and spending (G) deficit variables is removed. Doing so lowers the net tax deficit crowd out effect slightly from +.32 (t = 4.5) to .25 (t = 4.2). It turns the government spending deficit crowd out effect from +.39 (t = 6.0) to −.04 (t = −0.5). R 2 grows compared to model #2, but only returns to the same (.87) as in the unmodified model #1. The coefficient and t-statistic on the FR purchases stand-alone variable indicate increased FR purchases has a slight net negative effect on consumption: −.07 (t = 2.2), though it is not clear why since the model controls for the state of the economy through its disposable income control variable, and increases in the loanable funds pool resulting increasing FR purchases do not require reductions in the marginal propensity to consume as do increases in total loanable funds (S + FB) stemming from shifting income from consumption to savings. (4) We then tested the standard model with the FR securities purchase variable included as both a separate variable, and as a modifier of the crowd out variables (T , G). Estimated net crowd out effects rise slightly compared to model #3: .29 (t = 4.8) for tax cut deficits, and now have the negative sign expected in crowd out theory for government spending deficits: −.11 (t = −1.4). Significance levels for both increase, but not enough to make the spending deficit significant. The coefficient on the effect of the stand-alone FR purchases variable on consumption was −.45 (t = −4.3). This, of course, suggests there is a large positive effect on consumption of FR purchases by modifying the deficit variables (T ) and (G), but a slightly larger negative effect on consumption spending associated with this exogenous change in loanable funds, though the

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reason for this negative effect remains unclear. It may simply be that FR purchases are systematically countercyclical; it is win trying to fight off economic decline that the FR is most likely to increase FR purchases. The net effect of these two offsetting influences is identical to that given in Model #3 where we use only a stand-alone (Tr + A) variable. R 2 also remains the same as in Models #1 and #3: 87%. (5) We then switch the hypothesized channel through which increases in FR purchases of securities mitigate the crowd out problem. The new model increases the size of consumer borrowing variable from (C B ) to (C B + (Tr + A)). No separate stand-alone FR purchases variable was used. The estimated crowd out effects for this model are .36 (t = 8.9) for tax deficits, and −.18 (t = 4.2) for spending deficits. This is about the same as in Model #1, where there was no variable for FR purchases’ included, either as a stand alone, or as a modifier to the deficit variables. The statistical significance of the borrowing variable stayed about the same. R 2 dropped slightly to .85 compared to models 1, 3 and 4. Finally, (6) The test #5 model is repeated, except we add (Tr + A) as a standalone variable as well as include it in the consumer borrowing (C B ) variable. The coefficient and significance of the consumer borrowing variable, is more than restored (.14) with (t = 3.7) compared to those in models 1–4. Both the tax and spending variables again become statistically significant, with the theoretically expected sign. The coefficient and (significant) statistic on the stand-alone FR purchases variable were (−.24) (t = −3.2) The negative sign and significance of the FR purchases variable is similar to what was found in models #3 and #4. The tax deficit remains significant, the spending deficit returns to insignificance and R 2 grows compared to model #5, but still only equals the explanatory power of model #1, which hypothesized that changes in (Tr + A) had no effect on crowd out effects. Overall, these tests suggest FR efforts to stimulate the economy by increased purchases of securities do not affect consumer spending significantly. None of the models see R 2 increase when (TR + A) is added, and one declines. This may be because FR purchases do not significantly affect crowd out because historically 1960–2007 they have only been 1/8–2/4

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the size of the deficit. Or it may mean that the proceeds of security sales to the FR are channeled into either investment (which we test below), or other security purchases, which we do not test, and which would not affect consumption. Hence, the unmodified model would seem to be preferred because significance levels on the variables of interest are generally, but not always, higher, the model is simpler (Occam’s razor), and the unmodified model explains as much variance in consumption as the highest R 2 modified models. Putting it another way, adding only the Federal Reserve securities purchases part of total loanable funds does not increase the explanatory power of the consumption model. The limitation of the FR purchases modification models used in Table 13.1 is that they only examine the effect changes in the loanable funds pool caused by changes in the level of FR securities purchases. This may be the reason why it fails to outperform the model without any loanable funds variable. Other factors may also cause the loanable funds pool to change, namely, changes in economic conditions that vary personal and business income. This affects the national savings part of total loanable funds, since part of income changes is saved. These endogenous changes, historically, until the QE period, had by far the bigger effect on the yearly changes in loanable funds. Our Chapter 11 results did indicate that models with full (S + LF) modifiers did explain consumption behavior better than models without modifiers (better in terms of R 2 ; significance level results for the deficit variables were mixed). By retesting Table 13.1 models above, but including an additional, stand alone variable (S + FB) that controls for changes in the total loanable funds pool, is one way we can test whether the traditional definition of the pool of loanable funds, adequately capture the contribution of FR securities purchases in offsetting crowd out effects, or whether the additional variable, FR securities purchases (Tr + A), is also needed. Results are presented in Table 13.2. All the variables in the models in Table 13.2 were tested for stationarity and endogeneity with the dependent variable. All were found stationary except the dependent variable and the government spending variable, which were detrended. No endogeneity was found except for the government spending variable in Model 5. A Wald-strong instrument was substituted for it, and the instrument was found non-endogenous using the Sargan endogeneity test. Newey–West standard errors were used to address heteroskedasticity problems.

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Table 13.2 Results of different consumption models of the effects of loanable funds on crowd out Variable

Model 1

Model 2

Model 3

Model 4

Model 5

T Def :

.26 (4.2)

.19 (3.0)

.33 (6.2)

.33 (6.2)

.48 (8.2)

G Def :

.29 (4.2)

.26 (4.2)

S + FB + TR + A: C B:

.11 (1.9) .13 (2.7)

.14 (3.0)

R 2 = .80

R 2 = .82

2 = RAdj .76

2 = RAdj .77

Model 6

.35 (8.9) −.13 (1.8) −.13 (1.8) −.27 (2.9) −.15 (1.9) −.52 (5.3) −.06 −.17 (4.4) (−3.2) .13 (4.2) .13 (4.2) .04 (4.0) .02 (2.0) R 2 = .88 R 2 = .88 R 2 = .86 R 2 = .84 2 = 2 = 2 = 2 = RAdj RAdj RAdj RAdj .83 .80 .85.7 .85.8

Table 13.2, we will modify crowd out effects in the standard consumption model in several ways: (1) Model 1 modifies the deficit variables (T , G) with changes in loanable funds due to changes in national savings or foreign borrowing (S + FB), and changes due to changes in FR purchases of treasury or agency securities (Tr + A). These two separate variables are added directly to earlier measures of tax cut crowd out (T ) to give (T + (S + FB) + (Tr + A)) as our modified crowd out variable for tax cuts. We add these modifiers because changes in taxes which decrease taxes, increasing the deficit, have a negative sign. An increase in loanable funds reduces part or all of negative value of the change in total taxes, thereby reducing our estimate of the crowd out effect of tax cut deficits. The changes are subtracted from spending deficits G − (S + FB) − (Tr + A)) because they offset a deficit caused by a positive change in spending. These modified deficit variables become our variables measuring the crowd out effect of deficits net of loanable funds changes. In Model 1 there is no stand-alone variable for (S + FB) + (Tr + A), only deficit variables modified by this amount. Results indicate that after reducing the size of tax cut deficits by this amount, tax

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deficit crowd out effects still exist and are statistically significant: .26 (t = 4.3). However, spending crowd out effects disappear and become positive .29 (t = 4.2), a result similar to that obtained for the same model in Table 13.1. R 2 drops substantially to (.80). Both the R 2 and significance levels are below Table 13.1 model #2 of the same type. Hence it does not seem that adding total loanable funds to a model that already has the FR purchases portion increases its explanatory power, or the make the crowd out variables more statistically significant. The same model in Table 11.1, which used only (S + FB) as the modifier, also had lower R 2 and t-statistics on crowd out variables than did our earlier Table 13.1 model which used only FR purchases as a modifier. That said, recall from Table 13.1 that the coefficient and t-statistic for the unmodified tax cut crowd out variable was .32 (4.5) and for spending deficits was −.16 (2.2) and R 2 was .87, This unmodified model was better at explaining the data than the models that included a modifier on the crowd out variables, but no stand-alone modifier variable. (2) Model 2 replicates Model 1 with one addition: it adds (S + FB) as a separate variable to reflect the fact that, ceteris paribus, increases in saving have a negative effect on consumption. By this we mean holding disposable income constant (as the regression process does in estimating the specific effects of other variables), savings increases definitionally must reduce consumption. The separate (S + FB) variable, which prior evidence suggests affects consumption, is included to most accurately explain how the economy works, and maximize the model’s ability to explain consumption. Net tax cut crowd out variable effects are .19 (t = 3.0); net spending crowd out effects are +.26 (t = 4.2). R 2 = .82. These are noticeably lower than the comparable R 2 and t-statistics for the completely unmodified crowd out variable model with no separate (S + FB) variable (Model 1), and for the more comparable Model 3 in Table 10.1. Overall, this model seems less attractive than the comparable models from Tables 11.1 or 13.1, and less attractive than even the completely unmodified, no separate variable model in Table 13.1. (3) Model 3 repeats model two, except it adds a second (Tr + A) stand-alone loanable funds variable to (S + FB) included in Model 2. That said, we need a theory to justify using FR simulative policy

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(Tr + A) as a second separate influence, beside loanable funds, warranting including it as a separate part of the stand-alone variable. One theory might be that (TR + A), though it increases loanable funds, does not necessarily increase (S + FB), which is our traditional definition of the pool of loanable funds. Or we could argue that (TR + A) is included in (S + FB), but has a different impact on crowd out than other components. Hence, separately adding it as a modifier in addition to (S + FB) allows us to statistically estimate the additional effect. Adding the second stand-alone variable (Tr + A) this improves the R 2 slightly (.88) compared to model 3 in Table 13.1, and increases the significance of the tax cut crowd out variable: .33 (t = 6.2). It also switches the sign on the spending crowd out variable from positive to negative and leaves it significant −.13 (−1.8), which is more consistent with crowd out theory. In Table 10.1 it was insignificant, and in Table 11.1 it had a much larger negative coefficient and was highly statistically significant. Overall, the results suggest this model is slightly better than the comparable model (3) from Table 13.1, but less desirable than the comparable model (3) from Table 11.1, which used only (S + FB) as the modifier and has a higher R 2 . It has about the same explanatory power for the deficit variables and the whole model as the completely unmodified Model #1 from Tables 10.1 and 11.1. (4) Model #4 deletes the (S + FB) + (Tr + A) offsets from the (T ) and (G) deficit variables, but continues to include them as a single separate variable. Test results indicate both tax cut and spending deficit variables continue to have the same statistically significant crowd out effects and R 2 , as in the prior model (Model #3). Hence, our conclusions for model #3 hold for Model #4 as well: overall, the results suggest this model is slightly better than the comparable model (#3) from Table 10.1, but considerably less desirable than the comparable model (#3) from Table 11.1, which used only (S + FB) as the modifier. It has about the same explanatory power for the deficit variables and the whole model as the completely unmodified Model #1 from Tables 10.1 and 9.1. (5) Model#5 drops the loanable funds (S + FB) and accommodative monetary policy (Tr +A) modifiers from the crowd out variables, leaving (T ) and (G) alone as measures of crowd out. It adds the modifiers to the consumer borrowing variable (C B ) to explore

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another possible channel through which increases in loanable funds might influence consumption. The (S + FB) + (Tr + A) variable is left in the model as a separate variable as well. The net estimated crowd out effects for tax deficits becomes .48 (t = 8.2) and for spending deficits becomes −.27 (t = 2.9). R 2 is .86. The comparable models in Tables 10.1 and 11.1 is Model #6. This model #5 has stronger t-statistics on the deficit variables, but a slightly lower R 2 than the comparable Table 10.1 model. Model #6 from Table 9.1 explains three percent more variance and has a higher t-statistic on the government spending deficit variable. The tax variable significance level in this model is higher than in Table 9.1 model, but that model’s tax variable was highly significant also. These results suggest that Model 5, is also a reasonably successful way of modeling the effects of crowd out, though its Table 9.1 counterpart might still be preferred because it explains more of the variance in consumption (higher R 2 ) and has roughly equally high significance levels for the deficit variables. (6) Finally, we retested the “switched” Model 5, but without the standalone variable (S + FB) + (Tr + A). The net tax cut crowd out crowd out variable’s significance level increased from .48 (t = 8.2) to .36 (t = 8.9) and the significance level for government spending deficit declined from −27 (2.9) to −.16 (1.9). R 2 dropped to .84. Overall, this model does not seem to have the explanatory power of Model #5, in this Table, and is also inferior to the comparable model in Table 10.1. The comparable Table 9.1 model, has lower t-statistics but a higher R 2 than this model. Hence, we generally conclude the Chapter 11 approach of using only (S + FB) as a crowd out modifier is a better way is a better way of capturing the extent to which increases in loanable funds can modify crowd out problems than are this chapter approaches of either using FR securities purchases (Tr + A) alone, or in combination with the total loanable funds variable. Table 13.3 summarizes the key results obtained in Tables 11.1, 13.1, and 13.2. Modeling numbers can differ between Tables for the same type of model. The column header describes the type of model whose results are being reported. Table 13.3 headers use model numbers from Table 13.1 along with a brief description of the modifier used. Results from Tables 13.1 and 13.2 are listed under the column that describes the

.80

R2:

G:

−.13 9 (−1.8)

.26 (4.2) & −.13 (−1.8)a .82 & .88a 2 = 86.2 RAdj

.88

.35 (8.9)

87 2 = 84 RAdj

.29 (4.8) −.11 (−1.4)

.89 2 = 86.2 RAdj

.44 (6.8) −.25 (−3.3)

Model #4

Only Sd. Alone

.33 (6.2)

87 2 = 85. RAdj

82 2 = .84 RAdj .19 (3.0) & .33 (6.2)a .29 (4.2)

.25 (4.2) −.04 (−0.5)

.89 2 = 86.2 RAdj

.81 2 = .77 RAdj .32 (4.5) .39 (7.1)

.44 (6.8) −.25 (−3.3)

Def Mod & Sd. Alone Model #3

.14 (2.2) −.04 (−0.4)

T : .26 (4.2)

T : .32 (6.6) G: −.16 (−6.6) R 2 : .87 2 = .84 RAdj

T : .32 (6.6) G: −.16 (−6.6) R 2 : .87 2 = .84 RAdj

Model #2

Only Def Mod.

.84

−.15 (−1.9)

.48 (8.2)

85 2 = .82 RAdj

.36 (8.9) −.18 (−2.2)

.85 2 = .82 RAdj

.30 (5.3) −.12 (−1.5)

Model #5

Only CB Mod

.86

−.27 (−2.9)

87 2 = .84 RAdj

.25 (4.6) −.04 (−.05)

.89 2 = 86.2 RAdj

.43 (6.8) −.25 (3.3)

CB Mod & St. Alone Model #6

models

a Statistics for both Models #2 + #3 in Table 13.2 are those described at the top of this column. Only the stand-alone variables differ in those two

Table 13.2 (S + FB) + (Tr + A)

Table 13.1 (Tr + A) Mod.

Table 11.1 (S + FB Mod)

Modifier:

Totally Unmodified Model #1

Table 13.3 Statistical results for consumption crowd out models using different modifiers β (t-statistic), R 2 (1960– 2010 data sample only)

13 ALTERNATE WAYS OF MODELING HOW DEFICIT VARIABLES …

335

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J. J. HEIM

modifier used, regardless of what its model number is in Tables 13.1 and 13.2. For example, the results from Table 13.2 listed here in the column labeled “Model 2” are identified as “Model #1” results in Table 13.2, but use the modifier described here as the “Model #2” modifier. Overall, The Chapter 11 (S + B) consumption models had 3 R 2 s higher and 2 the same as this chapter (Tr + A) models, and these (Tr + A) models had higher R 2 s than the (S + FB + TR + A) models from this chapter. We conclude that the Chapter 11 total loanable funds modifier (S + FB) models best explains the variation in consumption that results from crowd out, and that using just FR security purchases (Tr + A) or that and (S + FB) explain less of the variation in consumption that resulted from crowd out.

13.2 Summary of Results and Conclusions for Chapter 13 The table summarizes the results and conclusions of tests of the hypothesis that it may only be the portion of changes in loanable funds attributable to FR actions that can offset the effects of crowd out on consumer spending. The conclusions are a little ambiguous: modifying the deficit variables shows no effect; but modifying the consumer borrowing by the amount of FR purchases does increase our ability to explain variation in consumer spending. This might be considered the preferred model, since it shows the structural mechanism (augmenting consumer borrowing) through which FR purchases serves to offset the effects of crowd out on consumption.

T13.1A

T13.3

T13.3

13 Unmodified (wo/s-a)

13 Def. Modified (wo/s-a)

13 CBor Modified (wo/s-a)

91

93

19 70 – 19 90 91 92

19 70 – 20 00 91

85

82

87

87

87

87

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

– – –

–

–

–

–

–

–

–

–

86

19 70 – 20 07 68

–

–

–

–

–

–

–

–

88

19 70 – 20 10 55

–

–

–

–

–

–

–

–

94

19 80 – 20 00 86

–

–

–

–

–

–

–

–

85

19 80 – 20 10 37

–

–

–

–

–

–

–

–

88

19 75 – 20 04 63

– – –

– – – – – – –

–

–

–

–

–

86

19 85 – 20 04 67

–

–

–

–

–

88

19 80 – 20 04 74

–

–

–

–

–

–

–

–

87

19 85 – 20 05 65

–

–

–

–

–

–

–

–

92

19 96 – 20 09 83

–

–

–

–

–

–

–

–

99

19 00 – 20 10 95

1/1

1/1 1/1

1/1 1/1

1/1 1/1

1/1 1/1

1/1*

1/1* 1/1

1/1* 1/1

1/1* 1/1

0/1* 1/1

0/1* 0/1

1/1 1/1

1/1 1/1

1/1 1/1

0/1

5/5*) 1/1

(5/5 1/1

1/1

5/11*

NA* 6/18*

NA

G

10/11

NA 15/18

NA

T

Test ratio

ALTERNATE WAYS OF MODELING HOW DEFICIT VARIABLES …

*No sample(s) with as much as 1/3 to 1/2 1990s data tested, so no change in results by dropping them

T13.3

T13.3

13 CBor Modified (w/s-a)

T11.1

11 Baseline Total LF Model (w/def. mod.& s-a) 13 Unmodified (w/s-a)

T13.3

87

T11.1A

11 Baseline (w/Def)

13 Def. Modified (w/s-a)

90

Eq.11.1A

11 Baseline (w/Def)

2

19 60 – 19 80 77

(Av. R2 = 89.4%; 0.87 for one period used below)

T11.1AA

11 Baseline (wo/Def) 89

19 60 – 20 07 72

(Av. R = 71.4%) 87 87 87 91

19 60 – 20 08 72 19 60 – 19 90 43

From Table#

Model

19 60 – 20 00 86

19 60 – 20 10 60

Cptr. 13 Consumption Summary Table (Tr+A) Deficit Modifier and (Tr + A) Stand-Alone Variable Models 13

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J. J. HEIM

For the one period tested (1960–2010): 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 =60%. 2. Baseline standard model with deficit variables added: average R 2 increases to 87%, an increase of 45%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects. 3. When the stand-alone loanable funds modifier (Tr + A) is added to the standard model with deficits, R 2 stays the same (87%). 4. Also Modifying the deficit by FR Purchases (Tr + A), while continuing to include the separate control variable for growth in exogenous loanable funds (Tr + A) again leaves R 2 unchanged. This suggests that over the 50 year sample period as a whole, FR purchases have not provided any significant offset to deficitgenerated crowd out. 5. By comparison, if we modifier (Tr + A) as a stand alone and a modifier of consumer borrowing, rather than the deficit variables, R 2 increases 2–89%, suggesting this may be a better way of modeling the crowd out offsetting effects of FR purchases. 6. For models without a stand-alone (TR + A) variable, R 2 declines noticeably when the baseline model is changed by modifying the deficit variables (82%), or the consumer borrowing variable (85%), making models without a stand-alone loanable funds variable the less preferred models.

References Bernanke, B. (2011, February 9). The Economic Outlook and Monetary and Fiscal Policy. Testimony before the Committee on the Budget. U.S. House of Representatives. Available at https://www.realclearpolitics.com/articles/2011/02/ 09/the_economic_outlook_and_monetary_and_fiscal_policy_108845.html. Economic Report of the President. (2018, 2012, 2013, 2010). Washington, DC: Government Publications Office. Goldberger, A. S. (1961, December). Stepwise Least Squares: Residual Analysis and Specification Error. Journal of the American Statistical Association, LVI, 998–1000. Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan. Mankiw, N. G. (2010). Macroeconomics (7th ed.). New York: Worth Publishers. Chapter 11.

CHAPTER 14

Does Modification of the Single Variable Deficit (T − G) by FR Purchases Better Measure Crowd Out, Controlling for Endogenous Loanable Funds Growth?

Equation 14.1 presents results for all variables in the standard consumption model using the single deficit variable (T − G) alone to define crowd out effects. This is done without the (Tr + A) modification to the deficit. In Eq. 14.2, the model is reestimated, with the crowd out variable defined as the deficit modified by FR securities purchases: (T − G) + (Tr + A). Both models contain a separate stand-alone variable to the regression to capture all other changes in loanable funds, namely (S + FB) – (Tr + A). This is done to ensure that (this definition of) other loanable funds effects are held constant when the effects of the deficit variable (with or without modification) on consumption are tested. In addition, a baseline model (BL) is also shown as Eq. 14.1A. This is identical to Eqs. 14.1 and 14.2. Except it has no stand-alone loanable funds variable, and no deficit modifying (Tr + A) variable. The deficit variables, with and without modification were found to be stationary (ADF test), and not endogenous with the dependent variable (Hausman test). For comparison the standard consumption model from the Heim (2017) large scale econometric model is presented. The Heim (2017) model differs from Eqs. 14.1 and 14.2 in that the deficit is divided into two variables (T , G), and coefficients for each type of deficit

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_14

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J. J. HEIM

effect are estimated separately, holding the other constant. Nonetheless, the average of the two coefficients is close to the single Eq. 14.1 coefficient estimated for (T − G). There are other differences because in Heim (2017). 1. There is no control variable ((S + FB) − (Tr + A)) for other factors influencing the pool of loanable funds, and 2. The modifier of T , and G for offsetting effects of changes in the loanable funds pool is somewhat different and less accurate a measure of the loanable funds effect. The Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT )− .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07POP16/65 + .020POP + 38.00M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

(3.7)

(4.9)

D.W. = 2.2

SE = 24.88 (4.4.TR)

This study’s baseline (=bl) standard consumption model with no deficit variables included, nor any loanable funds variables included (1960–2010 data:) (2SLS—strong inst. For (Y − T )) CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

(2.0)

(−0.1)

R = 60.3% 2

D.W. = 1.7

MSE = 43.98 (11.1AA)

This study’s standard baseline 1960–2010 consumption model with 1 variable crowd out (T − G), before adding separate endogenous loanable funds variable CD = .29(Y − TT ) + .28(T − G) − 7.30PR + .49DJ−2 − .579.55POP16/65 (t=)

(6.3)

(5.9)

(−3.1)

(4.8)

(−2.9)

+ .021POP + 43.55M2AV + .10CB2 (5.9)

R 2 = 85.9%

(4.7)

(4.1)

2 RAdj = 83.6%

D.W. = 2.1 MSE = 26.47 (14.1A)

14

DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

341

The standard 1960–2008 consumption model with 1 variable crowd out (T − G), with separate endogenous loanable funds variable, but before deficit modification by accommodating FR purchases CD = .29(Y − TT ) + .28(T − G) + .00(S + FB − (Tr + A)) (t=)

(3.9)

(4.7)

(0.1)

− 6.34PR + .39DJ−2 − .549.69 POP16/65 + .022POP (−2.7)

(3.1)

(5.4)

(−2.8)

+ 50.82M2AV + .09CB2 (2.9)

(6.1)

R = 87.2% 2

2 RAdj

= 84.3%

D.W. = 2.0

MSE = 25.87

AR(1) used (14.1)

Notice that adding the stand-alone endogenous LF variable increased the model’s ability to explain the data by 1.3% (Adj. R 2 increased by 0.7% on same model, with no instruments used). The coefficient (t-statistic) on the deficit (crowd out) variable is = .28 (t = 4.7), signifying a large, highly statistically significant, crowd out effect. Next, we examine the standard 1960–2008 consumption model with 1 variable crowd out (T − G), with separate endogenous loanable funds variable, after the deficit variable is modified by exogenous LF (FR security purchases), i.e., (T − G)-(Tr + A) = (T − G)m . CD = .22(Y − TT ) + .11(T − G)m + 16(S + FB − (Tr + A)) − 5.26PR (t=)

(5.3)

(3.8)

(−2.2)

(8.3)

+ .59DJ−2 − .546.98POP16/65 + .021POP + 48.90M2 AV + .09 CB2 (6.3)

R = 83.0% 2

(−2.7)

Adj. R = 78.8% 2

(10.3)

D.W. = 2.0

(6.3)

MSE = 30.08

(2.5)

AR(1) used (14.2)

Adding FR securities purchases to the model actually decreases the explanatory power of the model. Also, in this model, when the deficit is modified by any changes in FR securities purchases in the same period, i.e., (TR + A) the estimated effect drops in Eq. 14.2 significantly to +.13 (t = 3.7). Crowd out remains a highly statistically significant negative influence on consumption, but of lesser magnitude than when the deficit is unmodified. It seems to give a generally theory-consistent result. Modifying (T − G) by (TR + A) does reduce the explanatory power of the model by 3.4% points and reduce the statistical significance of the crowd out variable. These results suggest an “errors in variables” problem

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occurs, and that the deficit’s accuracy as a measure of crowd out’s effects is distorted, i.e., reduced by modifying it by the value of FR purchases. One explanation is that FR purchases, may either not increase loanable funds (perhaps because deposited in foreign banks) or though increasing loanable funds in US financial institutions, they tend to be investment banks and brokerages. Such entities are more likely to use the newly available funds to buy securities than consumer goods. Hence, subtracting them from the deficit just makes less correct our estimate of crowd out’s effects.

14.1 Summary of Consumption Test Results for Different Sample Periods Coefficients and significance levels of the crowd out variable in both unmodified and FR purchases modified form are presented in Table 14.1 for various time periods between 1961 and 2009. Two versions contain a separate, stand-alone control variable for endogenous loanable funds (LF) − (Tr + A), as in Eqs. 14.1 and 14.2 above. The baseline model does not have either a stand-alone (S + FB) − (TR + A) variable or a modified deficit (T − G) + (Tr + A) variable. Adding the stand-alone variable to the baseline model increased R 2 in 11 of 17 cases and left it unchanged in the other six. The average increase in the models in which it increased was 1.4 percentage points. For just the 11 that gained, it was 2.1 percentage points. Adding a variable to account for the effects of loanable funds on consumption did add to our ability to explain the data. To ensure the results were replicable, and not just spuriously related for reasons peculiar to the time period tested, the model was also separately tested in 16 other time periods. Though each time period is different, they do overlap. Results are also presented in Table 14.1. The results indicate that in 10 of the 17 time periods, the unmodified crowd out variable (T − G). had a statistically significant effect on consumption, negative in deficit years, positive in surplus years. After modification, 9 of 17 were significant. However, as shown in Chapter 11 above, data samples that include a third or more of their observations from the 1990s (a “crowd in” period) and the rest from other decades (“crowd out” periods), tend to be found statistically insignificant, even though the 1990s data, when run as a separate sample, or most of the other decades alone when run as a separate sample, are statistically significant. This is because when averaged in one sample, coefficients on the

BL

w/o

1961–1990

with

BL

w/o

1961–1980 with

BL

w/o

1961–2000 with

BL

w/o

1961–2007 with

BL

w/o

1961–2008 with

BL

w/o

1961–2009 with

(T − G) Coef: t-stat R2

Variable

.16 (2.9) .93

.23 (2.3) .95

.22 (2.4) .97

.09 (1.5) .92

.00 (0.3) .92

w/o

BL

with

BL

w/o

1970–2000

1970–1990

.01 (0.2) .92

with .25 (4.2) .85

BL .34 (2.7) .86

w/o

1970–2007

.15 (1.6) .84

with

.27 (5.3) .87

BL

.24 (4.0) .88

w/o

1970–2009

Comparing robustness over time of effects on consumption of crowd out, with and without accommodating FR securities purchases

.11 (1.6) .86

with

.25 (3.6) .85

BL

.06 (0.5) .85

with

(continued)

.11 (0.9) .87

w/o

1975–2004

(T − G) .28 .49 .44 .22 .30 .32* .16 .14 .12 .27 .39 .25 .27 .32 .21 .28 .28 .11* Coef: t-stat (6.3) (3.1) (2.6) (3.5) (4.0) (3.4) (2.4) (1.4) (1.5) (4.9) (4.4) (3.4) (5.0) (4.9) (3.2) (6.2) (4.7) (3.8) R2 .87 .89 .88 .87 .91 .92 .90 .90 .90 .86 .86 .83 .86 .86 .84 .87 .87 .83

Variable

Table 14.1 Effects of (S + FB) − (Tr + A) on consumption crowd out, with and without deficit modification by FR securities purchases (tr + a)*

14 DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

343

−.02

−.01

with .02

BL .11

w/o .07

with .28

BL .21

w/o

1980–2009

.10

with .28

BL .17

w/o

1985–2004

.01

with .30

BL .15

w/o

1985–2005 BL

−.04 .47

with

.63

w/o

1996–2009

.11

with

(0.2) (−0.2) (−0.2) (3.2) (1.0) (0.4) (5.0) (3.1) (1.0) (2.4) (0.7) (0.5) (2.7) (0.6) (0.1) (2.3) (1.8) (0.8) .93 .94 .94 .85 .86 .86 .86 .87 .86 .80 .84 .83 .80 .83 .83 .91 .92 .96

.02

w/o

1980–2004

*AR(1) control required in all regressions. BL = Baseline (Standard Model w/o deficit (Tr + A) deficit modifier or (S + FB) − (Tr + A) stand-alone variable

(T − G) Coef: t-stat R2

BL

Variable 1980–2000

Table 14.1 (continued)

344 J. J. HEIM

14

DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

345

same “crowd out” and “crowd in” variable tend to cancel out, and the statistical result is merely saying that on average the net effect is small, there is no tendency in the underlying data for individual observations to be close to this average. In the 17 periods sampled here, all that were found insignificant before modification (7 of 17) were samples in which 1990s data made up a third to half of all the data in the sample. If we exclude those, we find 10 of 10 samples showing significant negative crowd out effects before modification, and 9 of 10 after. However, even though significant crowd out remains, crowd out coefficients and t-statistics are smaller. This may indicate that FR purchases had some success in reducing crowd out, but not enough to eliminate it as a statistically significant problem. In general, this is an expected result; FR purchases only averaged 1/8 of deficit size from 1960 to 2000, and only ¼ of deficit size from 2001 to 2007. Only in 2009 did they exceed deficit size. Alternatively, it may mean FR has even less effect on crowd out than its numbers suggest; it may indicate the errors in variables problem discussed earlier, which occurs because part of FR purchases proceeds never finds its way to consumer or business borrowing; it is used to buy other securities or deposited in foreign banks. Our objective in this chapter is to determine the success of FR accommodative monetary policy, i.e., FR purchases of (TR + A) in offsetting the crowd out effects of deficits on consumption, controlling for other factors which could influence consumption. Since one of these other factors is any increases in loanable funds caused by factors other than FR purchases, we included that also as a control variable in the models tested in Table 14.1.

14.2 Summary of Investment Test Results for Different Periods In this section, we compare the effects of the unmodified crowd out variable, the deficit (T − G), with the same deficit reduced by (TR + A), the amount of FR securities purchases in the same period. The same 17 different though overlapping, time periods are tested as were used to test consumption in Sect. 14.1. The results indicate that in all time periods, crowd out, as measured by (T − G) alone, before modification, has a statistically significant negative effect on investment in years when deficits occur, and a positive effect in years when government budget surpluses occur.

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J. J. HEIM

However, when each year’s crowd out effect is hypothesized to be the deficit net of changes in FR securities purchases, i.e., (T − G) + (Tr +A), the coefficient and statistical significance reflecting the estimated effect of crowd out decline markedly. This suggests FR purchases are not effective in reducing crowd out, bet rather, have an “error in variables” effect. Below, this study’s results are compared to the crowd out effect found by Heim (2017, Eq. 5.4.TR) using a fairly typical (“standard”) investment model. There, the deficit was broken into two variables, one representing tax deficits (T ), ceteris paribus, and one representing government spending deficits (G), ceteris paribus. Each type of deficit was modified by the size of the total loanable funds pool (S + FB). No separate stand-alone control variable for the modifier was used. That model is presented to show continuity and allow comparison with this study’s “standard” model, given in Eqs. 14.3 and 14.4, which test the same 1960–2010 period. This study uses nearly the same standard model, modified only by a changed definition of the deficit modifier from total loanable funds (S + FB), to only FR purchases of securities (Tr + A). In addition, a stand-alone variable is added to the model capture all sources of change in loanable funds except for changes in resulting from FR security purchases. The stand-alone variable is given as (S + FB) − (Tr + A). The models shown in Eqs. 14.3 and 14.4 and Table 14.2 were all found stationary or cointegrated with the dependent variable; in the unmodified models, the GDP variable was found endogenously related to the dependent variable are replaced by a Wald strong instrument. In the modified models, the accelerator variable was found endogenous and replaced by a strong instrument. Both instruments were found not endogenously related to the dependent variable (Sargan test). Models were estimated in first differences of the data. Newey–West standard errors were used. Standard Investment Model from Heim (2017) ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

(1.7)

D.W. = 2.0

MSE = 28.25 (5.4.TR)

.04

.08

with .32

BL .13

w/o

1960–1990

.12

with .37

BL

with

.18 .17.

w/o

1960–2000

.29

BL .11

w/o

1960–2007

.14

with .33

BL .28

w/o

1960–2008

.51 (4.4) .86

BL

(T − G) Coef: t-stat

.33

BL

.31

w/o

1960–2009

.22

with

.27

w/o

.20

with .23

BL .06

w/o .08

with

.47 (6.1) .88

BL .21 (2.5) .91

with

.32

BL .31

w/o

1980–2009

.26 (2.5) .91

w/o

1970–2000

.20

with

.29 (2.9) .84

BL

.24

BL

.13

w/o

.12

.32 (2.9) .90

w/o

.24

BL

with

.12

with

.21 (4.1) .91

.13

w/o

1985–2005

.34 (3.7) .89

BL

1970–2009

with

.15 (1.4) .88

with

1985–2004

.12 (1.1) .88

w/o

1970–2007

.31

BL

with

.29

w/o

.15

with

.09 .10 (.09) (1.0) .90 .90

w/o

1996–2009

.25 (2.8) .87

BL

1970–2009

DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

(continued)

(5.1) (1.8) (1.6) (2.3) (0.5) (0.6) (3.2) (2.7) (3.8) (2.8) (0.8) (0.6) (2.9) (0.8) (0.6) (2.0) (1.0) (2.4)

.48

BL

.10 (0.8) .92

with

1980–2004

.15 (1.3) .92

w/o

1970–1990

Variable 1980–2000

(T − G) Coef: t-stat R2

Variable

.25

with

(2.9) (0.6) (1.1) (3.4) (1.8) (1.7) (4.8) (2.3) (2.5) (3.2) (1.2) (1.5) (3.6) (2.4) (5.4) (6.3) (3.1) (5.1) .93 . 95 .95 .85 .91 .91 .87 .90 .90 .83 .86 .86 .85 .88 .88 .89 .89 .89

.20

w/o

Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases

(T − G) Coef: t-stat R2

BL

Variable 1960–1980

Table 14.2 Effects on investment of crowd out, with and without FR securities purchases as deficit offset, with stand alone (S + FB) − (Tr + A)

14

347

.87

BL

.90

w/o

.90

with .86

BL .89

w/o

1980–2004

.89

with .89

BL .90

w/o

1980–2009

.92

with .85

BL .85

w/o

1985–2004

.85

with .85

BL .85

w/o

1985–2005

BL = Baseline (Standard Model w/o deficit (Tr + A) deficit modifier or (S + FB) − (Tr + A) stand-alone variable

R2

Variable 1980–2000

Table 14.2 (continued)

.85

with .96

BL

.96

w/o

1996–2009

.98

with

348 J. J. HEIM

14

DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

349

A baseline, standard investment model with no deficit or loanable funds variables (taken from Cptr. 10); (2SLS strong instrument for Accelerator used), and no GDP Variable Included to Control for the State of the Economy ID = + .48(ACC) + .008POP + .76PR−2 + 7.37XRAV + 14.08CAP−1 (t=)

(10.6)

(2.5)

(2.2)

(0.2)

R = 69.4% 2

D.W. = 1.6

(4.3)

MSE = 47.87

(10.3C)

This Study’s Baseline Model, With No Deficit Variables or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy ID = + .47(ACC) − .00POP − 0.85PR−2 + 5.21XRAV (t=)

(0.0)

(4.0)

(2.0)

(−0.3)

+ 10.39CAP−1 + .10 GDP (−1.3)

(2.9)

R 2 = 76.1%

D.W. = 2.1

MSE = 43.06 (10.3B)

Equation 10.3B; same as Eq. 11.10C. Equations 10.3C and 10.4C also cited as 13.3 and 13.4 in this chapter. Chapter 10s “Baseline” Standard Investment Model, Including 1 Variable Crowd out (T − G), before loanable funds modification. (Using 1961–2009 data—2SLS Used) ID = + .26(ACC) + .33(TT − G T&I ) + .011POP − 4.51PR−2 (t=)

(6.5)

(5.5)

(8.3)

(−2.4)

+ 8.86XRAV + 2.66CAP−1 (3.4)

R = 88.7% 2

(1.6)

Adj. R 2 = 87.4%

D.W. = 1.9

SE = 29.19 (10.5)

Adding the stand-alone variable for loanable funds net of the part attributable to FR purchases (endogenous LF), leaves R 2 unchanged and the new variable is statistically insignificant. This suggests adding endogenous loanable funds growth does help reduce crowd out (lower deficit coefficient and t-statistic) Next, we retest this same model, but modify the deficit variable modified by any changes in FR security purchases: Standard Investment Model with One Variable Crowd out (T − G), Modified by FR Security Purchases (Using 1962–2009 data)

350

J. J. HEIM

That said, we will not know if these results accurately reflect the underlying economics governing interactions of deficits and same-period changes in loanable funds to determine if our initial results above are replicable. In Table 21.3 below, we repeat the tests undertaken in Eqs. 14.4 and 10.5, for 17 different, though sometimes overlapping, time period samples, to evaluate the robustness over time of our initial results. Table 14.2 indicates all 17 models tested showed statistically significant negative relationships between deficits and investment in the “baseline” model, i.e., before any modification to show the effects of loanable funds on investment. Results suggest that adding the loanable funds pool variables generally increases our ability to explain variation in investment. When the variable “total loanable funds minus FR purchases” (or endogenous loanable funds) was added to the model as a separate variable, R 2 rose noticeably. R 2 increased in 13 of the 17 periods and stays the same in the other four. The average increase is 2.4 percentage points for all 17 periods. Clearly changes in the total endogenous portion of the loanable funds pool does help explain variation in investment. Also, when the loanable funds-FR purchases variable was added, the number of samples in which crowd out was found significant dropped from 17 to 8. At first blush, this would seem to result from endogenous growth in the loanable funds pool offsetting crowd out effects, but this isn’t really the way calculus works. Normally, we expect regression coefficients on two separate variables (partial derivatives) to represent their two separate effects. We go to great efforts to ensure multicollinearity between variables is kept low enough so that introducing the second into the equation does not unduly distort the coefficient on the first from what was obtained in previous tests when only the first variable was included. But with the one-variable deficit model it was impossible to do that. Hence the large reduction of the number of samples showing significant crowd out may not have occurred for an economically substantive reason, but only because reduced significance levels are a common side effect of introducing severe multicollinearity into a model. Here, our initial findings may have been due to originally overstating the effects of crowd out due to their strong correlation with growth in the loanable funds pool (T – G) is correlated (.74) with the endogenous portion of the pool; (.83 with the total pool), both driven by underlying changes in the economy.

14

DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

351

The simple correlation coefficient is (.74). In such cases, it is not uncommon when one of the highly correlated variables is added to a model with the other already in it, for the estimates of the first variable’s statistical significance to drops markedly, and sometimes the coefficient too. The high degree of multicollinearity leaves variable coefficients and significance levels unreliable estimates of marginal effects and significance. Further compounding the problem, there is no good basis in economic theory for saying that crowd out effects do not occur when loanable funds increase; they do occur with or without same-period increases in loanable funds. The increased loanable funds just offset a crowd out effect that is occurring; they don’t prevent it from occurring. If partial derivatives in regressions were able to do their job properly, they would show separate significant effects for the two variables. Hence, we cannot be sure whether adding the FR purchases net loanable funds variable really is offsetting enough crowd out to leave it insignificant in a majority of cases, or just causing a multicollinearity problem. Hence we reach no conclusions about the extent to which this model shows the effect of net loanable funds in offsetting crowd out, but since it raises R 2 noticeably when added to the model, take this as an indication that increases in loanable funds do have a positive effect on investment. Chapter 10 uses a different technique to examine the effects of loanable funds on crowd out for both the FR purchases part, and separately in the same equation for the endogenous part of loanable funds. There, no stand-alone model was used. The two separate variables were the deficit minus endogenous loanable funds (T − G) − (S + FB) – (Tr − A), and the deficit minus exogenous loanable funds (T − G) − (Tr + A). With this formulation, no multicollinearity problem exists; the correlation between the two variables was (r = −0.10) In all six periods tested, it found the deficit continued to have significant crowd out effects even after endogenous growth in loanable funds was subtracted (as well as before). But for the FR purchases part, the four periods tested before the QE period, when FR purchases were very small, showed no significant effect, but the two periods tested including QE period data, when FR purchases were very large, showed FR purchases having a positive effect on investment. This suggests FR purchases can have an effect on investment by offsetting crowd out, but only if large enough to fully offset the deficit (see Sect. 10.3.2, Table 10.6).

352

J. J. HEIM

Finally, if we then add the FR purchases modifier (Tr + A) to the deficit variable in the model with a separate endogenous crowd out variable, and reestimate the model, the number showing crowd out rises slightly to 9, but essentially is nearly unchanged. This suggests that though controlling for the changes in the endogenous part of the he pool of loanable funds seems to reduce crowd out, FR purchases efforts (accommodative monetary policy) has not. Also, modifying the deficit in the baseline model by this among reduces its R 2 significantly to 82.4%. This further suggests FR purchases have had no effect on crowd out, but are merely distorting the values of a variable that does, i.e., modifying the deficit is creating an “errors in variables” problem. Does this mean FR purchases can’t work to reduce crowd out? Possibly, but probably because of reasons we have shown earlier: (1) FR securities purchases have been to small to have much effect, (2) most FR purchases are through investment banks and brokerages, neither of which’s main business is extending loans to companies to finance new machinery and factory buildings, and (3) because as much as 40% of FR purchases in some periods have been from foreign banks and brokerages, and it is not clear how much of the proceeds paid these banks actually get deposited and spent in the United States. However, just because FR purchases haven’t done much to accommodate fiscal policy in the past, doesn’t mean it can’t in the future. Addressing the three problems could strengthen the FR’s ability to enact effective accommodative monetary policy.

14.3 Summary of Chapter 14 Consumption and Investment Findings and Conclusions

T10.2

T10.1

10 Baseline (w/Def)

10 Baseline Total LF Model (Modified (w/s-a) 14 Unmodified (w/s-a)

T14.1

91

90

86

91

89

87

88

88

92

90

83

84

83

(Av. R2 = 83.1%) (Adj. Av. R2 = 78.8)

88

(Av. R2 = 88.4%) (Adj. Av. R2 = 84.2%)

89

86

90

(Av. R2 = 88.8%) 87 87 87 (Av. R2 = 89.1%)

90

86

97

95

94

93

92

92

92

92

84

86

87

85

86

88

88

88

1960 1960 1960 1960 1960 1970 1970 1970 1970 – – – – – – – – – 2008 2007 2000 1990 1980 1990 2000 2007 2010 72 72 86 43 77 91 91 68 55 86

86

60

1960 – 2010

94

94

93

93

1980 – 2000 86

86

87

89

86

1980 – 2010 37

85

87

85

86

1975 – 2004 63

86

86

85

86

1980 – 2004 74

83

84

83

83

1985 – 2004 67

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 10 of 17

14 Modified (w/s-a)

Eq.11.1AA

11 Baseline (w/oDef)

T14.1

From Table#

Model

83

83

83

83

1985 – 2005 65

96

92

95

99

1996 – 2009 83

NA

NA

99

100

9/10

9/17

10/10

10/17

9/11

9/11 14/18

NA 14/18

(T − G)*

(T − G)

(T − G)*

(T − G)

(T − G)*

(T − G) (T − G)

NA* (T − G)

2000 Test ratio – G 2010 T 95 NA NA

Chapter 14 Consumption Summary Table ((Tr + A) Deficit Modifier, Separate (S + FB) − (Tr + A) Control Variable)

14 DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

353

354

J. J. HEIM

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R 2 increases to 88.8%, an increase of 24%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When the stand-alone loanable funds modifier (S + FB) − (Tr + A) is added to the standard model with deficits, R 2 decreases to 88.4%. This indicates that adding endogenous loanable funds in this single deficit variable model slightly decreased consumption model’s explanatory power. 4. When also adding a (Tr + A) modifier to the deficit, while continuing to include the stand-alone (S + FB − Tr − A) variable, reduced explained variation in consumption. For 17 tests, average R 2 dropped the unmodified (i.e., baseline) average of 88.8–87.8%, 1.0% points, in the deficit modified version. By comparison, in Chapter 10, consumption R 2 stayed constant at 89.4% when total loanable funds (S + FB) was added to the model). In short, in this chapter, adding the endogenous loanable funds variable to the consumption model decreased explained variance somewhat; then adding the FR purchases variable to the deficit variable reduced explained variance. Chapter. 14 Investment Summary Table (FR Purchases Deficit Modifier, Separate (S + FB – Tr − A) Control Variable) Model

R2 (18 Time Periods) From 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 Table# -2010 08 07 00 90 80 90 00 07 09 00 10 ‘04 04 04 05 10 10

10 Baseline (w/o Def) T10.3C 69 67 66 63 65 72 -61 56 65 72 69 77 -64 71 63 57 92 91 (Does not include GDP Control Variable) (Av. R2 = 68.3%) 10 Baseline (w/o Def) T10.3B 76 70 71 80 78 91 82 81 71 76 81 80 80 81 75 75 93 95 (includes GDP Control Variable) (Av. R2 = 79.8%) 10 Baseline (w/Def)

Sigif./Total Test Ratio T G. NA NA NA NA* NA NA

NA NA*

Eq.10.5 89 86 83 87 85 92 87 89 83 89 88 89 84 82 83 83 96 97 17/18 (T-G) 10/11 (T-G) (Av.R2= 87.3%) (Adj.R2=84.4)

10 Baseline Total LF T10.3 Model (Modified (w/s-a) 14 Unmodified (w/s-a) T14.3

90 88 87 91 91 96 90 91 87 91 90 90 88 87 84 87 97 96 11/18 (T-G) 9/11 (T-G)* (Av.R2= 90.1%) (Est.Adj.Av. R2 = 86.2%) 89 88 86 90 91 95 92 91 88 90 90 90 90 90 89 85 96 NA 11/18 (T-G) 9/11 (T-G)* (Av.R2= 90.0%) (Adj.R2=85.4%) 14 Modified (w/s-a) T14.3 89 88 86 90 91 95 92 91 88 91 90 90 92 90 89 85 98 NA 11/18 (T-G) 2 2 9/11 (T-G)* (Av.R = 90.3%) (Adj.R =86.4%) ___________________________________________________________________________________

14

DOES MODIFICATION OF THE SINGLE VARIABLE DEFICIT (T − G) …

355

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 10 of 17

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8% 2. When deficit variables only added to baseline standard model, R 2 increases to 87.3%, an increase of 9.4%, clearly indicating clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When the stand-alone endogenous loanable funds modifier is added to standard model with deficits, R 2 grows to 90.0% (or 2.7% points) compared to the standard deficit model without a loanable funds variable. This indicates that the adding the endogenous loanable funds variable explains noticeably more of investment’s variation than a model without it. The total loanable funds model in Chapter 11, except using a two variable deficit, explains more (91.2%) of the variance. 4. Adding a FR purchases modifier to the deficit, while retaining this stand-alone variable, left R 2 only slightly higher at 90.3%. With the Chapter 18 model, R 2 % was unchanged at 90.2% adding the deficit modifier (S + FB) while also keeping it as a stand-alone variable. In short, our results show that for both the consumption and investment models, adding crowd out variables increases explanatory power, as does adding changes in the endogenous and exogenous parts of loanable funds. When controlling for endogenous loanable funds levels, adding exogenous grow in loanable funds as a deficit variable modifier did not significantly add to the explanatory power of the model. The Chapter 10 model, which uses total loanable funds as both a stand-alone modifier and a deficit variable modifier appears to be the better model.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 15

Does Modification of the Two-Variable Deficit (T) (G) by FR Purchases Better Measure Crowd Out, Controlling for Endogenous Loanable Funds Growth?

In Sects. 15.1 and 15.2 below we test the standard consumption and investment models. Unlike Chapter 14, where we used one variable (T − G) to represent the government deficit, here we wish to determine whether tax (T ) and spending (G) deficits have different crowd out effects. Tests of crowd out’s effect will be made both before and after the deficit’s reduction by the amount of FR securities purchases (TR + A). This will allow us to test the hypothesis that such purchases increase the pool of loanable funds, and therefore reduce crowd out effects in years when deficits are incurred or increase in size. The methods of calculus insure us that the coefficients on each variable in a model are ceteris paribus estimates, i.e., estimates of marginal effect are arrived at holding all other variables constant. Hence, the coefficient estimating the effect of a change in (T ) on consumption or investment are made holding the value of (G) constant. Hence the change in (T ), i.e., (T ) represents a change in the deficit, i.e., (T − G constant ). The coefficient on this change in (T ) variable measures its marginal effect on consumption and investment. The same is true for the coefficient on the government spending variable (G). Its coefficient measures the effect on consumption or investment of a change in the deficit that is induced by a change in government spending (G − T constant ). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_15

357

358

J. J. HEIM

15.1 Testing the Two-Variable Deficit Consumption Model As was the case in Chapter 14, we hypothesize that (S + FB) − (Tr + A) may be the proper formulation of the portion of the total loanable funds that fluctuates for reasons other than FR securities purchases, i.e., for endogenous reasons. We use this as a stand-alone separate variable in the model to control to avoid confounding the effects on C or I from these endogenous changes in the loanable funds pool with the effects of growth in the exogenous part of the pool, or (Tr + A), on crowd out. Using just (Tr + A) as a measure of how changes in the loanable funds pool can be made which could offset crowd out is questionable as well. The deficit’s (T − G) crowd out effect can be modified not only by the exogenous factor (Tr + A), but by any of the other more endogenous factors that can change the size of the total loanable funds pool (S + FB) such as increases in income, or changes in the marginal propensity to consume. It may be that the Chapters 10 and 11 models, which uses total (S + FB) as a variable which might offset crowd out effects is a more theoryconsistent model. Of course, if there were no deficit, all the increase in loanable funds could be used to fund additional loans over previous period levels, financing additional consumer and investment demand. Using part of the growth to replace funds available for private borrowing in previous periods limits how much, if any, of the growth in the loan pool will be available for additional private borrowing, and how much will be needed just to replace previous levels of private borrowing now curtailed because of the need to fund the deficit. Below is the model we take as the “standard” consumption model, comprised of variables commonly thought to affect consumption. It is Eq. 4.4.TR taken from Heim (2017). Below that are Eq. 15.1 and 22.2. They show test results for the same standard model, but with an additional variable, used to control for endogenous changes in the pool of loanable funds. Also changed from Heim (2017) is the variable used to modify the crowd out effects of the deficit to reflect changes in loanable funds. In Heim (2017) the variable used was total loanable funds, i.e., total US savings plus foreign borrowing (S + B). In this chapter, we deduct FR purchases of government or agency securities (Tr + A) as the deduct from

15

DOES MODIFICATION OF THE TWO-VARIABLE DEFICIT …

359

the deficit, exactly as we did in Chapter 14, except here it is used twice, because we separate the deficit into two variables, one for tax cut deficits (T ) and one for government spending deficits (G). The modified crowd out variables become T + (Tr + A) and G − (Tr + A). They become our measure of the crowd out effect: i.e., the deficit’s effect in reducing the portion of the pool available to private borrowers, “net” of FR increases the loanable funds pool during the same period by purchasing government securities in the open market, Testing indicated how (Tr + A) was divided between the two deficit variables did not effect estimates of tax vs. spending crowd out variables, so the full value of (TR + A) was used as a modifier of each deficit variable. Equation 15.1 measures crowd out effects before modifying the deficit by the amount of FR securities purchases (Tr + A). Equation 15.2 measures crowd out effects after reduction by the FR securities purchases (i.e., the exogenous increase in the loanable funds pool). Both equations also include the stand-alone variable (S + FB) − (Tr + A). All three models were estimated using the full 1960–2009 Dataset. Standard Consumption Model from Heim (2017): C D = .29(Y − TT ) + .34(TT ) − .23(G T &I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07 POP16/65 + .020POP + 38.00 M2AV + .09 C B2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

(4.9)

MSE = 24.88

(3.7)

(Eq. 4.4.TR)

This study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included. (1960–2010 data) C D = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38 POP16/65 (t=)

(7.2)

(0.6)

(3.0)

(1.6)

+ .013POP − 1.58 M2AV + .13 C B2 (3.2)

R = 60.3% 2

(−0.1)

D.W. = 1.7

(2.0)

MSE = 43.98

(Eq. 11.1AA)

Below is this study’s baseline (bl) standard consumption model with 2 variable crowd out (T and G deficit effects estimated separately). This

360

J. J. HEIM

model is estimated before deducting loanable funds changes from (T ) or (G), and before endogenous LF is added as a stand-alone variable: C D = .31(Y − TT ) + .32(TT ) − .16(G T &I ) − 7.14PR + .49DJ−2 (t=)

(6.4)

(6.6)

(−3.1)

(−1.9)

(4.5)

− .459.68 POP16/65 + .017POP + 36.27 M2AV + .09 C B2 (4.0)

(2.4)

R 2 = 86.6%

D.W. = 2.1

(3.9)

(3.8)

MSE = 26.17

(Eq. 11.1A)

The next equation presents Standard Consumption Model with 2 variable crowd out (T ) and (G), before accommodating FR purchases used to modify the deficit variables, but including an endogenous LF stand-alone variable. C D = .21(Y − TT ) + .22(TT ) + 01(G T &I ) + .07( (ST + FB) − (Tr + A) ) (t=)

(3.7)

(3.0)

(0.6)

(2.0)

− 5.72PR + .50DJ−2 − 482.94 POP16/65 + .019POP + 53.13 M2AV (−2.3)

(4.0)

(−2.3)

(4.2)

(5.1)

+ .09 C B2 (3.3)

R = 85.3% 2

R 2 = 81.8%

Adj.

D.W. = 2.3 MSE = 27.76 (Eq. 15.1)

Standard Consumption Model with 2 Variable Crowd out (T ), (G), after accommodating FR purchases used to modify the deficit variables, and including an endogenous LF stand-alone variable. C D = .27(Y − TT ) + .27(TT )m + .20(G T &I )m + .10(ST + FB − (Tr + A)) (t=)

(3.0)

(3.0)

(1.7)

(1.5)

− 6.11PR + .42DJ−2 − 295.42 POP16/65 + .01POP + 39.44 M2AV (−2.1)

(3.2)

(−1.0)

(1.4)

(2.9)

+ .08 C B2 (2.0)

R = 83.8% 2

Adj.

R 2 = 80.1%

D.W. = 2.2

MSE = 29.11 (Eq. 15.2)

All results cited in Tables 15.1 below for different time periods were estimated using exactly these same models. Only the length and dates of the time periods tested changes. The variable use to control for changes in the private portion of the loanable fund pool was (S + FB) − (Tr + A). The modified government deficit variables were found endogenous

T Def : t-stat G Def : t-stat S + FB–SG t-stat

Variable

.26 .26 (2.2) (2.2) −.10 −.04 (−1.0) (−0.3) .04 .03 (−0.3) (0.2) .88 .88

w/o with

w/o with

.70 .63 (4.9) (3.0) −.30 −.22 (−2.5) (−1.1) −.50 −.48 (−1.4) (−1.2) .94 .92

1960–1990

1960–1980

.19 .12 (1.6) (1.2) −.02 .17 (−0.2) (0.9) .06 .13 (0.5) (1.1) .90 .88

w/o with

1960–2000

.33 .14 (2.1) (1.1) −.10 .25 (−0.8) (1.4) −.00 .19 (−0.0) (1.5) .87 .80

w/o with

1960–2007

.32 .24 (3.0) (2.7) −.09 .22 (−1.0) (1.2) .01 .10 (0.1) (1.2) .87 .82

w/o with

1960–2008

.21 .27 (3.0) (3.0) .01 .20 (0.1) (1.5) .08 .10 (2.0) (1.7) .85 .84

w/o with

1960–2009

Table 15.1 Crowd out effects of deficits on consumption W/ and W/O deficit modification by FR securities purchases; stand-alone (S + FB) − (Tr + A) control for endogenous sources of loanable funds

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and replaced by a Wald-strong instrument. All variables were found ADF stationary or DF cointegrated. Newey–West standard errors were used to avoid heteroskedasticity problems. All data were tested in first differences to reduce multicollinearity and improved stationarity. The endogenous loanable funds variable was correlated (−0.47) with the tax deficit variable and (0.78) with the spending deficit variable. The latter could result in low levels of significance for the spending variable. In Table 15.1 we use same standard model show in Eqs. 15.1 and 15.2 above, and test it in six different, though overlapping time periods. For each time period given in Table 15.1, two sets of statistics are presented, one with no modification of the deficit variables (T ) and (G) as a measure of crowd out effects, and one which reduces the deficit variables crowd out effect by the value of FR securities purchases, i.e., T + (Tr + A) or G − (Tr + A). R 2 in Table 15.1 for the unmodified model is slightly less than in the baseline deficit model with no loanable funds variables. Table 15.1 shows that tax cut deficits showed statistically significant crowd out problems, both before (6 of 6) and after (4 of 6) modification. By comparison, 1 of 6 tests show the unmodified value of government spending deficits causing a crowd out problem before modification, and 1 of 6 after. R 2 dropped after deficit modification in all but one model, where it stayed the same. The multicollinearity problem does not seem to be causing the results here, since the non-significant results for the spending variable were essentially the same before and after modification. Before modification, the multicollinearity problem for the spending and tax variables and loanable funds variables were nearly identical, yet the tax variable was significant in all tests. By comparison, the baseline model, with no loanable funds variable, showed crowd out to be a significant factor in all six-time periods. Compared to the baseline model (Table 15.2), R 2 with loanable funds was lower in 3 of the 6 “w/o” models and lower in 5 of the 6 “with” models. Because these two loanable funds model actually reduce the explanatory power of the consumption model when included, it strongly suggests changes in loanable funds are not channeled into consumer borrowing, i.e., do not offset consumer crowd out. Table 15.2 reruns the same “with” and “without” models as in Table 15.1, but without the separate, stand-alone endogenous loanable funds control variable. We are, in essence testing to see if controlling for

.28 .29 (3.2) (3.2) −.10 −.09 (−1.7) (−1.4) .89 .89

w/o with

w/o with

53 .50 (3.9) (3.4) −.21 −.17 (−1.6) (−1.2) .91 .91

1960–1990

1960–1980

.23 .19. (2.8) (2.5) −.03 .03 (−0.5) (0.6) .91 .90

w/o with

1960–2000

.33 .30 (5.6) (4.2) −08 .07 (−1.5) (1.0) .87 .84

w/o with

1960–2007

Note Single stage regression, since (S+FB2-Def) was the only endogenous variable. No AR(1) needed

T Def : t-stat G Def : t-stat

Variable

.33 .28 (5.5) (4.3) −.08 .10 (−1.6) (1.5) .87 .85

w/o with

1960–2008

.32 .22 (6.6) (3.3) −16 .29 (−1.6) (5.1) .87 .81 (.84Adj)

w/o with

1960–2010

Table 15.2 Effects of crowd out on consumption, with and without modification by FR securities purchases (no stand-alone [S + FB] − [Tr + A] control variable)

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factors which can affect the level of loanable funds available, other than the FR’s purchases, perhaps do not affect our crowd out effect estimates. Again, all tax cut samples show significant crowd out before and after deficit modification. Unlike before, government spending deficits tend to have marginally significant crowd out effects in four of the six tests. R 2 is lower in 4 of the 6 models with (TR + A) deficit modification, than in the baseline model with no loanable funds modifiers.

15.2 Testing the Two-Variable Deficit Investment Model Below is the model we take as the “standard” investment model. It is Eq. 5.4.TR taken from Heim (2017). Following that, Eqs. 15.3 and 15.4 show the same standard model with two changes: 1. The addition only of a control variable for changes in the pool of loanable funds for all reasons except changes in the FR securities purchases. 2. Also changed from Heim (2017) is the deduct from the tax or spending deficit to account for loanable funds changes. In Heim (2017), it was total loanable funds (S + FB). In this model, any deficit is reduced by the amount of FR purchases of government or agency securities, on the assumption that the entire FR purchase ends up as additional loanable reserves in banks that make loans for real goods and services. All variables were found Augmented Dickey Fuller (ADF) stationary or DF cointegrated; No Hausman endogeneity was found between the dependent and explanatory variables in the model using the stand-alone loanable funds variable (Eqs. 15.3 and 15.4, and Table 15.3), but the government spending variable was endogenous in the model without the stand-alone loanable funds variable (Table 15.4), and was replaced by a Wald strong instrument which was not itself endogenous (Sargan test). Newey–West standard errors were used to avoid heteroskedasticity. Variables were tested in first differences to reduce multicollinearity and nonstationarity effects.

T Def : t-stat G Def : t-stat LF-TR-A t-stat

Variable

.13 .10 (2.0) (1.4) −.10 −.08 (−1.1) (−0.6) .37 .38 (7.5) (9.5) .91 .91

w/o with

w/o with

.01 .05 (0.1) (0.7) −.09 −.16 (−0.7) (−1.2) .59 .52 (6.4) (4.2) .95 .96

1960–1990

1960–1980

.19 .16 (2.2) (2.2) −.17 −.17 (−1.9)(−1.5) .29 .27 (3.5) (3.1) .90 .89

w/o with

1960–2000

.10 .15 (1.1) (1.8) −.12 .−.20. (−1.2) (−1.5) .23 .17 (3.4) (2.2) .87 .86

w/o with

1960–2007

.29 .18 (2.5) (3.4) −23 −.23 (−2.1) (−2.0) .09 .15 (1.1) (2.8) .86 .89

w/o with

1960–2008

.32 .14 (3.1) (2.1) −.31 −.12 (−2.7) (−1.1) .02 .23 (0.6) (4.7) .89 .90

w/o with

1960–2009

Table 15.3 Crowd out effects of deficits on investment W/ and W/O deficit variable modification by FR securities purchases (controlling for endogenous sources of loanable funds (S + FB) − (Tr + A)

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T Def : t-stat G Def : t-stat

Variable

.25 .11 (1.6) (0.8) −.38 −.24 (−2.4) (−1.4) .87 .83

w/o with

w/o with

.12 .18 (1.5) (1.9) −.32 −.36 (−3.7) (−3.4) .94 .95

1960–1990

1960–1980

.36 .16 (2.6) (1.6) −.37 −.31 (−4.9)(−3.6) .88 .83

w/o with

1960–2000

.28 .16 (2.4) (2.4) −.30 −.31. (−2.7) (−2.9) .83 .80

w/o with

1960–2007

.35 .11 (2.9) (2.3) −.29 −.27 (−2.4) (−2.8) .85 .84

w/o with

1960–2008

.35 .04 (2.9) (0.4) −.30 −.02 (−3.4) (0.1) .88 .67

w/o with

1960–2009

Table 15.4 Effects on investment of crowd out, with and without accommodating FR securities purchases (no separate [STotal −SG ] control variable, but control for GDP included)

366 J. J. HEIM

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Standard Investment Model from Heim (2017) (Using 1960–2010 data): I D = + .26(ACC) + .27(TT ) − .30(G T &I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55 CAP−1 (2.9)

(−2.7)

R 2 = 83.3%

(1.7)

D.W. = 2.0

MSE = 28.25 (Eq. 5.4.TR)

This study’s baseline investment model, with no deficit or loanable funds variables included, and no GDP variable included to control for the state of the economy is given by: I D = + .48(ACC) + .008POP + .76PR−2 (t=)

(2.5)

(10.6)

(0.2)

+ 7.37XRAV + 14.08CAP−1 (2.2)

(4.3)

R = 69.4% 2

D.W. = 1.6

MSE = 47.87 (Same as Eq. 10.3C)

This study’s baseline investment model, with no deficit or loanable funds variables included, but GDP variable included to control for the state of the economy I D = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(0.0)

(4.0)

(−0.3)

+ 5.21XRAV + 10.39 CAP−1 + .10 GDP (2.0)

R 2 = 76.1%

(−1.3)

(2.9)

D.W. = 2.1

MSE = 43.06 (Same as Eq. 10.3B)

Baseline model with deficit and GDP control variable, but no loanable funds variables (1960–2010) I D = + .27(ACC) + .33TT − 33G T &I + .012POP − 4.95PR−2 (t=)

(6.4)

(2.6)

(−3.9)

(2.8)

(−2.5)

+ 6.68XRAV + 2.43 CAP−1 − .02 GDP (3.5)

R = 89.0% 2

(1.8)

D.W. = 1.9

(−0.2)

MSE = 29.87

(Eq. 11.4A)

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Standard Investment Model with 2 Variable Crowd out (T , G), with endogenous LF control variable, before accommodating FR purchases (Using 1960–2010 data): I D = + .22 (ACC) + .32TT − 31G T &I + .02( (S + FB) − (Tr + A) ) (t=)

(6.7)

(3.1)

(−2.7)

(0.6)

+ 1.06 CAP−1 − 4.78PR−2 + 6.51XRAV + .010POP (0.7)

R = 88.7% 2

(3.4)

(−2.3)

Adj.R = 86.9% 2

(2.8)

D.W. = 1.9 MSE = 30.01 (Eq. 15.3)

Standard Investment Model with 2 Variable Crowd out (T , G), with endogenous LF control variable, deficit variables adjusted for accommodating FR purchases) (Using 1960–2010 data): I D = + .22 (ACC) + .14TT − 13G T &I + .23( (S + FB) − (Tr + A) ) (t=)

(5.8)

(2.1)

(−1.1)

(4.7)

+ 3.13 CAP−1 − 1.82PR−2 + 8.24XRAV + .005POP (1.8)

R = 89.6% 2

(−0.9)

Adj.R = 88.1% 2

(2.9)

(1.6)

D.W. = 1.9 MSE = 28.71 (Eq. 15.4)

All results in Table 15.3 below for the other time periods estimated use exactly the same models shown in Eqs. 15.3 and 15.4. Only the length and dates of the period used to test the model changes. In Table 15.3 the models tested include the stand-alone loanable funds net of government savings variable. Any increases in these loanable funds in the same period a deficit occurs can be used to reduce crowd out effects. By using the FR open market purchases of securities a variable distinct from this, we are implicitly asserting that it too can increase loanable funds, but is not included in our stand-alone loanable funds variable. As noted earlier, this is a somewhat questionable assumption. In Table 15.3 below, for each time period given, two sets of statistics are presented. In one set, there is no modification of the crowd out variables (T , G) by FR purchases of treasuries and agency (Tr + A) securities, and one in which the same regression model is reestimated using crowd out variables modified by FR securities purchases T + (Tr + A) or G − (Tr + A). Adding the endogenous loanable funds variable to the model (the “w/o” column), increased R 2 between 1 and 4 percentage points compared to the baseline model which had no loanable funds variable of either the stand alone or deficit modifier type. The average increase was

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2.2 percentage points. We conclude growth in endogenous loanable funds does increase the ability of the model to explain variance in investment. In the baseline model, tax cut crowd out was significant in 5 of 6 samples, spending deficit crowd out was significant in 6 of 6. For tax deficit tests, in 4 of 6 tests of the model after adding the stand-alone endogenous loanable funds variable to the model,—with or without also adding the deficit modifier, indicate a continuing statistically significant tax deficit crowd out problem, though after modification generally with smaller coefficients and t-statistics. For spending deficits, 6 were significant in the baseline model, but drop to 3 of six significant after adding the stand-alone endogenous loanable funds variable, and drops further to 1 of 6 significant after further adding the FR purchases modification, to the deficit variables. When the deficit modifier, exogenous loanable funds (TR + A), was added to a model which already had a stand-alone endogenous loanable funds variable, R 2 effects of modification were mixed: 3 higher after modification, 2 lower (suggesting that the modification overall, did not add to explained variance). The number of significant tax deficits stayed the same—4 of 6, and the number of significant spending deficits technically dropped from 3 to 1, but two of the declines were so small as to leave the t-statistic barely below the 1.6 critical value used in this study (They dropped to 1.5). Essentially the result for spending deficits was also unchanged when deficits were modified by growth in FR security purchases. Table 15.4 reruns the same “with” and “without” models as in Table 22.3, but without the endogenous loanable funds control variable. We now testing to see if controlling for other factors which affect the level of loanable funds (as we did in Table 22.3) makes a difference in our crowd out effect estimates of the effects of FR purchases, and needs to be controlled for. In Table 15.4, before modification, tax cut crowd out had a statistically significant negative impact on investment in 5 of 6 cases and spending deficit crowd out in all 6 time periods tested. After modification of the deficit variables by any same-period change in loanable funds statistically significant crowd out remained in 4 of 6 periods tested, with roughly the same coefficients and t-statistics. However, R 2 s dropped markedly. If adding a loanable funds variable doesn’t change, or leads to reduced explained variance, we conclude it is less desirable model.

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In Table 15.4 when not controlling for endogenous sources of loanable funds, we found 4 tax cut and 5 spending deficits significant both in the baseline model and after modification by FR purchases. As we noted above, by comparison the model with the control variable for endogenous growth in the loanable funds pool, (Table 15.3) is considered the more theory-consistent, Hence, our best estimates of the extent to which FR security purchases have reduced the crowd out problem in the past are those produced by this model. In addition, the deficit modified by FR purchases model had noticeably smaller R 2 s in 5 of the 6 tests. Here again though, coefficient/significance levels in 15.4 were more what theory would lead us to expect. It is possible that absent multicollinearity, we would have gotten the same results with the model with a stand-alone endogenous loanable funds variable included.

15.3 Summary of Chapter 15 Results from 2 Variable Deficit Models Cptr. 15 Consumption Summary Table (Tr + A) 2 Variable Deficit Modifier; (S + FB − (Tr + A) Stand-Alone Variable Models Model

From Table#

11 Baseline(w/oDef)

Eq.11.1AA

11 Baseline (w/Def)

T11.1A

11 Baseline Total LF T11.1 Model (w/def. mod.& s-a)

1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 -2010 08 07 00 90 80 90 00 07 10 00 10 04 04 04 05 09 10 60 72 72 86 43 77 91 91 68 55 86 37 63 74 67 65 83 95 (Av. R2 = 71.4%) 87 87 87 91 89 91 93 92 86 88 94 85 88 88 86 87 92 99 (Av. R2 = 89.4%; Adj.R2= 84.3%) (R2=88.7% for only 6 samples) 90 (Av. R2 6 samples ) (Adj.R2= 85.2% ) --- --- ---

--- --- ----

Test T

Ratio G.

NA NA 15/18 10/11 (5/5

NA NA* 6/18 6/11 5/5**)

5/6

4/6

15 Unmodified (w/s-a)

T15.1

85 87 87 90 88 94 ---(88.5% Av.) (Adj.R2= 84.5% ) --- ---

6/6 6/6

1/6 1/6*

15

T15.1

84 82 80 88 88 92 ---(85.7% Av.) (Adj.R2= 81.0% ) --- ---

4/6 4/6

0/6 0/6*

6/6 6/6 6/6 6/6

4/6 4/6* 1/6** 1/6*

Modified (w/s-a)

15 Unmodified(wo/s-a)

T15.2

87 87 87 91 89 91 ---(88.7% Av.)--- --- --- --- --- --- --- ---

15 Modified (wo/s-a)

T15.2

81 85 84 90 89 91 --- (86.7% Av.) --- --- --- --- --- --- --- ---

*No samples with as much as 1/3 to 1/2 1990s data occurred, so no change in results by dropping them. **Significant only in sample with 2008-10 QE data on FR Purchases included (sign on spending coefficient: +, indicating “crowd in”)

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For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 68.3%. 2. Baseline standard model with deficit variables added: average R 2 increases to 88.7%, an increase of 30%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects. 3. When the stand-alone loanable funds modifier (S + FB) is added to the standard model with deficits, R 2 stays essentially the same, decreasing only from (88.7%) to (88.5%). 4. Modifying the deficit by FR Purchases (Tr + A), while continuing to include the separate control variable for growth in endogenous loanable funds causes R 2 to drop noticeably to (85.7%). Suggesting the (TR + A) modifier just distorts the estimates of the deficits’ crowd out effects. This may be because FR purchases are not generally from parties who will use the proceeds to purchase consumer goods and services (i.e., investment banks, brokerages), or from foreign banks who lend the proceeds outside the United States. 5. Without any deficit modifiers or stand-alone loanable funds variables added to the standard model with deficits, R 2 is 88.7%. Adding the FR purchases variable caused R 2 to drop to 86.7%. 6. Since R 2 remains nearly unchanged when the stand-alone endogenous loanable funds variable is added to the model, and declines if FR purchases are added, we conclude that increases in endogenous loanable funds has no impact on consumer spending, and that modifying the deficit variables’ effect (crowd out) by FR purchases also does not add to consumer spending (i.e., offset crowd out), but actually reduces the crowd out variables’ ability to properly account for the deficit’s crowd out effect on consumption.

Cptr. 15 Investment Summary Table (Tr + A) 2 Variable Deficit Modifier; (S + FB) − (Tr + A) Stand-Alone Variable Models

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J. J. HEIM

Model

From Table#

R2 (18 Time Periods) 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 -2010 08 07 00 90 80 90 00 07 09 00 10 04 04 04 05 10 10

Sigif./Total Test Ratio T G.

10 Baseline (w/o Def) Eq.10.3C 69 67 66 63 65 72 -61 56 65 72 69 77 -64 71 63 57 92 91 (Does not include GDP Control Variable) (Av. R2 = 68.3%)

NA NA

NA NA*

10 Baseline (w/o Def) Eq.10.3B 76 70 71 80 78 91 82 81 71 76 81 80 80 81 75 75 93 95 (include GDP Control Variable) (Av. R2 = 79.8%)--

NA NA

NA NA*

11 Baseline (w/Def)

Eq.11.4A

89 86 84 89 87 95 90 90 86 90 89 90 89 89 89 89 98 98 (Av. R2 = 89.8%) (Adj.R2=86.3% )

(6 sample av. = 85.3%) 11 Baseline Total LF T11.11 Model (w/def. mod.& s-a)

90 (Av. R2 6 samples ) --- --- --- --- --- --- --- --- ---

15 Unmodified (w/s-a)

15 Modified (w/s-a)

15 Unmodified (wo/s-a)

15 Modified (wo/s-a)

T.15.3

T15.3

T15.3

T15.3

11/18 16/18

---.--- --

6/6

4/6

89 86 87 90 91 95 ---(89.7% Av.) (Adj.R2 av.= 86.2) --- ---

4/6 4/6

3/6 3/6*

90 89 86 89 91 96 ---(90.2% Av.) (Adj.R2 av.= 87.5) --- ---

4/6 4/6

1/6 1/6*

88 85 83 88 87 94 ---(87.5% Av.)--- --- --- --- --- --- --- ---

5/6 5/6

6/6 6/6*

67 84 80 83 83 95 ---(82.0% Av.) --- --- --- --- --- --- --- ---

4/6 4/6

4/6 4/6*

*No samples dropped because 1990s crowd in data was 1/3 to 1/2 of total. Hence, results are unchanged.

For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 77.7%. 2. Baseline standard model with deficit variables added: average R 2 increases to 88.3%, an increase of 14%, clearly indicating investment cannot be explained without allowing for significant negative crowd out effects of deficits. 3. When the stand-alone loanable funds modifier (S + FB) − (Tr + A) is added to the investment standard model with deficits, R 2 increases from (88.3%) to (89.7%), indicating growth in endogenous loanable funds helps offset the crowd out effects of deficits. In Chapter 21, which used total loanable funds the stand alone and modifier, for 18 periods tested, adding the stand-alone variable (S + FB0 left the R 2 increased to 91.2%), indicating it was the better modifier. 4. Modifying the deficit by FR Purchases (Tr + A), while continuing to include the separate control variable for growth in endogenous loanable funds causes R 2 to again increase: this time to (90.2%), suggesting FR purchases (TR + A) also help offset the crowd out

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effects of deficits on investment. (In Chapter 18, adding deficit modifier left the R 2 unchanged at 91.2%. 5. Without any deficit modifiers or stand-alone loanable funds variables added to the standard model with deficits, R 2 is (85.9%), slightly below the standard deficit model’s (88.3%) before and loanable funds modification. Adding the FR purchases variable caused R 2 to drop to 82.0%. The Chapter 21 model adding the deficit modifier without the stand alone increased R 2 in all 18 tests over the baseline standard deficit model, up to%, an average increase of (0.9%). 6. Since the R 2 increases were large with the Chapter 14 model, and seems more theory consistent with its two effects of a change in loanable funds on consumption, we are inclined to favor that model.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 16

Do FR Purchases, Used as Deficit Modifiers, Reduce Crowd Out, Controlling for the Level of Private Saving and Foreign Borrowing

In Chapter 13 above we tested six different ways of structuring models that would allow us test for the crowd out effects of deficits and the ability of loanable funds to offset crowd out. The six models were tested on one sample of 1960–2010 data. The objective was to find the most data trends-consistent model possible to express crowd out effects and the ability of changes in loanable funds to offset crowd out. Our standard model, described in Chapters 10–11 above, contain what appear to be the best of those models, the ones that show the best ways to model crowd out and loanable funds variables so as to explain the most variance in consumption and investment. In short, the findings were that modifying the deficit variables by changes in the size of the total loanable fund pool was the best way, sometimes also including any changes in the total loanable funds variable as a separate stand-alone variable. In this and other chapters other hypotheses are tested about how best to determine what, if any, specific part of total loanable funds (the exogenous or endogenous parts) or the money supply can be used the crowd out effects of deficits. Initial results were obtained using 1960–2010 data. Additional tests are undertaken to determine if results could be replicated in from six to seventeen different time periods, each involving a subset of the years included in the 1960–2010 sample. Without replication, there is no science, and scientific answers to the questions about crowd out and loanable funds effects are what we are looking for. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_16

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In this chapter we use the one-variable definition of the deficit (T − G), to define the size of crowd out effect before reduction by a change in some part of the total loanable funds variable. The part of loanable funds tested as the crow out reducer (modifier) is the exogenous part of total loanable funds, FR security purchases (Tr + A). The hypothesis we are testing is that FR purchases of Treasury and Government Agency securities may create additional loanable funds in banks available to offset some or all crowd out. We also add to the standard model a separate, stand-alone loanable funds variable to control for changes in the private savings and foreign borrowing part of the loanable funds pool, i.e., endogenous growth in the loanable funds pool which we define as (S + FB) − (G − T ) + FR = national savings + foreign borrowing—public savings + Federal Reserve securities purchases. By using (S + FB) − (G − T ) as a control variable for private savings, we are arguing that while the total pool of loanable funds, (S + FB) includes all national savings public and private, the part that is available to finance private borrowing is given by (S + FB) − (T − G), the total pool minus the part required to finance the deficit (the public savings component). Using this net effect as a control variable when measuring the effects of (TR + A) reflects the fact that other factors affecting the private savings and foreign borrowing parts of the pool of loanable funds, should be separately controlled for when attempting to determine just how much a change in (TR + A) reduces the effects crowd out. Not doing so raises the possibility of misestimating the effects of (Tr + A) due to the “left out variables” problem discussed in Chapter 13. However, it can also be argued that subtracting the deficit (T − G) from (S + FB) is a logically weak hypothesis. The total loanable funds variable, (S + FB), for any period already reflects the decline in it caused by a same-period decline of government savings (the deficit). Therefore, to subtract the deficit again is redundant. The single deficit variable, (T − G) is included to measure the effect of crowd out on consumption or investment, before adjusting it for crowd out effects. As noted earlier in Chapter 13, also questionable is just using (Tr + A) as a measure of how changes in the loanable funds pool can offset the crowd out effects of a deficit. The crowd out effect can be modified not only by the exogenous component of loanable funds (Tr + A), but by any of the other factors that constitute its endogenous components, i.e., increases in income, or changes in the marginal propensity to consume.

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DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

377

Chapter 17 crowd out model, which uses total (S + FB) as the deficit modifying variable (and as a stand alone) may be a better model of how changes in loanable funds can mitigate crowd out. That said, in this chapter, we examine the extent that consumption and investment are affected by the crowd out effects of the one-variable deficit before and after it is modified by FR purchases, i.e., (T − G) + (Tr + A). The models tested also include a stand-alone variable to control for other factors which can affect the size of the pool of loanable funds available to private borrowers. It is defined as total loanable funds net of the government savings component: (S + FB) − (T − G). How successful the model is depends on whether it explains the data better or worse than other models tested. Equation 16.1 presents results for all variables in the standard consumption model using only the single deficit variable (T − G) alone to define crowd out effects. This is done without any (Tr + A) modification to the deficit variable. In Eq. 18.2, the model is reestimated, with the crowd out variable redefined as the deficit modified by FR securities purchases: (T − G) + (Tr + A). Both models contain a separate standalone variable to the regression to capture all other changes that can occur in the privately available part of the loanable funds pool, namely (S + FB) − (T − G). This is done to ensure that (this definition of) other loanable funds effects are held constant when the effects of the deficit variable (with or without modification) on consumption are tested. The deficit variables, with and without modification, were found to be stationary (ADF test), and not endogenous with the dependent variable (Hausman test). For comparison the standard consumption model from the Heim (2017) large scale econometric model is presented. The earlier Heim model differs from Eqs. 16.1 and 16.2 in that the deficit is divided into two variables (T , G), and coefficients for each type of deficit effect are estimated separately, holding the other constant. Nonetheless, the average of the two coefficients is close to the single 23.1 coefficient estimated for (T − G). There are other differences because in Heim (2017) 1. There is no control variable ((S + FB) − (T − G)) for other factors influencing the pool of loanable funds, and 2. The modifier of T , and G for offsetting effects of changes in the loanable funds pool is somewhat different and less accurate a measure of the loanable funds effect.

378

J. J. HEIM

Standard Consumption Model from Heim (2017) CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) (t=)

(6.2)

(6.5)

(−4.5)

− 5.44PR + .48DJ−2 − .515.07POP16/65 (−2.1)

(5.1)

(3.2)

+ .020POP + 38.00 M2AV + .09CB2 (6.0)

R = 87.8% 2

(3.7)

(4.9)

D.W. = 2.2

MSE = 24.88

(4.4.TR)

The Standard Consumption Model, with Deficit Variable, before Deficit Modified by (Tr + A) and Without Stand Alone (S + FB) − (T − G): CD = .29(Y − TT ) + .28(T − G) − 7.30PR (t=)

(5.9)

(6.3)

(−3.1)

+ .49DJ−2 − .579.55POP16/65 + .021POP (4.8)

(5.9)

(−2.9)

+ 43.55M2AV + .10 CB2 (4.1)

(4.7)

R = 85.9% 2

Adj. R = 83.6% D.W. = 2.1 2

MSE = 26.47 (10.1A)

The Standard 1960–2008 Consumption Model with 1 Variable deficit (Crowd out) (T − G), before deficit modification by accommodating FR purchases, but With a Stand Alone (S + FB) − (G − T ) Variable: CD = .33(Y − TT ) + .45(T − G) − .10 (S + FB − (T − G)) (t=)

(3.4)

(5.6)

(−1.6)

− 6.13PR + .32DJ−2 − .552.04POP16/65 + .022POP (−2.8)

(3.7)

(2.7)

(5.6)

+ 49.03M2AV + .10 CB2 (6.2)

R = 88.2% 2

(4.3)

Adj. R = 85.9% 2

D.W. = 2.0

MSE = 24.52 (16.1)

Generally, results are very similar to those obtained in Heim (2017). Standard 1960–2008 Consumption Model with 1 Variable Crowd out (T − G), after the deficit variable is modified by accommodating FR

16

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

379

purchases, i.e., (T − G) − (Tr + A) = (T − G)m : CD = .21(Y − TT ) − .01(T − G)m + 15(S + FB − (T − G)) (t=)

(2.6)

(6.1)

(0.5)

− 6.87PR + .44DJ−2 − .654.36POP16/65 + .023POP (−2.8)

(3.0)

(−3.7)

(5.5)

+ 54.46M2AV + .10 CB2 (6.2)

R = 82.0% 2

(2.4)

Adj. R = 78.4% 2

D.W. = 2.6

MSE = 30.30 (16.2)

Note in Eq. 16.1, though the deficit variable is unmodified, there is a variable controlling for changes in total loanable funds, net of the government savings component. The coefficient (t-statistic) on the deficit (crowd out) variable is =.45 (t = 3.4), signifying a large, highly statistically significant, crowd out effect. With accommodating purchases by the FR (TR + A), added to the deficit variable (T − G) and retaining the stand-alone modified total loanable funds variable, this drops in Eq. 16.2 to −.01 (t = 0.5) When defined this way, crowd out ceases to be a statistically significant negative influence on consumption. If reducing the deficit’s estimate of crowd out effects by (TR + A) gave a better explanation of how much crowd out actually occurred when there is a deficit, it should improve the model’s ability to explain variation in consumption. It did not. R 2 actually declined 6.2% when the deficit crowd out variable was reduced by the effects of FR purchases in the same period. It explained noticeably less variance than the standard model without either a deficit variable modifier, or a stand-alone control for the total loanable funds pool net of the deficit (85.9% in Eq. 10.1A). This result suggests an “errors in variables” problem occurs, and that the deficit’s accuracy as a measure of crowd out’s effects is distorted (reduced) by modifying it by FR purchases. I.e., exogenous changes in the loanable funds pool have not historically reduced crowd out, and just distort the real effects of crowd out when used to modify deficit values.

380

J. J. HEIM

16.1 Summary of Consumption Test Results for Different Sample Periods Coefficients and significance levels of the crowd out variable in both unmodified and FR purchases modified form are presented in Table 18.1 for various time periods between 1960 and 2009. Both versions contain a separate control variable for loanable funds net of government savings/deficits, as in Eqs. 16.1 and 16.2 above. To ensure the results were replicable, and not just spuriously related for reasons peculiar to the time period tested, the model was also separately tested in 16 other time periods, each representing a subset of the 1960– 2008 period tested above. Though each time period is different, they do overlap. Results are also presented in Table 16.1. Before modification, 15 of the 17 samples in Table 16.1 showed the deficit (T − G) had negative, statistically significant crowd out effects on consumption. This provides convincing evidence crowd out is a systemic problem in the US economy. However, when the value of FR purchases is deducted from the deficit, the new modified deficit variable is statistically significant in only 10 of 17 periods tested. In 12 of 17 cases, inclusion of the modifier causes the R 2 to drop, including 4 of the 5 cases where the crowd out effect dropped from significant to insignificant. In only in two cases does it rise. In eight of the 10 cases where crowd out remained statistically significant, the modified variable had lower t-statistics and model R 2 s. The predominance of lower R 2 s after suggest the modifier’s effects are more like a random variable distorting the true(r) value of crowd out (the deficit alone) than anything else. It suggests that FR open market purchases of securities, did not bring about reduce crowd out, though in theory FR security purchases should reduce crowd out. As noted in earlier chapters this unexpected result may be because 1. up until QE, FR purchases typically were only 1/8–1/4 of what was required to offset deficits. Hence even if they could offset crowd out, purchases were not large enough to achieve this objective until the QE years (Table 11.4), 2. most or all FR purchases are from investment banks and brokerages which do not in the main use proceeds to make loans to those who want to buy additional goods and services counted in the GDP (Chapter 7), and

2 RAdj

(T − G) Coef: t-stat R2

Variable

.78

.78

.71 (1.8) .87 .84

.34 (2.5) .89

w/o

.51 (2.9) .88

1960–1990

w/o

with

1960–1980

.85

.37 (2.8) .89

with

.87

.27 (1.4) .90

w/o

1960–2000

.86

.05 (0.3) .89

with

.84

.51 (3.2) .87

w/o

1960–2007

.80

.26 (1.3) .83

with

.85

.48 (3.5) .87

w/o

1960–2008

.80

.20 (1.8) .83

with

.78

−.02 (−0.5) .82

with

(continued)

.86

.45 (3.4) .88

w/o

1960–2009

Table 16.1 Comparing robustness over time of effects on consumption of crowd out, with and without deficit modification by accommodating FR securities purchases

16 DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

381

.90

.30 (1.4) .94 .92

.37 (2.1) .95 .89

.26 (1.1) .92

w/o

w/o

with

1970–2000

1970–1990

.89

.09 (0.4) .92

with

.83

.56 (3.4) .86

w/o

1970–2007

.78

.32 (1.5) .82

with

.85

.50 (3.6) .88

w/o

1970–2009

.78

−.02 (−0.6) .83

with

2 RAdj

(T − G) Coef: t-stat R2

Variable

.88

.05 (0.2) .93

w/o

1980–2000

.89

−.05 (−0.3) .93

with

.78

.30 (1.5) .85

w/o

1980–2004

.76

.09 (0.5) .84

with

.82

.54 (4.2) .87

w/o

1980–2010

.74

−.03 (−0.9) .81

with

.65

.28 (0.7) .80

w/o

1985–2004

.63

−.30 (−1.0) .79

with

.67

.34 (0.9) .80

w/o

1985–2005

.66

−.23 (−0.5) .79

with

Comparing robustness over time of effects on consumption of crowd out, with and without accommodating FR securities purchases

2 RAdj

(T − G) Coef: t-stat R2

Variable

Comparing robustness over time of effects on consumption of crowd out, with and without accommodating FR securities purchases

Table 16.1 (continued)

.89

.89 (3.3) .96

w/o

with

.68

−.14 (−1.5) .88

with

.78

−.02 (−0.1) .84

1996–2009

.80

.25 (1.8) .85

w/o

1975–2004

382 J. J. HEIM

16

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

383

3. a large portion of the FR purchases are from foreign banks, suggesting some or all of the proceeds may be deposited in European or Asian banks, and lent out to customers there. In a simple of FR purchases in 2014, about 40% were from foreign-owned banks (Chapter 7, Table 7.12). If these are the reasons we don’t see evidence that FR purchases do reduce crowd out, the problem is easily remedied. To remedy this, the FR could 1. Purchase at least enough securities to equal the deficit’s size 2. restrict its securities purchases to depository and other financial institutions catering to the retail loan needs of consumers and businesses desiring loans to buy real goods and services, i.e., do not purchase securities from banks that just use the proceeds to make loans used to by other securities or finance business takeovers, and 3. purchase securities only from financial institutions that will deposit all the proceeds in the US banking system. These results suggest monetary policy attempting to be accommodative to fiscal stimulus programs by reducing crowd out (and necessary in order for them to work) has not worked in the past (except perhaps during the quantitative easing period). Part of the problem may be the types of banks used to implement FR policy, but at least part, if not all, is just the inadequacy of the accommodative effort during the 1960–2007 period, when FR purchases were only a small fraction of the size of same-year deficits. From Chapter 10, we know that the baseline consumption model, before adding the deficit or loanable funds variables, explained only 71.4% of the variance. We also know from Chapter 10 that adding the one-variable deficit to the model increased R 2 to an average of 88.8% (Adjusted R 2 = 82.8%). When the stand-alone variable (S + FB − (T − G)) was added to the deficit model Average R 2 in the 17 samples fell to 87.8% (82.4% Adj.). In the Chapter 10 model, which used total loanable funds as the stand-alone modifier, adding the stand-alone raised R 2 to 89.1%. Hence, it appears to be a better modifier than this chapter’s stand-alone modifier (S + FB − (T − G).

384

J. J. HEIM

When Federal Reserve securities purchases were added as a modifier of the deficit values in this chapter’s model, average R 2 dropped from 87.8 to 85.5% (78.7% Adj.). In Chapter 10, when total loanable funds was used as both a stand alone and as a modifier of the deficit variable, R 2 was unchanged from the 89.1% obtained using it as only a stand alone; adjusted dropped to 78.6%. In short, this model does not explain as much consumption variance (or adjusted variance) as Chapter 10’s total loanable funds model, and for this reason the Chapter 10 model would be preferred. This chapter’s model also suggests increasing Federal Reserve securities purchases does not affect consumer crowd out, since the deficit variable minus FR purchases explains less variance than the deficit variable alone. For only 10 of the 17 tests, the unmodified crowd out variable (T − G) has a statistically significant positive relationship with consumption before the (Tr + A) modifier was added; in only 4 of 17 after the deficit variable was modified. Non-significant results can occur in an occasional sample even when the underlying relationship between variables is real and significant, for several reasons: 1. If during a certain period, one does not move. You can’t show correlation between two variables when one does not move appreciably. 2. If statistical problems arise in one sample not found in others, e.g., multicollinearity, or simply the selection of an “outlier” sample from the distribution of possible samples that can be drawn. Table 16.2 shows data on deficits starting in 1980 and continuing through 2000. The data for 13 of the 21 years involved show declining deficits (positive yearly changes in (T − G). Deficit reduction itself in these thirteen years was adding funds to the privately available portion the loanable funds pool, reducing crowd out, not adding to it. Hence, declining deficits should be associated, ceteris paribus, with increased demand by consumers and businesses (though offset by the decline in demand associated with the decline in the deficit).

16

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

Table 16.2 Yearly change in deficit and FR open market purchases (billions of 2005 dollars)

385

Year

Deficit*

FR securities Purchases

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1994 1995 1996 1997 1998 1999 2000

−116.12 15.67 −170.40 −66.62 43.28 −34.18 −45.79 62.27 39.81 10.00 −96.23 −68.10 −104.25 58.39 115.58 22.02 95.53 133.03 53.32 91.60

−16.50 −6.25 −1.14 15.60 4.03 21.62 24.22 23.72 10.46 −24.61 −1.29 30.20 27.99 37.82 30.57 6.15 6.09 37.06 22.05 26.20

* Negative sign denotes a year in which the deficit increased; positive sign a year of deficit decrease Source ERP (2010); Federal Reserve

16.2 Summary of Investment Test Results for Different Periods In this section, we compare the effects of the unmodified crowd out variable, the deficit (T − G), with the deficit modified by the amount of FR securities purchases in the same period on investment. The same 17 different though overlapping, time periods are tested as were used to test consumption in Sect. 16.1. The results indicate that in all 18 time periods, crowd out, as measured by the deficit (T − G) alone, before modification, has a statistically significant negative effect on investment in years when deficits occur, and a positive effect in years when government budget surpluses occur.

386

J. J. HEIM

However, when each year’s crowd out effect is hypothesized to be the deficit reduced by changes in FR securities purchases, i.e., (T − G) + (Tr + A), the coefficient and statistical significance reflecting the estimated effect of crowd out, as defined in this way, declines markedly. Below, this study’s results are compared to the crowd out effect found by Heim (2017, Eq. 5.4.TR) using a fairly typical (“standard”) investment model, as we have defined that before. In the 2017 study, the deficit was broken into two variables, one representing tax deficits (T ), ceteris paribus, and one representing government spending deficits (G), ceteris paribus. Each type of deficit was modified by the size of the total loanable funds pool (S + FB). No separate stand-alone control variable for the modifier was used. The Heim (2017) model is presented to show continuity and allow comparison with this study’s “standard” model, given in Eqs. 16.3 and 16.4, which test the same 1960–2010 period. This study uses nearly the same standard model, modified only by a changed definition of the deficit variable modifier from (S + FB), to only FR purchases of securities. In addition, in this study, an additional stand-alone variable is added to the model capture all sources of change in loanable funds except for changes in government saving, i.e., changes in personal and corporate savings, depreciation and foreign borrowing. The stand-alone variable is given as (S + FB) − (T − G). The Standard Investment Model Used in Heim (2017): ID = + .26(ACC) + .27 (TT ) − .30 (G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55 + CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(2.9)

MSE = 28.25

(5.4.TR)

Below is This Study’s Standard Investment Model with 1 Variable Crowd out (T − G), before Adding Deficit Modifiers and (S + FB) − (T − G) Variable (Using 1961–2009 data): ID =+ .26(ACC) + .32(TT −G T&I ) + .011POP (t=)

(6.5)

(5.5)

(8.3)

− 4.51PR−2 + 8.86XRAV + 2.66CAP−1 (−2.4)

R = 88.7% 2

(3.4)

D.W.= 1.9

(1.6)

MSE = 29.00

(10.3A)

16

387

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

The Standard Investment Model with 1 Variable Crowd out (T − G), before accommodating FR purchases, but including the (S + FB) − (T − G) variable. (Using 1962–2009 data) is given as: ID =+ .29(ACC) + .43(TT −G T&I ) + .15( (S + FB)−(T −G) ) (t=)

(6.2)

(5.0)

(1.8)

+ .020POP − 3.29PR−2 + 10.75XRAV + 4.30CAP−1 − .14GDP (3.3)

R = 85.5% 2

(−1.5)

2 RAdj =

83.0%

(3.0)

(1.6)

(−2.6)

(16.3)

D.W.= 1.6 MSE = 34.30

The Standard Investment Model with One Variable Crowd out (T − G), Modified by FR Security Purchases, and including the (S + FB) − (T − G) Variable (Using 1962–2009 data). ID =+ .26(ACC) + .08(TT −G T&I )m + .01( (S + FB)−(T −G) ) (t=)

(3.3)

(0.1)

(2.0)

− .012POP − 1.51PR−2 + 5.66XRAV + 4.80CAP−1 + .23GDP (−1.8)

R = 84.2% 2

(−0.4)

2 RAdj =

81.4%

(1.7)

D.W.= 1.4

(1.6)

MSE = 35.81

(3.3)

(16.4)

Note in Eq. 16.3 the coefficient (t-statistic) on the unmodified deficit (crowd out) variable is (.43) (t = 6.2), signifying a highly significant, large magnitude crowd out effect. In Eq. 16.3, with part of the deficit’s effects offset by FR securities purchases, the modified deficit variable coefficient drops to (.08) (t = 2.0), i.e., the magnitude of the crowd out effect is lower and becomes statistically insignificant. R 2 also noticeably drops, from 86 to 84%. The drop in R 2 indicates that investment varies more systematically with changes in the deficit alone than with changes in the FR purchases modified deficit. This suggests that (in this sample at least), FR securities purchases did not reduce the crowd out effects of government deficits, but just resulted in a “error in variables” problem discussed in Chapters 10 and 11, causing declining significance of the crowd out variable and model R 2 . In Table 16.3, we repeat the tests undertaken in Eqs. 16.3–16.4, for 17 different, though sometimes overlapping, time period samples. This is done to test the robustness over time of our initial results. Table 16.3 shows that, before modification of the deficit variable, in every period tested, deficit financing (crowd out) had a negative, statistically significant effect on investment. Even with modification, crowd out remains a

with

BL

w/o

1960–1990 with

BL

w/o

1960–2000 with

BL

w/o

1960–2007 with

BL

.94

.95

.87

.84

.87

.86

.81

.81

.43 (4.6) .87

BL

.85

.51 (5.1) .91

w/o

1970–1990

.82

.45 (3.2) .88

with

.43 (9.4) .89

BL

.87

.50 (4.9) .90

w/o

1970–2000

.86

.42 (4.2) .89

with

.30 (3.7) .83

BL

.82

.36 (4.6) .86

w/o

1970–2007

.82

.35 (5.3) .86

with

.33 (5.0) .89

BL

.83

.41 (4.9) .86

w/o

1970–2009

BL = Baseline (Standard Model w/o deficit (Tr + A) deficit modifier or (S + FB) − (T − G) stand-alone variable

2 RAdj

(T − G) Coef: t-stat R2

Variable

w/o

1960–2008 with

BL

w/o

1960–2009 with

.81

.08 (2.1) .84

with

.80

.29 (3.1) .84

BL

.83

.86

.31 (3.7) .89

w/o

1970–2004

.87

.85

.32 (3.3) .89

with

.81

.33 .64 .64 .38 .50 .45 .41 .49 .43 .30 .38 .37 .33 .43 .34 .33 .43 .08 (3.8) (7.2) (9.3) (4.0) (7.1) (3.8) (7.8) (6.0) (4.8) (3.9) (5.3) (6.0) (4.5) (5.7) (9.6) (5.5) (6.2) (2.0) .92 .96 .97 .85 .90 .88 .87 .89 .89 .83 .84 .84 .86 .83 .89 .89 .86 .84

w/o

BL = Baseline (Standard Model w/o deficit (Tr + A) deficit modifier or (S + FB) − (T − G) stand-alone variable

2 RAdj

(T − G) Coef: t-stat R2

BL

Variable 1960–1980

Table 16.3 Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases

388 J. J. HEIM

with

BL

w/o

with

BL

w/o

1980–2009 with

BL

w/o

1985–2004 with

BL

w/o

1985–2005 with

BL

w/o

1996–2009 with

.85

.83

.85

.84

.85

.82

.79

.78

.80

.79

.94

.95

.45 .41 .34 .25 .28 .28 .31 .36 .09 .24 .21 .21 .25 .21 .21 .29 .38 .10 (7.2) (4.1) (3.3) (2.4) (3.0) (2.8) (3.7) (3.6) (2.5) (3.0) (2.3) (2.1) (3.2) (2.4) (2.3) (1.7) (2.2) (3.7) .88 .90 .89 .82 .89 .89 .89 .88 .87 .83 .87 .86 .83 .87 .86 .96 .97 .98

w/o

1980–2004

BL = Baseline standard model without either (TR + A) deficit modifiers or stand-alone (S + FB) − (T − G) variable

2 RAdj

(T − G) Coef: t-stat R2

BL

Variable 1980–2000

16 DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

389

390

J. J. HEIM

significant factor in all 17 periods tested. Hence, the evidence is overwhelming that crowd caused by deficits out is a likely a real problem for investment. In Chapter 10, we found that the standard investment model with a GDP control variable, but with out deficit or loanable funds variables, explained 79.8% of the variance. Adding the deficit variable (but not a loanable funds variable) increased explained variance to R 2 = 87.4% (Adj. R 2 = 84.2%), clearly indicating investment behavior cannot be adequately explained without recognizing crowd out effects. In this chapter, when we add the stand-alone variable representing private savings and foreign borrowing, average R 2 rises slightly to 88.7% and Adjusted R 2 more noticeably to 84.9%, suggesting these variables can help offset crowd out. Modifying the deficit variable by any change in FR security purchases decreases R 2 to 88.3% and Adjusted R 2 markedly to 79.3%, suggesting increasing the loanable funds pool by increasing FR security purchases is ineffective in offsetting investment crowd out. In Chapter 10, using total loanable funds as the stand-alone modifier or as both the stand alone and as a deficit variable modifier, raised R 2 to 90.5%, which is greater than the 88.7% obtained in this chapter when using only the stand-alone modifier. For technical reasons involving the additivity of the deficit variable and stand-alone effects in Chapter 10, the model that includes both has the same 90.5% R 2 . We conclude the Chapter 10 model probably is to be preferred on both empirical and theoretical grounds. The theory chapter suggests that if the variable used to modify the deficit variable is truly a crowd out offset, and that the effect of the deficit on investment at different magnitudes is reasonably linear, that the modified deficit variable should remain statistically significant. This is the case here: before modification 17 of 17 samples showed significant crowd out effects of the deficit, and after modification, 16 of 17. We conclude that the data fully support the notion that this model, like the total loanable funds modifier model in Chapter 10, shows that the crowd out effects of deficits on investment can be offset by growth in (at least) some components of total loanable funds.

16.3

Conclusions

Tables summarizing Chapter 18 consumption and investment results, and conclusions regarding them, are presented below:

T16.1

16 Modified (w/s-a)

84

89

83

91

89

19 60 – 19 90 43

87

88

88

19 60 – 19 80 77

82

82

88

91

87

94

91

94

93

19 70 – 19 90 91

91

91

92

92

19 70 – 20 00 91

83

85

87

85

19 70 – 20 07 68

83

87

88

88

19 70 – 20 09 55

NA

NA

93

93

19 80 – 20 00 86

84

86

89

86

19 80 – 20 10 37

93

93

85

86

19 75 – 20 04 63

82

87

85

86

19 80 – 20 04 74

86

87

83

83

19 85 – 20 04 67

* 7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18

(Av. R2= 85.5%; Adj. Av. R2= 78.7%)

77

(Av. R2= 87.8%; Adj. Av. R2= 82.4%)

84

87

T16.1

90

16 Unmodif.d(w/s-a)

90

(Av. R2= 88.8%) 87 87 87

19 60 – 20 00 86

19 19 19 60 60 60 – – – 20 20 20 10 08 07 60 72 72 2 (Av. R = 71.4%) 86 86 86

(Av. R2 = 89.1%)

T10.2

Eq.11.1AA

From Table#

10 Baseline Total T16.1 LF Model (Modified (w/s-a))

17 Baseline (w/Def)

18 Baseline

Model

Cptr. 16 Consumption Summary Table (FR Purchases Deficit Modifier, Separate (S + FB-Deficit) Variable)

73

81

83

82

19 85 – 20 05 65

76

88

95

99

19 96 – 20 10 83

89

99

99

10 0

20 00 – 20 10 95

6/10

10/18

9/10

15/18

9/11

9/11 14/18

NA NA 14/18

T

(T-G)*

(T-G)

(T-G)*

(T-G)

(T-G)*

(T-G) (T-G)

NA NA* (T-G)

G

Test ratio

16 DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

391

392

J. J. HEIM

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R 2 increases to 88.8%, an increase of 24%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When the stand-alone loanable funds modifier is added to standard model with deficits, R 2 falls to 87.6% (1.2% points)) compared to the 88.8% for the standard deficit model without any standalone modifier. This suggest that private savings only and foreign borrowing loanable funds is a worse stand-alone explanatory variable than total loanable funds was in Chapter 11. 4. When adding a FR purchases modifier to the deficit, while retaining this stand-alone variable reduced explained variation in consumption even more. For 18 tests, average R 2 fell to 84.8%; By comparison, in the Chapter 11 model, which used total loanable funds for both the stand-alone variable and the deficit modifier, R 2 was 89.4%. This model clearly explains consumption less well.

From Table#

T10.4

T16.3

T16.3

10 Baseline Total LF (Modified (wo/s-a))

16 Unmodified(w/s-a)

16 Modified (w/s-a)

19 60 – 20 08 70 19 60 – 20 07 71 19 60 – 20 00 80 19 60 – 19 90 78 19 60 – 19 80 91 19 70 – 19 90 82

83

84

89

90

96

91 2

89

90 2

89

97

(Av.R = 88.3, Av. Adj R = 79.3%)

84

(Av.R2= 88.7%, Av. Adj R2= 84.9%)

86

(Av.R2 = 89.7%)

89

91

(Av. R2= 79.8%) 89 86 83 87 85 92 87 (Av. R2= 87.4%) (Av. Adj. R2= 84.2%) 91 88 87 90 90 95 90

19 60 – 20 10 76

90

90

91

89

19 70 – 20 00 81

89

86

87

83

19 70 – 20 07 71

85

86

91

89

19 70 – 20 09 76

N A

N A

90

88

19 80 – 20 00 81

89

89

90

89

19 80 – 20 10 80

89

90

87

84

19 75 – 20 04 80

89

89

86

82

19 80 – 20 04 81

87

88

84

83

19 85 – 20 04 75

* 7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18

T10.3

10 Baseline (w/Def)

11 Baseline (w/o Def) T11.4A

Model

R2 (18 Time Periods)

Cptr. 16 Investment Summary Table (FR Purchases Deficit Modifier, Separate (S + FB-Deficit) Variable)

86

87

84

83

19 85 – 20 05 75

87

87

97

96

19 96 – 20 10 93

98

97

96

97

20 00 – 20 10 95

10/10

17/17

10/10

17/17

10/11

NA 17/18 10/11 18/18

NA

T

(T-G)*

(T-G)

(T-G)*

(T-G)

(T-G)*

NA* (T-G) (T-G) (T-G)

NA

G

Test ratio

Sigif./Total

16 DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

393

394

J. J. HEIM

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8%. 2. When deficit variables only added to baseline standard model, average R 2 increases to 87.4%, an increase of 9.4%, clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When the stand-alone loanable funds modifier is added to standard model with deficits, average R 2 rises to 87.7% (0.3% points)) compared to the 87.4% for the standard deficit model. This suggest that private savings only and foreign borrowing loanable funds is a worse stand-alone explanatory variable than total loanable funds was in Chapter 10 (where R 2 grew to 91.2% when added, suggesting it is the better model). 4. Adding a FR purchases modifier to the deficit, while retaining this stand-alone variable, increased explained variation in investment to 89.2% in 18 tests, an increase of 1.8% points over the unmodified model. By comparison, in the Chapter 10 model, which used total loanable funds for both the stand-alone variable and the deficit modifier, R 2 was 91.2%. This model clearly explains investment less well; the Chapter 10 model appears to be the better model. The most likely reason the deficit’s crowd out effects were statistically significant in all 17 time periods tested, both before and after modification by (Tr + A), is that during most of the period sampled 1960–2007, the modifier, FR purchases, were only 1/8–¼ as large as the deficit. Hence, FR purchases simply were nowhere near large enough to offset crowd out.

16.4 Have FR Securities Purchases Been Pro or Contracyclical? If accommodating fiscal stimulus was a major monetary policy goal, we would expect to see deficits accompanied by same-sized increases in FR security purchases. Table 16.4 shows the yearly change the deficit’s size, and FR security purchases, 1960–2010.

16

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

Table 16.4 Real yearly changes in the deficit (T − G) and FR security purchases (Tr + A) (billions of 2005 dollars)

395

Year

( T − G)

(Tr + A)

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

46.9 −56.5 −28.4 26.3 −27.8 15.8 −17.7 −89.2 57.1 80.6 −120.4 −37.8 78.5 55.3 −53.4 −221.5 90.2 62.2 58.3 14.4 −116.1 15.7 −170.4 −66.6 43.3 −34.2 −45.8 62.3 39.8 10.0 −96.2 −68.1 −104.3 58.4 115.6 22.0 95.5 133.0 128.0

0.3 7.8 6.0 14.4 12.2 16.7 10.0 18.7 8.3 7.3 7.7 16.8 −5.2 19.1 −9.4 −0.1 5.6 6.4 2.1 −6.1 −16.5 −6.3 −1.1 15.6 4.0 21.6 24.2 23.7 10.5 −24.6 −1.3 30.2 28.0 37.8 30.6 6.2 6.1 37.1 18.9

(continued)

396

J. J. HEIM

Table 16.4 (continued)

Year

( T − G)

(Tr + A)

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

53.3 91.6 −255.2 −395.4 −102.0 47.4 155.9 99.3 −75.5 −379.0 −539.5 −23.6

22.1 26.2 31.2 74.7 25.2 33.3 2.4 10.1 −57.6 −239.1 1226.4 277.3

Statistical estimates of the simple model (T − G) = ƒ((Tr + A)) suggest such a relationship. (The sign on the coefficient for the FR purchases variable is negative because increases in the deficit show as rising (in absolute value) negative values for (T − G). The regression coefficient on (Tr + A) suggests there was an overall tendency for monetary policy to be accommodating in the data from 1960 to 2007. However, the negative relationship was only marginally statistically significant, i.e., the actual extent to which FR purchases matched changes in the deficit varied widely. Only after we add post-2007 data, i.e., data from the massive securities purchases of the Quantitative Easing (QE) period, did FR purchases equal or exceed deficit growth. Only when we add these years to the sample do we see a statistically significant relationship indicating increased FR securities purchases associated with growing deficits: Compare for example Eqs. 16.5 and 16.6 below.    (T − G) = −.27(Tr + A) + .37 AR(1) R 2 = .29 Using 1960−2011 data (t=)

(−1.8)

(2.8)

(16.5)

Before 2008, there was no statistically significant negative relationship.    (T − G) = −.63(Tr + A) + .31 AR(1) R 2 = .12 Using 1960−2007 data (t=)

(−0.9)

(2.3)

(16.6)

16

397

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

   (T − G) = +.54(Tr + A) R 2 = .01 Using 1960−1980 data (t=)

(0.3)

(16.7)

   (T − G) = −.56(Tr + A) + .36 AR(1) R 2 = .02 Using 1970−2007 data (t=)

(−0.7)

(2.2)

(16.8)    (T − G) = −1.32 (Tr + A) + .37 AR (1)R 2 = .17 Using 1975−2004 data (t=)

(−1.4)

(2.3)

(16.9)

All showed statistically insignificant relationships between deficits and FR purchases except the one containing the early QE period years. Hence, before the QE period, there was no systematic tendency for FR purchases to follow the ups and downs of the deficit over time. There was no systematically applied FR policy to accommodate fiscal stimulus efforts. Stimulative fiscal policy doesn’t work without accommodative monetary policy on the part of the FR. Therefore the FR has some responsibility for making sure that it takes place when deficits occur, unless they disagree with the fiscal stimulus being undertaken. It does not appear the FR undertook this responsibility in any systematic way during the years before, 1960–2007. This is probably why economists have had such a hard time since the 1930s reaching agreement on whether deficit driven fiscal policy works. In truth, even from within the framework of Keynesian analysis itself, a Keynesian stimulus shouldn’t without something enacted simultaneously to offset the “crowd out” effects of a deficit. That “something” is accommodative monetary policy. And it hasn’t been in any systematic way, and on occasions when it was, it was done in quantities way to small. We should not blame Keynes for the failure of Keynesian economics, we should blame the Fed. Do FR purchases increase in years when the deficit increases, but remain constant in years when deficits are declining? That would suggest monetary policy accommodates when it is needed most, even if it is not decreased (which may stimulate the economy or just be inflationary) when deficits are declining.

398

J. J. HEIM

Failure of the FR to contract reserves by selling securities when the deficit is declining also affects the economy, but in a good way. The declining deficit increases the amount of total loanable funds pool available for private borrowing, Since there is evidence demand for loans exceeds supply even in bad times, below full-employment economic conditions, additional private borrowing is likely to take place, stimulating the economy. At full employment, the additional private borrowing resulting from declining deficits is just likely to be inflationary. To examine the hypothesis that the FR may engage in accommodative money policy during recessions, but not in other years, the years above where the change in the deficit was increasing (had a negative sign) were examined. Equations 16.10 and 16.11 below presents the regression results.  (T − G) = −67.26 − 2.5(Tr + A)R 2 = .27 (t=)

(−2.9)

(−2.6)

  Using 1960−2006 deficit growth years data

(16.10)

 (T − G) = −116.57 + 0.64(Tr + A) R 2 = .12 (t=)

(−5.3)

(1.7)

  Using 1960−2008 deficit growth years data

(16.11)

For deficit years from 1960 to 2006, FR purchases increased as the deficit increased, which means it was partially accommodative. It would be fully accommodate only if the purchases equaled in size the deficits, which they did not. When the next two years are added to the sample, 2007 and 2008, the deficit increased but surprisingly, FR purchases markedly declined, worsening the crowd out problem. This caused the sign on the regression coefficient in Eq. 16.11 above to shift from negative to positive, indicating for that for these two years, FR purchase policy on average worsened the crowd out problem, not reduced it. Extraordinarily large purchases by the FR in 2009 and 2010 caused the average effect of FR purchase policy over the 50 year period to swing back negative, i.e., accommodative, but on average, the deficit growth in any one recession year was still 60% larger than the increase in FR purchases.  (T − G) = − 84.83 − 1.6(Tr + A) R 2 = .20 (t=)

(−4.1)

(−2.2)

16

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

  Using 1960−2010 deficit growthyears data

399

(16.12)

We conclude that while there has been a positive increase in securities purchases by the FR, possibly to accommodate the increase in deficits, the extent of the accommodation for both recession and non-recession years together has been paltry, about 20% of what was needed to completely offset the crowd out effects. The one exception was during 2009–2010 when purchases far exceeded deficit growth. We now examine whether FR purchases were systematically related to deficits in years when deficits were flat or declining. Declining deficits automatically increase the pool of loanable funds available for private borrowing, ceteris paribus. If FR purchases also increase, this plus the declining deficit would be increase the loanable funds pool beyond what the deficit’s reduction alone would allow. Equation 16.13 below shows the extent to which the FR continued buying securities even though the deficit was decreasing.  (T − G) = 53.97 + 0.97(Tr + A) R 2 = .13 (t=)

(0.0)

(2.0)

  Using 1960−2010 deficit decline years data

(16.13)

This positive relationship shown in Eq. 16.13 indicates a tendency for the FR to continue purchasing securities during periods of declining deficits, on nearly a one-to-one basis: a dollar increase in (Tr + A) is associated with a 0.97 cent decline in the deficit. The deficit declines automatically reduce crowd out, i.e., increase privately available loanable funds. Hence, the FR purchases occurring during this period on average almost doubled the increase in loanable funds available for private use solely because of the declining deficit. We have previously shown that during most of the 1960–2010 period, excess reserves were nearly zero, indicating the demand for loans was about the same as, and probably greater than supply. We suspect “greater” since prudentially, if banks allow excess reserves to fall to zero, they face the possibility that unforeseen circumstances will sometimes leave reserves below required levels. FR security purchases during periods of declining deficits, which are usually good times economically, represent pro-cyclical policy, and therefore are potentially inflationary. By comparison, during years of rising deficits, FR purchases were also increasing in a marginally statistically significant way.

400

J. J. HEIM

If FR purchases were a systematically successful way of reducing crowd out, we would expect that (TR + A) modified crowd out variables would have higher t-statistics reflecting this, as well as higher R 2 s for the whole modified model. This doesn’t seem to happen, and there are several reasons why this night not occur, some technical some substantive: 1. FR purchases were always way below the level need to fully accommodate deficit fiscal policy. 2. FR purchases were from Investment banks and brokerages, more likely to use the proceeds to buy other securities, than to lend it to those who would buy real goods and services. Hence the increase in the pool did not offset the reduction in loanable available to private borrowers caused by the deficit. 3. A large part of FR purchases may be from foreign banks. Some portion of the proceeds paid to them by the FR may have been deposited directly in foreign banks in Europe and Asia, and lent to customers there. 4. Spurious factors affecting consumption and investment may leave crowd out insignificant in any one period. 5. Differences in multicollinearity among explanatory variables in one sample compared to another may leave crowd out insignificant in any one period. 6. Mixing “Crowd In” and “Crowd Out” periods in the same sample, leaving net zero observable effects for the sample as a whole (see Chapter 11 for a more complete analysis of this problem). Finally, Sect. 16.3 tested to see if FR purchases policy was pro or contra cyclical. Results indicated that in recessions, FR policy worked to reduce crowd out, stimulating the economy, but that except for 2009, it efforts to accommodate were never large enough, and highly erratic in magnitude compared to what was needed. But even in declining deficit periods, FR purchases continued on a fairly regular basis, a policy that could be inflationary in periods of full employment, but stimulative if the economy is below that.

16

DO FR PURCHASES, USED AS DEFICIT MODIFIERS, REDUCE CROWD …

401

References Economic Report of the President. (2010). Washington: Government Printing Office. Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 17

Do FR Security Purchases, Used as 2 Variable Deficit Modifiers, Reduce Crowd Out, Controlling for Private Savings?

In Sects. 17.1 and 17.2 below we test the standard consumption and investment models. Unlike Chapter 16, where we used one variable (T − G) to represent the government deficit, here we wish to determine whether tax (T ) and spending (G) deficits have different crowd out effects. Tests of crowd out’s effect will be made both before and after the deficit’s reduction by the amount of FR securities purchases (TR + A). This will allow us to test the hypothesis that such purchases increase the pool of loanable funds, and therefore reduce crowd out effects in years when deficits are incurred or increase in size. We use the same stand-alone modifier, privates savings plus foreign borrowing, (S + FB) − (T − G) as in Chapter 16. The methods of calculus insure us that the coefficients on each variable in a model are ceteris paribus estimates, i.e., estimates of marginal effect are arrived at holding all other variables constant. Hence, the coefficient estimating the effect of a change in (T ) on consumption or investment are made holding the value of (G) constant. Hence the change in (T ), i.e., (T ) represents a change in the deficit, i.e., (T − G constant ). The coefficient on this change in (T ) variable measures its marginal effect on consumption and investment. The same is true for the coefficient on the government spending variable (G). Its coefficient measures the effect on consumption or investment of a change in the deficit that is induced by a change in government spending (G − T constant ). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_17

403

404

J. J. HEIM

17.1 Testing the Two-Variable Deficit Consumption Model (S + FB) − (T − G) is the portion of the total loanable funds that fluctuates for reasons other than the deficit. We use this as a stand alone separate variable in the model to control to avoid confounding the effects on C or I from this variable with the effects of crowd out, or (Tr + A) modified crowd out. However, as noted in Chapter 16, it can be argued that subtracting the deficit (T − G) from (S + FB) is a logically weak hypothesis. Total (S + FB) for any period already reflects the decline in it caused by a sameperiod negative level of government savings. To subtract the deficit again is redundant. (T − G) is included as a separate variable as a measure of the crowd out effects of a deficit. The test of this hypothesis is included for thoroughness of our example of possible options, not because of conviction it is correct. Using just (Tr + A) as a measure of how changes in the loanable funds pool can be made which could offset crowd out is questionable as well. The (T − G) crowd out effect can be modified not only by the exogenous factor (Tr + A), but by any of the other more endogenous factors that can change the size of the total loanable funds pool (S + FB) such as increases in income, or changes in the marginal propensity to consume. It may be that the Chapters 10 and 11 models, which uses total (S + FB) as a variable which might offset crowd out effects is a more theoryconsistent model. Of course, if there were no deficit, all the increase in loanable funds could be used to fund additional loans over previous period levels, financing additional consumer and investment demand. Using part of the growth to replace funds available for private borrowing in previous periods limits how much, if any, of the growth in the loan pool will be available for new private borrowing, and how much will be needed just to replace previous levels of private borrowing now curtailed because of the need to fund the deficit. This raises questions about the effect of deficits on the long term growth rate. The increase in government demand financed by the deficit will provide new stimulus to the economy. If it provides as much stimulus as the same portion of the growth in loanable funds would provide if left available for private borrowing, there may be no net effect on the overall long term growth rate. However, the choice of whether to use it

17

DO FR SECURITY PURCHASES …

405

to finance public versus private sector demand may change the composition of the growth. If allocated to public demand, i.e., used to finance deficits, there will be less private borrowing to buy cars, houses furniture in the long run, and more borrowing to finance public health, transfer programs, and infrastructure building. That said, the model we test below does use a stand-alone loanable funds control variable that nets out of total savings, the government savings component of total loanable funds, and does use (Tr + A) only as a modifier of the deficit variables. Below is the model we take as the “standard”consumption model, comprised of variables commonly thought to affect consumption. It is Eq. 4.4 TR taken from Heim (2017). The Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT )− .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−4.5)

(−2.1)

(5.1)

− .515.07POP16/65 + .020POP + 38.00M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

(4.9)

MSE = 24.88

(3.7)

(4.4TR)

Below that are Eqs. 17.1 and 17.2. They show this study’s test results for the same standard model, but with an additional variable, used to control for changes in the pool of loanable funds for all reasons except changes in the deficit (government savings), i.e., (Total US Savings + Foreign Borrowing)—the US consolidated Federal, State and Local government Deficit, i.e., (S + FB) − (T − G). It is exactly the same control variable used in Chapter 16. Changed from Heim (2017) is the variable used to modify the crowd out effects of the deficit to reflect changes in loanable funds. In Heim (2017) the variable used was total loanable funds, i.e., total US savings plus foreign borrowing (S + FB). In this chapter, we deduct FR purchases of government or agency securities (Tr + A) from the deficit, exactly as we did in Chapter 16, except here it is used twice, because we separate the deficit into two variables, one for tax cut deficits (T ) and one for government spending deficits (G). The modified crowd out variables become T + (Tr + A) and G–(Tr + A). They become our hypothesized measure of the crowd out effect: i.e., the deficit’s effect in reducing the portion of the pool available to private borrowers, “net” of FR increases the loanable

406

J. J. HEIM

funds pool during the same period by purchasing government securities in the open market, Testing indicated how FR purchases (Tr + A) were divided between the two deficit variables did not affect estimates of tax vs. spending crowd out, so the full value of (TR + A) was used as a modifier of each deficit variable. Equation 17.1 measures crowd out effects before modifying the deficit variable by the amount of FR securities purchases (Tr + A). Equation 17.2 measures crowd out effects after reduction of the deficit by the amount of FR securities purchases (i.e., the exogenous increase in the loanable funds pool). Both equations also include the stand-alone variable (S + FB) − (Tr + A). All three models were estimated using the full 1960–2009 Dataset. This study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included. (1960–2010 data) was found to be: CD = .54(Y − TT )+ 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58 M2AV + .13 CB2 (3.2)

(2.0)

(−0.1)

R = 60.3% 2

D.W. = 1.7

MSE = 43.98 (11.1AA)

This study’s Baseline (BL) Standard Consumption Model with 2 Variable Crowd Out (T and G Deficit Effects Estimated Separately). This Model is Estimated Before Deducting Any Loanable Funds Changes from (T ) or (G), and Before (S + FB) − (T − G) is Added as a Stand-Alone Variable: CD = .31(Y − TT ) + .32(TT ) − .16(G T&I )− 7.14PR+ .49DJ−2 (t=)

(6.4)

(6.6)

(−1.9)

(−3.1)

(4.5)

− .459.68POP16/65 + .017POP + 36.27M2 AV + .09CB2 (4.0)

(2.4)

R = 86.6% 2

(3.8)

D.W. = 2.1

(3.9)

MSE = 26.17 (11.1A)

This study’s Standard Consumption Model with 2 Variable Crowd out (T ) and (G), Including a Stand-Alone Control Variable for Loanable Funds Growth net of the deficit, but Before Modifying the Deficit by Accommodating FR Purchases): CD = .37(Y − TT ) + .30(TT ) − .07(G T&I ) (t=)

(6.9)

(7.2)

(−1.2)

17

407

DO FR SECURITY PURCHASES …

−13((ST + FB) − (T − G)) − 5.75PR+ .29DJ−2 (−2.8)

(1.9)

(4.0)

− 366.69POP16/65 +.022POP + 39.79 M2AV + 09CB2 (−1.8)

(3.7)

(5.0)

(3.5)

R 2 = 89.4%

D.W. = 1.9

MSE = 23.54

(17.1)

This study’s Standard Consumption Model with 2 Variable Crowd out (T − G), Including a Stand-Alone Control Variable for Endogenous Loanable Funds Growth, after Modifying Deficit Variables by Accommodating FR Purchases): C D = .42(Y − TT ) + .22(TT )m − .27(G T&I )m (t=)

(6.7)

(3.1)

(4.3)

−.22(ST + FB − (T − G)) − .77PR + .24DJ−2 − 206.50POP16/65 (−0.3)

(2.6)

(1.6)

(−0.9)

+ .010POP + 25.70M2 AV + 12 CB2 (3.2)

(3.3)

R = 85.7% 2

(2.9)

D.W. = 1.6 MSE = 27.30

(17.2)

All results cited in Table 17.1 for different time periods were estimated using exactly these same models. Only the length and dates of the time periods tested changes. The variable use to control for changes in the private portion of the loanable fund pool (S + FB) − (T − G) variable was found endogenously related to consumption and was replaced by a Wald-strong, Sargan-tested instrument. All variables were found ADF stationary or DF cointegrated. Newey–West standard errors were used to avoid heteroskedasticity problems. All data were tested in first differences to reduce multicollinearity and improved stationarity. Note that in Table 17.1, after accommodation by FR security purchases, the estimated crowd out effect of spending deficits changes from a negative effect to a statistically significant positive effect. A positive sign on this variable means the FR effect is not only fully negating the deficits crowd out effect, but there are net new loanable funds left over. Hence, it doesn’t just restore consumer spending to its pre-deficit level, it increases it. This may mean that accommodation is doing its job (and more— “crowd in”), but there is another explanation we will discuss further below. By comparison, the FR accommodation of tax cut deficits seems to reduce, the variables coefficient and t-statistic, but leave it statistically

.94 .88

.17 (0.7) .24 (0.8) −.56 (−0.5)

w/o

1960–1980

.94 .88

.18 (0.8) .24 (1.0) −.56 (−2.1)

with

.90 .85

.25 (3.1) −.09 (−1.2) −.07 (−0.8)

w/o

1960–1990

.90 .86

.25 (3.2) −.08 (−1.0) −.08 (−1.1)

with

.91 .88

.20 (2.5) −.01 (−1.2) −.07 (−0.4)

w/o

1960–2000

.90 .88

.16 (2.3) .06 (0.9) −.11 (−1.2)

with

.88 .86

.30 (4.9) −.04 (−0.6) −.18 (−2.3)

w/o

1960–2007

.87 .84

.28 (3.8) .06 (0.8) −.23 (−3.4)

with

.89 .86

.30 (4.9) −.06 (−0.9) −.14 (−2.0)

w/o

1960–2008

.86 .83

.25 (3.7) .11 (1.8) −.16 (−2.5)

with

.89 .87

.30 (7.2) −.07 (−1.2) −.13 (−1.9)

w/o

1960–2009

.86 .82

.22 (3.1) .27 (4.3) −.21 (2.6)

with

*2SLS regressions; (S + FB2 − Def) was endogenous. Instrument is Wald-strong, Sargan-valid. For 1960–2009 test w/(Tr + A), Durbin Watson was below 1.5, AR(1) used to raise it to 1.9

R2 R 2 Adj

T Def : t-stat G Def : t-stat S + FB−SG t-stat

Variable

Table 17.1 Crowd out effects of deficits on consumption with and without deficit modification by FR securities purchases*

408 J. J. HEIM

17

DO FR SECURITY PURCHASES …

409

significant. The crowd out coefficient drops, and adding the modification also reduces the significance levels of tax cut crowd out. The R 2 is also 3.7% points lower for the modified deficit model. Reduced significance levels for all variables in the model except one of the crowd out variables and reduced R 2 are generally taken to indicate the FR purchases modification actually hurt the model’s ability to explain variation in crowd out adequately. The implication is that FR security purchases do not significantly reduce consumption crowd out problem caused by the deficit, and when used to modify the deficit, just create an error in variables problem, reducing the explanatory power of the model. In Table 17.1 we use the same standard models shown in Eqs. 17.1 and 17.2 above, and test them in six different, though overlapping time periods. For each time period given in Table 17.1, two sets of statistics are presented, one with out modification (“w/o”) of the deficit variables (T ) and (G) as a measure of crowd out effects, and one which reduces the deficit variables crowd out effect by the value of FR securities purchases (“with”), i.e., T + (Tr + A) or G–(Tr + A). Recall from Chapter 11, Tables 11.1AA and 11.1B, that the standard model before adding the deficit and any loanable funds variable had an R 2 of 71.4%, which rose to 89.4% (Adj. = 84.3%) when the deficit variables were added. In Table 17.1, we see that adding only the stand-alone modifier variable to the standard model with deficit variables increases average R 2 for the six samples from 89.4 to 90.2% (Adj. R 2 rose noticeably from 84.3 to 86.6%). Growth in private savings(and foreign borrowing) does seem to offset some of the effects of crowd out on consumer spending. However, when the modified deficit variable was added to this model, R 2 and Adjusted R 2 dropped to 88.8 and 85.2%, respectively. As was the case in Chapter 16, growth in FR security purchases does not seem to affect consumer crowd out and creates an error in variables problem, by distorting the deficit’s more accurate measure of consumer crowd out effects. Table 17.1 shows that tax cut deficits show statistically significant crowd out problems, both before and after modification, in five of six tests. As noted in Chapter 16, if the crowd out effect is a real economic phenomenon, we would expect our tests to show a significant relationship, with the coefficient showing the marginal effect of an additional dollar of crowd out (deficit) on consumption. This seem to be the case for tax cut deficits. The fact that after modification by FR purchases, the

410

J. J. HEIM

tax cut deficits remain significant and usually with roughly the same coefficients is a result consistent with this. It means that the deduct from the tax cut value merely reduces the amount of dollars the marginal effect per dollar is multiplied against to get its estimated effect on consumption. In short, changes in FR purchases, don’t eliminate the crowd out problem, they just offset part of it. The rest still has the same marginal effect per dollar, i.e., the regression correctly estimated a linear relationship between crowd out and consumption that holds over a wide range of values. That said, significance levels on the modified tax cut crowd out variable are lower than for the unmodified variable. This may mean some portion of the increase in FR purchases is having no effect on consumption, and just the magnitude of (T ) and (G) alone are better measures of the crowd out effect of deficits. By comparison, 4 of 6 tests show the unmodified value of government spending deficits causing a crowd out problem, Finding two insignificant may mean one of five things: 1. Spending deficits crowd out effects are unpredictable and evidence may be spurious. 2. Spending deficits tend to be consumer oriented. They may be replacing in consumer’s pockets, money lost to unemployment they otherwise would have borrowed to purchase necessities, e.g., an unemployed person buying groceries with a credit card is buying consumer goods with borrowed money. A government spending program which increases unemployment insurance payments may not create crowd out “problem”; it may replace the need for the private borrowing this deficit created. Hence, the occurrence of a spending deficit will be uncorrelated with any change in spending, this period compared to last. Last period’s spending out of borrowed money is replaced this year by spending out of (e.g.) increased unemployment insurance benefits. The regression will show the relationship between deficits (crowd out) and spending to be insignificantly different from zero. This means some or all of Keynesian spending stimulus plans may not stimulate the economy (change spending levels) because it just replaces spending done previously out of somebody else’s savings (borrowed money). The extent to which this occurs may vary from period to period. If the increase in government spending does not fall into the hands of those who borrow, the crowd out effect will occur. If it does fall into the hands

17

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411

of those who borrow, it may just replace the borrowing, n which case there is no crowd out effect on private spending. 3. In periods of declining deficits, we have (definitionally) “crowd in,” i.e., increases in the pool of privately available loanable funds, which should have a positive effect on consumption. When such periods are mixed in a sample with a period that has deficit growth, we get a “crowd out” effect. Put them together and the average effect on consumption in the deficit decline years (+) is offset in large part by the effect in the deficit growth years (−), leaving a small net regression coefficient, i.e., average effect for the whole period. But is it likely to be statistically insignificant since have the yearly effects will have sizable positive coefficients (i.e., effects), and half will have sizable negative coefficients. Hence the standard deviation associated with the combined sample coefficient will be large, and therefore, its t-statistic small. In Chapter 11, we showed how this causes a series of different samples to show insignificant crowd out simply because they consist of two subsamples with deficits moving in opposite directions. 4. The theoretical model we are using to test crowd out may be bad. If so we should expect bad results, since all regressions can do is show if a hypothesis is consistent with the way the data say the world actually works. This appears to be the problem here. We noted above it is questionable on theoretical ground whether this model of the stand-alone variable (total loanable funds minus the government savings component) was correct. A more correct model might include total loanable funds as the stand-alone variable as a way of representing in ceteris paribus models the negative effect on consumption of increases saving. If we redo Table 17.1 using only (S + FB) as the stand alone, five of the six-time periods sampled show statistically significant negative effects on consumption of unmodified spending deficits. Three of six show significant spending crowd out after modification. All six tax cut deficits continue to show significant crowd out effects. 5. There is other evidence to the same effect. As we showed in Chapter 9’s consumption model (Table 9.1), a proper definition of the loanable funds offset, total (S + FB), may show spending deficits as well as tax cut deficits adversely affect consumption. Those tests were for only one sample period. Chapter 11 showed the Chapter 9 results for spending deficits are replicable in other time periods.

412

J. J. HEIM

6. There could be a multicollinearity problem between the government spending and loanable funds variables severe enough to cause the spending variable to appear insignificant when it really was significant. However, correlations between the separate crowd out net of the deficit variable and the tax variable (+.09) and the government spending variable (−.09) were not indicative of a multicollinearity problem. Hence, bad modeling may be the reason we find only three of six periods sampled show unmodified spending deficits have crowd out effects, when in most models studied, most or all do. Modifying the deficit by increasing FR security purchases results in even less samples (only one) showing spending deficits associated with crowd out of consumer spending. The one significant after-accommodation test shows statistically significant crowd out effects, but those were actually “crowd in” effects, which, as discussed earlier, may not be problems at all. The magnitude of FR securities purchases more than offsets the loss of part of the loanable funds pool previously used by private borrowers. This causes a net increase in privately available loanable funds. The positive sign and statistical significance of the relationship indicate consumers did borrow and spend some or all of the increase in loanable funds. The elimination of two of the three instances of significant crowd out by modifying (reducing) the deficit by the amount of FR security purchases shows the same thing: As the positive result just discussed; it is consistent with the hypothesis FR purchases can offset the spending deficit crowd out effects on consumption. Table 17.2 reruns the same “with” and “without” consumption models as in Table 17.1, but without the separate, stand-alone total loanable funds minus government deficit control variable. We are, in essence testing to see if controlling for factors which can affect the level of loanable funds available, other than the FR’s purchases, perhaps does not affect our crowd out effect estimates. In the unmodified model, all variables were found stationary or cointegrates; no variables were found endogenous, so OLS was used. Average R 2 before modifying deficit variable was 88.7%; after 84.8%. Adj. Average R 2 before modifying deficit variable was 85.0%; after 81.0%. Clearly this consumption crowd out model does not explain th data as

.53 (3.9) −.21 (−1.6) .91 .85

.27 (1.7) .02 (0.1) .86 .79

.28 (3.2) −.10 (−1.7) .89 .85

w/o

w/o

with

1960–1990

1960–1980

.14 (1.8) .03 (0.4) .84 .79

with .23 (2.8) −.03 (−0.5) .91 .88

w/o

1960–2000

.14 (2.7) .07 (1.5) .89 .87

with .33 (5.6) −08 (−1.5) .87 .84

w/o

1960–2007

.30 (4.2) .07 (1.0) .84 .80

with

*Single stage regression, since (S + FB2 − Def) was the only endogenous variable. No AR(1) needed

T Def : t-stat G Def : t-stat R2 R 2 Adj

Variable

.33 (5.6) −.08 (−1.6) .87 .85

w/o

1960–2008

.28 (4.3) .10 (1.5) .85 .83

with

.32 (6.6) −16 (−1.9) .87 .83

w/o

1960–2010

.22 (3.3) .29 (5.1) .81 .78

with

Table 17.2 Effects of crowd out on consumption, with and without modification by FR securities purchases (no separate (S + FB) − (T − G) control variable)*

17 DO FR SECURITY PURCHASES …

413

414

J. J. HEIM

well as the model in Table 17.1, which does have a stand-alone private savings and foreign borrowing variable.

17.2 Testing the Two-Variable Deficit Investment Model Below is the model we take as the “standard” investment model. It is Eq. 5.4.TR. taken from Heim (2017). The Standard Investment Model from Heim (2017) (Using 1960– 2010 data): I D = +.26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (−2.7)

R = 83.3% 2

(2.9)

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

Following that, Eqs. 17.3 and 17.4 show the same standard model with two changes: 1. the addition only of a control variable for changes in the pool of loanable funds for all reasons except changes in the government saving (the deficit). 2. Also changed from Heim (2017) is the deduct from the tax or spending deficit to account for loanable funds changes. In Heim (2017), it was total loanable funds (S + FB). In this model, any deficit is reduced by the amount of FRr purchases of government or agency securities, on the assumption that the entire FR purchase ends up as additional loanable reserves in banks that make loans for real goods and services. All variables were found Augmented Dickey Fuller (ADF) stationary or DF cointegrated; No Hausman endogeneity was found between the dependent and explanatory variables in the model using the stand-alone loanable funds variable (Eqs. 17.3 and 17.4, and Table 17.3), but the government spending variable was endogenous in the model without

.97 .94

.97 .95

.56 (8.0) −.70 (−6.9) .47 (3.6) .90 .86

.51 (2.6) −.48 (−2.8) .36 (0.6)

w/o

.6 (3.3) −.78 (−2.9) .6 (2.0)

1960–1990

w/o

with

1960–1980

a 1960–2009 figures very similar

R2 R 2 Adj

T Def : t-stat G Def : t-stat S T −S G − t-stat

Variable

.86 .79

.39 (5.2) −.32 (−2.3) .30 (2.7)

with

.90 .87

.47 (7.2) −.45 (−3.8) .30 (3.4)

w/o

1960–2000

.86 .83

.40 (5.3) −.35 (−2.6) .29 (2.7)

with

.87 .84

.34 (3.0) −.35 (−2.9) .22 (0.4)

w/o

1960–2007

.86 .83

.32 (5.2) −.29 (−3.0) .14 (2.8)

with

.88 .86

.39 (7.8) −34 (−2.8) .19 (3.3)

w/o

1960–2008

.89 .86

.28 (4.9) −21 (−2.2) .15 (2.8)

with

.90 .88

.38 (8.2) −.39 (−4.0) .06a (3.0)

w/o

1960–2010

.78a .73

.24a (3.0)a .24a (2.6)a .16 (0.9)a

with

Table 17.3 Effects on investment of crowd out, with and without FR securities purchases modifiers; separate private saving and foreign borrowing control variable included

17 DO FR SECURITY PURCHASES …

415

416

J. J. HEIM

the stand-alone loanable funds variable (Table 17.4), and was replaced by a Wald strong instrument which was not itself endogenous (Sargan test). Newey–West standard errors were used to avoid heteroskedasticity. Variables were tested in first differences to reduce multicollinearity and nonstationarity effects. Correlations between the separate crowd out net of the deficit variable and the tax variable (+.09) and the government spending variable (−.09) were not indicative of a multicollinearity problem. This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included: ID = +.48(ACC) + .008POP+ .76PR−2 (t=)

(2.5)

(10.6)

(0.2)

+ 7.37XRAV + 14.08CAP−1 (2.2)

(4.3)

R = 69.4% 2

D.W. = 1.6

MSE = 47.87

(10.3C)

Same as Eq. 10.3C This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy: ID = +.47(ACC)− .00POP − 0.85PR−2 + 5.21XR AV (t=)

(0.0)

(4.0)

(2.0)

(−0.3)

+ 10.39 CAP−1 + .10 GDP (−1.3)

(2.9)

R = 76.1% 2

D.W. = 2.1

MSE = 43.06

(10.3B)

Same as Eq. 10.3B This study’s Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010): ID = +.27(ACC) + .33TT − 33G T&I + .012POP (t=)

(2.6)

(6.4)

(−3.9)

(2.8)

− 4.95PR−2 + 6.68XRAV + 2.43CAP−1 − .02GDP (−2.5)

(3.5)

R 2 = 89.0%

D.W. = 1.9

(1.8)

(−0.2)

MSE = 29.87

(11.4A)

R2 R 2 Adj

T Def : t-stat G Def : t-stat

Variable

.90 .86

.31 (3.8) −.29 (−2.1)

.93 .89

.34 (4.6) −.38 (−2.1) .83 .79

.37 (4.0) −.30 (−2.9)

w/o

w/o

with

1960–1990

1960–1980

.80 .75

.30 (3.2) −.20 (−1.3)

with

.88 .83

.43 (6.2) −.37 (−3.8)

w/o

1960–2000

.83 .80

.37 (4.6) −.28 (−3.3)

with

.82 .80

.29 (5.0) −.29 (−2.8)

w/o

1960–2007

.83 .81

.31 (5.2) −.28 (−2.2)

with

.85 .83

.34 (5.7) −.30 (−1.9)

w/o

1960–2008

.87 .85

.25 (4.6) −.20 (−1.7)

with

.89 .87

.33 (6.3) −.36 (−4.2)

w/o

1960–2010

.73 .69

19 (4.1) +.22 (3.9)

with

Table 17.4 Comparing robustness over time of effects on investment of crowd out, with and without accommodating FR securities purchases (No separate (S Total −S G ) control variable)

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418

J. J. HEIM

Standard Investment Model with 2 Variable Crowd out (T , G), Before Deficit modifying FR purchases, but with a Stand-Alone Loanable Funds Variable (Using 1960–2010 data): ID = +.18(ACC) + .38TT − 39G T&I + .16((S + FB) − (T − G)) (t=)

(5.7)

(5.6)

(−5.0)

(2.1)

+ .007POP− 3.24PR−2 + 5.54XRAV + 1.00CAP−1 (2.7)

(2.7)

(−1.6

R = 90.4% 2

D.W. = 1.9

(0.7)

MSE = 27.50

(17.3)

Standard Investment Model with 2 Variable Crowd out (T , G), adjusted for accommodating FR purchases, and with a Stand-Alone Loanable Funds Variable: (Using 1960–2010 data): ID = +.25(ACC)+ .24TTm + 24G T&Im + .05((S + FB) − (T − G)) (t=)

(4.1)

(2.6)

(3.0)

(0.9)

+ .006POP− 6.46PR−2 + 3.76XRAV (0.9−)

(−1.2)

(1.1)

+ 3.25CAP−1 + .51 AR(1) (3.1)

(1.0)

R = 77.6% 2

D.W. = 2.1

MSE = 42.92 (17.4)

All results in Table 17.3 for the other time periods estimated use exactly the same models shown in Eqs. 17.3 and 17.4. Only the length and dates of the period used to test the model changes. In Table 17.3 the models tested include the stand-alone loanable funds net of government savings variable. Any increases in these loanable funds in the same period a deficit occurs can be used to reduce crowd out effects. By using the FR open market purchases of securities a variable distinct from this, we are implicitly asserting that it too can increase loanable funds, but is not included in our stand-alone loanable funds variable. As noted earlier, this is a somewhat questionable assumption. In Table 17.3, for each time period given, two sets of statistics are presented. In one set, there is no modification of the crowd out variables (T , G) by FR purchases of treasuries and agency (Tr + A) securities, and one in which the same regression model is reestimated using crowd out variables modified by FR securities purchases T + (Tr + A) or G–(Tr + A).

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419

From Chapter 11 we know the standard model without deficit or loanable funds variables explains 68.3% of the variance; when the deficit variables are added to the model, average R 2 increases to 88.3% for the six periods tested. Adding the stand-alone (S + FB) − (T − G) variable raises R 2 to 90.3%, indicating private saving and foreign borrowing can offset some investment crowd out; Adj. R 2 rises to 87.5%. Adding the modified deficit variable and the stand-alone (S + FB) − (T − G) variable lowers R 2 to 87.0; Adj. R 2 falls to 83.2%, indicating FR security purchases do not help offset investment crowd out. Table 24.4 reruns the same “with” and “without” models as in Table 17.3, but without the stand-alone (total loanable funds—government deficit) control variable. We are, in essence, testing to see if controlling for other factors which can affect the level of loanable funds available makes a difference in our crowd out effect estimates of the effects of FR purchases, and therefore needs to be controlled for. From Chapter 11 we know the standard model without deficit or loanable funds variables explains 68.3% of the variance; when the deficit variables are added to the model, average R 2 increases to 88.3% for the six periods tested. Adding the stand-alone (S + FB) − (T − G) variable to the deficit model lowers R 2 to 86.2%, indicating investment crowd out; Adj. R 2 is 83.5%. Adding the modified deficit variable and the stand-alone (S + FB) − (T − G) variable lowers R 2 further to 83.2; Adj. R 2 falls to 79.8%, indicating FR security purchases do not help offset investment crowd out. Both sets of results from Table 17.4 suggest Table 17.3 model is a better model. Including the private savings and foreign borrowing variable as a stand alone increases the model’s ability to explain variance. Both Tables 17.3 and 17.4 models, however, indicate changes in FR securities purchases do not affect the investment crowd out problem. In the 1960–2010 sample, quantitative easing was in full swing, and the tax cut deficit’s crowd out effect was little changed. But for spending deficits, the variable’s sign actually became positive when the 2009 data was added to the sample, and the variable became highly statistically significant. That said, the R 2 for the model dropped markedly, probably

420

J. J. HEIM

because so much of the QE increase in bank loanable funds remained as excess reserves, i.e., unused, leaving investment up, but not nearly as much as bank reserves increased. We noted earlier that FR accommodative monetary policy can offset deficits, but that increases in excess of this amount may lead to a “pushing on a string” problem unless the economy is growing and requires proportionately more lending, or banks lower lending standards. This appears to be the case in 2008–2010. 2010 also marks the first time when FR security purchases exceeded deficit size (see Table 15.3). Never before had purchases even come close to matching deficit size, averaging about 25–40% of deficit in the 1960–2007 period. Hence, you could look at the changed results when the 2009 data was included as indicating that for the first time, given the chance, accommodative monetary policy proved it can offset at least government spending induced deficits.

17.3 Summary of Chapter 17 Results from 2 Variable Deficit Models The two tables below and associated notes summarize this chapter’s findings: Cptr. 17 Consumption Summary Table: (FR Purchases Deficit Modifier, Separate (S + FB) − (T − G) Control Variable) Model

From Table#

11 Baseline (wo/Def

T11.1AA

11 Baseline (w/Def)

Eq.11.1A

1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 -2010 08 07 00 90 80 90 00 07 10 00 10 04 04 04 05 09 10

Test T

Ratio G.

60 72 72 86 43 77 91 91 68 55 86 37 63 74 67 65 83 95 (Av. R 2 = 71.4%) 87 87 87 91 89 91 93 92 86 88 94 85 88 88 86 87 92 99 (Av. R 2 = 89.4%; 88.7% for 6 periods tested below)

NA NA NA NA* 15/18 6/18* 10/11 5/11* ( 5/5 5/5**)

11 Baseline Total LF T11.1 Model (w/def. mod.& s-a)

90 (Av. R2 6 samples) --- --- --- --- --- --- --- --- ---

5/6 4/6

17 Unmodif.d(w/s-a)

T17.1

91 85 90 86 86 88 (Av. R2=00.3 Adj. Av. 07.7%)- --- ---

17 Modified (w/s-a)

T17.1

90 87 89 84 84 87 (Av. R =88.8 Adj. Av. 85.2%)---- --- ---

17 Unmodif.(wo/s-a)

T17.2

17 Modified (wo/s-a)

T17.2

---.--- --

6/6 6/6 6/6 6/6

3/6 3/6 1/6 1/6*

91 89 91 87 87 87 --- --- --- --- --- --- --- --- --- --- --- --- --6/6 6/6 (Av. R 2=88.7 Adj. Av. 85.0%) 91 89 90 84 85 81 --- --- --- --- --- --- --- --- --- --- --- --- --6/6 (Av. R 2=84.8 Adj. Av. 85.0%) 6/6 ___________________________________________________________________________________ *7 samples containing 1/3–½ of all observations from “Crowd In” yearsRemoved, leaving 11 of 18 **Modified spending deficit only significant when 2008-10 QE years included.

4/6 4/6* 1/6** 1/6*

2

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421

For the six periods tested: 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R 2 increases to 89.4%, an increase of 25%, clearly indicating consumption cannot be explained without allowing for significant negative crowd out effects. 3. When the stand-alone loanable funds modifier (S + FB) − (T − G) is added to the standard model with deficits, R 2 falls to (87.7%), (1.1%) below the unmodified standard deficit model. In Chapter 18, when a (S + FB) stand-alone modifier was added, R 2 increased from 89.4 to 90.7%). Because it explains more variance, the Chapter 18 stand-alone modifier (S + FB) appears to be the better modifier. 4. When also modifying the deficit by the amount of FR purchases (Tr + A), while continuing the stand-alone loanable funds variable, R 2 actually falls to 86.8%. For the Chapter 18 model, R 2 remained at 90.7% 5. When no stand-alone private savings plus foreign borrowing variable was included in the model, the unmodified deficit model had R 2 of 88.7%, and drops to 86.7% when modified. Essentially the results with and without including a stand-alone variable representing the private saving plus foreign borrowing portion of total loanable funds produce virtually identical results. Both results were similar to Chapter 18 results: the stand alone did not add to explained variance, and using only the deficit modifier without the stand alone caused R 2 to drop.

Cptr. 17 Investment Summary Table: (FR Purchases Deficit Modifier, Separate (S + FB) − (T − G) Control Variable)

422

J. J. HEIM

Model

From Table#

R2 (18 Time Periods) 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 -2010 08 07 00 90 80 90 00 07 09 00 10 04 04 04 05 10 10

Sigif./Total Test Ratio T G.

10 Baseline (w/o Def) T10.3C 69 67 66 63 65 72 -61 56 65 72 69 77 -64 71 63 57 92 91 (Does not include GDP Control Variable) (Av. R 2 = 68.3%)

NA NA

NA NA*

10 Baseline (w/o Def) T10.3B 76 70 71 80 78 91 82 81 71 76 81 80 80 81 75 75 93 95 (includes GDP Control Variable) (Av. R 2 = 79.8%)--

NA NA

NA NA*

11 Baseline (w/Def)

11/18 16/18

Eq.11.4A

89 86 84 89 87 95 90 90 86 90 89 90 89 89 89 89 98 98 (Av. R 2 = 89.8%; 88.3% for 6 periods tested below)

17 Unmodif.d(w/s-a) T1717.3 97 86 87 83 88 90 (Av. R 2 = 90.3%%; Adj. 87.5%) --- ---

6/6 6/6 6/6 6/6

6/6 6/6 6/6 6/6*

6/6 6/6 6/6 17 Modified (wo/s-a) T17.4 95 81 84 85 87 76 (Av. R = 83.2%; Adj. 79.8%) --- --- --- --6/6 ___________________________________________________________________________________ *7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 10 of 17

6/6 6/6* 6/6 6/6*

17 Modified (w/s-a)

17 Unmodif.(wo/s-a)

T17.3

T17.4

97 90 90 87 89 78 (Av. R 2 = 87.0%; Adj. 83.2%)--- --- --- --93 87 88 83 86 89 (Av. R 2 = 86.2%; Adj. 83.5%) --- --- --- --2

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 68.3%. 2. When deficit variables only added to baseline standard model, R 2 increases to 88.3%, for the six periods tested below with a modifier; an increase of 14%, clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When the stand-alone private savings & foreign borrowing loanable funds modifier is added to standard model with deficits, R 2 rises to 90.3% (Adj. 87.5%) when compared to the standard deficit model without any loanable funds variable. This indicates that the adding the private savings and foreign borrowing loanable funds adds to the explanatory power of the investment model. The same total loanable funds model in Chapter 11, except using total loanable funds as the stand-alone variable, explains considerably more (91.2%) of the variance. 4. Adding a FR purchases modifier to the deficit, while retaining this stand-alone variable, caused R 2 to drop, indicating they are not an effective way of expanding the pool of buyers. 5. When the FR purchases loanable funds modifier is added as a modifier of the deficit only, but not included as a stand-alone variable, R 2 decreases on average in the 6 periods tested, from its average of 88.3% before adding the private loanable funds deficit modifier to

17

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423

an average of 83.2% after modification of the deficit variables. Before modification, this model is basically the baseline model with deficit variables added. The decline in R 2 suggests the modification of the deficit variable by changes in FR purchases is creating an error in variables problem for our crowd out variable. And that the unmodified version (the deficit variables) is a better measure of crowd out. In the Chapter 11 model, modifying the deficit variables by the full value of loanable funds increased the R 2 noticeably, suggesting that is a better definition of the extent to which increases in loanable funds can offset the negative effects of crowd out. 6. The deficit variables remained significant after modification in all tests. The sign on the spending deficit variable changed from negative on the 5 pre-QE period tests to positive on the test including the 2008–2010 QE period data, providing evidence of the success of the QE effort in helping the economy.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 18

Do FR Purchases Reduce Crowd Out Effects, Controlling for Other Types of Loanable Funds?

18.1 Testing the Two---Variable Deficit Consumption Model This model is the same as the model used in Chapter 15, but uses a markedly different @SLS instrument, but one which is still Wald-Strong and Sargan tested.

18.2 Testing the Two-Variable Deficit Consumption Model As a connection to prior studies, we again take as a starting point, Eq. 4.4.TR taken from Heim (2017a) as a prototypical standard consumption model. An equation expressing this standard model, estimated using 1960–2010 data, is shown below: The Standard Consumption Model, with deficit variables added, from Heim (2017a): CD = 29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−4.5)

(−2.1)

(5.1)

− .515.07POP16/65 + .020POP + 38.00M2AV + .09CB2 (3.2)

R = 87.8% 2

(6.0)

(4.9)

D.W.= 2.2 MSE = 24.88

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_18

(3.7)

(4.4)

425

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J. J. HEIM

Two modifications of this standard consumption model, Eqs. 18.1 and 18.2, are given below. These new equations show test results for the model, with a stand-alone loanable funds variable added: the stand alone is endogenous changes in the pool of loanable funds, i.e., changes in (S + FB) except changes due to growth in FR purchases of securities. This new variable is comprised of total US savings and foreign borrowing minus FR purchases of securities, i.e., (ST + FB) – (Tr + A). The variable used to modify the tax or spending deficit is the exogenous part of total loanable funds, FR security purchases (Tr + A). Our objective is to measure the extent to which FR open market securities purchases can offset crowd out. It modifies the deficit only by FR security purchases, but acknowledges that there are other factors affecting the size of the pool of loanable funds, which can also offset crowd out, and therefore must be controlled for, i.e., (S + FB) − (Tr + A) if we are to get accurate estimates of how well FR purchases offset crowd out. The standard model from Heim (2017a) and these two equations, equation were estimated using the same 1960–2010 Dataset. Below is this study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included. (1960–2010 data) CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(7.2)

(0.6)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

R = 60.3% 2

(−0.1)

D.W.= 1.7

(2.0)

MSE = 43.98

(11.1AA)

(Recall from Chapter 11, Eq. 11.1AA, that adding the deficit variables to the baseline model increased R 2 from an 18-sample average of 71.4– 89.4%, an increase of 25%, strongly supporting the argument that deficits have crowd out effects which adversely affect consumer spending.) This study’s Baseline (BL) Standard Consumption Model with 2 Variable Crowd Out (T and G Deficit Effects Estimated Separately) is shown below. This Model is Estimated Before Deducting Loanable Funds Changes from (T ) or (G), and before (T + G) is Added as a Stand-Alone Variable (1960–2010 Data Sample Only):

18

427

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

CD = .31(Y − TT ) + .32(TT ) − .16(G T&I ) − 7.14PR + .49DJ−2 (t=)

(6.4)

(6.6)

(−3.1)

(−1.9)

(4.5)

− .459.68POP16/65 + .017POP + 36.27M2AV + .09CB2 (4.0)

(2.4)

R = 86.6% 2

D.W.= 2.1

(3.9)

(3.8)

(18.1A)

MSE = 26.17

Equation 18.1 below measures the crowd out effects of tax (T ) and spending (G) deficits before modification by FR securities purchases, but including the stand-alone endogenous loanable funds variable. Equation 18.2 measures the magnitude of these deficit variables as reduced by any same-period FR securities purchases, while continuing to include the stand-alone endogenous funds variable. The Standard Consumption Model with 2 Variable Crowd out (T , G), With a Stand-Alone Endogenous Loanable Funds Variable Before Accommodating FR Purchases Are Added as a Modifier to the Deficit Variables) is given as: CD = .14(Y − TT ) + .13(TT ) + .01(G T&I ) + .12(ST + FB − Tr − A)) (t=)

(2.6)

(1.7)

(0.1)

(2.6)

− 4.89PR + .66DJ−2 − 549.84POP16/65 + .023POP + 54.52M2AV + 15CB2 (−1.8)

(4.4)

R = 81.5%

(4.9)

(−2.8)

Adj.R = 77.2%

2

2

(5.1)

(4.1)

D.W.= 2.5 MSE = 30.86 (18.1)

The Standard Consumption Model with 2 Variable Crowd out (T , G), With a Stand-Alone Endogenous Loanable Funds Variable After Accommodating FR Purchases Are Also Added As a Deficit Variable Modifier: CD = .16(Y − T ) + .12(TT )m − .01(G T&I )m + .19(ST + FB − (Tr + A)) (t=)

(2.1)

(2.4)

(4.4)

(−0.2)

− 6.97PR + .65DJ−2 − 575.19POP16/65 + .022POP (−2.5)

(4.0)

(−2.9)

(4.3)

+ 48.01M2AV + .12CB2 (3.0)

(4.5)

R = 79.1% 2

Adj.R = 74.3% 2

D.W.= 2.7 MSE = 32.81

(18.2)

Clearly this model does not explain as much variation in consumer spending as does the total (S + FB) modifier model of Chapter 11, which explained 91.2%.

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J. J. HEIM

All results cited in Tables 18.1 and 18.2 below were estimated use the same models as the ones above. These tables show the results of attempts to replicate our initial results given above in five additional different time periods. Good science requires replication to ensure our initial results represent true underlying relationships, and not just spurious results. Only the length and dates of the time periods tested changes in the different tests; the model tested remains the same.

18.3 Adding a Separate Loanable Funds Variable to the Consumption Model Table 18.1 presents results using the standard model, with the addition of a stand-alone control variable for all loanable funds changes net of changes in FR security purchases. (S + FB − (Tr + A)). In Table 18.2, the model tested drops this additional variable, otherwise it is the same as the model whose results are presented in Table 18.1. All models tested in these tables have been tested for stationarity (ADF test), where necessary, cointegration (DF test), and for endogeneity. All variables tested are either stationary or cointegrated with the dependent variable. The stand-alone loanable funds variable (S + FB) − (Tr + A) was found endogenously related to the dependent variable (Hausman test), and replaced by a Wald-strong instrument, which itself was not endogenous (Sargan test). For each time period given in Table 18.1, two sets of results are presented. In one of them, labeled “w/o” there is no modification of the crowd out effects (T , G) by changes in FR securities purchases (Tr + A). In the other, labeled “with,” the same regression model is reestimated with the crowd out variables (T ) and (G) modified by exogenous changes in loanable funds (FR purchases). In both models there is a stand-alone endogenous loanable funds variable. R2 Results Recall from Chapter 11, Tables 11.1AA and 11.1B, that the standard model before adding the deficit and any loanable funds variable had an R 2 of 71.4%. When the deficit variables were added, R 2 rose to 89.4% (Adj. = 84.3%), indicating consumer crowd out was a real problem and has a negative effect on consumption. In Table 18.1, we see that adding only the stand-alone modifier variable to the standard model with deficit variables decreased average R 2 for the six samples from 89.4 to 82.0% (Adj. R 2 fell noticeably to 76.3%

.68 (4.9) −.28 (−2.4) −.59 (−1.8) .94

.88

2 RAdj

.87

.62 (4.7) −.23 (−1.8) −.55 (−1.7) .94 .86

.30 (3.1) −.16 (−2.3) −.07 (−0.7) .91 .87

.30 (4.1) −.16 (−2.2) −.12 (−1.3) .91

with

w/o

w/o

with

1960–1990

1960–1980

T Def : t-stat G Def : t-stat ST + FB −(Tr + A) R2

Variable

.87

.17 (1.5) −.01 (−0.7) .07 (0.5) .90

w/o

.86

.15 (1.6) .06 (−0.7) .11 (0.7) .89

with

1960–2000

.62

−.03 (−0.2) .26 (1.5) .40 (2.1) .70

−.12 (−0.4) .23 (0.8) .50 (1.5) .59 .49

with

w/o

1960–2007

.71

.12 (1.0) .07 (0.6) .25 (1.7) .77

w/o

.70

.16 (1.7) .14 (1.8) .25 (3.2) .76

with

1960–2008

Table 18.1 Effects of on consumption crowd out W/WO stand-alone endogenous LF variable

.77

.13 (1.7) .01 (0.1) .12 (2.6) .81

w/o

.74

.09 (1.6) −.03 (−0.3) .19 (3.8) .79

with

1960–2010

18 DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

429

.56 (7.5) .53 (4.1) −.21 (−1.6) .91

.85

2 RAdj

.84

.53 (5.4) .44 (2.9) −.05 (−0.2) .90 .85

.35 (4.1) .29 (3.6) .10 (−1.7) .89 .83

.35 (4.6) .29 (2.9) .05 (0.3) .88

with

w/o

w/o

with

1960–1990

1960–1980

(Y − T ) t-stat T Def : t-stat G Def : t-stat R2

Variable

.88

.33 (4.5) .22 (2.8) −.03 (−0.5) .91

w/o

.84

.33 (5.0) .25 (2.9) .27 (1.5) .87

with

1960–2000

.84

.31 (4.8) .33 (5.6) −.08 (−1.5) .87

w/o

.78

.34 (5.5) .45 (5.1) .21 (1.1) .81

with

1960–2007

.85

.32 (5.2) .33 (5.6) −.08 (−1.6) .87

w/o

.78

.37 (6.1) .41 (5.1) .27 (1.4) .82

with

1960–2008

.84

.31 (7.3) .32 (6.6) −16 (−1.9) .87

w/o

.74

.28 (4.2) .31 (3.7) .43 (5.4) .78

with

1960–2010

Table 18.2 Effects on consumption of crowd out, with and without compensating FR purchases (no separate (S + FB) − (T + A) control variable)

430 J. J. HEIM

18

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

431

86.6%). However, when the modified deficit variable was added to this model, R 2 and Adjusted R 2 rose to 83.2 and 78.2%, respectively. This suggests little effectiveness of FR purchases in reducing consumption crowd out. Adding a stand-alone loanable funds variable to the baseline model, reduced the model’s ability to explain variance, i.e., reduced R 2 , in 4 of the six periods tested, but raised it in two. The average for the six periods was a decline of 7.0 percentage points. Adding the deficit modifier variable to the model reduced explained variance further. At least part of the decline seems due to an econometric problem; The models in Table 18.1 were estimated using an instrument for the standalone loanable fund net of FR purchases variable, due to its endogenous relationship with the consumption variable. Though a Wald strong instrument was used, it had noticeably less explanatory power than the variable itself. When reestimated in OLS (just for comparison purposes; OLS is not really appropriate), R 2 for the six sample periods was about the same as without the endogenous loanable funds variable in the model. This would not seem as good a model to use the Chapter 11 model, which used total loanable funds as the stand-alone variable, and raised R 2 by doing so to 91.2%. Replacing the deficit with the modified deficit variable caused R 2 to increase slightly compared to just using the stand-alone loanable funds variable, but still left the model explaining less variance the standard model with a deficit variable, but no loanable funds variables at all. Overall, this suggests the FR purchases modifier is leaving unchanged or reducing our ability to explain variation in consumption.

18.4 The Consumption Model Without a Separate Loanable Funds Variable Table 18.2 reruns the same “with” and “without” models as in 18.1, but without the separate loanable funds control variable (total saving + foreign borrowing—FR purchases) in the model. We are, in essence testing to see if controlling for other factors beside FR purchases which may affect the level of loanable funds available makes a difference in our crowd out effect estimates. There are no stationarity problems with either the modified or unmodified variables not resolved by cointegration or detrending. The model without the deficit variables being modified was without endogeneity problems, so it was estimated using OLS. The

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J. J. HEIM

modified spending deficit G + (Tr + A) was found endogenous with the dependent variable and was replaced by a Wald-strong instrument, which was not endogenous (Sargan test). R2 Effects: The average R 2 for the baseline model with deficit, but no loanable funds variables, was 88.7%. the average adjusted R 2 was 85.2% Compared to the baseline model with deficit, but no loanable funds variables, R 2 falls in all six models after modifying the deficit variables by the amount of same-period FR securities purchases. Crowd Out and Loanable Funds Effects: In the baseline model, tax deficit crowd out was a significant problem in 6 of 6 periods tested. When the deficit variables were modified by same-period FR purchases, the number significant remained unchanged, though generally with slightly lower coefficients and significance levels, indicating growth in loanable funds may have reduced crowd out slightly, but nowhere near enough to eliminate it. In the baseline model, government spending deficits were statistically significant in 5 of 6 tests. After modification, in only 1 of 6 tests, the one including the large 2007, 2008, and 2010 data (QE era-level purchases), were significant, and there the effect is positive (i.e., crowd in, not crowd out). The insignificant earlier period results probably reflects an errors in variable problem stemming from the net effect of changes in loanable funds being very small and negative typically, because the increase comes out of reduced consumption. During the QE era it came from exogenously generated large increases in loanable reserves. The systematically lower R2 s found when the modifier is added to (T , G), suggests an errors in variables problem, i.e., the huge FR purchases of securities during the QE period may not only have (more than) covered crowd out, but may have far exceeded what consumers were in a position to borrow. Hence we have more variation than the change in consumer spending can explain, compared to the “without” model during QE. Overall Findings for Consumption, Adding the stand-alone loanable funds variable (net of FR purchases) was relate to substantially declining R 2 , a highly unusual response; almost always the result of adding a variable is to increase R 2 or leave it the same. The non-positive response suggesting increases in loanable funds may not affect consumer behavior. This could be because such increases are channeled into business rather than consumer borrowing.

18

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

433

In models without a stand-alone loanable funds variable, R 2 also generally declines when crowd out variable values are modified by FR purchases, again suggesting historically they have had no significant effect on consumption. Hence, we conclude consumption models fail to support the notion that increasing loanable funds can offset the crowd out effects of deficits.

18.5 Testing the Two-Variable Deficit Investment Model Below is the model we take as the “standard” investment model, Eq. (5.4.TR) taken from Heim (2017a), which includes variables commonly thought to be determinants of investment by many economists. The Standard Investment Model from Heim (2017a), (Using 1960– 2010 data): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W.= 2.0

(1.7)

(5.4.TR)

MSE = 28.25

Equations 10.3B and C are repeated below from Chapter 10. They show this study’s baseline investment model without either deficit or loanable funds variables yet added. They are the same except Eq. 17.3B has a GDP variable added to control for economic conditions. This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, and No GDP Variable Included to Control for the State of the Economy ID = + .48(ACC) + .008POP + .76PR−2 + 7.37XRAV (t=)

(10.6)

(2.5)

(0.2)

(2.2)

+ 14.08CAP−1 (4.3)

R 2 = 69.4% D.W.= 1.6 MSE = 47.87 (Same as Eq. 10.3C) This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy

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J. J. HEIM

ID = + .47(ACC) − .00POP − 0.85PR−2 + 5.21XRAV (t=)

(0.0)

(4.0)

(2.0)

(−0.3)

+ 10.39CAP−1 + .10GDP (−1.3)

(2.9)

R 2 = 76.1% D.W.= 2.1 MSE = 43.06 Same as Eq. 10.3B; and same as Eq. 11.10C) Equation 11.3A is repeated from Chapter 11. It shows the baseline investment model including deficit variables used in this study The Baseline Deficit Model: Before Adding Deficit Variables Modified by (S + FB), and Stand-Alone (S + FB) Variable I (1960–2010 Sample): ID = + .25(ACC) + .32TT − 33G T&I + .011POP − 4.91PR−2 (t=)

(7.2)

(3.9)

(2.9)

(−3.9)

(−2.6)

+ 6.53XRAV + 2.21CAP−1 (4.0)

R = 89.4% 2

(1.5)

D.W. = 1.9

MSE = 29.00

(11.3A)

The Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010): ID = + .27(ACC) + .33TT − 33G T&I + .012POP − 4.95PR−2 (t=)

(6.4)

(2.6)

(−3.9)

(2.8)

(2.5)

+ 6.68XRAV + 2.43CAP−1 − .02GDP (3.5)

R = 89.0% 2

(1.8)

D.W. = 1.9

(−0.2)

MSE = 29.87 (11.4A)

Table 11.3A shows the baseline model values of the deficit variables, their significance levels, and R 2 s in the baseline model shown in Eq. 11.4A above, before the addition of any loanable funds variables. Results are shown for the 18 time periods tested using one or the other of the two investment models tested in this chapter (Table 18.3A). Next, in Eq. 18.3 is the same standard model, with the addition of only a stand-alone control variable for changes in the pool of loanable funds, net of FR security purchases (S + LF) − (TR + A). Equation 18.4, shows the same model but with the deficit variables modified by FR purchases. All variables were found Augmented Dickey Fuller (ADF) stationary; No Hausman endogeneity was found between the dependent and explanatory variables, except for the variable capturing loanable funds effects except FR security purchases. Newey–West standard errors were

.13 .28 .32 .26 .33 .33

1960–1980 1960–1990 1960–2000 1960–2007 1960–2008 1960–2010

(0.9) (2.2) (2.7) (2.3) (2.7) (2.6)

T β(t)

Sample period

35 (−3.8) −.42 (−3.2) −.40 (−5.2) −.36 (−3.2) −.33 (−2.8) −.33 (−3.9)

G β(t) .95 .87 .89 .84 .86 .89

R2 1970–1990 1970–2000 1970–2007 1970–2009 1980–2000 1980–2010

Period .25 .33 .23 .32 .27 .30

(1.1) (2.5) (2.0) (2.3) (1.5) (2.0)

T β(t)

Table 18.3A A base line estimates of investment crowd out

1975–2004 1980–2004 1985–2004 1985–2005 1996–2010 2000–2010

.90 .90 .86 .90 .89 .85

−.55 −.45 −.37 −.34 −.42 −.31 (−2.8) (−4.5) (−3.1) (−3.5) (−3.3) (−2.4)

Period

G β(t) R2

.15 (1.8) .09 (1.1) .09 (1.3) .09 (1.3) 29 (2.6) .01 (0.0)

T β(t)

−.40 (−3.7) −.41 (−3.7) −.41 (−4.4) −.42 (4.5) .52 (1.1) 1.11 (1.8)

G β(t) R2 .89 .89 .89 .89 .98 .98

18 DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

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J. J. HEIM

used to avoid heteroskedasticity. As always in this book, models were tested in first differences of the data. Standard Investment Model with 2 Variable Crowd out (T , G), before modification by FR purchases, but with Endogenous Loanable Funds Variable (Using 1960–2010 data): ID = .27(ACC) + .33TT − 37G T&I (t=)

(−3.7)

(3.5)

(7.0)

− .016( (S + FB) − (Tr + A) ) − .012POP (3.9)

(−0.6)

− 4.40PR−2 + 6.78XRAV + 2.74CAP−1 (−2.1)

R = 89.1% 2

(3.8)

(1.9)

D.W.= 1.9

MSE = 29.74

(18.3)

The Standard Investment Model with 2 Variable Crowd out (T , G), modified by FR purchases, with Endogenous Loanable Funds Variable (Using 1960–2010 data): ID = + .17(ACC) + .13Tm − .16G m + .26( (S + FB) − (Tr + A)) (t=)

(5.0)

(2.3)

(−1.9)

(6.3)

+ .005POP − 1.47PR−2 + 5.06XRAV + 2.02CAP−1 (1.7)

R = 90.0% 2

(−0.7)

D.W. = 1.9

(2.6)

MSE = 27.97

(1.5)

(18.4)

Note that adding coefficients anon the deficit variables and the standalone loanable funds variable gives nearly identical result, indicating a net positive effect on investment of (.55) per dollar of increase in loanable funds. 18.5.1

Crowd Out Effects in Models with an Endogenous Loanable Funds Control Variable

All results in Tables 18.3 and 18.4 for the initial results shown above and five additional time periods are estimated use exactly the same model. Only the length and dates of the period used to test the model changes. In Table 18.3 we include the additional stand-alone variable to the standard model (Eq. 18.3A) when testing. The additional variable shows yearly changes in endogenous loanable funds, For each time period given, two sets of statistics are presented. In one set, there is no modification of

.01 (0.1) −.11 (−0.8) .56 (4.6) .95 .93 .31 .35 .93

.09 (1.4) −.21 (−1.4) .48 (4.3) .96 .94 (3.2) (−2.6)

.17 (2.2) −.17 (−1.5) .31 (3.5) .91 .89 .37 −.38 .86

.10 (1.5) −0.6 (−0.5) .40 (11.5) .91 .88 (4.0) (3.2)

with

w/o

w/o

with

1962–1990

1962–1980

*BL = Baseline Model Results

T Def : t-stat G Def : t-stat S + FB − Tr − A t-stat R2 Adj. R 2 BL T (t-stat) BL G(t-stat) BL R 2

Variable

.25 (2.0) −.25 (−2.2) .20 (1.3) .91 .89 .41 −.41 .88

w/o .15 (2.3) −.12 (−1.4) .32 (5.3) .90 .88 (5.7) (−4.9)

with

1962–2000

.28 (2.1) −.35 (−2.8) −.01 (−0.1) .83 .80 .27 −.33 .83

w/o .13 (1.7) −.15 (−1.4) .20 (2.5) .85 .82 (3.3) (−3.1)

with

1962–2007

.38 (5.0) −.42 (−4.4) −.11 (1.0) .84 .81 .32 −.33 .86

w/o

.37 (4.5) −.21 (−2.7) .16 (2.8) .90 .88 (3.8) (−2.9)

with

1962–2008

.33 (3.5) −.37 (−3.7) −.02 (−0.6) .89 .87 .32 −.33 .89

w/o

.13 (2.3) −.16 (−1.9) .26 (6.3) .91 .89 (3.9) (−3.9)

with

1962–2010

Table 18.3 Comparing robustness over time of Effects on investment of crowd out, with and without accommodating loanable funds modification

18 DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

437

T Def : t-stat G Def : t-stat R2 Adj. R 2 BL T (t-stat) BL G(t-stat) BL R 2

Variable

.31 (3.0) −.29 (−1.9) .90 .93 .30 −.35 .93

.34 (3.8) −.47 (−2.9) .94 .94 (2.8) (−2.0)

.37 (3.8) −.30 (−2.4) .83 .89 .42 −.46 .85

.31 (2.0) −.28 (−1.5) .82 .88 (2.7) (2.7)

with

w/o

w/o

with

1960–1990

1960–1980

.42 (5.4) −.37 (−4.2) .86 .89 .42 . − 37 .87

w/o .34 (3.6) −.23 (−1.4) .83 .88 (4.4) (2.4)

with

1960–2000

.29 (3.4) −.29 (−2.7) .82 .8 .28 −.23 .83

w/o .30 (4.2) −.20 (−1.1) .84 .82 (3.6) (−1.2)

with

1960–2007

.34 (4.0) −.29 (−2.6) .85 .81 .32 −.24 .86

w/o

.26 (4.1) −.10 (−0.8) .87 .88 (4.3) (1.4)

with

1960–2008

.33 (3.9) −.36 (−4.7) .89 .87 .33 −.23 .89

w/o

.20 (2.6) .21 (2.2) .76 .89 (4.3) (−1.5)

with

1962–2010

Table 18.4 Effects of rowd out on investment, with and without loanable funds accommodation (no separate (S + FB) − (Tr + A) or GDP control variable)

438 J. J. HEIM

18

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

439

the actual crowd out variables (T , G) by the same period change in FR purchases, and one in which there is modification. R2 Effects: Baseline model R 2 , before adding any loanable funds variable, was 87.5% For models including the stand-alone LF variable, but not the deficit variable modifier, average R 2 was found to be 88.8% (Adj. 86.5). When the deficit variable modifier was added, average R 2 was 90.5% (Adj. 88.2%). Adding the LF stand-alone added 1.3% to R 2 ; adding the deficit modifier to the stand-alone variable raised R 2 to 90.5%, 3.0% higher. After adding a separate loanable funds net of FR purchases variable to the baseline model (BL), R 2 increased in 3 of 6 time periods tested, stayed the same in one, and declined in two. However, Adding the variable increased R 2 1.3 percentage points on average. After adding the deficit variable modifier to this model, R 2 increased again in 4 of 6 periods tested, with the average increase in the six periods being (+2.5) points, mostly related to the big QE era purchases (which suggests that the exogenous portion of loanable funds changes (FR purchases) has a considerably more significant positive impact on investment than changes in the larger, endogenous part of the pool. Results indicate increases in endogenous loanable funds increased explanatory power, but that increases in exogenous loanable funds increased investment noticeably more. Effects on Crowd Out and Loanable Funds Comparing unmodified with modified crowd out results is based on the assumption that any modification of the size of tax or spending deficits should not lower their significance or the regression coefficient (if the underlying relationship between investment and modified deficits is linear). In fact, in theory, the significance levels of the crowd out variables will increase if the modification is a better estimate of the magnitude crowd out’s effect on consumption or investment. However, we have shown earlier in this book that there is evidence that suggests not all FR purchases end up lent out to borrowers who want to buy goods and services that will be counted in the GDP. Much of the borrowing may go to purchase securities sold to the FR. In this case, we may get a significant relationship of FR purchases to consumption or investment, but not as high a significance level, because part of the fluctuation in the crowd out variables due to FR purchases is not associated with movement in the

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dependent variable. Hence a lower significance level may be seen after modification. Also, if modification improves the accuracy of our estimates of crowd out effects, we expect to see the regression explain more variance in the data (higher R 2 ). Finally, if we modify a deficit variable and it goes from being statistically significant to insignificant, we may interpret this two ways. It may mean we have taken a good estimate of crowd out’s effects (the deficit), and added a random variable to it which affects investment (e.g., the FR purchases modifier). In this case, insignificance does not mean crowd out has been eliminated. In the present case we can show the modifier, FR purchases has only been big enough to offset a small portion of the deficit, about 1/8 on average from 1960–2000, about ¼ from 2000– 2007. Hence sample results covering this period shouldn’t turn the crowd out effect variables insignificant, because they could not offset most of the deficit’s crowd out effects. They could however, interrupt the systematic pattern with which deficits, ceteris paribus, move with consumption and investment, causing the relationship to appear unsystematic, i.e., statistically insignificant, which is what we see in Table 18.3. In the baseline model, both tax cut and spending deficits show statistically significant crowd out effects in all six-time periods examined. There can be little question but that crowd out is real. The question is, can increases in loanable funds offset the deficit’s negative effects? The increase in R 2 when adding the loanable funds variables suggests it can. For tax cut deficits when a stand-alone endogenous loanable funds variable is added to the baseline model, before modification by (Tr + A), crowd out was significant in 5 of 6 tests. After modification, it was only significant in 4 of 6 tests. Recall that modifying deficits by FR purchases increased explained variance in four of six cases, far more on average than did endogenous changes in loanable funds, but that the gain was concentrated in the samples containing data through 2007 and 2008. This is consistent with this “4 of 6” finding. For spending deficits, crowd out was found to be a crowd out problem before modification in 5 of 6 tests. After modification, it was only significant in 2 of 6 cases. This suggests FR purchases do not offset the crowd out effects of spending deficits (perhaps because they are not made available to consumers); they just distort the underlying relationship negative relationship between spending deficits and investment.

18

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

441

Overall, this model’s R 2 results suggest FR open market operations, but not private growth in loanable funds increase investment by offsetting (a relatively small part of) crowd out effect.

18.6 Crowd Out Effects in Models Without an Endogenous Loanable Funds Control Variable Table 18.4 reruns the same “with” and “without” models as in Table 18.3, but without the separate control variable for other factors which can affect the size of the endogenous loanable funds pool. We are in essence testing to see if controlling for factors besides FR purchases which can affect the level of loanable funds, as we did in Table 18.3, makes a significant difference in our crowd out effect estimates. R2 Effect Average R 2 (Adj. R 2 ) before deficit modification was 85.8% (83.0%). After deficit modification, average R 2 (Adj. R 2 ) fell to 84.3% (81.3%). He results suggest subtracting FR purchases from the deficit does not give as accurate an estimate of crowd out effects as does the deficit alone. Instead, it just causes an “errors in variables” problem. Results from the model using endogenous loanable funds modified deficit variables were compared with the base line model. Table 18.4 indicates that in 3 of the 6 periods tested, R 2 increased with the addition of the FR purchases deficit modifier, but in the other 3 it declined. The average over the 6 periods tested was a loss of (2.8) percentage points. This suggests the FR loanable funds variable had no effect on investment and when combined with the deficit variables, were just distorting the relationship of variables that do, i.e., creating an “error in variables” problem. Crowd Out and Loanable Funds Effects In Table 18.4, the tax deficit crowd out variable, was found to be statistically significant for all 6 sample periods before any modification by FR security purchases. After it was modified by any same period changes in FR purchases of securities, crowd out remained a statistically significant variable in all six sample periods for tax cut deficits. Spending deficits, before modification, were only significant in three of six periods tested. After modification it was 2 of 6. The significant samples were the 1960–80 sample and the full 1960–2009 sample periods:

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2009 marks the first time when FR security purchases exceeded deficit size. Never before had purchases even come close to matching deficit size. Hence, you could look at the statistically significant crowd out effect result that emerged when the 2009 data was added to the 1060– 2008 data as indicating that large FR purchases can offset deficit crowd out effects. The results may be indicting that for the first time, given the chance, accommodative monetary policy proved it can offset at least government spending induced deficits. Overall, results showed FR purchases slightly reduced coefficients on tax cut crowd out variables, but not significance levels, and for spending deficits reduced slightly the number of periods in which crowd out was found not significant. In Table 18.4, the strong showing of significance for crowd out variables, particularly the tax cut variable, may be because of misspecification of the model. By dropping our stand-alone loanable funds (net of FR purchases) variable), we allow increases in the (non-FR) loanable funds pool that positively affect investment to at the same time we are testing to see if taxes or spending also has an effect. Absent a business cycle control (and growth in loanable funds can serve that purpose, since it is highly correlated with economic conditions), we expect both loanable funds and tax collections to have separate, positive correlations with any rise as the economy (including investment). If the loanable funds variable is left out of the model, but is positively correlated with taxes (which it is), we expect the regression to assign loanable funds variable variance to the tax variable in addition to assigning to it the variance attributable to the tax variable itself. Hence, taxes may look stronger and more significantly related to investment in Table 25.4 than they really are due to crowd out effects of tax changes alone (the “left out variables” effect). Similarly, when economic conditions decline, investment and loanable funds decline and government spending typically increases. If the rise in spending is correlated with the decline in loanable funds, the decline in investment explained by declining loanable funds may be attributed by the regression to the rise in government spending. This would make the crowd out effect of rising government spending deficits look as though it were having a much stronger, more significant, negative effect on investment than truly belongs to crowd out alone.

18

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

443

To see if we have this problem, we retested the model in Table 18.4, adding a variable to control for changes in economic conditions (the current year GDP), as we estimated crowd out’s effects. Results are shown in Table 18.5 below. R2 Effects: In Table 18.5, with a GDP control variable, average R 2 before deficit modification was 84.3% (without the GDP control it was higher; 85.8% in Table 18.4). After deficit modification, average R 2 rose slightly to 84.5% (slightly more than without the GDP control: 84.3% in Table 18.4). Overall, adding the GDP control variable does not seem to add much to explanatory power. Replacing the deficit variables with FR purchases modified variables resulted in increased R 2 in 3 of 6 tests, declining R 2 in the other three. On average there was a (0.2) percentage point gain in R 2 in the six tests. If we compare Table 18.4 tests without the GDP control variable with Table 18.5 tests, which included it, we find baseline model drops heavily in 3 of 6 tests, rises slightly in two, and remains unchanged in one. On average R 2 in Table 18.5 baseline model drops (2.9) percentage points compared to the model in Table 18.4 without a GDP control. Comparing models using the modified deficit variables, R 2 declined in two tests, rose in three, and was unchanged in one. On average there was a net decline in R 2 of (0.2) percentage points using the model with the GDP control variable. We also note that in the 6 baseline and 6 modified deficit tests, the GDP variable was never found to be statistically significant. This and the fact that R 2 dropped notably in the baseline model when the GDP control was added, and stayed essentially the same in the modified deficit models suggest Table 18.4 model is already controlling adequately for fluctuating economic conditions, and that adding it here just distorts results.

T Def : t-stat G Def : t-stat R2

Variable

.08 (0.5) −.36 (−2.7) .90

.15 (0.9) −.46 (−4.1) .94

.24 (1.2) −.65 (−2.2) .83

.11 (0.5) −.52 (−1.6) .82

with

w/o

w/o

with

1960–1990

1960–1980

.38 (1.9) −.36 (−2.2) .86

w/o .22 (1.6) −.22 (−1.4) .83

with

1960–2000

.37 (2.2) −.30 (−1.4) .82

w/o .36 (3.4) −.21 (−1.0) .84

with

1960–2007

.44 (3.1) −.34 (−1.5) .85

w/o

.27 (3.2) −.10 (−0.6) .87

with

1960–2008

.44 (3.1) −.37 (−2.2) .89

w/o

.17 (1.3) .17 (1.0) .76

with

1962–2010

Table 18.5 Effects of on investment crowd out, with and without loanable funds accommodation (no separate (S + FB) − (Tr + A) control variable, but GDP control variable added)

444 J. J. HEIM

18

18.7

DO FR PURCHASES REDUCE CROWD OUT EFFECTS …

445

Chapter 18 Summary and Conclusions

Results are summarized in the following two tables: Cptr. 18 Consumption Summary Table Model

From Table#

10 Baseline (w/o Def)

Eq.11.1AA

11 Baseline (w/Def)

T11.1A

19 60 – 20 10 60

19 60 – 20 08 72

19 19 60 60 – – 20 20 07 00 72 86

19 60 – 19 90 43

19 60 – 19 80 77

19 19 70 70 – – 19 20 90 00 91 91

19 70 – 20 07 68

19 19 70 80 – – 20 20 10 00 55 86

19 80 – 20 10 37

18 Unmodif.d(w/s-a) 18 Modified (w/s-a)

19 85 – 20 04 67

19 19 85 96 – – 20 20 05 09 55 83

20 Test ratio 00 G – T 20 10 95 NA NA

2

(Av. R = 71.4%)

87 87 87

NA

91 89 91 93

92 86 88

94 85 88

2

11 Baseline Total LF Model (w/def. mod.& s-a)

19 19 75 80 – – 20 20 04 04 63 74

T11.11

T18.1 T18.1

88 86 87

NAa

92 99 15/18 6/18

(Av. R = 89.4% (Adj.84.3%) for18 samples; 88.7% (Adj.85.2%) for the 6 used below)

10/11 6/11

2 90 (Av. R 6 samples )

5/6

4/6

N/A

N/A

2

3/6 N/A

2/6 N/Aa

2

4/6

2/6

94 94

91 91

90 89

59 69

77 76

81 79

(Av. R = 82.0%; Adj. 76%) (Av. R = 83.0%; Adj.78%)

N/A

N/Aa

2

6/6 N/A

5/6 N/Aa

2

4/6

3/6

N/A

N/Aa

18 Unmodif.(wo/s-a)

T18.9

87

87

87

91

89

91

(Av. R = 88.7%; Adj.85.2%)

18 Modified (wo/s-a)

T18.9

78

81

83

88

89

90

(Av. R = 84.3%; Adj.80.2%)

a 7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving

11 of 18

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R2 increases to 89.4%, an increase of 25%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When loanable funds modifiers are added to standard model with deficits, as a stand-alone variable, average R 2 falls to 82.0%. When added as a stand alone and also as a deficit modifier, R 2 rises slightly to 83.0%, which is still considerably below the level of variance explained by the deficit model alone. This suggests that endogenous loanable funds only is not as good an explanatory variable as total loanable funds was in Chapter 11, where adding the total loanable funds variable as a stand-alone noticeably increased R 2 to 91.2%. Here, we have most likely just created an errors in variables problem.

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Adding the missing part of total loanable funds as a modifier to the deficit improves R 2 only slightly, still leaving it a poorer explanatory model than the standard model with deficit variables alone. 4. When the loanable funds modifier is added to the standard model as a modifier of the deficit only, without also being included as a stand-alone variable, the unmodified deficit model above is the same as the baseline model with deficit variables. When the deficit modifier is added, its R 2 drops in each of the six periods tested. The decline averages 4.1%. The effect of the endogenous part of loanable funds does not appear to reduce crowd out, but merely cause an error in variables problem (Or a left-out variables problem, since the endogenous part of loanable funds is negatively correlated with the exogenous part.

Cptr. 18 Investment Summary Table Model

From Table#

10 Baseline (w/o Def)

T10.3C

10 Baseline (w/o Def)

T10.3B

19 60 – 20 10 69

19 60 – 20 08 67

19 19 60 60 – – 20 20 07 00 66 63

19 60 – 19 90 65

19 60 – 19 80 72

19 19 70 70 – – 19 20 90 00 61 56

19 70 – 20 07 65

19 19 70 80 – – 20 20 10 00 72 69

19 80 – 20 10 77

19 19 75 80 – – 20 20 04 04 64 71

19 85 – 20 04 63

19 19 85 96 – – 20 20 05 09 57 92

2

(Does not include GDP Control Variable) (Av. R = 68.3%)

76 70 71

80 78 91 82

81 71 76

81 80 80 81 75 75

20 Test ratio 00 – T G 20 10 91 NA NA

NA 93 95 N/A

2

(includes GDP Control Variable) (Av. R = 79.8%) 11 Baseline (w/Def)

Eq.11.10A 89

86 84

89 87 95 90

90 86 90

2

89 90 89

2

T11.11

(Av. R = 89.8% for 18 samples); Av. R = 87.5 for 6 samples) 2 90 (Av. R 6 samples )

T18.3

89

81

82

91

91

95

(Av. R = 88.8%; Adj.R =86.5%)

18 Modified (w/s-a)

T18.3

90

90

87

90

91

96

(Av. R = 90.5%; Adj. R = 88.2%)

18 Unmodif.(wo/s -a)

T18.4

84

78

77

88

85

94

18 Modified (wo/s-a)

T18.4

11 Baseline Total LF Model (w/def. mod.; w/o s-a) 18 Unmodif.d(w/s -a)

89 89 89 98 98

NAa N/A

N/A N/Aa 11/18 16/18 8/11 6/6

9/11 4/6

N/A

N/A

5/6

5/6

N/A 4/6

N/Aa 4/6

(Av. R = 84.3%)

N/A 4/6

N/Aa 5/6

(Av. R = 85.8%; Adj. R = 83.0%) 78 86 81 85 82 95 (Av. R2 = 84.5%)

2

2

2

2

2

2

2

N/A 3/6

N/Aa 2/6

2

2

N/A

N/Aa

(Av. R = 84.3%; Adj. R = 81.3%)

a 7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18

18

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447

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8% 2. When deficit variables only added to baseline standard model, R 2 increases to 89.8%, an increase of 13%, clearly indicating clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When a stand-alone endogenous loanable funds variable is added to the standard investment model with deficits, average R 2 remains essentially constant. But when FR purchases is also added to the deficit variables, R 2 climbs to 90.7% suggesting that endogenous growth in loanable funds may not affect investment behavior, but increases in loanable funds due to FR purchases has a positive effect on investment (That said, the equivalent Chapter 11 model using total loanable funds as both a stand alone and a deficit modifier explains 92.1%), i.e., the combined effect of the two parts is greater than just the FR purchases part alone. 4. In investment models without a stand-alone endogenous loanable funds variable, when the deficit variables are modified by the FR purchases part of the loanable funds variable, average R 2 was about the same after modification as before. This suggests the part of loanable funds generated by FR securities purchases has no real effect on loanable funds, but may also mean we just can’t get a clear reading of its effect without controlling for endogenous growth in loanable funds, with which it is correlated. The model with a stand alone would seem to be the better model on the grounds it is more theory consistent with the notion loanable funds of any type can offset crowd out. In summary, this model does not seem to explain variation in consumption and investment as well as the Chapter 11 total loanable funds model does, though it does reach the same conclusions: crowd out is a problem reducing or eliminating the effectiveness of deficits, and increases in at least endogenous loanable funds can help offset crowd out. Where it differs from Chapter 18 is that it does indicate that FR securities purchases alone can stimulate investment, thereby offsetting crowd out.

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As in Chapter 11, increases in loanable funds do not seem to affect consumption crowd out.

Reference Heim, J. J. (2017a). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 19

Effects of Accommodative Monetary Policy on Crowd Out Before and After Quantitative Easing. Does “Pushing on a String” Occur?

In reviewing the large number of models tested so far in this study in Chapters 8–18, there has been a tendency for the sign on the modified government spending variable to change from negative to positive in many, though not all, tests when data from the QE period years (2009–10) is added to the sample being tested. Why this occurs was extensively dealt with in Chapter 11, and not much discussed since in the interests of brevity. However, it is an important finding about the core issue this study attempts to resolve: can/does “accommodative” monetary policy work? Such sign switching was predicted in the theory chapter (Chapter 4). The finding of switched signs on the government spending variable’s coefficient provides clear cut, theory consistent, statistical proof that if increases in loanable funds are large enough, accommodative monetary policy can fully offset the crowd out problem that tends to make fiscal stimulus programs ineffective. In brief, the Quantitative Easing program, which stated in 2008, led to large increases the pool of loanable funds due to the massive increase in securities purchases by the Federal Reserve. There is extensive evidence presented in this study to show that in the QE program’s early years, 2008–10, for the first time in the history of accommodative monetary policy program, at least as far back as 1960, the size of the accommodation in 2009 was more than adequate to fully eliminate crowd out caused by deficits. The increase in loanable funds more than restored the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_19

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borrowing power lost to consumers and businesses by the need to use part of the loanable funds pool to finance the deficit. There is also evidence the Fed’s accommodation program was far larger than needed to fully offset the crowd out problem. So, while the crowd out problem was resolved, the loanable funds increases under QE were much larger than what was needed to offset crowd out, and meet other borrowing needs. The excess increase in loanable funds created a “pushing on a string “effect, where much of the increase in lendable reserves created by the FR went unborrowed. This shows that there are bounds on the extent to which increasing loanable funds will stimulate the economy. The increase cannot exceed the economy’s desire to borrow money. A more detailed presentation of how the QE program showed accommodative monetary policy could be a fully effective way of offsetting crowd out, along with the “switched sign” statistical evidence for this conclusion, is presented in Chapters 5 and 11. Also discussed in Chapter 5 is the failure of accommodative monetary policy 1960–2007 to offset crowd out. During that period increases in loanable funds were far smaller than the deficit, i.e., far less than was needed to offset the crowd out problem caused by changes in the deficit.

PART VIII

Endogenous Increases in Loanable Funds: Effects on Crowd Out

CHAPTER 20

Is Endogenous Total Loanable Funds a Better Modifier Than Total Loanable Funds?

In Sects. 20.1 and 20.2 below we test the standard consumption and investment models in the same way we have previously done, but using a deficit variable modifier representing only the endogenous part of the total loanable funds variable, i.e., using (S + FB) − (Tr + A). This is total loanable funds minus the part of it created by the FR through open market purchases of government and government agency securities, i.e., the exogenous part. This is a variant of the Chapter 18 model, which tested to see if reductions in the magnitudes of deficit variables by increases in the exogenous part of the loanable funds pool, FR purchases, could explain variation in consumption and investment better than just the deficit variables alone, i.e., better indicate the true magnitude of crowd out effects. In Chapter 18, when testing for the effect of FR purchases, we also used a separate, “stand alone” variable, (S + FB) − (Tr + A), i.e., the endogenous part of the loanable funds pool to control for the influence of economic factors that can cause an endogenous increase in the pool, i.e., changes in the business cycle or national income. This chapter’s deficit modifiers will be the endogenous part of the loanable funds pool: T + (S + FB − Tr − A) and G − (S + FB − Tr − A). Each model also includes two separate stand-alone loanable funds variables: the endogenous (S + FB − Tr − A) part and exogenous part (Tr + A) of the total loanable funds pool. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_20

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All consumption and investment models tested below have been tested for stationarity and endogeneity problems. All variables were stationary or cointegrated with their dependent variables. Endogeneity problems of (S + FB − Tr − A) and (Tr + A) and the dependent variable were found in consumption models (Hausman test), and the variables were replaced by a Wald-strong instrument which was found not endogenous (Sargan test).

Testing the Consumption Model

20.1

Equation 4.4.TR below, from Heim (2017), is presented as a “standard“consumption model (i.e., comprised of widely accepted determinants of consumption) for ready comparison with prior statistical work on consumption. The Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) (t=)

(6.2)

(6.5)

(−4.5)

− 5.44PR + .48DJ−2 − .515.07POP16/65 (−2.1)

(5.1)

(3.2)

+ .020POP + 38.00 M2AV + .09CB2 (6.0)

R = 87.8% 2

(3.7)

(4.9)

D.W. = 2.2

MSE = 24.88

(4.4.TR)

Shown immediately below is this study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included (1960–2010 data). CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(7.2)

(0.6)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

R = 60.3% 2

(−0.1)

D.W. = 1.7

(2.0)

MSE = 43.98

(11.1AA)

This study’s Baseline (BL) Standard Consumption Model with 2 deficit (Crowd Out) Variables: (T ) and (G) Each Estimated Separately). This Model is Estimated Before Deducting Loanable Funds Changes from (T ) or (G), and before (T + G) is Added as a Stand-Alone Variable:

20

IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

455

CD = .31(Y − TT ) + .32(TT ) − .16(G T&I ) (t=)

(6.4)

(−1.9)

(6.6)

− 7.14PR + .49DJ−2 − .459.68POP16/65 (−3.1)

(4.5)

(2.4)

+ .017POP + 36.27M2AV + .09CB2 (4.0)

(3.9)

(3.8)

R = 86.6%

D.W. = 2.1

2

MSE = 26.17

(11.1A)

Also shown are Eqs. 20.1 and 20.2, which replicate models tested in Chapter 11, and use only the (S + FB) modifier as either a stand alone or as both a stand alone and deficit modifier in the same model. Equation 20.1 includes (S + FB) as a stand-alone variable, but not as a modifier to (T ) and (G). Equation 20.2 includes it both as a stand-alone variable and as a modifier to (T ) and (G). Instead of the total loanable funds stand-alone modifier used in Chapter 11, Eq. 20.3 divides the total into its endogenous (S + FB) − (Tr + A)) and exogenous parts (TR + A) and uses both as separate standalone loanable funds variables. In Eq. 20.4, (S + FB) − (Tr + A)) is also added as a modifier to (T ) and (G) as well as a stand-alone variable, with (TR + A) also included as a stand alone. All four models are estimated using the full 1960–2010 Dataset. Standard Consumption Model with 2 Variable Crowd out (T , G), before (S + FB only) modifications to T and G (1960–2010 Sample): CD = .38(Y − TT ) + .43(TT ) − .24(G T&I ) − .14(ST + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−4.1)

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.7)

(−1.9)

(3.7)

+ 33.67M2AV + .10 CB2 (4.5)

(3.5)

R = 88.3% 2

D.W. = 1.9

MSE = 24.68

  Taken from Cptr.18 (20.1)

Standard Consumption Model with 2 Variable Crowd out (T ), (G), after offsetting (S + FB) changes to T and G (1960–2010 Sample): CD = .38(Y − TT ) + .43(TT )m − .24(G T&I )m − .81(ST + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−5.6)

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.0)

(−1.9)

(3.7)

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J. J. HEIM

+ 33.67M2AV + .10 CB2 (4.5)

(3.5)

R = 88.3% 2

D.W. = 1.8

MSE = 24.89

  Taken from Cptr. 11 (20.2)

Standard Consumption Model with 2 Variable Crowd out (T , G), with (S + FB) − (Tr + A) and (Tr + A) stand-alone variables, but before (S + FB − Tr − A) modifications to (T ) and (G) (1960–2010 Sample):         CD = .33 Y − TT + .38 TT − .14 G T&I − .10 ST + FB − Tr − A (t=)

(5.0)

(−1.1)

(5.2)

(−1.8)

− .14(Tr + A) 4.83PR + .34DJ−2 − 380.32POP16/65 + .018POP (−2.2)

(2.2)

(−2.7)

(3.2)

(−1.9)

+ 43.04M2AV + .11CB2

(5.0) 2 R = 89.5%

(3.0)

D.W. = 2.0

MSE = 23.52

(20.3)

Standard Consumption Model with 2 Variable Crowd out (T − G), after offsetting (S + FB − Tr − A) changes to T and G, while keeping (S + FB − Tr − A) and (Tr + A) as stand-alone variables (1960–2010 Sample).         CD = .33 Y − TT + .38 TT m − .14 G T&I m − .62 ST + FB − Tr − A (t=)

(5.0)

(5.2)

(−1.8)

(−1.1)

− .14(Tr + A) 4.83PR + .34DJ−2 − 380.32POP16/65 (−2.2)

(2.2)

(−2.7)

(−1.9)

+ .018POP + 43.04M2AV + .11CB2 (3.2)

R 2 = 89.5%

(5.0)

D.W. = 2.0

(3.0)

MSE = 23.52

(20.4)

As you can see, results in this chapter, using the (S + FB − Tr − A) modifier, are similar to those using only the (S + FB) modifier from Chapter. 11, though unlike Chapter 11, the (G) deficit variable in this specific sample does not show significant crowd out effects before or after modification. This we think is due to including the early QE years in the same tested, when the market was flooded with FR generated LF. Finally, note that the models with the (S + FB − Tr − A) modifier have a much lower significance level, and a nearly identical R 2 values when compared to the (S + FB) model. This we attribute to the fact that both models are

20

IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

457

very similar; only the FR purchases part of total LF is missing from the deficit variable modifiers, and not missing from the stand-alone modifiers. Note that after modification of the crowd out effect by adding (S + FB) to the tax deficit variable (T), and subtracting it from the spending deficit variable (G), and also including it as a stand-alone variable, results for all variables except the stand-alone (S + FB) variable remain the same, as does R 2 . The same is true for the (S + FB − Tr − A) modifier. Earlier chapters explain that this is the expected result: the crowd out reducing effect of changes in the loanable funds variable on crowd out are given by the modified crowd out variable coefficients; the negative effect on mpc of increasing the loanable funds by increasing savings is given by the coefficient on the stand-alone loanable funds variable of the same type. All results shown in Table 20.1 for different time periods were estimated use the same models as the ones above. Only the time periods tested change. For each time period given in Table 20.1, two sets of statistics are presented. One in which there is no direct modification of the deficit variables (T , G) by changes in endogenous loanable funds, and one in which there is modification that yields modified deficit variables: T + (S + FB − Tr − A) and G − (S + FB − Tr − A). In both models, the stand-alone variables (TR + A) and (S + FB) − (TR + A) are used. We may summarize Table 20.1 results as follows: (S + FB) Model From Cptr. 11: Adding a stand alone (S + FB) to the base increases R 2 in 5 of 6 time periods tested. The average R 2 for all six periods is 90.7% (Av. R 2 Adj. = 85.4%) For tax cut deficits, 6 of 6 (T ) periods tested showed statistically significant crowd out for both the baseline and modified models. Significance levels on the (T ) variable stayed about the same after modification. For spending deficits, 4 of 6 (G) show statistically significant crowd out, using the baseline model, and 5 of 6 after modification. After modification of (G), significance levels were markedly higher. When, after modification by (S + FB), a deficit variable shows constant or increased significance levels, in most cases, we also expect to see rising R 2 , and that is what occurs when a stand-alone (S + FB) variable is added to the baseline model. (The exception would be in cases where loanable funds growth is so large, it completely or more than completely offsets crowd out; reducing the effect of crowd out on consumption to zero or near zero statistical significance).

1960–1990 w/o

w/o

with

1960–1980 with

w/o

1960–2000 with

w/o

1960–2007

.44 (5.7) −.17 (−2.4) −.74 (−4.7) .89

with

BL T Def BL t-stat BL G Def

.53 (3.9) −.21

.28 (3.2) −.10

.23 (2.8) −.03

.33 (5.6) −.08

Baseline Model (Same as Above, Except No Stand Alone or Deficit Modifiers, from Table 11.1A)

(S + FB) Modification Only; repeats Model used in Cptr. 11, Table 11.1 T Def : .72 .72 .36 .36 .29 .29 .44 t-stat (5.3) (5.3) (2.7) (2.7) (2.6) (2.6) (5.7) GDef : −.27 −.27 −.16 −.16 −.09 −.09 −.17 t-stat (−2.8) (−2.8) (−2.2) (−2.2) (−0.9) (−0.9) (−2.4) ST + FB− −.47 −1.46 −.13 −.65 −.10 −.48 −.13 t-stat (−2.6) (−4.2) (−1.3) (−2.5) (−1.2) (−1.8) (−3.6) R2 .94 .94 .90 .90 .91 .91 .89 (Av. R 2 = 90.7%; Av. Adj. R 2 = 85.4%)

Variable

.33 (5.6) −.08

.42 (5.5) −.16 (−2.4) −.11 (−3.4) .89

w/o

1960–2008

.42 (5.5) −.16 (−2.4) −.69 (−4.4) .89

with

.32 (6.6) −.16

.43 (6.7) −.24 (−2.8) −.14 (−4.1) .88

w/o

with

.43 (6.7) −.24 (−2.8) −.82 (5.6) .88

1960–2010

Table 20.1 Comparing robustness over time of effects of crowd out on consumption, with and without modification of deficit variables by loanable funds

458 J. J. HEIM

2 RAdj

.87

.85

.85

.88

.88

.22 (1.4) −.07 (−0.4) −.31 (−0.6) .91 .86

.30 (2.9) −.10 (−0.8) −.02 (−0.2) .89

(−1.5) .87

.86

.30 (2.9) −.10 (−0.8) −.42 (−1.3) .89 .87

.41 (5.6) −.20 (−1.6) −.12 (−2.0) .90

(−1.6) .87

.87

.41 (5.6) −.20 (−1.6) −.73 (−3.1) .90

(Av. Unmodified R 2 = 91.0%; Av. Adj. R 2 = 86.5%) (Av. Modified R 2 = 91.0; Av Adj. R 2 = 86.5%)

.87

BL t-stat (−1.6) (−1.7) (−0.5) .91 .89 .91 BL R 2 (S + FB − Tr − A) Modification Model from Cptr. 20 T Def : .67 .67 .32 .32 .22 t-stat (5.3) (4.1) (4.2) (4.2) (1.4) G Def : −.27 −.27 −.15 −.15 −.07 t-stat (−3.0) (−3.0) (−1.9) (−1.9) (−0.4) S + FB – Tr − A .56 −1.50 −.13 −.60 −.02 t-stat (−1.8) (−2.9) (−1.7) (−3.5) (−0.1) .94 .94 .92 .92 .91 R2

Baseline Model (Same as Above, Except No Stand Alone or Deficit Modifiers, from Table 11.1A)

.86

.86

.38 .38 (5.2) (5.2) −.14 −.14 (−1.1) (−1.1) −.10 −.62 (−1.8) (−2.7) .90 .90

(−1.9) .87 20 IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

459

460

J. J. HEIM

(S + FB − Tr − A) Model From This Cptr.: The average R 2 for all six periods is 91.0%, 0.3% points higher than for the total loanable funds model (S + FB). Av. Adj. R 2 = 86.5%, which is 1.1% higher than the (S + FB) model. The increase in explanatory power seems attributable to diving the stand-alone loanable funds variable into its two parts, and recognizing that the two have different marginal effects. In essence, but dividing the stand-alone variable into two variables, we have eliminated an “errors in variables” problem due to averaging the two effects. Adding the stand-alone (S + FB − Tr − A) and (Tr + A) variables to the base line model increases R 2 in 5 of 6 time periods tested. The average increase for all 6 periods tested is 2.3 percentage points. However, when compared to the (S + FB) model, the (S + FB) model had higher R 2 in 2 of 6 tests, lower in 1, and the same in 3 of 6, indicating that separating the endogenous and exogenous parts of total loanable funds adds little to the explanatory power of the consumption model. For tax cut deficits, 6 of 6 (T ) periods tested showed statistically significant crowd out for both the baseline model and 5 of 6 for the modified model. For spending deficits, 4 of 6 (G) show statistically significant crowd out using the baseline model, and 3 of 6 after modification. The slight reduction may mean that in one period, endogenous growth in loanable funds may large enough to eliminate crowd out. And in the three periods that remained significant, significance levels were down (though coefficients were up). In short, all results suggest endogenous growth has some ability to at least partially offset spending deficit crowd out. For tax cut deficits, results for the (S + FB) and (S + FB − Tr − A) models are about the same. We note here that when a modifier is added to (T), (G) deficits , and it turns the modified variable insignificant, it is not necessarily indicating the modifier has eliminated the crowd out problem. In periods like the 1990s, the deficit was declining most years. The decline should have had a positive effect on consumption (“ crowd in”). As noted elsewhere, even though the deficit was declining in the 1990s, both spending and taxes continued to grow; taxes just grew faster. The result is, if we test just the 1990s decade, the coefficient on the spending deficit variable is positive, and the coefficient on the tax deficit stays positive and grows. In other cases, the modifier may be one that does not have a significant relationship with the dependent variable. Using it as a deficit modifier creates an “errors in variables” problem.

w/o

w/o*

with

1960–1990

1960–1980 with

w/o

1960–2000

.84

.75

.84

.80

.88

.87

.31 (6.5) −.11 (−2.4) .89

.14 (2.9) .07 (1.4) .90 .87

.33 (5.6) −.08 (−1.5) .87

w/o

.11 (1.8) .04 (0.6) .90

with

1960–2007

.84

.19 (5.0) .09 (1.8) .87

.16 (2.2) .07 (0.6) .82

with

.86

.34 (6.4) −.09 (−1.7) .89

.33 (5.6) −.08 (−1.6) .87

w/o

1960–2008

(Av. Unmodified R 2 = 88.7%, Adj. R 2 = 85.5%; Av. Modified R 2 = 85.2%, Adj. R 2 = 81.2%)

2 RAdj

(S + FB Only) Model from Cptr. 11: T Def : .53 .24 .28 .14 .23 t-stat (3.9) (2.2) (3.2) (2.7) (2.8) G Def : −.21 +.06 −.10 .08 −.03 t-stat (−1.6) (0.5) (−1.7) (1.3) (−0.5) R2 .91 .86 .89 .87 .91 (Av. Unmodified R 2 = 88.7%; Av. Modified R 2 = 85.2%) (S + FB – Tr − A) Modification Model from Cptr. 20: T Def : .52 .25 .29 .16 .24 t-stat (3.8) (2.6) (3.1) (2.8) (3.1) G Def : −.21 .05 −.09 .10 −.07 t-stat (−1.5) (0.3) (−1.6) (1.8) (−1.5) R2 .91 .86 .89 .86 .91

Variable

.81

.24 (4.2) .19 (2.0) .85

.18 (2.5) .19 (0.7) .83

with

.84

.29 (4.8) −.11 (−1.4) .87

.32 (6.6) −16 (−1.9) .87

w/o

1960–2010

.80

.20 (4.2) .15 (2.3) .84

.15 (2.3) .02 (0.1) .83

with

Table 20.2 Robustness over time of effects on consumption of crowd out, with and without offsetting loanable funds (no stand-alone (S + FB) or (S + FB – Tr − A) control variable)

20 IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

461

462

J. J. HEIM

Table 20.2 retests the same “with” and “without” models as in Table 20.1, but without the separate loanable funds (total saving + foreign borrowing − Tr − A) control variable. We are testing to see if controlling for loanable funds as a separate variable, as well as in the tax and spending crowd out variables makes a difference in our crowd out variable estimates. There are no stationarity problems with either the modified or unmodified variables. The model, with and without the deficit variables being modified, was without endogeneity problems, so it was run in OLS. We may summarize Table 20.2 results as follows: Average R 2 and modified R 2 was the same for both the total loanable funds and endogenous loanable funds only models. This result is perhaps not surprising since the endogenous part of loanable funds is by far the biggest, and strongly influences the value of the total loanable funds estimate. (S + FB) Model From Cptr. 11: Adding (S + FB) to the baseline model as a deficit modifier decreased R 2 in 6 of the 6 models tested. The average decline was 3.5 percentage points. Modeling the effects of loanable funds on crowd out and consumption this way is clearly not as good as the model used in Table 20.1, which also included (S + FB) as a stand-alone variable, allowing the model to capture separately (or in net) the two competing effects of a change in loanable funds on consumption: the positive effect of reducing crowd out, and the negative effect of reducing the marginal propensity to consume. Adding (S + FB) there increased R 2 an average of 1.5 percentage points in the six periods tested, For tax cut deficits, The baseline model showed 6 of 6 (T ) deficits associated with statistically significant crowd out problems. With the (S + FB) variable added, the tax cut deficit model still showed significant crowd out in 6 of 6 periods tested. For spending deficits, the baseline model still showed 5 of 6 (G) with statistically significant crowd out. With (S + FB) added, this fell to 0 of 6 spending deficits. Since this change in significance levels caused a decline in R 2 , adding the (S + FB) variable as a modifier is though to have created an error in variable problem, and that that cause the decline in significance, not success in reducing crowd out. (Recall that S + FB has both a positive and a negative effect on consumption, and that using the variable just once in the model forces the regression to assign to it its net impact on consumption, which is

20

IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

463

near zero and negative.) As explained in Chapter 11, increases in loanable funds have two effects on consumption: a positive effect because they offset crowd out, and a negative effect because the increase in mps requires an offsetting decline I mpc, ceteris paribus. The crowd out variables marginal crowd out-offsetting effect is given by the net of the positive values of the coefficients on the (T ) and (G) variables; the negative effect by the coefficient on the stand-alone (S + FB) variable in the same equation. (S + FB − Tr − A) Model: Adding the (S + FB − Tr − A) total loanable funds variable to the baseline model left R 2 lower in all 6 periods tested, i.e., reduced the model’s ability to explain year-to-year fluctuations in consumption. The average decline was 3.2 percentage points. Here again, this suggests this consumption model is inferior to Table 20.1 model, which also contains a stand-alone (S + FB − Tr − A) variable, and produces separate estimates of the crowd out reducing and mpc reducing effects of an increase in loanable funds. For tax cut deficits, the baseline model showed 6 of 6 periods tested having significant crowd out, and after adding (S + FB − Tr − A) to the model, 6 of 6 (T ) continued to show significant crowd out, but with lower coefficients and significance levels. For spending deficits, baseline model which showed 3 of 6 (G) significant, and increases to 4 of 6 (G) after adding the deficit modifier (S + FB − Tr − A) to the model (but the sign on three of these, from samples including 2007 or QE year data, is positive). Because adding (S + FB − Tr − A) did decreases consumption, changes in the number of significant tax crowd out effects relative to the baseline, and the (S + FB)-only model, is taken to reflect an error in variables problem, not a more accurate explanation of crowd out effects. Overall, the rise in the number of significant crowd out findings for spending deficits, with only a slight decline in the number of significant tax deficits, is more consistent with a finding of rising R 2 than the finding for the model using total loanable funds (S + FB). In the (S + FB) model, adding (S + FB) left the number of significant tax deficits unchanged, but reduced the number of significant spending deficits from 5 to zero with a smaller increase in R 2 , though neither result fits the theory perfectly. R 2 was higher for the (S + FB − Tr − A) model in 3 of 6 tests, lower in 2 and the same in 1 test. But this consumption model, without the standalone modifier, is less preferred than Table 27.1 model on theoretical grounds and empirically because the six tests explain so much less variance (R 2 ) than Table 27.1 model that includes a stand-alone modifier variable.

464

J. J. HEIM

20.2 Investment Models Using the (S + FB) or (S + FB) − (Tr + a) Modifier Below is the model we take as the “standard“investment model, representing a summary of the variables found to be significant determinants of investment in a wide range of prior studies undertaken in the last half of the twentieth century, reduced to show just those that were both time period and model-type robust. It is Eq. 5.4.TR taken from Heim (2017). Many other variables found in the literature were initially tested to determine if they were determinants of investment. However, the criteria used in Heim 2017 to determine if a variable was to be included in the standard model was that they had to be found significant 3 of 4 different, though sometimes overlapping time periods between 1960 and 2010, and coefficient values could vary no more than 30% when two variables were added or subtracted from the model. Needless to say, many variables sometimes thought to be determinants of consumption could not meet this standard and were excluded. Good science requires the ability to replicate initial results in different time periods and models. The Standard Investment Model from Heim (2017) (Using 1960– 2010 data): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, and No GDP Variable Included to Control for the State of the Economy: ID = + .48(ACC) + .008POP + .76PR−2 + 7.37XRAV + 14.08CAP−1 (t=)

(10.6)

R 2 = 69.4%

(2.5)

(0.2)

(2.2)

(4.3)

D.W. = 1.6 MSE = 47.87

Same as Eq. 10.3C This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy:

20

IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

465

ID = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(0.0)

(4.0)

(−0.3)

+ 5.21XRAV + 10.39CAP−1 + .10 GDP (2.0)

(−1.3)

(2.9)

R = 76.1% 2

D.W. = 2.1

MSE = 43.06

Same as Eq. 10.3B; and Eq. 18.10C below Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010): ID = + .27(ACC) + .33TT − 33 G T&I + .012POP (t=)

(6.4)

(2.6)

(2.8)

(−3.9)

− 4.95PR−2 + 6.68XRAV + 2.43CAP−1 − .02GDP (−2.5)

R = 89.0% 2

(3.5)

D.W. = 1.9

(1.8)

MSE = 29.87

(−0.2)

(11.4A)

The next models (Eqs. 20.5 and 20.6) represent the same standard model, with the addition only of a control variable for changes in the total pool of loanable funds (S + FB). In both Heim (2017), and here the crowd out effects of the deficit are modified by changes in loanable funds during the same period (S + FB), but in Heim (2017), these were incorporated into the crowd out definition in a somewhat different way. Here, we simply add the change in loanable funds to the effects of any tax cut, reducing the estimated crowd out effect, and we subtract it from any change in the spending deficit, also reducing the estimated crowd out effect. In Eq. 20.5, we only use (S + FB) as a stand alone. In Eq. 20.6 it is used as a stand alone and as a modifier to (T ) and (G). After that, In Eqs. 27.7 and 27.8, the standard model equations are repeated, but this time using (S + FB) − (Tr + A) as the stand-alone variable (20.7), along with a second stand alone (Tr + A), or, as a stand alone (with Tr + A) and also to modify the deficit variables (T ) and (G) in Eq. 20.8. All variables were found Augmented Dickey Fuller (ADF) stationary; No Hausman endogeneity was found between the dependent and explanatory variables, and Newey–West standard errors were used to avoid heteroskedasticity. The Standard Investment Model with 2 Variable Crowd out (T , G) and a Stand-Alone (S + FB) Variable, before Modifying the Deficit Variables with (S + FB) (Using 1960–2010 data):

466

J. J. HEIM

ID = + .18(ACC) + .21TT − 23G T&I + .16( (S + FB)) (t=)

(1.8)

(5.6)

(−2.6)

(2.1)

+ .007POP − 3.24PR−2 + 5.54XRAV + 1.00 CAP−1 (2.7)

(2.8)

(−1.6)

R = 90.4% 2

D.W. = 1.9

(0.7)

MSE = 27.49

(20.5)

(Equation 20.5) (same as Eq. 11.3) The Standard Investment Model with 2 Variable Crowd out and a Stand-Alone (S + FB) Variable, with (T , G), modified by (S + FB) (Using 1960–2010 data): ID = + .18(ACC) + .21TT − 23G T&I − .28( (S + FB)) (t=)

(1.8)

(5.6)

(−2.6)

(1.1)

+ .007POP − 3.24PR−2 + 5.54XRAV + 1.00 CAP−1 (2.7)

(2.7)

(−1.6)

R = 90.4% 2

D.W. = 1.9

(0.7)

MSE = 27.50

(20.6)

(Equation 20.6) (same as Eq. 11.4) The Standard Investment Model with 2 Variable Crowd out (T , G), with (S + FB − Tr − A) added as a stand-alone variable, but before modifying (T ) and (G) with (S + FB − Tr − A) (Using 1960–2010 data): ID = + .18(ACC) + .20TT − 27 G T&I + .18( (S + FB − Tr − A)) (t=)

(6.0)

(1.8)

(−2.1)

(2.3)

+ .20  (Tr + A) + .008POP − 2.12PR−2 + 5.64XRAV + 1.67CAP−1 (2.8)

(2.6)

(−1.1)

(2.7)

(1.2)

R = 90.6% D.W. = 1.8 MSE = 27.48

(20.7)

2

Standard Investment Model with 2 Variable Crowd out (T , G), with (S + FB − Tr − A) added as a stand-alone variable, and modifying (T ) and (G) with (S + FB − Tr − A) (Using 1960–2010 data): ID = + .18(ACC) + .20TT(m) − 27 G T&(m)I − .30( (S + FB − Tr − A)) (t=)

(6.0)

(1.8)

(−2.1)

(−1.1)

+ .20 (Tr + A) + .008POP − 2.12PR−2 + 5.64XRAV + 1.67CAP−1 (2.8)

(−1.1)

(2.7)

R = 90.6% D.W. = 1.8 MSE = 27.48 2

(2.7)

(1.2)

(20.8)

w/o

with

1960–1980 w/o

with

1960–1990 w/o

with

1960–2000

.12 (1.2) −.17 (−1.7) .20 (3.6) .88

w/o

.12 (1.2) −.17 (−1.7) −.08 (−0.4) .88

with

1960–2007

.13 (0.9) −.35 (−3.8) .95

.28 (2.2) −.42 (−3.2) .87

T Def : t-stat G Def :

.05 (1.2) −.20

.05 (1.2) −.20

.14 (1.6) −.10

(S + FB − Tr − A) Model from Cptr. 20:

BLT Def : BLt-stat BLG Def : BLt-stat BL R 2

.14 (1.6) −.10

.18 (1.7) −.16

.32 (2.6) −.40 (−5.2) .89

.18 (1.7) −.16

.13 (1.5) −.14

.26 (2.3) −.34 (−3.2) .84

.13 (1.5) −.14

Baseline Model—No (S + FB) or (S + FB − Tr − A) variable included (from Table 20.4)

(S + FB only) Model from Table 11.4: T Def : −.10 −.10 .09 .09 .20 .20 t-stat (−1.2) (−1.2) (0.9) (0.9) (1.5) (1.5) G Def : −.12 −.12 −.21 −.21 −.19 −.19 t-stat (−1.3) (−1.3) (−2.4) (−2.4) (−1.9) (−1.9) S + FB .59 .57 .30 .00 .27 −.12 t-stat (5.4) (2.8) (3.1) (0.0) (2.4) (−0.4) R2 .98 .98 .92 .92 .90 .90 (Unmodified and modified av. R 2 = 91.2%, av. adj. R 2 = 87.5%)

Variable

.16 (2.3) −.16

.33 (2.7) −.33 (−2.8) .86

.21 (1.6) −.18 (−2.5) .19 (2.8) .88

w/o

.16 (2.3) −.16

.21 (1.6) −.18 (−1.6) −.21 (−0.8) .88

with

1960–2008

.20 (1.8) −.27

.33 (2.6) −.33 (−3.9) .89

.20 (1.8) −.27

467 (continued)

with IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

.22 (1.6) −.16 (−1.9) −.19 (−0.8) .91

.22 (1.6) −.16 (−1.9) .16 (1.9) .91

w/o

1960–2010

Table 20.3 Comparing robustness over time of effects on investment of crowd out, with and without accommodating loanable funds modification, net of FR purchases

20

.96

(−1.9) .55 (10.0) .98 .96

(−1.9) .30 (1.8) .98 .88

(−1.1) .36 (4.7) .91 .88

(−1.1) .12 (0.6) .91 .88

(−1.8) .29 (2.9) .90

(Unmodified and modified av. R 2 = 91.2%, av. adj. R 2 = 89.0%)

2 RAdj

t-stat S + FB – Tr − A t-stat R2

(S + FB − Tr − A) Model from Cptr. 20:

Table 20.3 (continued)

.88

(−1.8) −.05 (−0.2) .90 .85

(−1.3) .21 (2.4) .87 .85

(−1.3) −.07 (−0.3) .87 .88

(−1.7) .18 (2.3) .90 .88

(−1.7) −.14 (0.7) .90

.89

(−2.1) .18 (2.3) .91

.89

(−2.1) −.30 (1.1) .91

468 J. J. HEIM

w/o

w/o

with

1960–1990

1960–1980 with

.91

.96

.83

.89

.89

.16 (2.8) −.14 (−1.9) .91

.42 (5.7) −.49 (−5.2) .88 .86

.16 (1.9) −.14 (−2.2) .90

with

.32 (2.6) −.40 (−5.2) .89

w/o

1960–2000

.82

.29 (4.5) −.31 (−2.4) .85

.26 (2.3) −.34 (−3.2) .84

w/o

1960–2007

.85

.11 (2.3) −.10 (−1.4) .88

.10 (1.7) −.13 (−1.8) .88

with

.86

.28 (4.2) −.26 (−1.8) .88

.33 (2.7) −.33 (−2.8) .86

w/o

1960–2008 with

.89

.13 (2.1) −.08 (−0.8) .90

.17 (1.9) −.07 (−0.7) .87

Av. R 2 , unmodified model = 88.7%; (Adj. R 2 = 85.8%); Av. R 2 , modified model = 89.8% (Adj. R 2 = 89.7%)

2 RAdj

(S + FB only) Model from Cptr. 11.5: T Def : .13 .05 .28 .10 NWt-stat (0.9) (0.6) (2.2) (1.9) G Def : −.35 −.27 −.42 −.20 NWt-stat (−3.8) (−4.1) (−3.2) (−3.1) R2 .95 .97 .87 .91 (S + FB – Tr − A) Model from Cptr. 20: T Def : .35 .13 .38 .16 t-stat (4.2) (3.6) (4.1) (3.1) G Def : −.48 −.28 −.42 −.15 t-stat (−3.5) (−3.9) (−4.1) (−1.8) R2 .95 .97 .87 .92

Variable

.87

.33 (4.1) −.24 (−1.5) .89

.33 (2.6) −.33 (−3.9) .89

w/o

with

.90

.17 (2.4) −.06 (−0.6) .91

.18 (2.0) (−.06) (−0.7) .90

1960–2010

Table 20.4 Comparing robustness over time of effects on investment of crowd out, with and without accommodating loanable funds modification

20 IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

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J. J. HEIM

All results in Tables 20.3 and 20.4 for the other time periods estimated use exactly the same model, except 20.4 drops the stand-alone (S + FB − Tr − A) and (Tr + A) variables. Only the length and dates of the period used to test the model changes. In Table 20.3 we use the standard model, adding to it, either (S + FB) or (S + FB − Tr − A) and (Tr + A). The additional variables shows how yearly changes in total loanable funds, or total loanable funds net of changes in FR security purchases (S + FB − Tr − A), can reduce crowd out effects. For each time period given, two sets of statistics are presented. In one set, there is no modification of the crowd out variables (T , G) by the same period change in loanable funds net of FR purchases, and one in which there is modification. In both cases (S + FB − Tr − A) is kept as a stand-alone control variable. (Tr + A) is also kept as a stand-alone variable. All variables were found Augmented Dickey Fuller (ADF) stationary; No Hausman endogeneity was found between the dependent and explanatory variables, and Newey–West standard errors were used to avoid heteroskedasticity. We may summarize Table 20.3 results as follows: Average R 2 for both the total LF model and the endogenous LF model were the same, but adjusted R 2 was 1.5% higher for the endogenous LF model. This appears to be a result of dividing the total LF variable into two parts, where, because the two parts have different marginal effects, yield a higher adjusted R 2 for the model with the tow stand-alone parts compared to the model with only one stand-alone loanable funds variable: (S + FB). (S + FB) Model From Cptr. 11: Adding the (S + FB) modifier increased R 2 in all six periods tested. The average increases was 2.8 percentage points. The increase indicates growth in loanable funds can does offset crowd out. For tax cut deficits, 5 of 6 (T ) show significant crowd out in the baseline model, only 2 of 6 after modification. For spending deficits, 6 of 6 (G) show significant crowd out in the baseline model, and 5 of 6 after modification. The baseline data show tax cut and spending crowd out was a statistically significant problem in almost every period tested. The “net” effect shown by the coefficient on the stand-alone variable in the “w/o” modification column does indicate increases in (S + B) have

20

IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

471

a large and highly statistically significant positive relationship with investment. This implies they are also effective in offsetting the negative effects of crowd out. However, when also added to the model as a deficit variable modifier, in 5 of 6 tests, the stand-alone (S + FB) variable becomes statistically insignificant. This suggests (unlike consumption), that increases in loanable funds has only one positive effect on investment; they offset crowd out. Hence the need to also include a stand alone is questionable and will be tested in Table 20.4. (S + FB − Tr − A) Model: Adding the (S + FB − Tr − A) modifier also increased R 2 in all six periods tested, and the average increase was also 2.8 percentage points. The increase indicates growth in just the endogenous part of loanable funds can does offset crowd out, and add as much explanatory power to the model as did adding total loanable funds, implying that little or no part of the increase in (S + FB) was due to increases in the exogenously driven part resulting from FR security purchases (which is consistent with data presented earlier indicating that FR security purchases (accommodative monetary policy) historically have only averaged about 25–44% of what was needed to fully accommodate deficits. For tax cut deficits, the baseline model showed tax cut deficits associated with significant crowd out in 5 of 6 (T ), and in 5 of 6 tests after deficit modification. For spending deficits, 6 of 6 showed significant crowd out problems in the baseline model, and this fell to 4 of 6 after modification. Here again, The “net” effect of the stand alone (S + FB − Tr − A) shown in the “w/o” modification results does indicate increases in (S + B) have a large and highly statistically significant positive relationship, but that when the same variable is also added as a deficit modifier, the stand-alone version becomes insignificant, again suggesting (unlike consumption) that changes in endogenous loanable funds only have one effect on investment: they increase it by offsetting crowd out caused by deficits. Overall, R 2 was higher for the (S + FB) model in 2 of 6 tests, lower in 1, and the same in 3 tests. We conclude these models do not typically indicate that that adding the exogenous part of loanable funds to endogenous loanable funds increases explanatory power of the model any more than just the endogenous part alone.

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The Same Investment Models Without Stand-Alone Modifier Variables All variables were found Augmented Dickey Fuller (ADF) stationary. Hausman endogeneity was found between the dependent and government spending variable, so it was replaced with a Wald-strong instrument that was not itself endogenous (Sargan test). Newey–West standard errors were used to avoid heteroskedasticity. All results in Table 20.4 use exactly the same investment models tested in Table 20.3, except 20.4 drops the stand-alone variables (S + FB) and (S + FB − Tr − A). The lack of statistical significance of the stand-alone version of these variables in Table 20.3 suggested it may not be needed if the variable is already included as a deficit modifier. In the six tests below, only the time period used to test the models changes. For each time period given, two sets of statistics are presented. In one set, the baseline, or “w/o” model), there is neither a stand alone or modification of the crowd out variables (T , G). In the other column of results (“with”), there is no stand alone, but the deficit variables are modified by (S + FB) for the Chapter 11.5 model, and (S + FB − Tr − A) for this chapter’s model. The modifications are designed to reduce the deficit’s magnitude by any growth in total or endogenous loanable funds that occurs in the same period. We may summarize Table 20.4 results as follows: R 2 for the unmodified model was virtually identical to R 2 after the deficit variables were modified by the endogenous portion of total loanable funds, which suggests growth in the endogenous part of the LF pool does not offset crowd out. However, Adj. R 2 , a better measure of how much explanatory power grew when we included the endogenous funds modifier, rose 3.9%. This is a significant increase indicating that growth in the endogenous portion of loanable funds can significantly help offset investment crowd out. (S + FB) Model From Cptr. 11: Adding the (S + FB) modifier increased R 2 in all six periods tested. The average increases was 2.2 percentage points. The increase indicates growth in the total pool of loanable funds can offset crowd out. For tax cut deficits, 5 of 6 (T ) show significant crowd out in the baseline model, and 5 of 6 after modification. For spending deficits, 6 of 6 (G) show significant crowd out in the baseline model, but only 4 of 6 after modification (insignificant were the 2008 and 2010 QE-period samples).

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The baseline data show tax cut and spending crowd out was a statistically significant problem in almost every period tested. (Though not shown, when also controlling for business cycle effects (the GDP), we obtained the same results for both the tax and spending deficits.) (S + FB − Tr − A) Model: Adding the (S + FB − Tr − A) modifier increased R 2 in 6 of 6 periods tested. The average increase was 2.8 percentage points. The increase, when compared to the average growth in R 2 of 2.2 points when modifying the deficits’ effect by total loanable funds, indicates the endogenous loanable funds-only variable better explains the extent to which crowd out affected investment levels during the periods tested. R 2 using the endogenous loanable funds modifier was higher in 4 of 6 tests than obtained using the total loanable funds modifier, lower in 1, and the same in one. 6 of 6 (T ) significant before and after modification. Five of 6 (G) show significant crowd out, and one marginally significant crowd out, before, but only 3 of 6 shows statistically significant crowd out after modification. Those turning insignificant were in tests including data from the 2007– 2010 era, the QE or near QE era. Compared to the (S + FB) model where 5 of 6 (S + FB) modified deficits were found significant, with (S + FB − Tr − A) all six modified deficits were significant, For spending deficits, using (S + FB), 4 of 6 were significant compared to 6 of 6 using (S + FB − Tr − A). However, because the changes in significance levels on the modified deficit variables in the endogenous loanable funds models resulted in a reduced ability to explain variance in investment, it appears more likely they resulted from an error in variables problem caused by thinking only the endogenous part of the loanable funds pool, not the whole pool, could offset crowd out.

20.3

Summary and Conclusions

Summary of results are presented in the table:

87

84

T20.2

20 Unmodif.(wo/s-a)

20 Modified (wo/s-a) T20.2

85

89

90

87

89

89

89

90

91

91

91

86

89

92

92

84

87

94

94

77

91

68

55

(Av. R2 = 85.2%, Adj. R2 = 81.2%)

(Av. R2 = 88.7%, Adj. R2 = 85.5%)

(Av. R2 = 90.7%; Av. Adj. R2 = 85.4%)

(Av. R2 = 90.7%; Av. Adj. R2 = 85.4%)

91

88

63

88

74

86

67

*7 samples containing 1/3–½ of observations from “Crowd In” years (1990s) Removed, leaving 11 of 18 **13 of 18 samples containing more than 42% observations from 1990s “crowd in” or 1980s “little variation in G” years.

90

T20.1

20 Modified (w/s-a)

90

90 (Av. R2 6 samples )

43

85

90

Eq.11.1A

11 Baseline (w/Def)

86

37

72

86

72

(Av. R2 = 71.4%) 87 87 87 91 89 91 93 92 86 88 94 (Av. R2 = 89.4% for 18 samples; 88.7% for the 6 samples used below)

60

87

65

92

83

99

95

NA

NA NA* 3/6 NA* 3/6 NA* 4/6 NA*

NA 5/6 NA 6/6 NA 6/6 NA

NA* 6/18* 5/11* 5/5** 4/6

NA

NA 15/18 10/11 5/5 5/6

NA

1960 1960 1960 1960 1960 1960 1970 1970 1970 1970 1980 1980 1975 1980 1985 1985 1996 2000 Test ratio – – – – – – – – – – – – – – – – – – 2010 2008 2007 2000 1990 1980 1990 2000 2007 2009 2000 2010 2004 2004 2004 2005 2010 2010 T G

11 Baseline Total T11.1 LF Model (w/def. mod.& s-a) 20 Unmodif.d(w/s-a) T20.1

T11.1AA

From Table#

11 Baseline (wo/Def)

Model

Cptr. 20 Consumption Summary Table (Endogenous Deficit Modifier, Separate Endog. and Exog. LF Variables)

474 J. J. HEIM

20

IS ENDOGENOUS TOTAL LOANABLE FUNDS A BETTER …

475

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4% 2. When deficit variables only added to standard model, R 2 increases to 89.4%, an increase of 25%, clearly indicating clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When both loanable funds modifiers are added to standard model with deficits, as two stand-alone variables, and if the endogenous part is added as a deficit modifier, R 2 rises to 90.7% compared to the 90.2% for the standard deficit model. This indicates that endogenous loanable funds only is a slightly better explanatory variable as total loanable funds was in Chapter 11 (91.2% for the same six test periods). Separating the two parts of total loanable funds into two separate stand alones may have increased explanatory power slightly. 4. When no stand-alone variable included, and without adding the endogenous loanable funds modifier to the deficit variables, R 2 is 88.7% (for just these six samples). When endogenous loanable funds is added to the standard model as a modifier of the deficit only, but no stand-alone loanable funds variables are included, the average R 2 drops to 86%, a decline of 5. We conclude that for consumption, where increases in loanable funds have both a positive (crowd out reduction) and negative (mpc declines) using the loanable funds variable as both a deficit modifier and a stand alone is necessary to pick up both effects, i.e., best explain the data.

65

72

−61 2

56

65

91

20 Modified (wo/s-a) T20.4

72

87

85

91

88

92

87

97

95

91

89

90

80

77

(Av. R2 = 89.8%; Adj. R2 = 89.7%)

(Av. R2 = 88.7%; Adj. R2 = 85.8%)

(Av. R2 = 91.2%, Av. adj. R2 = 87.5%)

(Av. R2 = 91.2%, Av. adj. R2 = 87.5%)

90

81

69

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18

90

88

90

89

87

T20.4

90

20 Unmodif.(wo/s-a)

91

91

(includes GDP Control Variable) (Av. R2 = 79.8%) 89 86 84 89 87 95 90 90 86 (Av. R2 = 91.2% for 18 periods; 88.3% for 6 used below) 90 (Av. R2 6 samples)

98

T11.11

11 Baseline Total LF

63

T20.3

Eq.18.10A

18 Baseline (w/Def)

66

(Does not include GDP Control Variable) (Av. R = 68.3%) 76 70 71 80 78 91 82 81 71 76

67

20 Modified (w/s-a)

T17.3B

17 Baseline (w/o Def)

69

89

80

−64

89

81

71

89

75

63

89

75

57

98

93

92

98

95

91

4/6 NA* 4/6 NA* 5/6 NA* 3/6 NA*

NA 4/6 NA 6/6 NA 6/6 NA

NA* 16/18 9/11 4/6

NA* NA

NA

G

4/6

NA 11/18 8/11 6/6

NA NA

NA

2010 2008 2007 2000 1990 1980 1990 2000 2007 2009 2000 2010 2004 2004 2004 2005 2010 2010 T

Model (w/def. mod.; w/o s-a) 98 91 90 87 90

T17.3C

17 Baseline (w/o Def)

ratio

Sigif./Total

1960 1960 1960 1960 1960 1960 1970 1970 1970 1970 1980 1980 1975 1980 1985 1985 1996 2000 Test – – – – – – – – – – – – – – – – – –

20 Unmodif. d(w/s-a) T20.3

From Table#

Model

R2 (18 Time Periods)

Cptr. 20 Investment Summary Table (Endogenous Deficit Modifier, Separate Endog. and Exog. LF Variables)

476 J. J. HEIM

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1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8%. 2. When deficit variables only added to baseline standard model, R 2 increases to 89.8%, an increase of 13%, clearly indicating clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When endogenous loanable funds modifiers are added to the standard model with deficits as a stand alone, and also as a stand alone and a deficit modifier, average R 2 is 91.2%, (1.4%) points above the level explained by the standard deficit model alone (89.8%). This is the same as Chapter 11, which showed adding total loanable funds in this way left investment R 2 = 91.2%. This suggests that the exogenous part of total loanable funds has had little or no effect historically (until the QE program started). 4. When the loanable funds modifier is added as a modifier of the deficit only, but not included as a stand-alone variable, R 2 increases in all six periods tested, from its average of 88.7% before adding the endogenous loanable funds deficit modifier to an average of 91.2% after.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 21

Comparing Various Stand-Alone Endogenous Loanable Funds, and FR Securities Purchases Variables Models

Six different combinations of endogenous, exogenous, and total loanable funds models are tested as stand-alone variables in consumption and investment models. The six combinations are Total loanable funds (S + FB) Exogenous Loanable Funds Total + Exogenous Loanable Funds Total, Exogenous Loanable Funds National Savings + Exogenous Loanable Funds Endogenous Loanable Funds, Exogenous Loanable Funds No deficit variable modifiers are used in these models. Tests for consumption are given in Sects. 21.1–21.6 below. Tests for investment are given in Sects. 21.7–21.12 below. As has been the case in prior chapters, when testing these models we will find some instances variables of interest, the deficit, and crowd out variables, will be found significant and others when they are found insignificant. It is worth explaining again how adding a deficit modifier, such as (S + FB) or (Tr + A) can cause a decline in deficit significance levels previously associated with the unmodified deficit variables, but not because the crowd out problem has been eliminated. The newly modified

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_21

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deficit variable will turn insignificant and R 2 can decline if adding the modifier to the deficit causes an “error in variables” problem. Previous chapters have involved testing the unmodified deficit variables (T ) and (G) separately, or as one variable (T − G), to determine the crowd out effects of deficits. The same models were then retested after modifying the deficit variables by either 1. total loanable funds (S + FB), and/or 2. FR purchases of securities (Tr + A), or 3. changes in the endogenous part of loanable funds pool. The tests generally indicate that there are negative effects of crowd out, and that changes in the pool of loanable funds can offset them (not that they always do, for reasons cited below). Generally we find consumption crowd out in most models is not reduced, but investment crowd out is reduced by changes in loanable funds. The failure of increased loanable funds to offset crowd out can be due to a number of factors: 1. It may be that the increase in loanable funds in some periods was not as large as the deficit, or 2. Increase in the deficit. 3. It may be the increase that goes unborrowed, 4. It may be borrowed, but spent on something other than goods and services; i.e., spending that does not enter the GDP, like stocks and bonds, or loans to one firm so that it can purchase the assets of another. 5. The increase in LF occurs in foreign, not US banks. This can occur if the increase results from FR purchases of securities from foreign banks, with the Fed’s payment being deposited in the foreign bank’s home country, or some other non-US country. In these cases, reducing the deficit by any same-period growth in (S + FB) creates a variable that erroneously states the facts: crowd out (the deficit) was not in fact reduced by the growth in loanable funds, or not reduced adequately. While it is true the crowd out effects of a deficit could potentially have been reduced by the change in loanable funds (S + FB), they were not. Hence, when we look at real world data, we may find the

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COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

481

correlation between loanable funds (S + FB) and purchases of goods and services may be real, but not perfect, i.e., not one-to-one. In fact, it may be substantially less than one-to-one. As a result, sometimes the relationship may be statistically insignificant. Fluctuations in the deficit loanable funds modifier (S + FB) may not lead to changes in GDP or its components. The change may be seen by the regression calculus as adding unexplainable variance to the model when the crowd out variable used is the deficit as modified by the change in loanable funds. It will report lower significance levels or statistical insignificance for the variable, especially when compared to those obtained using the deficit variable(s) alone. Suppose, for example, the regression coefficient on the deficit variable (T − G) is, say 0.5 (T − G), where (T − G) is the magnitude of the deficit. This is also the magnitude of the crowd out effect, provided there is no change in the level of loanable funds. If the magnitude of the deficit variable is reduced dollar for dollar by any increase in loanable funds, i.e., (T − G) + (S + FB), the crowd out effect becomes 0.5 (T − G + S + FB) because (T − G + S + FB) now more accurately reflects how much the pool of loanable funds available for private borrowing declines when a government deficit is incurred at the same time the loanable funds pool is changing: we are just multiplying a smaller number by (0.5) than before. But if changes in (S + FB) do not get lent out, or do not get lent out to buy goods and services, we get a different story. The changes in (S + FB) reduce the amount we define as crowd out, i.e., (T − G) + (S + FB), without changing GDP. The variable, which before had accurately measured crowd out’s effect on GDP, now defines crowd out less accurately. The variable we define as “crowd out” has now declined in value, but the crowd out problem has not. No more is available to offset crowd, because the increase in loanable funds is either staying unborrowed, or is borrowed for non-GDP related uses (like buying stocks and bonds). In short, even though increases in loanable funds can help reduce crowd out, doesn’t mean they will. The relationship may not be oneto-one, or even close to one-to-one. Even though increases in loanable funds may reduce the amount our modified crowd out variable measures as crowd out, the change will be unrelated to change in GDP. Therefore, significance levels of the modified crowd out variables may decline because we now have an “errors in variables” problem, not because the increase in loanable funds has offset crowd out by replacing the part of the pool of loanable funds available for private borrowing that was lost

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to finance the deficit. This may also cause R 2 s to drop in the modified model. A decline in R 2 will occur when change in variation of the crowd out variable (due to modification) is not matched by an increase in the model’s dependent variable, e.g., if the model explained 50% of the variation in consumption or investment before, it may explain only 40% now, simply because changes in crowd out (as redefined) are less in sync in variation in GDP than before. We also discussed in Chapter 11 how mixing data from periods of crowd in (like the 1990s) with periods of crowd out can leave the combined sample insignificant, even though each individually is highly significant. The reader is referred to that chapter for more information on that topic. Hence, in evaluating our test results we must remember 1. We could get lower significance levels on the (modified) crowd out variable, and lower R 2 for the modified deficit variable for an economically sensible, though not desirable, economic reason: the modifier may or may not be ultimately used to purchase goods that increase the GDP, or 2. We may have an “errors in variables” problem when we modify the initial deficit variable. Variables with errors in their data characteristically show lower coefficients and significance levels than the “true” non-error ridden data series underlying them. As a result, data only imperfectly reflects the variation from period to period of the true modifying variable, and by adding variance to an explanatory variable not correlated with the dependent variable, will likely reduce the variable’s statistical significance compared to the unmodified variable. Substitution of a modifier when the true variable is the unmodified version may lower deficit significance levels and also lower R 2 as well as deficit significance levels. 3. With the type models we use, mixing statistically significant crowd out years data with statistically significant crowd in years data may leave the combined (i.e., the average crowd out effect for the whole period) near zero and statistically insignificant. This happens because we are mixing periods when there are no or declining deficits (“crowd in” periods), even though the tax variable (T ) may be declining or the government spending variable (G) increasing. In such cases, the regression will see consumption or investment rising while taxes are declining to give the regression coefficient a

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

483

negative sign to show this relationship. Similarly, when government spending is rising, creating or increasing the deficit, we normally expect the sign on its effect to be negative. But if government spending increases while the deficit is declining, consumption and investment will be rising, and the regression will give a positive sign to the relationship between them and government spending. Mixing crowd in and crowd out year can cause the half of your data with positive signs to negate the half with negative signs, causing near-zero regression coefficients and lack of statistical significance. 4. In the period tested, there may not have been enough variation in the variable to leave it correlated with another variable 5. Multicollinearity, which typically lowers significance levels of the affected variables 6. Spurious effects present in one sample but not others. To evaluate these first two of these alternatives, we will separately test • Total loanable funds (S + FB), i.e., both its exogenous and endogenous parts together, and • The exogenous part of loanable funds only (Tr + A). • We will also test a combination of the two, (S + FB) + (Tr + A) which is essentially a test of the hypothesis that additions to loanable funds resulting from FR purchases do not raise the level of national saving (the core of the loanable funds pool) on a one-to-one basis, if at all, but do increase the system’s liquidity beyond what an increase in loanable funds (S + FB) can do. • In fact, we will test six different combinations of parts of total loanable funds. The six combinations are: 1. Total loanable funds (S + FB) 2. Exogenous Loanable Funds 3. Total + Exogenous Loanable Funds 4. Total, Exogenous Loanable Funds 5. National Savings + Exogenous Loanable Funds 6. Endogenous Loanable Funds, Exogenous Loanable Funds.

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Consumption Model Tests Below we again show three standard consumption models based on the “standard” model taken from (Heim 2017, Eq. 4.4.TR). One additional variable is added to the standard model: either the total loanable funds (S + FB) variable; the FR Purchases of Treasuries and Agency securities (Tr + A) variable, or a combination of both. All variables in the models are ADF stationary, DF cointegrated, or detrended as required, and Hausman—endogenous explanatory variables are replaced by Waldstrong instruments, which themselves were tested for endogeneity and found not endogenous (Sargan test). As always, models are estimated in first differences to reduce multicollinearity effects and enhance variable stationarity.

21.1 Statistical Significance of the Total Loanable Funds Variable When Added to the Standard Consumption Model No endogeneity problems were found when testing the loanable funds variable (S + FB) model, where loanable funds is defined as total national saving from personal, corporate, and depreciation allowance sources, plus any borrowing from foreign sources that takes place. Equation 21.1 below shows estimation results, using the full 1960–2010 data set. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods, each representing a part of the full 1960–2010 period used in the initial test. Results of retesting are shown in Table 21.1. The individual deficit (crowd out) variables (T ) and (G) are not modified by (S + FB). Standard Consumption Model from Heim (2017) Estimated Using 1960–2010 data: CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−4.5)

(−2.1)

(5.1)

− .515.07POP16/65 + .020POP + 38.00 M2AV + .09CB2 (3.2)

R = 87.8% D.W. = 2.2 2

(6.0)

MSE = 24.88

(4.9)

(3.7)

(4.4.TR)

This study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

485

(1960–2010 data): CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38 POP16/65 (t=)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

R = 60.3% 2

(2.0)

(−0.1)

D.W. = 1.7

MSE = 43.98

(11.1AA)

Standard Consumption Model With Deficit Variables Used in This Study for the Same Time Period; Deficit Variables are Unmodified, and no Stand-alone LF Modifiers are Used: CD = .31(Y − TT ) + .32(TT ) − .16(G T&I ) − 7.14 PR (t=)

(6.4)

(−1.9)

(6.6)

(−3.1)

+ .49 DJ−2 − .459.68 POP16/65 + .017 POP (4.5)

(2.4)

(4.0)

+ 36.27 M2AV + .09 CB2 (3.8)

R = 86.6% 2

(3.9)

D.W. = 2.1

MSE = 26.17

(21.1A)

The same no modifier model was tested in five additional periods and results are given in Table 21.1A: Tests used OLS. Without modification by any growth in loanable funds, 6 of 6 time periods sampled show tax deficits have a statistically significant crowd out effect, and 4 of 6 samples showed spending deficits had significant crowd out effects. Average R 2 for the six tests is .87. Average R 2 is 87%. Table 21.1A Consistency of coefficient and t-statistic on loanable funds variable in six different time periods, using model given in Eq. 21.1A Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.) NA NA NA NA NA NA

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

.32(6.6) .32(5.5) .33(5.6) .23(2.8) .29(3.2) .53(3.9)

−.16(−1.9) −.08(−1.6) −.08(−1.5) −.03(−0.5) −.10(−1.7) −.21(−1.6)

.87 .87 .87 .81 .89 .91

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J. J. HEIM

Table 21.1 Consistency of coefficient and t-statistic on total loanable funds variable in six different time periods, using model given in Eq. 21.1 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.)

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

−.14(−4.13) −.12(−3.37) −.13(−3.61) −.10(−1.19) −.13(−1.28) −.47(−2.55)

.43(6.7) .42(5.5) .44(5.7) .29(2.6) .35(2.7) .72(5.3)

−.24(−2.9) −.16(−2.5) −.17(−2.4) −.09(−0.9) −.16(−2.2) −.28(−2.8)

.88 .89 .89 .91 .90 .94 Av. = 90.2% Adj.R 2 Av. = 86.5%

Standard Consumption Model With Added Stand-Alone Total Loanable Funds Control Variable (1960–2010 data): CD = .38(Y − TT ) + .43(TT ) − .24(G T&I ) − 14(S + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−4.1)

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.0)

(−1.9)

(3.7)

+ 33.67M2AV + .10 CB2 (3.5)

R = 88.3% 2

(4.5)

D.W. = 1.8

MSE = 24.68

(21.1)

Average R 2 is 90.2, about 3 points higher than in the unmodified version. The results for all six time periods consistently show a negative relationship between loanable funds pool size variable and consumption (probably because we are controlling for disposable income levels in the model, so any increase in the personal saving component definitionally has to be offset by declines in consumption). The coefficient uniformly shows the net effect of loanable funds growth to have a negative effect on consumption, even though one of its two effects is the positive effect on consumption of reducing crowd out’s negative impact. (The other, obviously larger impact is that holding disposable income constant, increases in savings, which is most to the pool, definitionally required cuts in

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

487

consumption. The sum of these two effects are what we hypothesize the (net) negative results here are showing.) Even after modification by any growth in loanable funds, 6 of 6 time periods sampled show tax deficits have a statistically significant crowd out effect, and 5 of 6 samples showed spending deficits had significant crowd out effects. Results for tax deficits were the same as before modification, but only four significant for government spending deficits. Hence, we have something of a textbook result for a modifier that yields a more accurate measure of crowd out effects: R 2 is higher as is the level of statistical significance of the modified deficit variable, compared to the unmodified version. Average R 2 was 90%, 3% higher than before modification (87%), suggesting modifying deficits’ effects on consumption by any changes in total loanable funds does increase explanatory power noticeable.

21.2 Statistical Significance of the FR Security Purchases Variable When Added to the Standard Consumption Model FR securities purchases variable is defined as FR purchases of treasuries, agency bonds, and mortgage-backed securities (Tr + A). The variable was found Hausman-endogenous with consumption and was replaced by a Wald-strong, non-endogenous (Sargan test) instrument. Estimation results, using the full 1960–2010 data set, are shown in Eq. 28.2 below. The variable is added to the standard consumption model as a stand-alone variable. The individual crowd out variables (T ) and (G) in the model are not modified by (Tr + A). To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are shown in Table 21.2. Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07 POP16/65 + .020 POP + 38.00 M2AV + .09CB2 (3.2)

R = 87.8% D.W. = 2.2 2

(6.0)

(4.9)

MSE = 24.88

(3.7)

(4.4.TR)

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J. J. HEIM

Table 21.2 Consistency of coefficient and t-statistic on FR purchases variable in six different time periods, using model given in Eq. 21.2 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.)

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

−.08(−2.2) −.79(−2.1) −1.20(−2.5) −1.22(−2.3) .11(0.2) −.27(−0.2)

.28(4.6) .36(6.5) .30(6.9) .27(3.2) .29(3.2) .53(3.9)

−.02(−0.4) −.11(−1.4) −.14(−2.2) −.14(−2.2) −.10(−1.5) −.22(−1.6)

.87 .86 .88 .89 .89 .91 Av. = 88.3% Adj.R 2 Av. = 82.2%

Standard Consumption Model with Added FR Securities Purchases Control Variable: CD = .25(Y − TT ) + .28(TT ) − .02(G T&I ) − .08(Tr + A) (t=)

(5.0)

(4.6)

(−0.4)

(−2.2)

− 5.28PR + .48DJ−2 − 430.43 POP16/65 (−2.2)

(4.0)

(−2.1)

+ .017POP + 50.59 M2AV + .10 CB2 (3.9)

R = 87.4% 2

(5.1)

D.W. = 2.0

(4.5)

MSE = 25.69

(21.2)

Average R 2 is 88.3%, a drop from the 90.3% for the model using total loanable funds. The results for five of the six time periods consistently show a negative relationship between FR securities purchases and consumption. In two cases, the negative sign maybe because FR purchases during the quantitative easing period (2008–2010) were higher than ever before, and this just happened to also be years of economic decline. But it does not explain the other three periods’ results. FR purchases may occur mostly when the economy is in a slump and the FR is trying to stimulate it. If so, the negative signs may simply mean we are not adequately controlling for the state of the economy. To test this hypothesis, we added two variables as additional controls (we are already controlling for

21

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489

disposable income) for the state of the economy: the current year unemployment rate and the level of the GDP, lagged one year. This changed the results noticeably; the first three tests in Table 21.2, which included sample data from 2007 to 2010 remained negative and significant, the 1960–2000 test was insignificantly different from zero, and the last two tests, covering 3/5ths of the total period tested, became positive. Hence, we conclude the negative relationship was most likely an abnormality of the fiscal difficulties occurring during the 2007–2010 period. Even after modification by any growth in loanable funds, 6 of 6 time periods sampled show tax deficits have a statistically significant crowd out effect, and 3 of 6 samples showed spending deficits had significant crowd out effects. For tax cut crowd out, results are the same as before modification. For spending deficits, the number of period found to have significant crowd out dropped slightly. Notice the spending deficit variables turn statistically insignificant in the samples containing the QE years, the years when FR purchases rose hugely, but consumption did not. This was because the huge increase in banks stayed mostly in banks; unlent loanable funds grew from an average of 2.2% of total reserves before QE to 96% after. Average R 2 was 88.1% a little higher than before modification, suggesting using FR purchases to modify deficits’ effects on consumption does increase explanatory power, but noticeably less than when the modifier used is total loanable funds.

21.3 Statistical Significance of the Combined Loanable Funds and FR Security Purchases Variable When Added to the Standard Consumption Model Endogeneity problems were found when testing the combined loanable funds and FR securities purchases variable (S + FB) + (Tr + A) model. That variable, the government receipts (T ) variable and prime interest rate (PR) found endogenously related to consumption in the model tested here. All three variables were replaced by a single Wald-strong, nonendogenous (Sargan test) instrument. Estimation results, using the full 1960–2010 data set, are shown in Eq. 21.3 below. The combined loanable funds and FR purchases variable was tested as a stand-alone variable.

490

J. J. HEIM

(T ) and (G) were not modified by (S + FB) + (Tr + A). To see if these results could be replicated, the same model was retested in five additional different but somewhat overlapping time periods. Results of retesting are shown in Table 28.3. Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−4.5)

(−2.1)

(5.1)

− .515.07POP16/65 + .020POP + 38.00 M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

(3.7)

(4.9)

MSE = 24.88

(4.4.TR)

Standard Consumption Model with Added Loanable Funds and FR Securities Purchases Control Variable: CD = .38(Y − TT ) + .47(TT ) − .14(G T&I ) − .16(S + FB + T + A) (t=)

(6.5)

(5.0)

(−1.3)

(−1.8)

− 3.50PR + .28DJ−2 − 230.28 POP16/65 + .014POP (−1.3)

(2.6)

(−1.2)

(3.1)

+ 38.07M2AV + .12CB2 (4.6)

R = 88.8% 2

(2.9)

D.W. = 1.8

MSE = 23.57

(21.3)

Average R 2 was 88.8%. For the tax variable, levels of statistical significance are lower in all five periods than those obtained using (S + FB) alone; for the spending variable, 3 of 5 are lower. This may indicate either that FR purchases add nothing to loanable funds, and just distort the data, or that FR purchases are already counted in (S + FB). The later explanation is more theory consistent. The results for four of the five time periods show a negative relationship between loanable funds pool size and consumption. This may be principally because, ceteris paribus, as national savings increase out of after tax personal or business income, spending must definitionally decline. Even after modification by any growth in loanable funds, 5 of 5 time periods sampled show tax deficits have a statistically significant crowd out effect, but only 1 of 6 samples showed spending deficits had significant crowd out effects. As discussed earlier, this is most likely a sign of the “errors in variables” problem than an indicator that this modifier was reducing crowd out.

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COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

491

Table 21.3 Consistency of coefficient and t-statistic on combined loanable funds and FR purchases variable in five different time periods, using model given in Eq. 21.3 Time period Tested 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.)

Tax deficit

Spending deficit

Coefficient ( t-Stat.)

Coefficient ( t-stat.)

R2

−.16(−1.8) −.18(−2.1) −.21(−1.5) .06(0.5) −.56(−1.5)

.47(5.0) .50(5.2) .43(4.1) .45(3.1) .84(3.8)

−.14(−1.3) −.15(−1.3) −.17(−1.7) −.08(−0.9) −.35(−2.6)

.89 .88 .90 .84 .93 Av. = 88.8% Adj.R 2 Av. = 85.2%

Average R 2 was .89%, higher than before modification (87%), suggesting using a combination of (S + FB) and FR purchases to modify deficits’ effects on consumption does increase explanatory power, but less than when the modifier used is total loanable funds alone (90%). This suggests the total loanable funds modifier is the better modifier, and that adding FR purchases to it creates an error in variables problem. We conclude Tables 21.1, 21.2, 21.3 indicated (S + FB) is a better measure of the effect of an increase in loanable funds on consumption than is just the FR purchases variable (or both).

Statistical Significance of Separate Loanable Funds and FR Security Purchases Variables When Added to the Standard Consumption Model

21.4

No endogeneity problems were found when testing separate stand-alone loanable funds (S + FB) and FR securities purchases (Tr + A) variables in the standard consumption model. Possible stationarity issues were removed through cointegration or with detrending. Estimation results, using the full 1960–2010 data set, are shown in Eq. 21.4 below. To see if these results could be replicated, the same model was retested in five

492

J. J. HEIM

additional different but somewhat overlapping time periods. Results of retesting are shown in Table 21.4. Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07POP16/65 + .020POP + 38.00 M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

(3.7)

(4.9)

MSE = 24.88

(4.4.TR)

Standard Consumption Model with Added Separate Loanable Funds and FR Securities Purchases Control Variables: CD = .34(Y − TT ) + .41(TT ) − .20(G T&I ) − .14(S + FB) (t=)

(5.8)

(5.3)

(−2.1)

(−4.2)

− .04(T + A) − 5.22PR + .44DJ−2 − 395.17POP16/65 (−2.1)

(−1.5)

(4.4)

(−2.1)

Table 21.4 Consistency of coefficient and t-statistic on total loanable funds and FR purchases variable in six different time periods, using model given in Eq. 21.4 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.) −.14(−4.2) −.04(−1.5) −.11(−2.9) −.29(−2.4) −.07(−1.5) −.51(−2.2) −.08(−0.8) −.38(−1.3) −.16(−2.3) −.16(−2.0) −.48(−2.3) −.28(−0.4)

LF FR LF FR LF FR LF FR LF FR LF FR

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

.41(5.3)

−.20(−2.2)

.89

.43(6.3)

−.17(−2.7)

.90

.38(4.9)

−.16(−2.7)

.90

.29(2.4)

−.11(−1.3)

.91

.38(3.2)

−.16(−2.3)

.90

.73(5.3)

−.29(−3.0)

.94 Av. = 90.7% Adj.R 2 Av. = 86.3%

21

493

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

+ .017POP + 39.15M2AV + .12CB2 (3.5)

R = 88.9% 2

(4.2)

D.W. = 1.8

(2.9)

MSE = 24.35

(21.4)

The results for all six time periods consistently show a negative relationship between loanable funds pool size and consumption. For (S + FB), his may be simply because, ceteris paribus, as national savings increase out of after tax personal or business income, spending must definitionally decline. The net of this negative effect and the positive effect of and increase in (S + FB) reducing crowd out simply seems negative (but near zero. For (Tr + A), it may just reflect the tendency of FR purchases to be large when the economy is declining. Comparing the single variable (S + FB) + (Tr + A) stand-alone variable models (Table 21.3) with results when both were included as separate variables in the Table 23.4 model, we see that (S + FB) and (TR + A) were both significant in 4 of 6 in four of six time periods in both models. In the model with these two variables combined into one, it was significant in only two of six tests, though it is not clear why the decline occurs. Tax deficits were statistically significant in all 6 test periods, spending deficits in 5 of 6. This is the same result obtained using just total loanable funds as the modifier (Table 21.1), and the coefficients on the tax and spending variables are very similar. Average R 2 was 90.7% compared to 90.3% when only the total loanable funds variable was used. Adding the loanable funds variable slightly raises R 2 , but not enough to suggest it is contributing more to our ability to explain consumption variance than just using total loanable funds alone as a deficit modifier.

21.5 Statistical Significance of Separate National Savings (Instead of (S + FB)) and FR Security Purchases Variables When Added to the Standard Consumption Model No endogeneity problems were found when testing separate national savings (S) and FR securities purchases (Tr + A) variables in the standard consumption model. Possible stationarity issues were removed through

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cointegration or with detrending. Estimation results, using the full 1960– 2010 data set, are shown in Eq. 28.5 below. To see if these results could be replicated, the same model was retested in five additional different but somewhat overlapping time periods. Results of retesting are shown in Table 21.5. Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t =)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07POP16/65 + .020POP + 38.00 M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

(3.7)

(4.9)

MSE = 24.88

(4.4.TR)

Standard Consumption Model with Added National Savings and FR Securities Purchases Control Variables: CD = .33(Y − TT ) + .40(TT ) − .21(G T&I ) − .17(S) (t =)

(5.5)

(5.2)

(−2.4)

(−2.9)

Table 21.5 Consistency of coefficient and t-statistic on national savings and FR purchases variable in six different time periods, using model given in Eq. 21.5 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.) −.17(−2.9) S −.02(−0.7) FR −.14(−2.4) S −.28(−2.5) FR −.10(−1.6) S −.53(−2.9) FR −.10(−1.1) S −.38(−1.5) FR −.12(−1.2) S .47(1.2) FR −.14(−0.4) S .22(0.2) FR

Tax deficit Coefficient ( t-stat.)

Spending deficit Coefficient ( t-stat.)

R2

.40(5.2)

−.21(−2.4)

.89

.42(6.0)

−.18(−2.7)

.90

.38(5.1)

−.17(−2.5)

.90

.30(2.5)

−.14(−1.6)

.91

.36(2.8)

−.12(−2.2)

.90

.57(2.6)

−.23(−1.4)

.91 Av. = 90.2% Adj.R 2 = 85.8%

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

495

− .02(Tr + A) − 4.80PR + .45DJ−2 − 433.08 POP16/65 (−0.7)

(−1.8)

(4.5)

(−2.5)

+ .019POP + 37.31M2AV + .10 CB2 (4.2)

R = 88.9% 2

(4.6)

D.W. = 2.0

(3.0)

MSE = 24.35

(21.5)

The average R 2 was 90.2 (essentially the same as when using (S + FB)). The results for all six time periods consistently show a negative relationship between national savings and consumption, but only three of the six coefficients are statistically significant. In Table 21.4, the model which was identical to this one except its loanable funds variable included foreign borrowing (S + FB), four of the six were statistically significant, suggesting it is a better representation of what the bounds are of the loanable funds pool that affects consumption. For (Tr + A), in this table, only two of six coefficients on (Tr + A) are significantly different from zero; in Table 21.4, we had the same result. Tax deficits were statistically significant in all 6 test periods, spending deficits in 5 of 6. This is the same result obtained using just total loanable funds as the modifier (Table 21.1), or the total loanable funds and FR purchases model (Table 23.4) and the coefficients on the tax and spending variables are very similar. Average R 2 was 90.2% compared to 90.3% when only the total loanable funds variable was used, or 90.7% when both the total loanable funds and, separately, the FR purchases variables were included (Table 21.4). Deleting foreign borrowing from the loanable funds variable to get national saving slightly lowers R 2 , but not enough to suggest FB is a major contributor to our ability to explain consumption variance. Using just the total loanable funds modifier remains the best option, since it is the more theory consistent than the Table 21.4 model. We also reran this exact model, with the addition of a separate foreign borrowing (FB) variable. Details of regression findings are not shown here, but the foreign borrowing variable was found negatively related to consumer spending in all six tests, but the coefficient was only significantly different from zero in the oldest period sampled, 1960–1980. Combined into one variable (S) and (FB) were significant in four of six tests; but separately in only one or two. The combined variable is also the most theory consistent explanation of how loanable funds growth may mitigate crowd out effects on consumption.

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J. J. HEIM

21.6 Statistical Significance When Separate Loanable Funds Net of FR Security Purchases and Separate FR Security Purchases Variables When Added to the Standard Consumption Model Loanable funds, net of FR purchases, was found endogenous with domestic consumption in the standard (domestic) consumption model; it was replaced by a Wald-strong instrument which was not endogenous. Possible stationarity issues were removed through cointegration or with detrending. Estimation results, using the full 1960–2010 data set, are shown in Eq. 28.6 below. To see if these results could be replicated, the same model was retested in five additional different but somewhat overlapping time periods. Results of retesting are shown in Table 21.6. Table 21.6 Consistency of coefficient and t-statistic on separate loanable funds (net of FR purchases) and FR purchases variables in six different time periods, using model given in Eq. 21.6 Time period Tested 1960–2010

1960–2008

1960–2007

1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.)

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

−.04(−0.4) LF−FR −.06(−0.6) FR −.05(−0.5) LF−FR −.35(−2.5) FR −.04(−0.3) LF−FR −.69(−3.3) FR .07(0.3) LF−FR −.41(−1.6) FR .01(0.1) LF−FR .47(1.2) FR −.28(−3.0) LF−FR −.72(−0.9) FR

.36(3.1)

−.10(−1.1)

.89

.38(3.4)

−.12(−1.4)

.89

.27(2.0)

−.09(−1.0)

.89

.20(1.7)

−.04(−0.4)

.91

.29(3.1)

−.09(−1.1)

.89

.34(3.6)

−.10(−1.4)

.91

R2

Av. = 89.7% Av.Adj.R 2 = 86.0%

21

497

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−2.1)

(−4.5)

(5.1)

− .515.07 POP16/65 + .020POP + 38.00 M2AV + .09CB2 (3.2)

R = 87.8% 2

(6.0)

D.W. = 2.2

(3.7)

(4.9)

MSE = 24.88

(4.4.TR)

Standard Consumption Model with Separate Endogenous Loanable Funds and FR Securities Purchases Control Variables: CD = .35(Y − TT ) + .40(TT ) − .15(G T&I ) − .10(S + FB − Tr − A) − .14(Tr + A) (t=)

(4.8)

(3.5)

(−1.5)

(−1.0)

(−1.1)

− 5.70PR + .33DJ−2 − 362.92 POP16/65 + .017POP + 43.78M2AV + .10 CB2 (−2.5)

(3.3)

(−1.8)

R = 89.6% D.W. = 1.9 MSE = 23.64 2

(3.3)

(5.0)

(2.9)

(21.6)

Average R 2 was 89.7%, slightly lower than the model using (S + FB). Only one of the six coefficients on the endogenous loanable funds variable (S + FB) − (Tr + A) was statistically significant, suggesting growth in the endogenous portion of the loanable funds pool is seldom directed toward consumers. By comparison, 3 of 6 periods tested showed FR purchases significant. In Table 21.6, three of six coefficients on (Tr + A) are significantly different from zero, indicating that exogenous increases in loanable funds offset the negative effects of consumption crowd out more often than endogenous increases in loanable funds. However, the poor showing of both total loanable funds net of FR purchases, and FR purchases may not be a substantive finding that neither affect consumption. It may be the result of a technical factor, namely, that when the correlation between two explanatory variables becomes very high, the standard errors on both tend to become very high, reducing or eliminating their statistical significance. This is what appears to have happened here. The simple correlation between the two variables is r = .87, which is very high. Hence, we think the other consumption models give results regarding significance levels more likely to be accurate than this model. Tax deficits were statistically significant in all 6 test periods, spending deficits in 0 of 6. For spending, this is a considerably different result than that obtained using just total loanable funds as the modifier (Table 21.1), or the total loanable funds and FR purchases model (Table 21.4). In those

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models 6 of 6 tax deficit variables were significant, as were 5 of 6 spending variables. Average R 2 was 89.7% compared to 90.3% when only the total loanable funds variable was used, or 90.7% when both the total loanable funds and, separately, the FR purchases variables were included in Table 21.4). Using the total loanable funds modifier remains the best option, since it explains more variance and it is the more theory consistent than the Table 21.6 model. Conclusions for Consumption Model In the search for which of a number of variants of loanable funds might be most systematically related to consumption, and therefore most likely represent the variable that can offset crowd out, the total loanable funds variable (S + B), was statistically significant most often, had the highest R 2 and adjusted R 2 , and appears to contain the effect of FR purchases on total loanable funds as one of its components. FR purchases alone, in some periods, also seem related negatively to consumption, but this may because of their tendency to rise when the economy is in decline, not because they are driving consumption downward. 21.6.1

Investment Model Tests

Below we modify the standard investment models taken from (Heim 2017, Eq. 5.4.TR), by adding one additional variable either total loanable funds (S + FB), FR Purchases of Treasuries and Agency bonds (Tr + A), or a combination of both. All variables in the models are ADF stationary, DF cointegrated, or detrended as required, and Hausman—endogenous explanatory variables are replaced by Wald-strong instruments, which themselves were tested for endogeneity and found not endogenous (Sargan test). Models are estimated in first differences to reduce multicollinearity effects and enhance variable stationarity.

21.7 Statistical Significance of the Total Loanable Funds Variable (S + FB) When Added to the Standard Investment Model Some variables in Eq. 21.7 below had stationarity issues, but these were resolved through cointegration or detrending. No endogeneity problems were found when testing the total loanable funds variable (S + FB) model, where loanable funds is defined as total national saving from personal,

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

499

corporate, and depreciation allowance sources, plus any borrowing of funds from foreign sources that takes place. Nor were any of the other explanatory variables found endogenous with the investment dependent variable (ID ). Estimation results, using the full 1960–2010 data set available, are shown in Eq. 21.7 below. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are shown in Table 21.7. The Standard Investment Model from Heim (2017): (Using 1960–2010 data) ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, and No GDP Variable Included to Control for the State of the Economy: ID = + .48(ACC) + .008POP + .76PR−2 (t=)

(10.6)

(2.5)

(0.2)

Table 21.7 Consistency of coefficient and t-statistic on loanable funds variable (S + FB) in six different time periods, using model given in Eq. 21.7 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.) .16(2.1) .19(2.4) .22(3.1) .30(3.1) .36(4.2) .65(9.7)

LF LF LF LF LF LF

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

.21(1.8) .20(1.8) .12(1.4) .17(1.8) .13(1.6) −.01(−0.4)

−.23(−2.5) −.16(−1.5) −.13(−1.3) −.15(−1.7) −.10(−1.2) −.12(−1.3)

.90 .88 .87 .90 .89 .97 Av. = 90.2% Av.Adj.R 2 = 88.3%

500

J. J. HEIM

+ 7.37XRAV + 14.08CAP−1 (2.2)

(4.3)

R = 69.4%

D.W. = 1.6

2

MSE = 47.87

Same as Eq. 10.3C This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy: ID = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(0.0)

(4.0)

(−0.3)

+ 5.21XRAV + 10.39CAP−1 + .10 GDP (2.0)

(−1.3)

(2.9)

R = 76.1% 2

D.W. = 2.1

MSE = 43.06

Same as Eq. 10.3B; and same as Eq. 11.10C below The Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010): ID = + .27(ACC) + .33TT − 33 G T&I + .012POP (t=)

(2.6)

(6.4)

(2.8)

(−3.9)

− 4.95PR−2 + 6.68XRAV + 2.43CAP−1 − .02GDP (3.5)

(−2.5)

R = 89.0% 2

D.W. = 1.9

(−0.2)

(1.8)

MSE = 29.87

(11.4A)

The Standard Investment Model with 2 Variable Crowd out (T , G), with stand-alone loanable funds variable (Using 1960–2010 data): ID = + .18(ACC) + .21TT − 23 G T&I + .16( (S + FB)) + .007POP (t=)

(5.6)

(1.8)

(−2.6)

(2.1)

(2.7)

− 3.24PR−2 + 5.54XRAV + 1.00 CAP−1 (−1.6)

R = 90.4% 2

(2.7)

D.W. = 1.9

(0.7)

MSE = 27.50

(21.7)

Notice that the loanable funds variable in Eq. 21.7 has a positive sign, unlike our consumption models where it was negative. Unlike consumption, an increase in loanable funds does not have two competing effects (reduces income available for consumption when disposable income is held constant, but simultaneously increases funds available to offset crowd out). An increase in loanable funds only increases funds available for

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

501

investment, thereby allowing it to serve as an offset to crowd out effects on investment without any offsetting negative effect. Because of the savings/investment identity, every increase is definitionally associated with an increase in investment. Average R 2 was 90.2%. The results for all six time periods consistently show a positive and highly statistically significant relationship between loanable funds pool size and investment levels, as we might expect, since the loanable funds pool is largely national savings, and savings is required to finance investment. For the baseline investment model with deficits, but before any modifiers were added, 5 of 6 tax deficit and 6 of 6 spending deficit variables were statistically significant (Table 11.10A). (A baseline model including a GDP control variable yielded nearly identical results: 4 of 6 tax deficits significant and 6 of 6 spending deficits significant.) After the stand-alone loanable funds variable was added to the model (without a GDP control), tax deficits were only statistically significant in 4 of 6 test periods, spending deficits in 2 of 6. But the significance of deficit variables changes dramatically when a control variable for GDP is added to the model (see Table 11.10). There, only 1 of 6 tax deficits remains significant, but 5 of 6 spending deficits stay significant. Adding the control variable for economic conditions (GDP) is appealing on theoretical grounds. There is an argument to be made that tax deficits are mostly saved (since they accrue to those with higher incomes who save significant portions of their income), and therefore fund their own offset to crowd out, as discussed in conjunction with Table 11.10). In addition, we know that in addition to crowd out, a declining in the business cycle affect both deficits and investment spending. Hence, that model may better describe the loanable funds effects. Before modification, average R 2 was 88.3%. After modification, it rose to 90.2%, indicating the effect of deficits on crowd out is better given as the size of the deficit net of any change in loanable funds that occurs. The growth in loanable funds clearly significantly offsets crowd out as shown by the coefficient and significance levels on the loanable funds variable and increased R 2 . It is not clear why the significance levels on the crowd out variables declined so much, except for the “errors in variables” reason discussed earlier, which suggest only some of loanable funds makes its way into lending to those who wish to buy real goods and services (which raises R 2 ), but the rest goes unspent or is spent on things like securities which do not enter the GDP.

502

J. J. HEIM

21.8 Statistical Significance of the FR Securities Purchases Variable (Tr + A) When Added to the Standard Investment Model Some variables in the FR purchases (Tr + A) model in Eq. 21.8 below had stationarity issues, but these were resolved through cointegration or detrending. Endogeneity problems were found with the accelerator (ACC) and government spending (G) variables, and they were replaced by a Wald-strong, Sargan tested, instrument. Estimation results, using the full 1960–2010 data set available, are shown in Eq. 21.8 below. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are shown in Table 21.8. The Standard Investment Model from Heim (2017): (Using 1960–2010 data): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

Table 21.8 Consistency of coefficient and t-statistic on FR security purchases variable in six different time periods, using model given in Eq. 21.8 (investment) Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable Coefficient ( t-stat.)

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

.02(0.7) FR .30(2.4) FR .54(1.6) FR −.32(−0.6) FR −.40(−0.5) FR 1.43(2.7) FR

.32(3.6) .31(3.5) .35(3.9) .42(4.3) .47(2.3) .34(3.6)

−.38(−1.8) −.30(−1.2) −.25(−0.9) −.38(−1.8) −.41(−2.0) −.45(−3.2)

.89 .87 .83 .86 .82 .93 Av. = 86.7% Adj.R 2 Av. = 84.3%

21

503

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

The Baseline Model With Deficit Variables Added: Before Adding Stand Alone (S + FB) (1960–2010 Sample): ID = + .27(ACC) + .33TT − 33 G T&I + .012POP (t=)

(2.6)

(6.4)

(2.8)

(−3.9)

− 4.95PR−2 + 6.68XRAV + 2.43CAP−1 − .02GDP (3.5)

(−2.5)

R = 89.0% 2

D.W. = 1.9

(1.8)

MSE = 29.87

(−0.2)

(11.4A)

The Standard Investment Model with 2 Variable Crowd out (T , G), including a stand-alone accommodating FR purchases variable. (Estimated using 1960–2010 data): ID = .26(ACC) + .32TT − 38 G T&I + .02( (Tr + A)) + .011POP (t=)

(3.0)

(3.8)

(−1.8)

(0.7)

(1.6)

− 3.88PR−2 + 6.52XRAV + 2.03CAP−1 (−1.4)

R = 88.7% 2

(3.7)

D.W. = 1.8

(0.7)

MSE = 29.67

(21.8)

Average R 2 was 86.7%, markedly less than for the model using (S + FB). The results for all six time periods are decidedly mixed. The effect of increases in loanable funds on investment is positive (unlike consumption) in only four time periods, and statistically significant for only three. Clearly exogenous increases in the loanable funds pool by FR open market operations has a less reliable positive effect on investment than increases from the total loanable funds pool, which is comprised mostly of funds that vary for endogenous reasons. All six tax deficits were found significant, but only three of the six spending deficits were significant. Average R 2 was only 86.7%, less than the model without any deficit modifier (88.3%).

21.9 Statistical Significance of the Combined Loanable Funds (S + FB) and FR Securities Purchases Variable (Tr + A) When Added to the Standard Investment Model Some variables in Eq. 21.9 below had stationarity issues, but these were resolved through cointegration or detrending. Endogeneity problems

504

J. J. HEIM

were found with the foreign exchange rate average variable and it was replaced by a Wald-strong, Sargan tested instrument. Estimation results, using the full 1960–2010 data set available, are shown in Eq. 21.9 below. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are shown in Table 21.9. Standard Investment Model from Heim (2017) (Using 1960–2010 data): ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(5.7)

(−3.8)

(2.9)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

Standard Investment Model with 2 Variable Crowd out (T , G), using 1960–2010 data: ID = .25(ACC) + .28TT − 43 G T&I + .05( (S + FB + Tr + A)) (t=)

(−3.1)

(3.1)

(6.4)

(1.4)

+ .013POP − 1.68PR−2 + 10.59XRAV + 4.22CAP−1 (3.6)

(−0.8)

(3.3)

(2.1)

Table 21.9 Consistency of coefficient and t-statistic on single loanable funds and FR security purchases variable in six different time periods, using model given in Eq. 21.9 Time period Tested

Loanable funds variable Coefficient ( t-stat.)

1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

.05(1.4) .14(2.4) .13(2.3) .10(0.5) .28(1.6) .63(6.1)

LF LF LF LF LF LF

+ + + + + +

FR FR FR FR FR FR

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

.28(3.1) .20(2.3) .18(2.2) .31(1.7) .19(1.4) .01(0.1)

−.43(−3.1) −.28(−2.0) −.26(−2.2) −.34(−2.5) −.20(−1.4) −.13(−1.9)

.89 .88 .85 .88 .89 .97 Av. = 89.3% Av.Adj.R 2 = 87.2%

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

R 2 = 88.6%

D.W. = 1.7

MSE = 30.63

505

(21.9)

Average R 2 was 89.3, again lower than the (S + FB) model. The results for all six time periods show a positive relationship between (S + FB + Tr + A) and investment. Four of the six are statistically significant. Coefficients and t-statistics in Table 21.7 (S + FB alone) tended to be larger, and much more statistically significant, and were significant in all six periods. This suggests that adding the FR purchases component to total loanable funds, reduced explanatory power, by distorting the values of the “true” loanable funds variable. This finding suggests that either the FR purchases are already picked up in the loanable funds variable (S + FB), or that (Tr + A) has no effect on investment and is simply distorting a data set that does have a systematic effects. The first explanation is more theory consistent and suggests that adding (Tr + A to (S + FB) is redundant, and just over weights its effects in the new variable, bringing down its significance levels. Results from Table 21.8 (FR purchases only) as to the extent to which (Tr + A) had a systematic positive effect were very mixed, both as to the sign of the effect, and the statistical significance. Four of 6 tax deficit variables were statistically significant and 5 of 6 spending deficit variables. Average R 2 was 89.3, the same as the model without any modifier, and below the 90.2% R 2 obtained using only the total loanable funds variable as the modifier. Table 21.7 model variable (S + FB) provides our best definition of how changes in loanable funds can offset crowd out effects in investment. It is the most consistent with the data. Looking at FR purchases alone (Table 21.8), without consideration of other loanable funds factors which can increase funds available for investment, is the worst. Addendum: Table 21.9A model is Table 21.9 with GDP variable added to the model to control for economic conditions. Adding the GDP control variable leaves the results essentially unchanged from those reported earlier in Table 21.9.

506

J. J. HEIM

Table 21.9A Consistency of coefficient and t-statistic on single loanable funds and FR security purchases variable in six different time periods, using model given in Eq. 21.9 with a GDP control variable added Time period Tested

Loanable funds variable Coefficient ( t-stat.)

1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

.05(1.2) .14(2.6) .14(2.5) .11(0.5) .21(1.1) .61(6.4)

LF LF LF LF LF LF

+ + + + + +

FR FR FR FR FR FR

Tax deficit

Spending deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

R2

.29(2.4) .21(2.0) .19(1.9) .33(1.9) .12(1.1) −.01(0.1)

−.43(−3.0) −.25(−1.8) −.26(−2.0) −.34(−2.4) −.31(−1.9) −.13(−1.7)

.88 .88 .85 .87 .90 .98 Av. = 89.3% Av.Adj.R 2 = 87.2%

21.10 Statistical Significance When Separate Loanable Funds and FR Securities Purchases Variables Are Added to the Standard Investment Model When two stand-alone variables, total loanable funds, and FR purchases, were added to the standard investment model, some variables had stationarity issues, but these were resolved through cointegration or detrending. Endogeneity problems were found with the foreign exchange rate average variable and it was replaced by a Wald-strong, Sargan tested instrument. Estimation results, using the full 1960–2010 data set available, are shown in Eq. 21.10 below. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are also shown in Table 21.10. The Standard Investment Model from Heim (2017): (Using 1960–2010 data) ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (−2.7)

R = 83.3% 2

(2.9)

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

507

Table 21.10 Consistency of coefficient and t-statistic on total loanable funds and FR security purchases variables in six different time periods, using model given in Eq. 21.10 Time period

Loanable funds variable

Tax deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

Spending deficit Coefficient ( t-stat.)

10(1.3) S + FB .04(1.1) TR + A .12(1.9) S + FB .21(2.4) TR + A .16(2.2) S + FB .03(0.1) TR + A .16(1.0) S + FB −.50(−1.2) TR + A .31(3.3) S + FB −.57(0.9) TR + A .67(1.7) S + FB .45(1.4) TR + A

.24(2.1)

−.37(−2.7)

.89

.20(2.4)

−.28(−2.2)

.89

.15(1.8)

−.23(−1.7)

.86

.28(2.0)

−.31(−2.4)

.90

.17(1.6)

−.17(−1.6)

.92

−.01(−0.6)

−.11(−1.4)

.98

Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

R2

Av. = 90.7% Av.Adj.R 2 = 87.7%

The Standard Investment Model with 2 Variable Crowd out (T , G), With Separate Total Loanable Funds and FR purchases Variables. (Using 1960–2010 data): ID = .23(ACC) + .24TT − 37G T&I + .10(S + FB) + 04(Tr + A) (t=)

(5.3)

(2.2)

(−2.7)

(1.3)

(1.2)

+ .012POP − 1.59PR−2 + 10.73XRAV + 3.79CAP−1 (3.7)

R = 88.7% 2

(−0.7)

D.W. = 1.6

(3.2)

MSE = 30.84

(1.8)

(21.10)

Average R 2 was 90.7%. The results for all six time periods show a positive relationship between (S + FB) and investment. Four of the six (S + FB) variables are at least marginally statistically significant. (Tr + A) is positively related to investment in four of the six samples, and negatively related in two. Only one of six (Tr + A) is statistically significant. This indicates fluctuations in the total loanable funds pool are more systematically related to investment than fluctuations in FR purchases.

508

J. J. HEIM

Tax deficit variables are significant in 5 of 6 periods sampled; for spending deficits it is also 5 of 6. Average R 2 for the six samples here is 90.7%; using only total loanable funds as the modifier gave an average R 2 of 90.2% for the same six test periods, and significance levels for the tax and spending variables that were very different from the 5 of 6 tax deficit and 6 of 6 spending deficit significance levels of the crowd out variables before any modification. These results suggest that adding the additional liquidity represented to total loanable funds may in fact be indicating FR purchases add something to liquidity beyond what our traditional definition of loanable funds provides (though the fact that it was a significant addition in only one of six cases would argue against this interpretation). Coefficients and t-statistics on the (S + FB) variable in Table 21.7, where only the (S + FB) variable was used, tended to be larger, and statistically significant in all six tests. The model tested in Table 21.10 is identical except the FR securities purchases variable is also added as a stand-alone variable. The smaller magnitude of coefficients on (S + FB) in all but one of the six periods, and lower statistical significance levels, and less frequent findings of significance (one of six tests) suggests that adding the FR purchases to the same model dilutes the clear relationship of the variation in (S + FB) to investment. This finding suggests that either (1) the FR security purchases variation relationship to investment is already picked up in the loanable funds variable (S + FB), or (2) that (Tr + A) has no effect on investment aside from that shared with (S + FB), and is simply distorting a data set that does have a systematic effects. We lean toward the interpretation that the Table 21.7 model variable (S + FB) provides our best definition of how changes in loanable funds can offset crowd out effects in investment.

21.11 Statistical Significance of Separate National Savings and FR Securities Purchases Variables When Added to the Standard Investment Model In testing the model with separate savings (S) and FR purchases (Tr + A) variables, some variables in Eq. 21.11 below had stationarity issues, that were resolved through cointegration or detrending. Endogeneity problems were found with the foreign exchange rate average variable and it was

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

509

replaced by a Wald-strong, Sargan tested instrument. Estimation results, using the full 1960–2010 data set available, are shown in Eq. 21.11 below. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are also shown in Table 21.11. The Standard Investment Model from Heim (2017): (Using 1960–2010 data) ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

Table 21.11 Consistency of coefficient and t-statistic on separate (S) and FR security purchases variables in six different time periods, using model given in Eq. 21.11 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable

Tax deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

.12(1.2) S .02(0.8) TR + A .14(1.5) S .21(2.2) TR + A .16(1.7) S .15(0.6) TR + A .09(0.6) S −.58(−1.3) TR + A .21(1.3) S −.62(1.1) TR + A .25(0.9) S .84(1.6) TR + A

Spending deficit Coefficient ( t-stat.)

R2

.24(2.1)

−.35(−2.8)

.88

.21(2.1)

−.26(−2.4)

.88

.19(2.0)

−.23(−2.1)

.84

.36(3.0)

−.37(−3.7)

.88

.27(2.1)

−.22−(1.6)

.89

.23(1.4)

−.18(−1.7)

.95 Av. = .88.7% Av.Adj.R 2 = 85.3%

510

J. J. HEIM

The Standard Investment Model with 2 Variable Crowd out (T , G), With Separate National Savings and FR Purchases Variables, But Without Including the Foreign Borrowing Component of Loanable Funds (Using 1960–2010 data): ID = .23(ACC) + .25TT − 35G T&I + .12(S) (t=)

(2.1)

(5.2)

(−2.8)

(1.2)

+ .02(Tr + A) + .012POP − 2.17PR−2 (0.8)

(3.6)

(−1.0)

+ 11.83XRAV + 3.37CAP−1 (3.5)

R = 87.6% 2

(1.4)

D.W. = 1.6

MSE = 32.34

(21.11)

The results for all six time periods show a positive relationship between (S) and investment, but only one of the six tests of (S) was even marginally statistically significant, compared to four out of six in the identical model except that (S) was augmented by adding foreign borrowing, i.e. (S + FB) was used (Table 21.10), and in Table 21.7 where only (S + FB) was tested, all six were statistically significant. The much weaker findings for (S) alone as compared to (S + FB) indicate our definition of loanable funds effect in reducing crowd out effects on investment are flawed unless we use (S + FB). i.e., also account for the substantial effect on investment of foreign borrowing. Only two tests of (Tr + A) were statistically significant. This model, like the others in this chapter, finds little evidence FR purchases have significantly impacted investment in the past. The tax deficit variable was significant in 5 of 6 periods tested, and the spending deficit variable was significant in all six. Average R 2 fell to 88.7%, noticeably below the 90.7% obtained when using separate total loanable funds and FR purchases variables, or the 90.2% obtained using total loanable funds alone as the modifier. Hence, our results of nonsignificance for the two loanable funds variables, low average R 2 (about the same as the unmodified model) indicate this is not a good model of how loanable funds variables affect crowd out. The number of significant tax and spending deficit variables also is identical to that found in the unmodified model.

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

511

21.12 Statistical Significance of a Separate Endogenous Loanable Funds Variable (LF − FR Purchases), and a Separate FR Securities Purchases Variables When Added to the Standard Investment Model Some variables in Eq. 21.12 below had stationarity issues, but these were resolved through cointegration or detrending. Endogeneity problems were found with the foreign exchange rate average variable and it was replaced by a Wald-strong, Sargan tested instrument. Estimation results, using the full 1960–2010 data set available, are shown in Eq. 21.12 below. To see if these results could be replicated, the same model was retested in five additional different but overlapping time periods. Results of retesting are also shown in Table 21.12. The Standard Investment Model from Heim (2017): Table 21.12 Coefficients and t-statistics on loanable funds (net of Tr + A) and FR security purchases variables in six different time periods, using model given in Eq. 21.12 Time period Tested 1960–2010 1960–2008 1960–2007 1960–2000 1960–1990 1960–1980

Loanable funds variable

Tax deficit

Coefficient ( t-stat.)

Coefficient ( t-stat.)

.15(2.1) S + FB−FR .19(2.1) TR + A .15(2.2) S + FB−FR .37(3.5) TR + A .18(2.4) S + FB−FR .21(1.0) TR + A .24(1.9) S + FB−FR −.09(−0.2) TR + A .37(4.6) S + FB−FR −.07(−0.9) TR + A .61(10.3) S + FB−FR 1.12(3.3) TR + A

Spending deficit Coefficient ( t-stat.)

R2

.22(2.2)

−.24(−1.7)

.90

.19(2.5)

−.22(−1.7)

.90

.16(1.8)

−.19(−1.4)

.86

.23(1.9)

−.21(−1.9)

.90

.12(1.2)

−.08(−0.8)

.91

.01(0.4)

−.15(−1.6)

.98 Av. = 90.8% Av.Adj.R 2 = 88.2%

512

J. J. HEIM

(Using 1960–2010 data) ID = + .26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (2.9)

(−2.7)

R = 83.3% 2

D.W. = 2.0

(1.7)

MSE = 28.25

(5.4.TR)

The Standard Investment Model with 2 Variable Crowd out (T , G), with stand-alone LF variables, but no deficit variable modifiers) (Using 1960–2010 data) ID = .23(ACC) + .22TT − 24G T&I + .15(S + FB − (Tr + A)) (t=)

(2.2)

(5.7)

(−1.7)

(2.1)

+ 19(Tr + A) + .008POP − 2.31PR−2 (2.2)

(2.2)

(−1.2)

+ 8.78XRAV + 2.27CAP−1 (3.0)

R = 89.8% 2

(1.3)

D.W. = 1.7

MSE = 28.49

(21.12)

The results for all six time periods show a positive relationship between (S + FB − (Tr + A)) and investment, and all six effects were statistically significant. This and the Table 21.7 model (S + FB alone) are our only models in which the loanable funds variable (S + FB alone), or its largest component part (S + FB) − (Tr + A), are significant in all six models. This is a much better showing than the Table 21.10 model, an identical model except that (Tr + A) was not netted out of (S + FB). With (T + A), only three of the six test results were statistically significant, including the two for purchases during the Quantitative Easing sample years. We have previously assumed (T + A) was included as a part of total loanable funds. If so, adding the separate (Tr + A) variable should be viewed as merely a logically faulty attempt to explain the same variance twice in the model, and show as insignificant, as in Table 21.10 where the two loanable funds variables tested were total loanable funds and FR purchases, and the separate FR purchases variable was found insignificant in 5 of 6 tests. That said, this model is a good way of assessing the relative importance to investment of the two components of total loanable funds since 1960. The results above suggest the endogenous part has been far more important than the FR purchases part, but the strong QE period results suggest that in large enough quantities, FR purchases

21

COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

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can also have a significant positive impact on investment. In investment Table 21.12, where endogenous and exogenous components are tested in the same model as stand alones, the average 6-test coefficients on the endogenous part and the exogenous part were the same (.28), and both were statistically significant, but the average t-statistic was higher on the endogenous coefficient than on the exogenous coefficient. However, the exogenous component was much weaker in 2 of the 3 samples covering periods between 1960 and 2000. The tax deficit variable was significant in 5 of 6 periods tested, and the spending deficit variable was significant in 4 of 6 periods tested. Average R 2 was 90.8%, slightly above the 90.7% obtained when using separate total loanable funds and FR purchases variables, or the 90.2% obtained using total loanable funds alone as the modifier. Overall, this model suggests that in the past, the endogenous growth in the loanable funds pool has mainly been what has at least partially offset crowd out effects, but the unusually large increase in FR purchases during the QE period also significantly helped offset crowd out.

21.13 Summary of Chapter Results and Conclusions The two tables and comments below summarize the findings and conclusions of this chapter for consumption and investment. The findings indicate the same increase in the pool of loanable funds has a net negative effect on consumption, but a net positive effect on investment. A comparison of Tables 21.1 and 21.7 will show that the positive effect on investment of a change in loanable funds (S + FB), more than offsets the negative effect on consumption. This of course, is good news, but still understates the net effect. The reason the effect on consumption is negative is that ceteris paribus, for loanable funds (savings) to increase, consumption must decline due to the associated reduction in mpc necessary to increase saving. But this neglects the stimulus effects of the deficit on consumption, which work by increasing income. This needs to be added into get the true net effect on consumption. By the same reasoning the positive effect of an increase in loanable funds on investment, also obtained ceteris paribus, also understates the net effect because it does not factor in the positive effects on investment of the growth in income associated with the deficit. In the investment model, this is seen as an increase in the accelerator.

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The bad news is that the opposite holds for changes in loanable funds due solely to FR security purchases. There, the negative effects on consumption swamp the positive effects on investment (see Tables 21.7 and 21.8). It is not clear why an increase in FR purchases leaves a net negative effect on consumption. It does not seem to be because declining economic conditions are associated with increased FR purchases. We have tried several controls for economic conditions and get the same result (the standard consumption model already uses a measure of disposable income as a control). Cptr. 21 Investment Summary Table (Six Stand-Alone Modifier Models Tested, No Modification of Deficit Variables Used) ___________________________________________________________________________________

Model

R2 (18 Time Periods) From 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 Table# -2010 08 07 00 90 80 90 00 07 09 00 10 04 04 04 05 10 10

Sigif./Total Test Ratio T G.

10 Baseline (w/o Def) T10.3C 69 67 66 63 65 72 -61 56 65 72 69 77 -64 71 63 57 92 91 (Does not include GDP Control Variable) (Av. R2 = 68.3%)

NA NA

NA NA*

10 Baseline (w/o Def) T10.3B 76 70 71 80 78 91 82 81 71 76 81 80 80 81 75 75 93 95 (includes GDP Control Variable) (Av. R2 = 79.8%)

NA NA

NA NA*

11 Baseline (w/Def) Eq.11.10A 89 86 84 89 87 95 90 90 86 90 89 90 89 89 89 89 98 98 11/18 16/18 (Av. R2 = 91.2% for 18 samples; 88.3% for 6 samples used below) 8/11 9/11 Variant(s) of loanable Funds Used 21 (S+FB)

T21.7

90 88 87 90 89 97 (90.2% Av. ; Adj.R2=88.3%) --- --- ---

4/6 2/6 4/6 2/6*

21 (Tr+A)

T21.8

89 87 83 86 82 93 (86.7% Av. ; Adj.R2=84.3%) --- --- ---

6/6 4/6 6/6 4/6*

21 (S+FB)+(Tr+A)

T21.9

89 88 85 88 89 97 (89.3% Av. ; Adj.R2=87.2%) --- --- ---

4/6 5/6 4/6 5/6*

21 (S+FB), (Tr+A)

T21.10

89 89 86 90 92 98 (90.7% Av. ; Adj.R2=87.7%) --- --- ---

5/6 5/6

21 (S), (Tr+A)

T21.11

88 88 84 88 89 95 (88.7% Av. ; Adj.R2=85.3%) --- --- ---

5/6 5/6*

5/6 6/6 5/6 6/6*

90 90 86 90 91 98 (90.8% Av. ; Adj.R2=88.2%)

--- --- --4/6 4/6 4/6 4/6* ___________________________________________________________________________________ 21 (S+FB-FR),(Tr+A) T21.12

*Excludes test periods with 1/3–½ of observations from 1990s (crowd in periods). See Cptr. 11 for explanation

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COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

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1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8% 2. When deficit variables only added to standard model, R 2 increases to 89.8%, an increase of 13%, clearly indicating variation in investment is better explained by models that allow for significant crowd out effects. 3. The investment model with the most explanatory power was the total loanable fund model (R 2 = 91.2%), the model with total loanable fund’s two parts estimated separately (90.8%), but the adjusted R 2 , the better measure, is slightly greater for the total loanable funds model. 4. Four of the 6 investment models tested with modifiers explained substantially more variance than the no modifier model. The four that explain more variance all have total loanable funds as their only LF variable, or that and the FR purchases modifier combined. The other two models explained less variance, and are rejected for that reason (the (Tr + A) and (S, Tr + A) models. When added to the model, they explain either less or only slightly more variance than the model with no loanable funds variable at all. Basically, we conclude that for these six sample periods, increases in total loanable funds pool can offset some investment crowd out effects. 5. Of the four with the total loanable funds modifier, the two that explained the most variance were the models that included separate total LF and FR purchases modifiers, or total LF net of FR purchases and a separate FR purchases variable. Both suggest FR purchases has something to add not captured by just including it as part of the total LF variable. This “something” appears to be the strong positive effect of FR purchases during the QE period, but not at any other time. 6. With no loanable funds modifier, the standard investment model with deficit variables included for the 6 periods tested here had an average R 2 of 88.3%; 5 of 6 tax deficit variables and 6 of 6 spending deficit variables were statistically significant (Table 11.10A). In

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general, adding one of the six modifiers left the number of significant tax or spending deficits roughly the same. The one exception came when only the total loanable funds variable was used. There, tax deficits remained roughly the same (4 of 6), but significant spending deficits dropped to 2 of 6. The problem seems to be multicollinearity between the (S + FB) variable and the tax deficit variable (r = .79). The effects can distort the significance of other variables as well and this appears to be happening here. The highest correlation between the loanable funds variant in the other models (S, S + FB − FR), (S + FB + FR) is r = .43.

Cptr. 21 Consumption Summary Table (Six Stand-Alone Modifier Models Tested, No Modification of Deficit Variables Used) ___________________________________________________________________________________ Sigif./Total R2 (18 Time Periods) From 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 Test Ratio Model Table# -2010 08 07 00 90 80 90 00 07 09 00 10 04 04 04 05 10 10 T G. 11 Baseline (wo/Def T11.1AA 60 72 72 86 43 77 91 91 68 55 86 37 63 74 67 65 83 95 (Av. R2 = 71.4%) 11 Baseline (w/Def) Eq.11.1A 87 87 87 91 89 91 93 92 86 88 94 85 88 88 86 87 92 99 (Av. R2 = 89.4%; 88.7% for the 6 periods used below)

Variant(s) of loanable Funds Used 21 (S+FB) T21.1 89 89 89 91 90 94 (90.2% A; Adj.R2=86.5%v.) --- --- ---

NA NA 15/18 10/11 ( 5/5

NA NA* 6/18* 5/11* 5/5**)

6/6 5/6 6/6 5/6*

21 (Tr+A)

T21.2

87 86 88 89 89 91 (88.3% Av. ; Adj.R2=82.2%) --- --- ---

6/6 3/6 6/6 3/6*

21 (S+FB)+(Tr+A)

T21.3

--- 89 88 90 84 93 (88.8% Av. ; Adj.R2=85.2%)- --- --- ---

5/5 2/5 5/5 2/5*

21 (S+FB), (Tr+A)

T21.4

89 90 90 91 90 94 (90.7% Av. ; Adj.R2=86.3%)- --- --- ---

6/6 5/6 6/6 5/6*

21 (S), (Tr+A)

T21.5

89 90 90 91 90 91 (90.2% Av; Adj.R2=85.8%.)

21 (S+FB-FR),(Tr+A) T21.6

--- --- ---

6/6 6/6

5/6 5/6*

89 89 89 91 89 91 (89.7% Av. ; Adj.R2=86.0%) --- --- ---

6/6 0/6 6/6 0/6* ___________________________________________________________________________________

*Excludes test periods with 1/3–½ of observations from 1990s (crowd in periods). See Cptr. 11 for explanation

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COMPARING VARIOUS STAND-ALONE ENDOGENOUS …

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1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4% 2. When deficit variables only added to standard model, R 2 increases to 89.4%, an increase of 25%, clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When total loanable funds modifiers are added to standard model with deficits, either as a stand-alone variable, average R 2 increases from 88.3 to 90.2% (Adj. R 2 = 86.5%) for the six periods tested, indicating increases in loanable funds do help offset consumption crowd out. This model explained more variance than any other model tested. For all five models that contain either all of (T + FB) as a control, or at least the largest part of it (national savings (S)), the addition of the loanable funds variable increases the explanatory power of the model, indicating the results are consistent with the theory that the true crowd out effects of a deficit are the deficit itself net of any growth in the total loanable funds pool during the same period. 4. When only FR purchases added to the model, R 2 remained the same as in the no loanable funds deficit modifier model. 5. Model 21.4 shows R 2 rising one half percent when FR purchases are added as a separate variable, in addition to total loanable funds, to the model. This may mean the usual definition of total loanable funds does not fully account for the effect of an increase in FR purchases on loanable funds. But it is difficult to see how this could occur. The national saving part of savings = investment identity is comprised of personal and corporate savings (and depreciation allowances). The FR must purchase securities from either persons or corporations, and the payment must add initially to personal or corporate savings, even if paid into an M1 account, since it represents unspent disposable income (savings). Hence, the higher R 2 could be spurious, especially given the small size of the increase. 6. We do note that in model 21.5, where we rerun the Table 21.4 model except without including foreign borrowing, we get a one half percent decline in explanatory power. This suggests that access to foreign borrowing can help offset crowd out, but again, given its small size, may just be spurious. 7. Basically, we conclude that for these six sample periods, increases in total loanable funds pool can best explain the extent to which

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consumption crowd out effects can be offset by adding some form of additional liquidity to the system.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

CHAPTER 22

Total and Endogenous Parts of Loanable Funds as a Stand Alone Deficit Modifiers: Comparison of Cptrs. 11, 18, 21 and 24 Test Results

In Sect. 22.1 we compare stand-alone total loanable funds modifiers used in Chapter 11 (S + FB) with endogenous only loanable funds variable used in Chapter 18 (S + FB) − (Tr + A). Our focus will be which variable explains the most variance and is most statistically significant (highest R 2 and t-statistics on deficit variables) in otherwise identical standard consumer and investment models, and therefore likely to be the most accurate modifiers on tax and government spending variables to use to show how much crowd out is modified by changes in loanable funds. In Sect. 22.2 we compare Chapter 11 modifier with the Chapter 18 modifier (S + FB) – (Tr + A). Here our focus is which modifier yields the most statistically significant estimate of how modified tax and spending deficits affect consumption and investment.

22.1 Comparing Chapters 11 and 18 Stand-Alone Loanable Funds Variables Below we summarize and compare results for the stand-alone loanable funds modifiers tested in 6 time periods in Chapters 11 and 18. In Chapter 11, the total loanable funds modifier (S + FB) was tested as a separate explanatory variable for its effects on standard models of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_22

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consumption and investment. In Chapter 25, the total loanable funds (S + FB) variable net of FR purchases was tested as a separate explanatory variable, i.e., the endogenous part. We wish to test which of these two has the higher level of statistical significance and gives its model the higher R 2 . Results are shown in Table 22.1 for six different time periods. Results shown are for models with stand-alone loanable funds variables only, no modifiers on the (T ) and (G) deficit variables are used. Table 22.1 Comparisons of Totalloanable Funds to Endogenous Loanable Funds Consumption

1960–1980 LF coefficient (t-stat.) R2 1960–1990 LF coefficient (t-stat.) R2 1960–2000 LF coefficient (t-stat.) R2 1960–2007 LF coefficient (t-stat.) R2 1960–2008 LF coefficient (t-stat.) R2 1960–2010 LF coefficient (t-stat.) R2 Av. R 2 = Av Adj. R 2 =

Investment

T.18.1 End. LF

T.11.1 Total LF

T.18.3 End. LF

T.11.3 Total LF

−.59 (−1.8) .94

−.47 (−2.6) .94

.56 (4.6) .95

.59 (5.4) .98

−.07 (−0.7) .91

−.13 (−1.3) .90

.32 (3.9) .91

.30 (3.1) .92

.07 (0.5) .90

−.10 (−1.2) .91

.22 (1.4) .91

.27 (2.4) .90

.50 (1.5) .59

−.13 (−3.6) .89

−.03 (−0.2) .82

.20 (3.6) .88

.25 (1.7) .77

−.11 (−3.4) .89

−.16 (1.6) .81

.19 (2.8) .88

.12 (2.6) .81 81.7% 76.3%

−.14 (−4.1) .88 90.7%; 85.2%

−.02 (−0.6) .89 88.8% 86.5%

.16 (1.9) .91 91.2% Av. 87.5% Av. Adj.

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In Table 22.1, results are shown for identical consumption and investment models, except for the choice of loanable funds variable used. Regression coefficients, t-statistics, and R 2 for the stand-alone total loanable funds (S + FB) variable taken from Chapter 11, Tables 11.1 (consumption), and 11.3 (investment) are compared with the more limited endogenous stand-alone loanable funds variable (S + FB) − (Tr + A) coefficient, t-statistic and R 2 results taken from Chapter 18, Tables 18.1 (consumption), and 18.3 (investment). For consumption, test results in Table 22.1 indicate that average R 2 s and adjusted R 2 s on the total loanable funds model were markedly larger than the endogenous LF-only model. All six of six t-statistics on the loanable funds variable in consumption models were significantly higher when using the total loanable funds version (S + FB) of the variable found in Chapter 11. For investment, test results in Table 22.1 indicate that R 2 s and adjusted R 2 s using Chapter 11’s total loanable funds model explained more variance than endogenous loanable funds only. We conclude that when examining the effect of loanable funds on consumption or investment, only using endogenous changes in the pool as the loanable funds variable does not explain as much variance or produce as high t-statistics as when we use total loanable funds. This by inference provides statistical evidence that FR purchases, can also increase the loanable funds pool, thereby helping offset the crowd out effects of deficits.

22.2 Comparing Chapters 11, 18, 21, and 24 Results on What Type of Loanable Fund Best Offsets Crowd Out The question then becomes: which of the two parts of total loanable funds (S + FB) is the more important in offsetting crowd out effects? The endogenous part (S + FB) − (Tr + A), or the exogenous part (Tr + A)? For consumption, recall that in Chapter 21, Table 21.4 finding was that in standard consumption models, when both total loanable funds (S + FB) and exogenous loanable funds (Tr + A) variables were included as separate variables in the same model, total (S + FB), which includes the exogenous part, was significant in four of the same six sample periods

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tested but the exogenous part (FR purchases) was significant only in three of the six samples. The slight difference in numbers of tests significant when adding the endogenous part to the exogenous part suggests the exogenous part may be the most important. The stronger finding for the total loanable funds variable (S + FB) was also found compared to just its endogenous part in consumption models in Sect. 22.1 immediately above. These two findings suggest that total loanable funds (S + FB), which is comprised of both is better at explaining how loanable funds can offset crowd out than either of the two parts alone. That is, both types of loanable funds increases can reduce the crowd out effects of deficits, and that the FR security purchases portion can be more important than any same-period endogenous growth. For investment, recall that models where both the endogenous and exogenous parts were tested in the same model (Chapter 21, Table 21.10), differences were even more pronounced: (S + FB) was again significant in four of six tests, and (Tr + A) in only one. Chapter 21 also indicated that when only one of these two loanable funds variables was tested in the standard models (S + FB) was more likely to be found significant than just (TR + A) alone. Section 22.1 also showed (S + FB) models more frequently had higher R 2 and higher t-statistics than the endogenous loanable funds portion alone. Hence, for investment as well as consumption, total loanable funds (S + FB) better explains the extent to which loanable funds can offset the crowd out effects of deficits than either its endogenous or exogenous component separately. Our Chapter 24 finding (presented in detail further below) for consumption was the same. In Chapter 24 we compared: 1. the standard model with only a stand-alone (S + FB) variable, 2. a second model with the stand alone (S + FB), and with (T ) and (G) modified by (S + FB), 3. and a third model, with a stand alone (S + FB) − (Tr + A), and both (T ) and (G) are modified by the same (S + FB) − (Tr + A) modifier (unlike this chapter, where the stand alone was the same, but the (T ) and (G) modifier was only (Tr + A)).

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For consumption, adding the total loanable funds variable to the baseline model from Chapter 11 generally increased R 2 . The third model, using only an endogenous loanable funds variable (Cptr. 18) had lower R 2 s generally. For Chapter 24 investment, models, the total loanable funds models again generally raise R 2 compared to the baseline model. Lower R 2 s were generally obtained using only the endogenous loanable funds variable.

Chapter 22 Conclusions

22.3

This chapter’s comparisons of the effectiveness of total loanable funds compared to only the endogenous portion are summarized in the table. Cptr. 22 Consumption Summary Table (Stand-Alone Total vs. Endogenous LF Modifier Only) Model

11 Baseline (wo/Def 11 Baseline (w/Def)

From Table#

19 60 – 20 08 72

19 60 – 20 07 72

19 60 – 20 00 86

T11.1AA

19 60 – 20 10 60

Eq.11.1A

(Av. R2 = 71.4%) 87 87 87 91

19 60 – 19 90 43

19 60 – 19 80 77

19 70 – 19 90 91

19 70 – 20 00 91

19 70 – 20 07 68

19 70 – 20 10 55

19 80 – 20 00 86

19 80 – 20 10 37

19 75 – 20 04 63

19 80 – 20 04 74

19 85 – 20 05 65

19 96 – 20 09 83

20 00 – 20 10 95

Test ratio T

G

NA

NA

NA 15/1 8 10/1 1 (5/5

T22.

88

89

89

91

90

94

(Av. R2 = 90.3%;4/6 Total LF Var. Sig.)

NA

NA* 6/18 * 5/11 * 5/5* *) NA

T22.1

81

77

59

91

91

94

(Av. R2 = 82.2%; 3/6 Endog. LF Var. Sig.)

NA NA

NA* NA

NA

NA

89

91

93

92

86

88

94

85

88

88

2

(18 Sample Av. R = 89.4%; for 6 Periods used below 88.7%)

22 Modified (w/s-a) (Total LF) 22 Modified (w/s-a) (Endogenous LF)

19 85 – 20 04 67 86

87

92

99

*7 samples containing 1/3 – ½ of all observations from “Crowd In” years Removed, leaving 11 of 18

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%. 2. When deficit variables only added to standard model, R 2 increases to 89.4%, an increase of 25%, clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When loanable funds modifiers are added to standard model with deficits as a stand-alone variable average R 2 rises to 90.2%, an

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increase of 0.8%, and the loanable funds variable was statistically significant in 4 of 6 periods tested. The two periods tested not significant were the 1960–1990 and 1960–2000 periods. When only the endogenous part of loanable funds modifiers was added to standard model with deficits as a stand-alone variable, average R 2 falls to 82.2% and the endogenous loanable funds variable was statistically significant in 3 of 6 periods tested. 1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8%. 2. When deficit variables only added to baseline standard model, R 2 increases to 89.8%, an increase of 13%, clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When loanable funds modifiers are added to standard model with deficits as a stand-alone variable average R 2 rises to 91.2%, an increase of 1.4%, and it was statistically significant in 5 of 6 periods tested. When only the endogenous part of loanable funds modifiers was added to standard model with deficits as a stand-alone variable, average R 2 falls to 82.2% and the endogenous loanable funds variable was statistically significant in 3 of 6 periods tested.

Cptr. 22 Investment Summary Table (Endogenous LF Modifier Only) R2 (18 Time periods) Model

10 Baseline (w/o Def)

From Table#

T10.3C

Sigif./Total

19 19 19 19 19 70 70 70 70 80 – – – – – 19 20 20 20 20 90 00 07 10 00 −6 56 65 72 69 1 (Does not include GDP Control Variable) (Av. R2 = 68.3%) 76 70 71 80 78 91 82 81 71 76 81 19 60 – 20 10 69

19 60 – 20 08 67

19 60 – 20 07 66

19 60 – 20 00 63

19 60 – 19 90 65

19 60 – 19 80 72

19 80 – 20 10 77

19 75 – 20 04 −6 4

19 80 – 20 04 71

10 Baseline (w/o Def)

T10.3B

11 Baseline (w/Def)

Eq.11.10 A

29 Modified (w/s-a) (Total LF) 29 Modified (wo/s-a) (Endogenous LF)

T22.1

(18 Sample Av. R = 89.8%; for 6 used below, 88.3%) 91 88 88 90 92 98 (Av.R2 = 91.2%;6/6 Total LF Var. Sig.)

T22.1

89

(includes GDP Control Variable) (Av. R2 = 79.8%) 89 86 84 89 87 95 90 90 86 90

89

82

91

91

95

19 85 – 20 05 57

19 96 – 20 09 92

20 00 – 20 10 91

80

80

81

75

75

93

95

90

89

89

89

89

98

98

2

81

19 85 – 20 04 63

(Av. R2 = 88.2%; 3/6 Endog. LF Var. Sig.)

Test ratio T

G

NA

NA

NA NA

NA* NA

NA 11/1 8 8/11 NA

NA* 16/1 8 9/11 NA

NA NA

NA* NA

NA

NA*

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18

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Comparisons of the impact of the endogenous and exogenous portions of the loanable funds pool on crowd out indicated in 1. Chapter 11 (total) versus Chapter 18 tests (exogenous only) 2. Chapter 21 tests (Endogenous vs. exogenous) 3. Chapter 24 tests (total loanable funds vs. endogenous part only) That total loanable funds explained more variation in consumption and investment than just the endogenous part alone. This also indicates variation in loanable funds due to FR purchases had an important impact on consumption and investment, particularly during the only QE years in the samples: 2008–2010. Total loanable funds also explained more variance than the exogenous part of loanable funds alone.

CHAPTER 23

Difficulties Comparatively Testing Total Loanable Funds and Endogenous Loanable Funds Only in the Same Model

As another test, we had wished to test two variants of the modified crowd out variables, (S + FB)–(Tr + A) and (Tr + A), by inserting both of them in the same standard consumption and investment models to see which proved statistically significant (or more significant). This would show us which type of change in loanable funds, endogenous or exogenous, was had the largest and most systematic effect in reducing crowd out. The variables to be tested were T + (S + FB–Tr–A), T + (Tr + A), G–(S + FB–Tr–A), and G–(Tr + A). We wished to determine which type of loanable funds modification of deficit effects explained the most variance. Unfortunately, the variables were so highly multicollinear the regression would not run. Hence, for results showing the effect of each of these two modifications on consumption and investment, we refer the reader to Chapters 28, 31 and 29 where as separate, stand-alone variables, they are tested in models without any modification of the deficit variables (T, G) by them. Those tests indicate both the endogenous and exogenous parts of the loanable funds pool can play a role in offsetting crowd out. For the exogenous part (FR open market security purchases), this was especially true in the early QE years included in the sample.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_23

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CHAPTER 24

Comparing Endogenous and Total Loanable Funds Modifiers to Deficit Variables

There was strong statistical evidence in Chapter 11 that growth in total loanable funds (LF), can offset crowd out effects, provided the growth (in the same period the deficit occurs) is large enough. This chapter tests the hypothesis that it is not “total” loanable funds (S + FB), but endogenous LF, i.e., total LF minus FR securities purchases (Tr + A) which defines most accurately how much loanable funds offsets crowd out. This hypothesis is based on indications in prior chapters that FR purchases historically were small compared to deficit size, and some indication that much of FR purchases may be from investment banks or foreign banks, leaving problematic what % of FR purchases actually is channeled to US consumers and businesses who want to buy goods that will affect the GDP. By subtracting FR purchases (Tr + A) from total loanable funds, this chapter’s models are testing the hypothesis that only the endogenous part of total loanable funds (S + FB) − (Tr + A) can offset the funds lost by crowd out. Endogenous LF is used to modify the two deficit variables, and also included as a stand alone in some models. In Sects. 24.1 and 24.2 below we test the standard consumption and investment models as we did in earlier chapters. The models use two separate deficit variables, one for tax deficits (T ) and one for government spending deficits (G), are measures of crowd out. The deficit modifier tested is total loanable funds variable (S + FB) minus the amount of FR

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_24

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securities purchases (Tr + A). This gives a modified tax cut deficit variable of T + (S + FB − Tr − A), and a modified spending deficit variable G − (S + FB − Tr − A) used to represent crowd out effects. We also include (S + FB − Tr − A) as a stand-alone variable. In tests below, models modifying the deficit variables a (S + FB − TR − A) modifier, and including it as a stand alone, will be labelled as “with modifier 2” models, or “w/m2.” We will compare these results with results previously obtained from models tested in Chapter 11, which indicated total loanable funds alone was a good modifier. In Chapter 18 we tested whether (T ) and (G) had different crowd out effects either before (labelled “without modification” (w/o) and after modification of the deficit variables (labelled “w/m”) by same—period changes in the total loanable funds pool (S + FB). Here, in this chapter, we compare the crowd out findings of Chapter 11, with and without the modifier used there, i.e., (S + FB), to results obtained here using the (S + FB − Tr − A) deficit variable modifier labelled “m/2.” Our objective is to see which is more systematically related to movement in consumption or investment, and therefore, more likely to represent the true way in which crowd out can be offset by increases in the loanable funds pool. All consumption and investment models tested below have been tested for stationarity and endogeneity problems. All variables are either stationary or cointegrated with their dependent variables. No endogeneity problems were found (Hausman test) with any of the consumption or investment models.

24.1 Testing the Two-Variable Deficit Consumption Model Below is the model we have previously identified as a “standard” consumption model. It is Eq. 4.4.TR taken from Heim (2017). Standard Consumption Model from Heim (2017): CD = .29(Y − TT ) + .34(TT ) − .23(G T&I ) − 5.44PR + .48DJ−2 (t=)

(6.2)

(6.5)

(−4.5)

(−2.1)

(5.1)

− .515.07POP16/65 + .020POP + 38.00 M2AV + .09CB2 (6.0)

(3.2)

R = 87.8% 2

D.W. = 2.2

MSE = 24.88

(4.9)

(3.7)

(4.4.TR)

24

531

COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

Equations 24.1, 24.2, and 24.3 are shown next. They show test results for variables in the standard model, including crowd out (deficit) variables, with and without modifications. Equation 24.1 measures crowd out effects before modifying the deficit variables (T ) and (G) by any loanable variable. Equation 24.2 measures crowd out effects as the effect of the deficit variables (T ) and (G) reduced by any changes in total loanable funds (S + FB) in the same period. Equation 24.3 shows the crowd out effects resulting from modifying the deficit by the change in total loanable funds net of (Tr + A), and also modifying the stand-alone variable the same way, i.e., to give a modifier of (S + FB) − (Tr + A) for the deficit variables (T ) and (G), and also include it as a stand-alone variable. All three models are estimated using the full 1960–2010 dataset. Below is this study’s Baseline (BL) Standard Consumption Model with no Deficit Variables Included, nor any loanable funds variables included, taken from Chapter 11 (1960–2010 data): CD = .54(Y − TT ) + 2.70PR + .27DJ−2 − .714.38POP16/65 (t=)

(0.6)

(7.2)

(3.0)

(1.6)

+ .013POP − 1.58M2AV + .13CB2 (3.2)

(2.0)

(−0.1)

R = 60.3% 2

D.W. = 1.7

MSE = 43.98

(11.1AA)

Next we present this study’s Baseline (BL) Standard Consumption Model with 2 Variable Crowd Out (T and G Deficit Effects Estimated Separately). This Model is Estimated Before Deducting Loanable Funds Changes from (T ) or (G), and Before (T + G) is Added as a Stand-Alone Variable: CD = .31(Y − TT ) + .32(TT ) − .16(G T&I ) − 7.14PR + .49DJ−2 (t=)

(6.4)

(6.6)

(−1.9)

(−3.1)

(4.5)

− .459.68POP16/65 + .017POP + 36.27M2AV + .09CB2 (4.0)

(2.4)

R = 86.6% 2

D.W. = 2.1

(3.8)

(3.9)

MSE = 26.17

(11.1A)

Next we present the Standard Consumption Model with 2 Variable Crowd out (T , G), before deficit variable modification by loanable funds changes, but including (S + FB) as a Stand-alone Variable (Test Results Taken from Chapter 11): CD = .38(Y − TT ) + .43(TT ) − .24(G T&I ) − .14(S + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−4.1)

532

J. J. HEIM

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.0)

(3.7)

(−1.9)

+ 33.67M2AV + .10 CB2 (4.5)

(3.5)

R = 88.3% 2

D.W. = 1.9

MSE = 24.68

(24.1)

Adding the total loanable funds variable increases explained variance from 86.6 to 88.3%, a significant increase. Also shown is the Standard Consumption Model with 2 Variable Crowd out (T ), (G), after offsetting loanable funds changes T + (S + FB, G − (S + FB) and stand-alone variable +(S + FB). (Also Taken from Chapter 11): CD = .38(Y − TT ) + .43(TT )m − .24(G T&I )m − .81(ST + FB) (t=)

(8.0)

(6.7)

(−5.6)

(−2.8)

− 6.09PR + .40DJ−2 − 398.48POP16/65 + .016POP (−2.8)

(5.0)

(3.7)

(−1.9)

+ 33.67M2AV + .10 CB2 (4.5)

(3.5)

R = 88.3%

D.W. = 1.8

2

MSE = 24.89

(24.2)

Finally, Eq. 24.3, which shows the: Standard Consumption Model with 2 Variable Crowd out (T ), (G), after offsetting loanable funds changes T + (S + FB) − (Tr + A), G − (S + FB − Tr − A), and using a standalone variable (S + FB) − (Tr + A), This is slightly different from the (S + FB) stand alone used in Eqs. 24.1 and 24.2. All three test variables were Hausman endogenous, so Wald-strong instruments used. The instrument was not itself endogenous (Sargan test). Stationarity issues were resolved by detrending or cointegration. As usual, models are tested in first differences of the data and use Newey West standard errors. CD = .22(Y − TT ) + .19(TT )m2 + .01(G T&I )m2 (t=)

(2.5)

(1.7)

(0.0)

− .11(ST + FB − Tr − A) − 4.99PR + .49DJ−2 (−1.7)

(−0.4)

(3.2)

− 506.01POP16/65 + .019POP + 51.98M2AV + .12CB2 (2.8)

(−1.7)

R 2 = 85.2%

D.W. = 2.3

(3.6)

MSE = 27.76

(2.8)

(24.3)

24

COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

533

Notice the 3.1% drop in explained variance when only the endogenous portion of loanable funds was used as a stand-alone variable and as deficit modifiers. This sizable decline indicates that FR purchases, the exogenous part of total loanable funds also has some systematic ability to offset consumption crowd out. Without including the FR purchases portion, the model defining crowd out as the deficit minus endogenous growth in LF explains crowd out less well than the model which defines it as precisely equal to the size of the deficit.

24.2 Consumption Comparisons in Models with a Separate Loanable Funds Control Variable All results cited in Table 24.1 were estimated using the same models as the ones above. Only the length and dates of the time periods tested changes. Note that after modification of the crowd out effect to the model with an (S + FB) stand alone by adding (S + FB) to the tax deficit variable (T), and subtracting it from the spending deficit variable (G), results for all variables except the stand-alone (S + FB) variable remain the same, as does R 2 . Results after subtracting (Tr + A)) from (S + FB) are substantially different and explain much less variation. This suggests FR securities purchases (Tr + A) is an important part of (S + FB), so when (Tr + A) is subtracted from the loanable funds modifier (S + FB), it creates insufficient variation in the crowd out variable to match the variation in consumption caused by the deficit net of all loanable funds changes. Hence, variation in the model less effectively explains variation in the dependent variable, lowering R 2 , than does just using (S + FB) alone. For each time period given in Table 24.1, three sets of statistics are presented. One in which there is no modification of the crowd out effects of (T , G) by changes in loanable funds, though (S + FB) is included as a stand alone, labeled “w/o.” There is also one set of results in which the same regression model is reestimated defining the crowd out variables as the deficit modified by the change in loanable funds: T + (S + FB) and G − (S + FB), and continuing to include a separate (S + FB) variable. It is labelled “w/m.” Both of these sets of results just repeat here results originally obtained testing these two models in Chapter 11. The third set of results shown in Table 24.1 are from the model labelled

T Def : t-stat G Def : t-stat ST + FB t-stat R2 Adj. R2

w/m

w/m2 w/o

w/m

1960–1990 w/m2 w/o

w/m

1960–2000 w/m2 w/o

w/m

1960–2007 w/m2 w/o

w/m

1960–2008

w/m2 w/o

w/m

1960–2009 w/m2

(−2.6) (−4.2) (3.5) .94 .94 .94 .88 .88 .86

(−1.3) (−2.5) (−2.7) (−1.2) (−1.8) (−0.8) (−3.6) (−4.7) (1.7) .90 .90 .90 .91 .91 .90 .89 .89 .88 .85 .85 .85 .88 .88 .87 .86 .86 .84

(−3.4) (−4.4) (−1.3) (−4.1) (5.6) .89 .89 .87 .88 .88 .86 .86 .83 .86 .86

(−0.4) .84 .80

.72 .72 .72 .36 .36 .36 .29 .29 .26 .44 .44 .39 .42 .42 .31 .45 .45 .15 (5.3) (5.3) (5.1) (2.7) (2.7) (3.1) (2.6) (2.6) (1.8) (5.7) (5.7) (3.2) (5.5) (5.5) (3.1) (6.7) (6.7) (1.3) −.27 −.27 −.31 −.16 −.16 −.16 −.09 −.09 −.08 −.17 −.17 −.13 −.16 −.16 −.06 −.24 −.24 −.02 (−2.8) (−2.8) (−2.2) (−2.2) (−2.2) (−1.4) (−0.9) (−0.9) (−0.3) (−2.4) (−2.4) (−0.8) (−2.4) (−2.4) (−0.3) (−2.8) (−2.8) (−0.1) −.47 −1.46 −1.52 −.13 −.65 −.63 −.10 −.48 −.40 −.13 −.74 −.59 −.11 −.69 −.38 −.14 −.82 −.09

w/o

Variable 1960–1980

Table 24.1 Comparing robustness over time of effects on consumption of crowd out, with and without compensating loanable funds and (Tr + A) modifications

534 J. J. HEIM

24

COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

535

“w/m2,” showing (T ) and (G) each modified by (S + FB) − (Tr + A), and containing a separate (S + FB) − (Tr + A) variable. R2 Effects For the 6 periods tested, average R 2 for the total loanable funds model was 90.2%; average adjusted R 2 was 86.5%. The endogenous-only model explained less variance, average R 2 was 88.8%; average adjusted R 2 was 84.2%. The total loanable funds models better explained consumption than models without a total loanable funds variable. R 2 s on the model with a loanable funds variable (Table 11.1B) were higher than the baseline model in 5 of the 6 periods tested. The baseline model R 2 s were also lower than in the endogenous loanable funds—only models in 3 of the six time periods tested, and the higher in three others. Differences were very marginal suggesting adding the endogenous-only variable added nothing to explained variance in consumption (which implies increases in exogenous loanable funds explains it all. R 2 s were also below total loanable funds models in 5 of 6 tests. Hence, the total loanable funds model is considered the better model. Crowd Out and Loanable funds Effects For tax cut deficits, the baseline model (Table 11.1B), containing no loanable funds variable, showed significant tax crowd out in 6 of 6 periods examined. After adding the stand-alone total loanable funds variable, all six tests, either with or without deficit modification, tax cut deficits consistently lead to crowd out problems. In the endogenous-only loanable funds model, 5 of 6 tests also showed tax deficits crowd out effects to be statistically significant, before and after modification. For spending deficits, the baseline model (Table 11.1B), containing no loanable funds variable, showed significant spending crowd out in 5 of 6 periods examined. After adding the stand-alone total loanable funds variable, 5 of 6 tests spending deficits continued to show a crowd out problem, both before and after deficit modification by (S + FB). The one exception is again the sample with 1990s data added to the sample. In all six cases using the full (S + FB) modifier, explained variance is unchanged by adding the modifier. By comparison, with the endogenous-only loanable funds model, only 1 of 6 tests showed spending deficits crowd out effects to be statistically significant, even with modification for changes in the endogenous portion of the loanable funds pool.

536

J. J. HEIM

The lower R 2 of endogenous loanable funds models compared to total loanable funds models probably indicates using the endogenousonly funds variable as a modifier of deficits is creating an error in variables problem: endogenous growth in loanable funds may not get channeled into consumer lending, and therefore don’t affect consumption.

24.3 Consumption Comparisons in Models Without a Separate Loanable Funds Control Variable Table 24.2 retests the same “with” and “without” models as in Table 24.1, but without the separate loanable funds (S + FB) or (S + FB − Tr + A) control variable. We will compare results with Table 24.1 to testing if controlling for loanable funds as a separate variable, as well as using it as a modifier in the tax and spending crowd out variables, makes a difference in our crowd out variable estimates. There are no stationarity problems with either the modified or unmodified variables. The model without the deficit variables being modified was without endogeneity problems, so it was run in OLS. In the modified model, G) − (S + FB) was found endogenous with the dependent variable, and was replaced by a Wald-strong instrument, which was not endogenous (Sargan test) This was also true for the model using the (S + FB) − (Tr + A) modifier. R2 Effects For the 6 periods tested, average R 2 for the unmodified total loanable funds model was 88.7%; average adjusted R 2 was 84.8%. For the modified model, R 2 was 85.2%; average adjusted R 2 was 79.8%. For the endogenous model, average R 2 was 84.7%; average adjusted 2 R was 79.0%. Compared to earlier models with a stand-alone total loanable funds variable, dropping the stand alone leads to a decline in R 2 s in all 6 of 6 models tested. It also leads to a decline for the (S + FB − (Tr + A) model in all 6 of 6 periods tested. The likely reason is that without the standalone loanable funds variable to (separately) pick up the negative effects on consumption of a rise in savings while holding consumption constant, the negative and positive effects must be lumped together into one variable—the deficit modifier. Since when lumped together, their effects on consumption largely cancel out, we are again faced with a situation where

T Def : t-stat G Def : t-stat R2 Adj. R2

.53 (3.9) −.21 (−1.6) .91 .82

w/o

.24 (2.2) .06 (0.5) .86 .73

.26 (2.2) .03 (0.2) .85 .72

.28 (3.2) −.10 (−1.7) .89 .86

.14 (2.7) −.16 (−1.3) .87 .82

w/m

1960–1990

w/m w/m2 w/o

Variable 1960–1980

.16 (1.8) .08 (0.9) .85 .79

.23 (2.8) −.03 (−0.5) .91 .88

w/m2 w/o .11 (1.8) .04 (0.6) .90 .87

.16 (2.0) .09 (0.8) .89 .86

.33 (5.6) −.08 (−1.5) .87 .84

.16 (2.2) −.07 (0.6) .82 .79

.22 (2.2) .10 (0.7) .83 .79

.33 (5.6) −.08 (−1.6) .87 .84

.18 (2.5) −19 (0.7) .83 .79

.21 (2.2) .10 (0.7) .83 .79

.32 (6.6) −.16 (−1.9) .87 .85

.15 (2.3) .02 (0.1) .83 .79

.13 (1.3) .03 (0.2) .83 .79

w/m w/m2

1960–2009 w/m w/m2 w/o

1960–2008

w/m w/m2 w/o

1960–2007

w/m w/m2 w/o

1960–2000

Table 24.2 Robustness over time of effects on consumption of crowd out, with and without offsetting loanable funds and (Tr + A) modifications. No stand-alone (S + FB) control variable

24 COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

537

538

J. J. HEIM

we are subtracting from variables known to be statistically significant (the deficit variables) an essentially random variable, reducing the ability of the deficit variable to explain variance. This reduces the model’s R 2 (as well as the significance levels of the deficit variables). Clearly, the model with the stand-alone loanable funds variable is the preferred model. Crowd Out and Loanable Funds Effects For tax cut effects, the baseline (S + FB) model indicates significant crowd out in 6 of 6 periods tested. With the deficit variable modified by (S + FB), this remains 6 of 6, but even though significant, with lower significance levels than before. Using (S + FB) − (TR + A) as the deficit modifier, again the baseline model, showed significant tax cut crowd out in 6 of 6 tests, and the endogenous loanable funds model also showed 5 of 6 significant, but with lower levels of significance than before. On average, the results of the total and endogenous-only loanable funds models were about the same (both models mainly showing deterioration of significance levels and R 2 s due to errors in variable problems). For spending deficits, the baseline showed significant crowd out effects in 5 of 6 tests. After modification by total loanable funds, that dropped to 0 of 6 showing statistically significant crowd out. Modification by only endogenous loanable funds also led to 0 of 6 tests showing significant crowd out (both models mainly showing deterioration of significance levels and R 2 s due to errors in variable problems). As we have explained in other chapters, a change in loanable funds has two effects in a ceteris paribus model like this: a negative effect resulting from the need to reduce consumption to increase savings (most of loanable funds), and a positive effect associated with crowd out reduction. Without the stand alone, the modifiers (S + FB) and (S + FB) + (Tr + A) estimate the effects of the modifier on crowd out without controlling for the offsetting negative effect on consumption caused by the same modifier, Hence, consumption’s increase resulting from increases in the modifier on (T ) and (G) occurs while its other effect is causing an offsetting decline in consumption. This reduces the net amount of movement in the consumption variable observed with any given (and often sizeable) change in the modifier compared to Table 24.1, reducing the statistical significance of the modified deficit variables.

24

COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

539

Consumption Conclusions Without loanable funds modification, 6 of 6 time periods tested showed statistically significant tax deficit crowd out; 5 of 6 periods showed significant spending deficit crowd out. In models with a stand-alone loanable funds variable, when the total loanable funds variable was added, it increased R 2 . The endogenous loanable funds—only model did also, but generally not as much. For the total loanable funds variable, tax deficit crowd out remained significant in 6 of 6 tests for both types of loanable funds. Spending deficits remained significant in 5 of 6 periods. For endogenous-only loanable funds models, adding the loanable funds variable increased R 2 in half the time periods tested, but not the other half. 6 of 6 tax deficits continued to show significant, but less significant after modification, but none of the spending deficits were significant. In models without a stand alone, R 2 generally declined and crowd out was significant in 6 of 6 tax deficit and 5 of 6 spending deficit models; after modification by either the total or endogenous loanable funds variable, 6 of 6 tax cut deficits continued to show significant crowd out (but at lower levels of significance), and 0 of 6 spending deficits remained significant. The decline seems mainly due to errors in variables problems associated with estimating both consumption effects with one loanable funds variable when it is used as a deficit modifier rather than a stand alone.

24.4 Testing the Two-Variable Deficit Investment Model 24.4.1

Investment Comparisons in Models with a Separate Loanable Funds Control Variable

Below is the model we take as the “standard” investment model, Eq. 5.4.TR taken from Heim (2017): The Standard Investment Model from Heim (2017) Using 1960–2010 data ID = +.26(ACC) + .27(TT ) − .30(G T&I ) + .011POP (t=)

(8.7)

(2.9)

(5.7)

(−3.8)

− 4.72PR−2 + 6.81XRAV + 2.55CAP−1 (−2.7)

(2.9)

(1.7)

540

J. J. HEIM

R 2 = 83.3%

D.W. = 2.0

MSE = 28.25

(5.4.TR)

Next is this Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, and No GDP Variable Included to Control for the State of the Economy: ID = +.48(ACC) + .008POP + .76PR−2 (t=)

(2.5)

(10.6)

(0.2)

+ 7.37XRAV + 14.08CAP−1 (2.2)

(4.3)

R = 69.4% 2

D.W. = 1.6

MSE = 47.87

Same as Eq. 10.3C This Study’s Baseline Investment Model, With No Deficit or Loanable Funds Variables Included, but GDP Variable Included to Control for the State of the Economy: ID = + .47(ACC) − .00POP − 0.85PR−2 (t=)

(0.0)

(4.0)

(−0.3)

+ 5.21XRAV + 10.39CAP−1 + .10 GDP (2.0)

R 2 = 76.1%

(−1.3)

(2.9)

D.W. = 2.1

MSE = 43.06

Same as Eq. 10.3B; and same as Eq. 11.10C This study’s Baseline Model With Deficit and GDP Control Variable, but No Loanable Funds Variables (1960–2010): ID = + .27(ACC) + .33TT − 33 G T&I + .012POP − 4.95PR−2 (t=)

(6.4)

(2.6)

(2.8)

(−3.9)

(−2.5)

+ 6.68XRAV + 2.43CAP−1 − .02GDP (3.5)

R = 89.0% 2

(1.8)

(−0.2)

D.W. = 1.9

MSE = 29.87

(11.4A)

Next, taken from Chapter 11, are Eqs. 11.4 and 11.5. These equations constitute the same standard model, with the addition only of a standalone control variable for changes in the pool of loanable funds (S + FB), and in 11.5, also includes (S + FB) as a deficit modifier. All variables were found Augmented Dickey–Fuller (ADF) stationary; No Hausman-endogeneity was found between the dependent and explanatory variables, and Newey–West standard errors were used to avoid heteroskedasticity.

24

COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

541

Standard Cptr. 11 Investment Model with 2 Variable Crowd out (T , G), before (S + FB) and used to modify (T ), (G), but including a stand-alone loanable funds variable, (S + FB) (Estimation uses the full 1960–2010 data set): ID = + .23(ACC) + .22TT − 16 G T&I + .19( (S + FB)) + .008POP (t=)

(1.6)

(5.1)

(−1.9)

(2.0)

(2.8)

− 4.25PR−2 + 5.25XRAV + 1.48CAP−1 − .04GDP (2.3)

(−2.1)

R = 90.6% 2

(0.6)

(1.2)

Adj. R = 88.7%

D.W. = 2.0

2

MSE = 27.93 (11.4)

Standard Investment Model with 2 Variable Crowd out (T , G), adjusted for only stand-alone endogenous Loanable Funds Changes (S + FB) − (Tr + A) (Using 1962–2010 data): ID = + .23(ACC) + .22TT − 16 G T&I + .19( (S + FB)) (t=)

(1.6)

(5.1)

(−1.9)

(2.8)

+ .008POP − 4.25PR−2 + 5.25XRAV (2.0)

(2.3)

(−2.1)

+ 1.48CAP−1 − .04GDP (0.6)

(1.2)

R = 90.6% 2

Adj. R = 88.7% 2

D.W. = 2.0

MSE = 27.93 (11.4)

Standard Cptr. 11 Investment Model with 2 Variable Crowd out (T , G), after (T ), (G) are adjusted for accommodating (S + FB), and including (S + FB) as a stand-alone variable (Using 1960–2010 data): ID = + .23(ACC) + .22TT − 16 G T&I − .19( (S + FB)) + .008POP (t=)

(5.1)

(1.6)

(−1.9)

(2.0)

(−2.8)

− 4.25PR−2 + 5.25XRAV + 1.48CAP−1 − .04GDP (−2.1)

R = 90.6% 2

(2.3)

Adj. R = 88.7% 2

(1.2)

D.W. = 2.0

(0.6)

MSE = 27.93 (11.5)

*Note: If we test 24.4 as an OLS models, as was the comparable Cptr 11 model, R 2 is 90.4%, identical to Cptr. 11 model. But the modified (G) deficit variable G − (S + FB − Tr − A) and the exchange rate

542

J. J. HEIM

variable XRav were found endogenous and had to be replaced by a instrument. The instrument, though Wald-strong, was an imperfect substitute for these two variables, lowering R 2 . For that reason, we feel that here we cannot with confidence conclude that it is the endogenous modifier that caused the drop in R 2 , rather than the difference in modeling technique, so we decline to state that the models indicated endogenous loanable funds explained any less (or more) variance than total loanable funds for this sample period. All test results in Tables 24.3 and 24.4 for the other time periods estimated use exactly the same model. Only the length and dates of the period used to test the model changes. Comparing Chapter 11’s Eqs. 11.4 and 11.5, we find that all coefficients and t-statistics, except one, are the same before and after modification. The exception is the stand-alone (S + FB) variable, whose value changes from (+.19 (t = 2.8)) to (−.19 (t = −1.1)) R 2 also remains the same. This was the same result we obtained with our consumption models earlier. In Table 24.3 we present results for several test periods using explanatory variables from the standard investment model in Heim 2017, with the addition of the stand-alone total loanable funds (S + FB) variable. The additional variable shows clearly that changes in the pool of loanable funds can offset crowd out. This result is shown most clearly in the “without modification” column, labelled (“w/o”), but the identical result, presented in a different way, is shown in the “with modification” column next to it, labelled (“w/m”). Additional results showing the deficit variables modified by only the endogenous part of (S + FB), i. e, (S + FB) − (Tr + A), labelled (“w/m2”). R2 Effects For the 6 periods tested, average R 2 for the total loanable funds model was 91.2%; average adjusted R 2 was 88.7%. For the endogenous model, average R 2 was 88.3%; average adjusted R 2 was 84.3%. Compared to the baseline model without any loanable funds variable (Table 11.10A), R 2 s were higher for models with a total loanable funds (S + FB) variable added in 6 of 6 models tested For models with only the endogenous loanable funds control variable added (Table 24.3, “w/m2), in 5 of the 6 periods, more variance in investment was explained, but not rise as much as when using the Chapter 11 (S + FB) modifier.

T Def : t-stat G Def : t-stat ST + FB− t-stat R2 Adj. R2

w/m

w/m2 w/o

w/m

1962–1990 w/m2 w/o

w/m

1962–2000 w/m2 w/o

w/m

1962–2007 w/m2 w/o

w/m

1962–2008

w/m2 w/o

w/m

1962–2010 w/m2

(5.4) .98 .96

(2.8) .98 .96

(1.3) .90 .83

(3.1) .92 .88

(0.0) .92 .88

(0.6) .91 .88

(3.1) .90 .88

(0.9) .90 .88

(−0.1) (3.6) .89 .88 .87 .85

(−0.4) (−1.0) (2.8) .88 .85 .88 .85 .82 .86

(−0.8) (−2.4) (2.8) .88 .84 .91 .86 .81 .89

(−1.0) (−3.7) .91 .87 .89 .85

−.10 −.10 −.30 .09 .09 .11 .20 .20 .24 .12 .12 .15 .21 .21 .29 .22 .22 .32 (1.2) (1.2) (−0.9) (0.9) (0.9) (0.8) (1.8) (1.8) (2.1) (1.2) (1.2) (1.6) (1.6) (1.6) (2.9) (1.6) (1.6) (3.4) −.12 −.12 −.37 −.21 −.21 −.04 −.19 −.19 −.25 −.17 −.17 −.24 −.18 −.18 −.31 −.16 −.16 −.39 (−1.3) (−1.3) (0.7) (−2.1) (−2.1) (−0.2) (−1.7) (−1.7) (−1.9) (−1.7) (−1.7) (−1.6) (−1.6) (−1.6) (−1.5) (−1.9) (−1.9) (−2.8) .59 .56 1.73 .31 .00 .23 .27 −.12 −.30 .20 −.08 −.23 .19 −.21 −.55 .19 −.19 −.70

w/o

Variable 1962–1980

Table 24.3 Effects crowd out on investment, with and without compensating loanable funds modifications

24 COMPARING ENDOGENOUS AND TOTAL LOANABLE FUNDS …

543

T Def : t-stat G Def : t-stat R2

w/m

w/m2 w/o

w/m

1960–1990 w/m2 w/o

w/m

1960–2007

w/m w/m2 w/o

1960–2000 w/m2 w/o

w/m

1960–2008

w/m2 .33 .14 .21 (3.9) (2.2) (2.4) −.36 −.11 .10 (−4.7) (−1.5) (1.0) .89 .90 .84

w/m

1960–2010 w/m2 w/o

.31 .14 .14 .37 .17 .18 .42 .17 .17 .29 .11 .10 .33 .16 .20 (3.0) (2.7) (2.5) (3.8) (3.6) (3.7) (5.4) (3.5) (3.7) (3.4) (2.5) (2.3) (4.0) (2.6) (2.2) −.29 −.26 −.22 −.30 −.16 −.15 −.37 −.14 −.14 −.29 −.12 −.12 −.30 −.07 .00 (−1.9) (−3.1) (−2.5) (−2.3) (−2.2) (−2.6) (−4.2) (2.6) (−2.9) (−2.7) (−1.9) (−2.2) (−2.6) (−0.9) (0.0) .90 .96 .94 .83 .90 .91 .86 .90 .90 .82 .87 .87 .85 .88 .84

w/o

Variable1960–1980

Table 24.4 Robustness over time of effects on investment of crowd out, with and without offsetting loanable funds and (Tr + A) modifications. No stand-alone (S + FB) control variable

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Note: Table 24.4 models were run as OLS models, as was comparable the Cptr 11 model, R 2 is 90.4%, identical to Cptr. 11 model. But the modified (G) deficit variable G − (S + FB − Tr − A) and the exchange rate variable XRav were found endogenous and had to be replaced by a instrument. The instrument, though Wald-strong, was an imperfect substitute for these two variables, lowering R 2 . For that reason, we feel that here we cannot with confidence conclude that it is the endogenous modifier that caused the drop in R 2 , rather than the difference in modeling technique, so we decline to state that the models indicated endogenous loanable funds explained any less (or more) variance than total loanable funds. Crowd Out Effects The baseline model in Table 11.10A without any loanable funds variable show tax crowd out in 5 of 6 periods tested. For spending deficits, it was 6 of 6. Loanable Funds Effects For tax cut deficits, with the total loanable funds variable added, 5 of 6 tax crowd out variables showed statistically significant crowd out effects (but with lower significance levels), for both modified and unmodified versions. For the endogenous—only loanable funds model, 4 of 6 tests showed continued significant crowd out (also with lower significance levels). For spending deficits, the baseline model, 6 of 6 tests showed significant crowd out effects of spending deficits. After the total loanable funds variable was added, this dropped to only 2 of 6 spending crowd out variables. For the model using endogenous loanable funds, only 3 of 6 spending crowd out variables were significant. 24.4.2

Investment Comparisons in Models Without a Separate Loanable Funds Control Variable

Table 24.4 retests the same “with” and “without” models as in Table 24.3, but without the separate loanable funds (S + FB) or (S + FB) − (Tr + A) control variables. We are testing to see if controlling for loanable funds as a separate variable, in addition to separate tax and spending crowd out variables makes a difference in our crowd out variable estimates. Table 24.4 allows comparisons with Table 24.3 for this purpose. There are no stationarity problems with either the modified or unmodified variables. The “w/o” model without the deficit variables being

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modified was without endogeneity problems, so it was run in OLS. In the modified (“w/m”) model, G − (S + FB) was found endogenous with the dependent variable and was replaced by a Wald-strong instrument, which was not endogenous (Sargan test). With modification (w/m2) both the modified government spending deficit variable and the exchange rate variable were found endogenous, and were replaced with a Wald-strong, Sargan non-endogenous instrument. R2 Effects Compared to the baseline model without any loanable funds variable (the “w/o” model), R 2 s were higher for 6 of 6 models tested that added total loanable funds (S + FB) as a deficit variable modifier. Models with the modified total loanable funds variable has higher R 2 s than the endogenous—only loanable funds modifier in 3 of 6 tests, the endogenous model only had a higher R 2 in one of 6 tests. Crowd Out Effects In the baseline model before any loanable funds variable added (“w/o” model), 6 of 6 periods tested showed significant crowd out effects for tax cut deficits, and also 6 of 6 for spending deficits. These models strongly support the hypothesis that deficits “crowd out” private spending. But that does not address the issue of whether increases in loanable funds can “crowd out crowd out.” Loanable funds Effects For models with total loanable funds added as the deficit modifier variable (“with” models), tax cut deficit crowd out effects were found statistically significant in 6 of 6 periods tested, but at lower significance levels. Since R 2 in these models increased when adding the loanable funds variable, we take this as indicating it was partially successful in reducing crowd out. For the models using only endogenous loanable funds as a deficit modifier, 6 of 6 also showed significant tax cut crowd out. Since significance levels were lower after deficit variable modification, indicating the modification had some, but not complete success in offsetting crowd out. (There is an explanation for why we see rising R 2 s, but declining deficit variable significance levels. If some, but not all loanable funds help offset crowd out, perhaps because part is used to buy securities or is spent on foreign goods, R 2 could go up, but when the increase in loanable funds modify the deficit variables, its full value only imperfectly measures the offsetting effect, creating something of a error in variables problem, reducing the modified deficit variable’s statistical significance.)

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The spending deficit crowd out effects are statistically significant in all six tests for the (S + FB) model denoted “w/o,” and for 4 of 6 of the (S + FB) modified deficit labelled “w/m” (the 2 not significant are associated with the huge increases in FR purchases in the 2008 and 2009 QE years); since R 2 was also up, we take this as indicating that the FR purchases in those years were successful in offsetting crowd out. Four of 6 were also significant for spending deficits modified with (S + FB) − (Tr + A), denoted “w/m2” (again, the two not significant were the periods including the 2008 or 2008 and 2009 QE years). Compared to Table 24.3, coefficients and significance levels are higher for all 6 samples. In general, coefficients and significance levels vary very little between the two types of modifications, (S + FB) and (S + FB) − (TR + A). This is as it should be if both endogenous and exogenous loanable funds changes have the same effect on crowd out. Since (unlike consumption), there are not two separate, offsetting effects of an increase in loanable funds on investment, this model without the stand-alone loanable funds variable would seem to be the most theory-consistent. 24.4.3

Investment Comparisons in Models Without a Separate Loanable Funds Control Variable, but with an Added GDP Control Variable

The investment model with no stand-alone loanable funds variable may inadequately control for the effects of fluctuating economic conditions on our estimates of crowd outs effects, as noted earlier in Chapter 11. But, because of the positive correlation of tax revenue and investment simply because they move in the same direction as the overall economy, they tend to overstate crowd out effects of deficits. To remedy this, in Table 24.5, we add a variable to the model tested to control for the level of the GDP when testing for the effects of tax deficits. Similarly, as economic conditions decline, government spending, especially on transfer payments tends to increase. Hence, spending and investment tend to be negatively correlated as the general economy fluctuates, as well as simply because the deficit has increased. The GDP control variable added to the (original) Chapter 11 model should control for these fluctuations and give us more accurate estimates of crowd out’s effect on investment. (The results presented in Table 24.5 as taken from Chapter 11 are the results that currently are presented in Table 24.5.)

T Def : t-stat G Def : t-stat R2 Adj. R2

w/m

w/m2 w/o

w/m

1960–1990 w/m2 w/o

w/m

1960–2007

w/m w/m2 w/o

1960–2000 w/m2 w/o

w/m

1960–2008

w/m2 w/o

w/m

1960–2010 w/m2

.13 .04 .05 .28 .10 .09 .32 .16 .14 .26 .10 .08 .33 .17 .20 .33 .18 .24 (0.9) (0.6) (0.5) (2.2) (1.9) (1.6) (2.6) (1.9) (1.8) (2.3) (1.7) (1.3) (2.7) (1.9) (1.6) (2.6) (2.0) (1.9) −.35 −.27 −25 −.42 −.20 −.21 −.40 −.14 −.15 −.34 −.12 −.14 −.33 −.07 −.00 −.33 −.06 .14 (−3.8) (−4.1) (−3.4) (−3.2) (−3.1) (−3.6) (−5.2) (2.6) (−2.5) (−3.2) (−1.9) (−2.1) (−2.8) (−0.7) (−0.0) (−3.9) (−0.7) (1.1) .95 .97 .96 .87 .91 .92 .89 .90 .91 .84 .87 .88 .86 .87 .84 .89 .90 .84 .91 .95 .93 .83 .89 .90 .86 .88 .89 .81 .85 .85 .83 .85 .81 .87 .89 .82

w/o

Variable 1960–1980

Table 24.5 Robustness over time of effects on investment of crowd out, with and without (S + FB) and (Tr + A) modifications (No stand-alone (S + FB − Tr − A) control variable; GDP control added)

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R2 Effects For the 6 periods tested, average R 2 for the total loanable funds model before modification was 88.3% after modification 88.3%; average adjusted R 2 before modification was 85.2%. Average R 2 for the total loanable funds model after modification was 90.3%; average adjusted R 2 after modification was 88.5%. Both R 2 and adjusted R 2 averages were higher after modification. For the endogenous-only loanable funds model, average R 2 was 88.3%; average adjusted R 2 was 84.3%. Clearly the total loanable funds variable explained more variance than did just using its endogenous portion. R 2 increased in 6 of 6 periods tested when the total loanable funds (S + FB) modifier was added to the deficit variables. When the endogenous loanable funds only modifier was added as both a stand alone and a deficit modifier, R 2 increased over total loanable funds values in 2 of 6 cases, but declined in 3 of 6 tests. The lack of consistency leaves unclear which is more accurately designated the “real” modifier of crowd out effects. Hence, from this test, we, cannot be sure that both endogenous and exogenous parts of the loanable funds pool can offset investment crowd out effects, or whether it is just the endogenous part. Crowd Out Effects For tax cut deficits, the baseline model (Table 11.10A) without any loanable funds variable indicates statistically significant crowd out effects of in 5 of 6 periods tested. Spending deficits showed significant crowd out effects of in 6 of 6 periods tested. Loanable Funds Effects For tax cut deficits, after adding total loanable funds to the baseline model, 5 of 6 periods tested continued to show significant crowd out, though at lower levels of significance, this may indicate increases in loanable funds had some, but not complete success in reducing crowd out. (But, as before, there is an alternative explanation: if some, but not all loanable funds help offset crowd out, perhaps because part is used to buy securities or is spent on foreign goods, R 2 could go up, but when the increase in loanable funds modify the deficit variables, its full value only imperfectly measures the offsetting effect, creating something of a error in variables problem, reducing the modified deficit variable’s statistical significance.) For tax cut deficits, 4 of the 6 models using the endogenous loanable funds modifier showed remaining significant tax deficit crowd out.

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Recall in Table 24.4, after modification by both total and endogenousonly types of loanable funds, tax cut crowd out remained significant in all 6 of 6 periods tested. In Table 24.5 it was 6 of 6 for total loanable funds and still 4 of 6 for endogenous loanable funds holding income constant. This suggests that tax deficits have large crowd out effects, net of any growth in loanable funds, when taking into consideration growth in deficits related to fluctuations in the economy. Put another way, results indicate, non-business cycle growth in deficits seems more than adequately offset by non-business cycle levels of growth in endogenous loanable funds. But declining business cycles cause deficits at the same time they are causing declines in endogenous loanable funds, hence they do not eliminate the crowd out problem. For spending deficits, results for the Chapter 11 model without modification show six of six spending deficits having significant tax crowd out effects, and after modification by (S + FB), 4 of 6 continued to be significant, but not the two QE samples. Four of the 6 models using the endogenous loanable funds modifier also showed and significant crowd out (again, excepting the two QE time period models). The similarity of results again leaves ambiguous whether total or just endogenous loanable funds is the true measure of how much crowd out can be offset by endogenous vs. endogenous plus exogenous increases in loanable funds. Investment Conclusions For models with a stand-alone loanable funds variable, investment crowd out is real, but definitely can be offset in some time periods by same-period increases in the loanable funds pool. Comparisons of the models using total loanable funds and models using only the endogenous portion of total loanable funds indicate both can offset crowd out to some extent, but total loanable funds tends to better explain the offsets total effect on explained variance. The model with a stand-alone variable did not include a control variable for economic conditions. But, as noted in the paragraph below, holding economic conditions constant, both seem to do an equivalent job. This does imply the exogenous part of loanable funds also has a role to play, particularly in recessions, when deficits are rising as the same tie the endogenous part of the loanable funds pool is declining. The models without a stand alone loanable funds variable provides a more theory—consistent way of modeling the effects of loanable funds on investment, since unlike consumption, increases in loanable funds increase investment by reducing crowd out without simultaneously

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reducing investment for some other reason. Hence, there is no need to model a second effect by including a stand-alone variable in addition to deficit-variable modifiers. Rerunning the no-stand-alone models with a variable controlling for fluctuations in the business cycle, deficit crowd out results were the same for both endogenous and total loanable funds models. But economic conditions are not always constant, and the higher R 2 for the total loanable funds models in models without the control suggests the Federal Reserve’s securities purchases, which are largest in recessions, do offset declines in the endogenous part of the loanable funds pool during recessions, and hence explains why the total loanable funds variable better explains the real extent to which crowd out can be offset than just the endogenous part.

24.5

Summary and Conclusions

Cptr. 24 Consumption Summary Table (Endogenous LF Modifier Only) Model

From 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 Table# -2010 08 07 00 90 80 90 00 07 09 00 10 04 04 04 05 10 10

11 Baseline (wo/Def T11.1AA

60 72 72 86 43 77 91 91 68 55 86 37 63 74 67 65 83 95 (Av. R2 = 71.4%) 11 Baseline (w/Def) Eq.11.1A 87 87 87 91 89 91 93 92 86 88 94 85 88 88 86 87 92 99 (Av. R2 = 89.4% for 18 samples; 88.7% for 6 samples used below) 11 Baseline Total LF T11.1 Model (w/def. mod.& s-a)

90 (Av. R2 6 samples ) --- --- --- --- --- --- --- --- --- ---.--- --

Test Ratio T G. NA NA NA NA* 15/18 6/18* 10/11 5/11* ( 5/5 5/5**) 5/6 4/6

24 Modified (w/s-a) T24.1w/m2 85 87 87 90 90 93 (Av. R2 = 88.8%; Adj.R2= 86.5% ) -- --- 6/6 1/6 T24.1w/m 88 89 89 91 90 94 (Av. R2 = 90.2%; Adj.R2= 84.2% )-- -- -- 6/6 5/6* 24 Modified (wo/s-a) T24.2 w/m2 84 83 83 89 85 85 (Av. R2 = 84.7%; Adj.R2= 79% )-- --- 5/6 0/6 T24.2 wo/m 91 89 91 87 87 87 (Av. R2 = 88.7%; Adj.R2= 84.8%)-- -- 6/6 5/6 T24.2 w/m 86 87 90 82 83 83 (Av. R2 = 85.2%%; Adj.R2= 79.8%) --- 6/6 0/6 ___________________________________________________________________________________

*7 samples containing 1/3–½ of all observations from “Crowd In” years Removed, leaving 11 of 18 *Cptr. 11 models using (S + FB) modifier

1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 71.4%

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2. When deficit variables only added to standard model, R 2 increases to 89.4%, an increase of 25%, clearly indicating consumption cannot be explained without allowing for significant crowd out effects. 3. When total loanable funds modifiers are added to standard model with deficits, as a stand alone and also as a deficit modifier, average R 2 is 90.2%, well above the level of variance explained by the standard deficit model alone. For the exogenous modifier; the comparable statistic is lower: 88.8%. 4. When the loanable funds modifier is added as a modifier of the deficit only, but not included as a stand-alone variable, R 2 drops in each of the six periods tested, to an average of 88.7%. The decline averages 1.5%. from the model with a stand-alone variable. The finding is consistent with the Chapter 11 model which on both empirical and theoretical grounds found that for consumption models, a second loanable funds effect needed to be accounted for by using a stand-alone loanable funds variable. The endogenousonly model R 2 dropped even more to 84.7%

Cptr. 24 Investment Summary Table (Endogenous LF Modifier Only) Model

R2 (18 Time Periods) From 1960 60 60 60 60 60 70 70 70 70 80 80 75 80 85 85 96 00 Table# -2010 08 07 00 90 80 90 00 07 09 00 10 04 04 04 05 10 10

Sigif./Total Test Ratio T G.

17 Baseline (w/o Def) T17.3C 69 67 66 63 65 72 -61 56 65 72 69 77 -64 71 63 57 92 91 (Does not include GDP Control Variable) (Av. R2 = 68.3%)

NA NA NA NA*

17 Baseline (w/o Def) T17.3B 76 70 71 80 78 91 82 81 71 76 81 80 80 81 75 75 93 95 (includes GDP Control Variable) (Av. R2 = 79.8%)

NA NA

NA NA*

18 Baseline (w/Def) Eq.18.10A 89 86 84 89 87 95 90 90 86 90 89 90 89 89 89 89 98 98 11/18 16/18 (Av. R2 = 91.2% for 18 samples; 88.3% for 6 samples used below ) 8/11 9/11 11 Baseline Total LF T11.11 90 (Av. R2 6 samples ) --- --- --- --- --- --- --- --- --- ---.--- -Model (w/def. mod.; w/o s-a) 24 Modified (w/s-a) T24.3w/m2 87 84 85 89 91 90 (Av. R2 = 88.3%; Adj.R2=84.3%) --- --T24.3w/m 90 88 87 90 90 97 (Av. R2 =91.2%; Adj.R2= 88.7%) --- ---

6/6 4/6

4/6 5/6

2/6 3/6

24 Modified (wo/s-a) T24.5w/m2 86 85 89 91 93 96 (Av. R2 = 88.3%; Adj.R2=84.3%) -- --- 0/6 4/6 T24.5wo/m 89 86 84 89 87 95 (Av. R2 =88.3% ; Adj.R2=85.2%) -- --- 5/6 6/6 T24.5w/m 90 87 87 90 91 97 (Av. R2 = 90.3%; Adj.R2=88.3%) -- --- 4/6 4/6 ___________________________________________________________________________________

*7 samples containing 1/3—½ of all observations from “Crowd In” years Removed, leaving 11 of 18

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1. Baseline standard model (no deficit or loanable funds variables included): Average R 2 = 79.8% 2. When deficit variables only added to baseline standard model, R 2 increases to 89.8%, an increase of 13%, clearly indicating investment cannot be explained without allowing for significant crowd out effects. 3. When endogenous loanable funds modifiers are added to standard model with deficits, as a stand alone and also as a deficit modifier, average R 2 is 88.3%, the same as the level of variance explained by the standard deficit model alone, which for the 6 periods tested here, which also was 88.3%. By comparison, Chapter 11 showed adding total loanable funds left investment R 2 higher, averaging 91.2%. Adding just the endogenous part of total loanable funds as a modifier to the deficit explains less of the variance in investment, but this may be in part for econometric, not substantive reasons related to the use of OLS in Chapter 11 models and 2SLS in this chapter models. The 2SLS model was Wald-strong, but still a very imperfect substitute for the modified G deficit and exchange rate variables it replaced. 4. When the loanable funds modifier is added as a modifier of the deficit only, but not included as a stand-alone variable, R 2 increases in five of the six periods tested, to an average of 88.3%, again below the Chapter 11 figure for the same model of 90.3%, suggesting total loanable funds is the better measure of how much crowd out can be offset when system liquidity is increased.

Reference Heim, J. J. (2017). An Econometric Model of the U.S. Economy. Hoboken: Palgrave Macmillan.

PART IX

Summary Chapters

CHAPTER 25

Summary of Introductory. Literature Review, and Methodology Chapters (Cptrs 1–3)

25.1 Cptr. 1. Deficits, Crowd Out, and Accommodative Monetary Theory Keynes (1936) asserted that the economy was demand, not supply, driven. The theory implied government fiscal policy could be used to stimulate the economy. It was recognized that for such stimulus programs to work, the increased spending or tax cuts involved required increasing the government’s budget deficit. It was recognized that money borrowed to fund deficits is taken from the same pool of funds from which consumers and businesses borrow to finance their spending needs. Government borrowing from the pool reduces consumers’ or businesses’ ability to borrow by a like amount (“crowd out”), forcing a cut in their spending of equal magnitude to the stimulus effect of the deficit. This reduces the stimulus effect of the deficit to zero or near zero. Using fiscal policy to stimulate the economy becomes impossible. It has long been thought that increasing the size of the loanable funds pool from which borrowing takes place could solve this problem, and size of this pool can be increased by the Federal Reserve purchasing government bonds. The proceeds received by bond sellers, once deposited in the banking system, can restore to the pool the funds lost to private borrowers due to the deficit This is called “accommodate monetary policy” and it allows fiscal stimulus programs to take place successfully, i.e., without reducing private spending and offsetting the stimulus effect. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_25

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25.1.1

Actual Accommodative Monetary Policy—Chapters 4–5

The money bond sellers receive from the Federal Reserve must be used to increase borrowing on real goods and services, like cars and machines, that will increase the GDP and lower unemployment. Unfortunately, three problems have kept accommodative monetary policy from being affective: 1. most sellers of bonds to the Federal Reserve are investment banks or brokerages, whose main reason for selling securities is to get funds to buy other securities. But buying securities does not, in any direct way, increase GDP or cut unemployment. 2. In addition, some are foreign banks; when the Fed buys securities from them, there is no guarantee the funds will be spent in the U.S., and in some cases they haven’t been. 3. Finally, from 1960 until the start of the Quantitative Easing program in 2008, The Fed’s purchases of securities were never more than 23% to 44% of the deficit. So even if the Fed had been buying from the right sources (commercial and savings banks, individuals), the fiscal stimulus programs would not have worked, or not worked well. To the extent the Federal Reserve was trying to accommodate, it was only replacing a small fraction of the loss in funds available to private borrowers caused by the deficit. 25.1.2

Accommodative Monetary Science Chapters 6–24

In an exhaustive series of over 1000 statistical tests of the 1960–2010 period, this book examines whether there is a real connection between FR security purchases and/or the money supply and the GDP (Yes). Most of these tests are of whether deficits really do cut private spending (yes), and whether increases in the loanable funds pool can keep these cuts in private spending from happening (Yes). All initial findings are tested in numerous time periods to ensure initial findings are replicable. Good science requires replicability of results, and economic science is no exception.

25

25.2

SUMMARY OF INTRODUCTORY. LITERATURE …

559

Cptr. 2 Summary---Literature Review

For bonds, both the business press and the academic/professional press agree examination of the 1960–2010 period indicates that bond and mortgage market prices are positively related to Federal Reserve (FR) purchases of securities in the credit markets, For stocks, both the business and the academic/professional press agree that at least since the start of quantitative easing (QE) in 2008, increases in FR purchases have also led to increases in stock market prices. Academic and professional studies do not find any effect on the stock markets before 2008. For the GDP, the business press found no significant effect of the large FR purchases during the QE period. Most of the academic/professional studies found some positive effect of FR purchases.

25.3

Cptr. 3: Methodology

In Chapters 6–24, all tests of crowd out and loanable funds effects are made in models that control for a wide range of other variables commonly thought to affect consumption, investment, their specific subcomponents, or the GDP. These are referred to in the text as the “standard” economic models in which crowd out and loanable funds effects are tested. All models are tested for stationarity, endogeneity, serial correlation, and multicollinearity. Stationarity problems if found, using ADF or DF tests, are resolved by trending or because of cointegration, do not need to be further addressed. Hausman endogeneity tests are used, and if, instruments are needed, the ones used are Wald-strong and Sargon—tested to ensure they are not endogenous. Multicollinearity is addressed by only testing in first differences of the data. There are occasional exceptions, like dummy variables where other techniques are more effective, as noted in the text. Prior tests on this same data set indicate first differencing reduces the multicollinearity level by about half, reducing almost all correlations between explanatory variables to less than ±(0.50). A range of other problems commonly encountered in serious regression studies, and how they were resolved are also discussed, including: 3.2.1. Mixing Periods of Deficit Increase and Decrease 3.2.2. Statistical Insignificance Caused by Lack of Variation in the Data 3.2.3. Left-Out Variables

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3.2.4. Multicollinearity 3.2.5. Insufficient Sample Size 3.2.6. Spurious Results Indicating Insignificance. All results obtained on issues of deficits, crowd out, and loanable funds offsets to crowd out are tested in from 6–18 different time periods to ensure replicability of results, a requirement of good science.

CHAPTER 26

Summary of Crowd Out Theory and Accommodative Monetary Policy Theory (Chapters 4–5)

26.1 Chapter 4---Theory of Crowd Out and Accommodative Monetary Policy A general theory of how deficits create a “crowd out” problem is presented, along with modifications to show the extent to which increasing the size of the pool of loanable funds can eliminate the problem. Topics covered include: 4.1. How Deficits Crowd Out Consumer and Business Spending 4.2. How “Accommodating” Monetary Policy Can Offset Crowd Out Effects 4.3. How the Theory Shows Tax Cut and Spending Deficits Having Different Crowd Out Effects 4.4. Alternative Ways of Modeling Crowd Out Effects 4.5. How Declining Deficits Create “Crowd In” Effects 4.6. Should We Use Accommodative Monetary Policy to Offset Crowd Out?

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_26

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26.2 Chapter 5: The Effectiveness of Accommodating Monetary Policy---The Mechanics Describes the role of primary dealers in open market attempts to increase the money supply. Describes the type of financial institution typically selected by the FR to be a primary dealer over the 1960–2010 period (investment banks and brokerages). Discusses the inherent limitations of using such dealers compared to using commercial and savings banks. Provides a list of Primary Dealers Used in Selected Years 1960–2010. Notes whether each primary dealer is the U.S. or foreign dealer.

CHAPTER 27

Summary of the Science Showing “Crowd Out” Exists and Accommodative Monetary Policy Can Offset It

Chapters 6–24 detail the results of approximately 1000 statistical tests undertaken to determine the relationship of government deficits, loanable funds, and the money supply to the real economy. To ensure the findings are reliable, all significant test results were required to be replicable in most of six to 18 other time periods tested, and often in a variety of different models. We summarize the results of this scientific effort in the form of answers to nine key questions. These questions ask about whether deficits and “crowd out” affect the GDP, whether any negative effects of deficits (crowd out) can be offset by increasing loanable funds and/or the money supply, and whether changes in loanable funds, particularly changes from increased Federal Reserve Security purchases, push up stock and bond market prices. The seven questions and the chapters and where they are answered are as follows: 1. Do Changes in the money supply or monetary base to stimulate the economy lead to “pushing on a string” effects? (Cptr. 19) 2. Does deficit financing of stimulative fiscal programs create a “crowd out” problem that reduces consumer and investment spending, causing the fiscal programs to fail? (Cptrs 6–7, 10–11)

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_27

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3. Does growth in M1 offset crowd out as well as growth in total loanable funds pool? (Cptr. 12) 4. Can increases in the total loanable funds pool, either through natural growth in the economy, or through accommodative FR open market operations to increase reserves, offset the crowd out effects of stimulative (i.e., deficit-financed) fiscal policy? (Cptrs. 6–7, 10–11) 5. Are alternative versions of the LF Variable Better Crowd Out Offsets than the total Loanable Funds Version? (Cptrs. 12–24) 6. Is it Changes in the endogenous or exogenous parts of the loanable funds pool, or changes in the money supply or that affects the real economy and financial markets? (Cptrs. 10, 20, 21) 7. Is Growth in total loanable funds a more effective way of reducing crowd out than Alternative Modifiers? Each of these seven questions was subjected to dozens, and in some cases, hundreds of statistical tests. The findings of these tests are summarized in Sects. 27.1–27.7 below along with reference to the chapters that provide more detailed analysis of the models tested, periods tested, and findings obtained.

27.1 Do Changes in Federal Reserve Security Purchases to Offset Crowd Out and Stimulate the Economy Lead to “Pushing on a String” Effects? (Chapter 19) Before 2008, there was no “pushing on a string” problem; excess reserves were only a miniscule part (2.2%) of total reserves; most lendable funds were lent out as evidenced by the limited amount of loanable funds left in banks 1060–2007. After 2007, huge levels of bank reserves remained unlent at year’s end 2008–2017, averaging 93.6% of total reserves (Table 27.1). Table 27.1 U.S. banking system excess reserves (% of total reserves)

Average, 1960–1907: 2.2% Average 2008–2017: 93.6%

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27.2 Does Stimulative Fiscal Policy Create a “Crowd Out” Problem that Reduces Consumer and Investment Spending, Causing the Fiscal Policies to Be Ineffective? (Cptrs 6, 7, 10–11) Chapters 6 and 7 show that adding a “crowd out” variable, equal to the size of the government deficit, to standard consumption and investment equations results in significant increases the explanatory power of the model. One time period was sampled in Chapter 6, 6 periods were sampled in Chapter 7. Chapters 10 and 11 run the same tests in eighteen different, but sometimes overlapping time periods In virtually every test, increased deficits were found significantly related to declining consumer spending and investment spending.

27.3 Does Growth in M1 Offset Crowd Out as Well as Growth in Total Loanable Funds Pool? (Cptr. 12) No. Statistical tests in Chapter 12 clearly shows growth in total loanable funds more accurately measures how much crowd out affects consumption and investment that M 1 alone.

Can Increases in the Total Loanable Funds Pool, Either Endogenously, or Exogenously Through Accommodative FR Increases in Bank Reserves, Offset the Crowd Out Effects of Stimulative Fiscal Policy? (Chapters 8–9, 10–11, 19)

27.4

Yes, increases in loanable funds can fully offset crowd out if they are large enough, but before Quantitative Easing, they were not; after QE they were. Prior to QE, accommodative monetary policy must be considered a failure. Chapter 8 examines whether increases in the total loanable funds pool can offset crowd out and concludes it does, but tests for only one time period Chapter 9 compares five different models in which different ways are used to show how changes in total crowd out affected consumption

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and investment. Models are evaluated principally on the basis of how much adding the loanable funds modifier to the standard deficit model increases explained variance (R 2 ). Chapters 10 and 11 show effects of three of the best of these models for the 1960–2010 period and then tests them for replicability in 5–17 smaller time periods within this 50 year time frame. All these chapters find strong statistical evidence increases in the total loanable funds can offset the negative effects of crowd out.

27.5 Are Alternatives to the Total LF Variable Better Crowd Out Modifiers? (Cptrs. 12–24) Tests of the effects of just the exogenous, or just the endogenous parts of total loanable funds, or of just M 1 show that they do not generally capture the extent actual crowd out is reduced from its deficit size to something less than that as well as total loanable funds measures the actual reduction. Table 27.2 Explanatory power of models with total loanable funds (LF) variables, compared to baseline R2 R2 Consumption Investment Baseline (1 Var.Deficit, No Modifier) (T.10.2, 10.4) (18 Periods 88.2% 89.8% Sampled) (6 Periods 87.5% 87.0 Sampled) Baseline (2 Var.Deficit, No Modifier) (T.11.10B) (18 Periods 89.4% 89.8% Sampled) (6 Periods 88.7% 88.3% Sampled) 1 Var. Deficit With Total LF Modifier Cptr. 10 88.3 90.2 (T.10.1&4) 2 Var. Deficit With Total LF Modifier Cptr. 11 90.2 90.5 (T.21.1&4) Alternative Modifier Models:* Cptr. 24 Mod: (S 89.7 88.5 + FB + M 1)

Deficit Significant Consumption 14/18 (9/11) 6/6 (6/6)

14/18 (9/11) T:4/6 (4/6)

Investment 17/18 (10/11) 6/6 (6/6)

17/18 (10/11) G:6/6 (6/6) (CK!!!)

6/6

6/6

T:6/6; G:(5/6)

T:5/6; G:(4/6)

T:6/6; G:5/6

T:1/6; G:4/6 (continued)

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(continued) (T.24.1&4) (M 1)

88.7

81.8

Cptr. 16 Model: (T − G) + FR, LF-DEF (T.16.1&3) 87.6 89.3

T:6/6; G:2/6

T:1/6; G:2/6

(T − G); 10/18

(T − G); 17/17

(Table 16.4: Compares 50 years of Deficits and FR purchases, which allows comparison of the size of accommodative monetary policy needed (before LF considerations) with what the FR actually provided.) (Eq, 16.13 shows positive. sign on Gdef when 2008–2010 data added, explains it is “crowd in” effect) Cptr. 15 Model : (T + FR, G − FR, LF − FR) 85.7 90.2 (T.22.1&4)

T : 4/6, G : 0/6 T : 4/6, G : 1/6

Cptr. 17 Model : (T + FR, G − FR, LF − DEF) 86.8 84.6 (T.17.1&4)

T : 6/6, G : 1/6 T : 6/6, G : 6/6

Cptr. 18 Model : (T + FR, G − FR, LF − FR) 83.0 84.5 (T.18.1&5)

T : 4/6, G : 2/6, T : 3/6, G : 2/6

(Cptrs 17 & 18 test the exact same models on the same 6 time periods. Only the Wald-strong instrument used to deal with an endogeneity problem is different, and the difference does lead to some noticeable differences in results.) Cptr. 20 Model : T + (LF − FR), G − (LF − FR), (LF − FR) 91.0 91.2 (T.20.1&3) T : 5/6, G : 3/6

T : 4/6, G : 4/6

Cptr. 21 Model : FR only as stand − alone (S − A) variable 88.3 86.6 T : 6/6, G : 3/6 (T.21.2&8)

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T : 6/6, G : 4/6 Note: Only one part of Chapter 21 results are cited above. Chapter 21 also compared the explanatory power of total LF with five other alternative models that replaced the total LF variable with either the exogenous or endogenous parts of LF, or both, or in some cases tested one of the parts plus total LF as a single variable in the same model. For these models: 1. The total loanable funds-only model had the highest R 2 for investment compared to the other models tested. 2. For consumption, total LF alone had the highest R 2 (90.2%) compared to the other models except one in which separate total LF and exogenous LF variables were both included in the same model. This gave a R 2 (90.7%) which slightly exceeded that obtained for total LF alone. This difference may be spurious but may also be indicating that not all of the effect of FR purchases on consumption are captured by same period changes in total LF.

Cptr. 24 (T + Endog, G − Endog, Endog) 88.7 87.7 (T24.1)

T : 6/6, G : 1/6 T : 4/6, G : 3/6

(T22.1)

Cptr. 22(LF) vs. (LF − FR) (just compares Cptr. 21 and 22 results above; concludes LF explains morevariance)

Cptr. 13 (T + FR)(, G − FR), (FR) 87.0 NA (T.13.1)

T : 1/1, G : 0/1 T : NA , G : NA

*Read model descriptor as indicating (e.g.,) deficit variable modified by LF = (T + LF), (G − LF). If a stand-alone LF modifier is used, it will just read (LF). If model has both deficit modifiers and stand-alone LF modifiers, all will be shown as follows: (T + LF) (G − LF) (LF).

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There are a total of 53 R 2 , or ratio of significant t-tests/total t-tests results shown for the alternative consumption and investment models being compared with the total loanable funds model. Out of 53 R 2 or t-statistics obtained for the alternate models, the total loanable funds model had the better t-statistic in 43 of the 53 cases, equally significant in four cases, and less significant in only six cases. In some cases the results indicated both the total LF model and the alternative modifier model both explained variation better than the baseline deficit model without any modifier; but that the total loanable funds modifier (LF, or S + FB) explained more of the variation in the data than did the alternative model being compared with it. In others cases, the results were worse: the alternative modifier model explained less variance than the base line crowd out model without any modifier at all. The reader wishing to examine in more detail any of the alternative models tested can find exhaustive test details in the chapters cited.

27.6 Comparing the Effects of Endogenous and Exogenous Loanable Funds on the Real Economy and Financial Markets? (Cptrs. 10, 20, 21) The best tests we have of whether the endogenous (economy determined) or the exogenous (FR determined) part of the total loanable funds variable (S + FB) is more important in offsetting crowd out (explains more variance) comes from Chapter 10, Tables 10.5 and 10.6). Six time periods were tested to ensure replicability of the initial results: For consumption: 1. The deficit variable modified by the endogenous part of total LF was found significantly and positively related to consumption in 6 of 6 periods tested; the exogenous part only a significant influence on consumption in 1 of 6 (the one including QE period data where FR purchases were far greater than ever before). 2. Average R 2 in the models tested was 88.2%, only a bit more than the 87.5% obtained for the same six periods in the baseline crowd out model without any modifier, This indicates changes in loanable funds do reduce the impact of crowd out in consumption models and that examination of its two parts was helpful. (R 2 using one

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total LF variable, instead of the two parts, was 88.3%, so essentially, breaking it into two parts neither added or reduced our information significantly.) For investment, results were similar: 1. Endogenous loanable funds growth was positively and significantly related to investment growth in 5 of 6 periods tested. Exogenous growth was only positively significant in the 2 of six samples, those containing QE period data. 2. Average R 2 in the models tested was 90.5%, noticeably more than the 89.0% obtained for the same six periods in the baseline crowd out model without any modifier, again indicating LF has some effect in reducing crowd out, and that examination of its two parts was helpful. (R 2 using one total LF variable was 90.2%, so essentially, breaking it into two parts added, but only slightly to our information.) Consumption results above are based on testing standard consumption models with one variable modified deficits (T − G) + (total LF) and a stand-alone total LF variable. The signs on the modified deficit and stand alone were consistently positive (as they were on unmodified deficit, T − G), indicating deficits have a negative effect on consumption, as do modified deficits, unless the loanable funds modifier exceed the deficit, then the effect on consumption of the modified deficit is positive. The consumption model also contained a stand-alone total LF variable, and its sign was consistently negative, as in Chapter 28 below, indicating that ceteris paribus, raising savings (most of the LF pool) can only occur when holding income and taxes constant by lowering consumption since the marginal propensity to consume (mpc) and marginal propensity to save (mps) have to add to 1.00. In Chapter 21, for consumption, results generally indicated neither the endogenous or exogenous parts reduced crowd out. For investment, when endogenous LF and exogenous LF were tested as separate variables in the same model, the endogenous part was found significant in all 6 of 6 tests. The exogenous part in only 3 of 6 tests. Hence, the endogenous part of total loanable funds does reduce crowd out; the exogenous part only inconsistently reduces crowd out.

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Cptr. 20 compares the total LF models from Chapter 11 to models in which total LF is divided into its endogenous and exogenous parts, both tested only as s separate stand-alone variables in the same model. Six time periods were tested. For consumption, Endogenous LF was negative in all six tests, statistically significant in 4 of 6 (Table 20.1), reflecting the need for the mpc to decline when loanable funds increased in ceteris paribus models (discussed in earlier chapters, including Chapter 11). The Exogenous LF variable information was unavailable. For investment, endogenous LF, like total LF was positively related to investment and significant in all 6 periods tested (Table 20.3). Exogenous LF variable information was unavailable. In short, Chapter 20 indicates that either adding total LF to the model as one variable, or dividing it into its endogenous and exogenous parts in the model, results will be virtually identical to those obtained in Chapter 11 using only the one variable, total LF, to determine the ability of LF to offset crowd out. The significance of total LF is because its endogenous part was found significant. Exogenous LF was not typically significant, or its results were mixed. We conclude that growth in the endogenous part of loanable funds has been most responsible for offsetting crowd out during the 1960– 2010 period. The poor showing for the exogenous part may be because growth in this part has been small (except during QE).

27.7 Total Loanable Funds Compared to Alternative Modifiers Offsetting the crowd out resulting from budget deficits requires restoring the funds available for consumer and business borrowing to pre-deficit levels. This requires increasing the system’s loanable funds, which can be done endogenously or exogenously. Chapters 10–24 look at several different ways this might be done to determine which is the best. Chapters 10–11 tested to see if increasing the total loanable funds pool offset crowd out. Chapters 12 tested whether increasing the M1 money supply offset crowd out as well as increasing total loanable funds. Chapters 13–19 tested whether increasing just the exogenous part of the pool, through Federal Reserve securities purchases (“accommodative monetary policy”) reduced crowd out as well as increases in total loanable funds. Different models of how this might occur are tested in each of these

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chapters. Chapters 20–24 tested whether increasing just the endogenous part of the pool, (which grows when savings increase due to growing income, a growing marginal propensity to save [mps], or growing foreign borrowing) reduced crowd out as well as increases in total loanable funds. Different models of how this might occur are tested in each of these chapters. Results are presented in Table 27.1. All consumption models tested models tested use test variable as both a modifier of deficit variable values, and as a stand-alone variable. Investment models just use the variable tested as a deficit variable modifier; no stand-alone variable is included, except in Chapter 21, where only stand-alone variables are tested. Table 27.3 Statistical models tested to determine what form of increased liquidity best offset crowd out Are % of Tests with Significant Cptr#/ Is R 2 Higher Than

Model

No Modifier At All?

10 Total LF (Baseline Model) 11 Total LF (Baseline Model ) 12 M1 Model

C I C I C I C

13 Exog Def Exog S-A 14 Exog Def Endog s-a 15 Exog Def Endog s-a 16 Exog Def SPriv +FB s-a 17 Exog Def SPriv s-a 18 Exog Def Endog s-a 19 NA 20 Endog. Def Endog. S-a 21 Compares s-a

Yes Yes Yes Yes Same Lower Same

Is R 2 Higher for Total Loanable funds Model? Same Same Same Same Yes Yes Yes

Modified Deficit Variable Higher in the Total Loanable Funds Model? Same Same Same Same Yes Yes Yes

C Same Yes Yes I Yes Same Same as LF C Same Same Yes I Lower Same Yes C Lower Yes Yes I Lower Yes Same as LF C Yes Yes Yes I Yes Yes Lower as LF C Yes Yes Yes I Yes Yes Yes (Just Repeats Results of Earlier statistical Testing) C Yes Lower Yes I Yes Yes Yes C Yes Yes Yes, generally (continued)

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(continued) LF To 5 Others: Exog, (LF+Exog), (LF, Exog), (Savings + Exog) (Endog, Exog) 22 Compares LF to Endog (s-a only; no Def. modifier) 23 NA 24 Endog Def Endog s-a

I

Yes

Yes

Lower in LF

C I

Lower Lower

Yes Yes

NA NA

C I C I

(Just Repeats Results of Earlier statistical Testing) Lower Lower

Yes Yes

Yes Yes

Reading Table model identifiers: e.g., “15 Exog Def, Endog. s-a” = Chapter 15 model used exogenous loanable funds as the deficit modifier and endogenous loanable funds as the stand-alone variable. “LF” = Loanable Funds. In answer to the questions posed in Table 27.3, we have the following results: 1. Do alternate modifiers tested reduce crowd out, at least to some extent? Yes for the total loanable funds modifiers, but only yes in about half the models tested (9/21) cases for the alternate models tested, generally in the ones most similar to the loanable funs model. 2. Do alternate modifiers tested reduce crowd out as much as the total loanable funds modifier? Almost all (17 of the 21) alternate models tested had lower R 2 s than the total loanable funds model. Only 1 explained more variance (the one that used only endogenous LF as the deficit modifier and the stand alone. We have pointed out in earlier chapters that this was the far stronger of the tow parts of total loanable funds, the other part being exogenous (Federal Reserve securities purchases) part. 3. Are the number of cases in which the modified deficit variable(s) was found statistically significant (and predicted by Chapter 4 theory) higher for the total loanable funds model than for the alternate models?

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Yes. In 15 of 19 cases tested, the percent of all tests resulting in statistically significant modified deficit (i.e., crowd out) variables was higher in the loanable funds models than in the alternatives. Only in 2 of the 19 cases was the percentage significant higher. Based on the answers to these questions, it seems clear that public policies aimed at reducing the level of crowd out should be focused on raising the total level of loanable funds, not just M 1 or either the endogenous or exogenous parts alone.

Reference Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. London: Macmillan.

PART X

Overall Conclusions, Definitions and Engineering Equations

CHAPTER 28

Overall Conclusions

Even in the summary form presented in Chapters 25–27, this book’s findings are highly detailed, and it can be difficult to tell from looking at the individual trees what the forest in genera looks like. To summarize this book’s major findings in as brief a way as possible (a summary of summaries, if you will), we summarize the books six major findings here: 1. Fiscal stimulus programs definitely can stimulate the economy, but in doing so, they create crowd out problems which usually leaves fiscal stimulus programs ineffective. 2. If the pool of loanable funds grows sufficiently, it can offset crowd out completely, leaving fiscal stimulus programs effective. There is evidence a complete offsetting of crowd out occurred during the Quantitative Easing (QE) period due to Federal Reserve actions. The size of the pool is policy controllable by the Federal Reserve. 3. Total loanable funds is a better measure of the actual crowd out modifying effect than either its endogenous part or its exogenous part (FR security purchases) alone, though endogenous explains most of the variation in total loanable funds. Increases in endogenous loanable funds, per dollar of increase, have a much larger positive impact on investment. For consumption, tests were ambiguous regarding as to which type of increase in loanable funds had the

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_28

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greatest effect. Total loanable funds is also a better modifier than M1. 4. While the level of loanable funds is policy controllable by the Federal Reserve, it is not likely that its current methods of exercising this control have much positive effect on the GDP or lowering unemployment. This may be because the Federal Reserve historically, has relied on purchasing securities from investment banks and brokerages. These institutions typically only sell securities to the Fed (or anybody else) to obtain funds to buy other securities. Securities trading is what they do for a living. This helps inflate bond market prices, helping Wall Street. The Federal Reserve, historically, has relied on purchasing securities from investment banks and brokerages. Such institutions most typically only sell securities to the Fed (or anybody else) to obtain funds to buy other securities. After all, securities trading is what they do for a living. This helps inflate bond market prices, helping Wall Street, but does little to increase the demand for real goods and services necessary to raise GDP and lower unemployment, which is what is needed if Federal Reserve actions are to help Main Street. If this hypothesis is correct, the results should indicate a smaller marginal effect on consumption and investment of a dollar’s increase in loanable funds due to FR security purchases than by a dollar’s increase due to growth in the endogenous portion of the loanable funds pool. And this is exactly what we see. For consumption, in 6 of 6 periods tested, the estimated marginal effect is lower for increases in FR purchases than for increases in the endogenous part of the loanable funds pool. For investment the marginal effect of an increase in loanable funds is lower for FR purchases compared to endogenous growth in 5 of 6 periods tested (Chapter 17, Tables 17.5 and 17.6). The Federal Reserve’s purchases of securities would more likely stimulate the GDP and reduce unemployment if its purchases of securities were restricted to purchases from U.S. commercial and savings banks. It is these banks, not investment banks, and brokerages, that are in the business of directly lending money to consumers and businesses that want to buy, cars, houses, machinery, and other goods and services, the very actions which will raise GDP and reduce unemployment.

28

OVERALL CONCLUSIONS

579

5. In addition, many are foreign banks with less incentive to invest Federal Reserve money in the U.S. than U.S. banks would have to invest in the U.S. 6. To deficit or not is a policy choice which has huge implications as to whether growth in the future is skewed toward growth in private or public goods. With no deficit, growth in loanable funds increases the GDP by increasing private investment and spending. With a deficit created by a fiscal stimulus program, the increase in loanable funds go to offset crowd out effects (i.e., keep private spending at old levels so the stimulus program works), which also raises GDP. The increase in GDP due to the fiscal stimulus is likely to be more oriented toward production of public goods than the no deficit increase in private spending characterizing that leads to that increase in GDP. Hence doing deficits amounts to policy decision about private vs public goods, as well as comparative magnitudes of the effects.

CHAPTER 29

Acronyms Used to Define Variables in Equations

ACC= The accelerator ( U.S. GDP) Adj R2 = Adjusted R2 AR(n) = nth Order Autocorrelation Control CAP-1 = U.S. Capacity utilization lagged one year CapUtil = Level of capacity utilization (Table B54) C B2 = Consumer borrowing (FR Flow of Funds Accounts:  Consumer Debt) C D = Domestically produced consumer goods. = Total consumption—(Total imports−Capital goods, Industrial supplies and materials) (Tables B2, 104)  = Denotes Variable Data are in First Differences, not Levels (e.g., GDP) (Y ) = The change in current year GDP (the accelerator) (B2) DJ-2 = Wealth measure; NYSE composite average lagged two years (B95) D.W. = Durbin Watson Test ER = Excess Reserves FB = Foreign Borrowing (B32) FR = Federal Reserve G = Consolidated Government Spending in U.S. (or, depending on context:) = G = Deficits generated by total government spending on

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_29

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goods, services and transfers (our initial measure of crowd out caused by spending deficits) (B83) GDP = U.S. GDP G T&I = Total consolidated U.S. federal, state and local government spending, including transfers I B = I BOR = Business Borrowing (FR Flow of Funds Accounts:  Business Debt) = Domestically produced investment goods (total ID investment−(imported capital goods + industrial supplies and materials)) (B2, B104) I P&E = Plant and Equipment Investment Infl = Inflation FB = For.Bor. = Foreign Borrowing (B32) LF = Pool of Loanable Funds = (S + FB) = National Saving Plus Foreign Borrowing M 1 = M 1 Money Supply (B69) M 2-2-4 = M 2 money supply (or M 2–M 1 component): a measure of recent year (liquid) saving (B69) Mort = Mortgage interest Rate (M − X )/Y ) = the trade deficit (expressed as Imports-Exports) divided by the GDP NYSE = NY Stock Exchange Composite Index OLS = Ordinary Least Squares PerSav = Personal Saving POP = U.S. population (B34) POP20/65 = Ratio of those 20–24 to those 65 or older in the population (B34) PR = the Prime interest rate (B73) PR-2 = the Prime interest rate, lagged two periods (B73) Prof = Level of Profits (B28) Reces = Recession R 2 = % of Total Variance Explained by the Model S = Gross national U.S. saving = personal, + corporate + depreciation + government (B32) (S + FB) = Total U.S. loanable funds: pool = national savings plus foreign borrowing T = Consolidated Government Revenues in U.S. or, depending on context: T = Deficits generated by tax or other revenue cuts (our initial measure of crowd out caused by tax cuts) (B83)

29

ACRONYMS USED TO DEFINE VARIABLES IN EQUATIONS

583

(T − G) = the consolidated deficit for all U.S. governmental entities taken collectively (B83) TR = Total U.S. Bank Reserves (Tr + A) = FR Holdings of Treasury and Agency Securities 2SLS = Two Stage Least Squares Treas10 = 10 Year U.S. Treasury Bond Treas30 = 30 Year U.S. Treasury Bond T T = Total consolidated U.S. federal, state and local government revenues XRav = U.S. real exchange rate average for current and past three years Y = GDP (Y − T ) = Disposable income (B2, B83) *Tables cited starting with “B” are taken from the Appendix B of the Economic Report of the President, 2012 and other years.

CHAPTER 30

Summary of Engineering Quality Equations in This Book

Economic questions raised in this book were answered by testing an initial hypothesis containing the variable(s) of interest and other known determinants of the dependent variable, usually consumption or investment. The initial hypothesis was then tested on the full 50 year 1960–2010 data set. Then, to ensure the finding on any particular variable in the model said something of a truly scientific nature, i.e., was replicable, the same model was retested in from 5 to 17 additional shorter time periods taken from within the larger 1960–2010 timeframe. This was done to ensure the initial findings were not spurious. Average coefficients and t-statistics for the full 6–18 different time period tests became the engineering coefficients. By “engineering coefficients” we mean coefficients that provide very stable estimates of the marginal effects of one variable on another, and the standard deviations associated with them. Only equations whose variables of interest were found statistically significant in most or all 6–18 tests are reported below. Because of how they were arrived at, he coefficient averages and average significance levels provide roughly the same results as would be obtained by future researchers testing the same thing and controlling for the same other variables (or justify why a model without them is a better model). Hence our reference to these results as “engineering – quality” coefficients and confidence levels.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8_30

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It has been close to four centuries since the birth of the scientific revolution and Isaac Newton. Given that, engineering quality results should not be too much to ask economics researchers to provide readers at the time of publication of initial results. We believe that the key findings of this book achieve that standard, and hope the reader will agree as well.

30.1

Do Deficits Really Cause Crowd out?

A previous work, Heim 2017a examined this question exhaustively, replicating initial results in at least two of three additional periods sampled. Other known determinants of the dependent variable were controlled for. Findings for crowd out’s effect on various parts of consumption and investment for the 1960–2010 test period were as follows: Total Consumption C T = .57(T ) − .38(G) (−7.9) (t =) (11.0)

(Eq. 4.1T.TR)

Domestic Consumption C D = .34(T ) − .23(G) (−4.5) (t =) (6.5)

(Eq. 4.4.TR)

Imports Consumption C M = .25(T ) − .18(G) (−5.4) (t =) (7.4)

(Eq. 4.2.TR)

Consumer Durables CDur = .24(T ) − .14(G) (−5.4) (t =) (5.9)

(Eq. 4.9.TR)

Consumer Nondurables CND = .18(T ) − .12(G) (−4.7) (t =) (7.2)

(Eq. 4.11.TR)

Consumer Services CSer = .45(T ) − .25(G) (−5.4) (t =) (8.5)

(Eq. 5.2.TR)

Total Investment IT = .30(T ) − .32(G) (−4.4) (t =) (2.7)

(Eq. 5.2.TR)

Domestic Investment I D = .27(T ) − .30(G) (−3.8) (t =) (2.9)

(Eq. 5.4.TR)

Imports Investment I M = .05(T ) − (NS)(G) (NS) (t =) (2.0)

(Eq. 5.6.TR)

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

587

Plant and Equipment I P&E = .14(T ) − .14(G) (−2.0) (t =) (NS)

(Eq. 5.10.TR)

Residential Const. IRes = .21(T ) − .21(G) (−7.5) (t =) (5.6)

(Eq. 5.11.TR)

These tests clearly indicate both tax cut deficits and spending increases have negative “crowd out” effects on consumption and investment, and usually, but not always, statistically significant results. (“NS” indicates not significant). For the current study, as we note that in the Summary Table for Chapter 10, for 18 periods tested, adding the deficit (crowd out) variables to the consumption function increases R 2 by 15.9%, and increases investment R 2 by 19.0%. Clearly government deficits crowd out, i.e., reduce, both consumption and investment spending. In the current study, the standard structural models presented in Chapter 10 of this book, which use the one variable definition of the deficit (T − G), in 18 different (but overlapping) time periods tested, the crowd out variable had a statistically significant negative effect on consumption in 16 of those tests, and was significant for 17 of the 18 investment time periods tested (Tables 10.1, 10.3). Examples of the equations tested are presented below, showing results of testing the full 1960–2010 data set: C D = .36(Y − TT ) + .38(T − G)m − .51 (S + FB) − 6.37PR (t=)

(6.3)

(7.3)

(−2.8)

(−4.3)

+ .40DJ−2 − .533.54 POP16/65 + .021POP + 42.35 M2 AV (−2.5)

(5.3)

(4.7)

(5.4)

+ .11 C B2 (4.6)

R = 87.4% 2

Adj.R 2 = 85.0%

D.W. = 1.8

MSE = 25.29 (Eq. 10.2)

(6 Time period average coefficient, t-statistic, R 2 /Adj.R 2 ): (As discussed in the text, the ceteris paribus nature of the consumption model leads us to expect a negative sign on the stand-alone loanable funds variable). I D = +.22(ACC) + .18(TT − G T &I )m + .007POP (t=)

(6.1)

(7.8)

(5.0)

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J. J. HEIM

− 3.39PR−2 + 7.40XRAV + 2.05 CAP−1 (2.7)

(1.9)

(1.2)

(Eq. 10.6)

(6 Time period average coefficient, t-statistic, R 2 /Adj.R 2 ): Two Variable Deficit Models: Consumption Modified by Stand Alone Loanable Funds Variable (1960–2010 Sample) C D = .38(Y − TT ) + .43(TT ) − .24(G T &I ) − .14(ST + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−4.1)

− 6.09PR + .40DJ−2 − 398.48 POP16/65 + .016POP (−2.8)

(5.0)

(3.7)

(−1.9)

+ 33.67 M2AV (3.5)

+ .10 C B2 R 2 = 88.3% MSE = 24.68

Adj.R 2 = 85.8%

D.W. = 1.9 (Eq. 11.1)

(4.5)

The 6-period average regression coefficients, (t-statistics), and R 2 /Adj.R 2 for this model were (Table 12.5): (S + FB) modified deficit variable model:

C = $-0.44 (4.8) per dollar of  tax cut 2 = or deficits. R 2 / RAd. $-0.18 (2.3) per dollar of  spending deficits 90.4/86.5%

I D = + .22(ACC) + .18TT (m) − .06G T &I (m) + .008POP (t=)

(4.9)

(2.0)

(−0.7)

(2.0)

− 4.11PR−2 + 4.77XRAV + 1.50 CAP−1 − .05 GDP (−2.2)

R 2 = 90.2%

(2.4)

Adj.R 2 = 88.5%

(1.2)

D.W. = 2.0

(−0.7)

MSE = 28.20 (Eq. 12.5)

Six time periods were tested to ensure replicability of results: 1960– 1980, 1990, 2000, 2007, 2008, and 2010. The average regression coefficient (t-statistic), and R 2 for the three models were:

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

(S + FB) modified deficit variable model:

589

I = $-0.08 (1.7) per dollar of  tax cut 2 = or deficits. R 2 / RAd. $-0.14 (2.1) per dollar of  spending def. 90.5/88.7%

30.2 Changes in M1, or Loanable Funds: Which Affect the GDP’s Components More?---Using Full Structural Models to Control for Other Variables’ Effects (Table 12.5) Consumption: Baseline Model—No Deficit Modifiers of LF or M1 C D = .31(Y − TT ) + .32(TT ) − .16(G T &I ) − 7.14PR + .49DJ−2 (t=)

(6.4)

(6.6)

(−3.1)

(−1.9)

(4.5)

− .459.68 POP16/65 + .017POP + 36.27 M2AV + .09 C B2 (4.0)

(2.4)

R = 86.6 2

Adj.R = 83.9% 2

(3.9)

(3.8)

D.W. = 2.1 MSE = 26.17

(Eq. 11.1A)

Consumption Modified by Stand Alone Loanable Funds Variable (1960–2010 Sample) C D = .38(Y − TT ) + .43(TT ) − .24(G T &I ) − .14(ST + FB) − 6.09PR (t=)

(8.0)

(6.7)

(−2.8)

(−2.8)

(−4.1)

+ .40DJ−2 − 398.48 POP16/65 + .016POP + 33.67 M2AV (5.0)

+ .10 C B2

(3.7)

(−1.9)

R = 88.3%Adj.R = 85.8% 2

(4.5)

2

D.W. = 1.9

(3.5)

MSE = 24.68 (Eq. 11.1)

Comparing Models tested: Standard Consumption Model with deficit variables modified by (S + FB), (S + FB + M1), or (M1) alone. (6 time periods tested). The average regression coefficient (and t-statistic) and R 2 for the three models were (Table 12.5): (S + FB) modified deficit variable model:

C = $-0.44 (4.8) per dollar of  tax cut 2 = or deficits. R 2 / RAd. $-0.18 (2.3) per dollar of  spending deficits 90.4/86.5%

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J. J. HEIM

C = $-0.39 (4.8) per dollar of  tax cut 2 = deficits, R 2 / RAd. .15 (2.0) per dollar of  spending deficits 89.5/85.5%

(S + FB + M1) modified deficit variable model:

(M1) modified deficit variable model:

C = $-0.32 (4.3) per dollar of  tax cut 2 = or deficits, R 2 / RAd. $-0.11 (1.5) per dollar of  spending deficits 89/84.8%

Baseline standard investment model with deficit variables, but no LF or other liquidity modifiers: I D = + .27(ACC) + .33TT − 33G T &I + .012POP − 4.95PR−2 (t=)

(2.6)

(6.4)

(2.8)

(−3.9)

(−2.5)

+ 6.68XRAV + 2.43 CAP−1 − .02 GDP (3.5)

(−0.2)

(1.8)

R = 89.0% 2

Adj.R = 85.9% 2

D.W. = 1.9 MSE = 29.87

(Eq. 12.4A)

(6 period average R 2 = 88.3%) Models tested: Standard Investment Model with deficit variables modified by (S + FB), (S + FB + M1), or (M1) alone. No stand-alone version of these variables variable included. General 2SLS Model Tested, Using 1960–2010 Data (Using Total Loanable Funds as Deficit Variable Modifier 1960–2010 Sample) I D = + .22(ACC) + .18TT (m) − .06G T &I (m) + .008POP (t=)

(4.9)

(2.0)

(−0.7)

(2.0)

− 4.11PR−2 + 4.77XRAV + 1.50 CAP−1 − .05 GDP (−2.2)

R = 90.2% 2

(2.4)

Adj.R = 88.5% 2

(1.2)

D.W. = 2.0

(−0.7)

MSE = 28.20 (Eq. 12.5)

Six time periods were tested to ensure replicability of results: 1960– 1980, 1990, 2000, 2007, 2008, and 2010. The average regression coefficient, (t-statistic), and R 2 for the three models were:

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

591

(S + FB) modified deficit variable model:

I = $-0.08 (1.7) per dollar of  tax cut 2 deficits. R 2 / RAd. = $-0.14 (2.1) per dollar of  spending def. 90.5/88.7%

(S + FB + M!1) modified deficit variable model:

I = $-0.08 (0.9) per dollar of  tax cut 2 deficits, R 2 / RAd. = $-0.14 (1.8) per dollar of  spending def. 88.5/84.8%

(M1) modified deficit variable model:

I = $-0.08 (0.8) per dollar of  tax cut 2 deficits, R 2 / RAd. = $-0.15 (1.3) per dollar of  spending def. 83.7/79.5%

30.3 Which is the More Accurate Measure of Consumer Crowd Out? The Size of the Deficit alone, or the Deficit Minus any Same Period Increase in the Pool of Loanable Funds? (1 and 2 Variable Deficit Models Tested) 1. Variable Standard Consumption Model with Deficit Variables, but no crowd out modifier (i.e., no loanable funds Variable) (1960–2010 data): C D = .29(Y − TT ) + .28(T − G) − 7.30PR + .49DJ−2 (t=)

(6.3)

(5.9)

(−3.1)

(4.8)

− .579.55 POP16/65 + .021POP + 43.55 M2AV + .10 C B2 (5.9)

(−2.9)

R = 85.9% 2

Adj.R = 83.6% 2

(4.7)

D.W. = 2.1

(4.1)

MSE = 26.47

(10.1A) Standard Consumption Model with Deficit Variables, but With Same-Period Separate Loanable Funds Modifier Variable (1960–2010 data): C D = .36(Y − TT ) + .38(T − G) − .13 (S + FB) − 6.37PR (t =)

(7.3)

(6.3)

(−6.1)

(−2.8)

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+ .40DJ−2 − .533.54 POP16/65 + .021POP + 42.35 M2AV (5.3)

(5.4)

(−2.5)

(4.7)

+.11 C B2 (4.6)

R = 87.4% 2

Adj.R 2 = 85.0%

D.W. = 1.8

MSE = 25.29

(10.1) To ensure consistency over time, the six sample periods 1960–1980, 1990, 2000, 2007, 2008, 2010, were tested. Average coefficient, t-statistic and R2 Findings were Unmodified deficit model Modified deficit model

regression coefficient (t-statistic) = −.27 (4.2); R 2 /Adj.R 2 = 88.0%/83.8% est. regression coefficient (t-statistic) = .35 (3.4); R 2 /Adj.R 2 = 88.3%/86.5% (Tables 10.1, 10.2, 10.1A)

2 Deficit Variable Consumption Model Standard Consumption Model with Deficit Variables, but no loanable funds modifier (1960–2010 data): C D = .31(Y − TT ) + .32(TT ) − .16(G T &I ) − 7.14PR + .49DJ−2 (t =)

(6.4)

(6.6)

(−3.1)

(−1.9)

(4.5)

− .459.68 POP16/65 + .017POP + 36.27 M2AV (4.0)

(2.4)

(3.8)

+.09 C B2

(3.9) R 2 = 86.6%

Adj.R 2 = 83.9%

D.W. = 2.1 MSE = 26.17 (Eq. 11.1A)

Standard Consumption Model with Deficit Variables, but With Same-Period Separate Loanable Funds modifier Variable (1960–2010 data): C D = .38(Y − TT ) + .43(TT ) − .24(G T &I ) − .14(ST + FB) (t=)

(8.0)

(6.7)

(−2.8)

(−4.1)

− 6.09PR + .40DJ−2 − 398.48 POP16/65 + .016POP (−2.8)

(5.0)

+ 33.67 M2AV +.10 C B2 (3.5)

(4.5)

(−1.9)

(3.7)

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

R 2 = 88.3%

Adj.R 2 = 85.8%

593

D.W. = 1.9

MSE = 24.68

(Eq. 11.2)

Average effects for the 6 sample periods cited above were: Unmodified deficit model Tax deficit coefficient

(t-statistic) = −.34 (4.6); R 2 /Adj.R 2 = 88.7%/84.7% est. Spending deficit coefficient (t-statistic) = −.11 (1.5) (Table 11.1B)

Modified deficit model Tax deficit coefficient

(t-statistic) = −.44 (4.8); R 2 /Adj.R 2 = 90.2%/86.5% est. Spending deficit coefficient (t-statistic) = −.18 (2.3);

30.4 Which is a Better Measure of Investment Crowd Out? The Deficit, or the Deficit Reduced by any Same Period Growth in the Pool of Loanable Funds (1 and 2 Variable Deficit Models)? This Study’s Standard “Baseline” Investment Model with 1 Variable Deficit Variable (T − G), before Adding Deficit Modifiers (Using 1961–2009 data): I D = + .26(ACC) + .32(TT − G T &I ) + .011POP (t=)

(6.5)

(5.5)

(8.3)

− 4.51PR−2 + 8.86XRAV + 2.66 CAP−1 (−2.4)

(3.4)

(1.6)

R = 88.7% Adj.R = 87.4 D.W. = 1.9   87.5% = six period average. 2

2

MSE = 29.00 (Eq. 10.3A)

Standard Investment Model with 1 Variable Crowd out (T − G) modified by (S + FB). No Separate Stand-Alone (S + FB) Variable Used. (Using 1961–2009 data) I D = + .22(ACC) + .18(TT − G T &I )m + .007POP (t=)

(6.1)

(7.8)

(5.0)

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− 3.39PR−2 + 7.40XRAV + 2.05 CAP−1 (2.7)

(1.9)

R = 90.5% 2

(1.2)

Adj.R = 89.3%

D.W. = 1.9

2

MSE = 26.90 (Eq. 10.6)

The average 6—sample periods (same as used above) negative marginal effect (coefficient), (t-stat), and R 2 /Adj.R 2 results were regression coefficient (t-statistic) = .28 (4.6); R 2 /Adj.R 2 = 87.0%/85.8% est.

Unmodified deficit model

Modified deficit model

regression coefficient (t-statistic) = .21(7.1); R 2 /Adj.R 2 = 90.2%/88.5% (Table 10.4)

2-Variable Standard Investment Model with Deficit Variables, but no loanable funds modifier (1960–2010 data): I D = + .27(ACC) + .33TT − 33G T &I + .012POP − 4.95PR−2 (t=)

(2.6)

(6.4)

(2.8)

(−3.9)

(−2.5)

+ 6.68XRAV + 2.43 CAP−1 − .02 GDP (1.8)

(−0.2)

Adj.R = 85.9%

D.W. = 1.9

(3.5)

R = 89.0% 2

2

MSE = 29.87 (Eq. 11.4A)

Standard Investment Model with deficit variables Modified by Loanable Funds Variable (1960–2010 data): I D = + .22(ACC) + .18TT (m) − 06G T &I (m) + .007POP (t=)

(5.0)

(2.0)

(−0.7)

(2.1)

− 4.12PR−2 + 4.77XRAV + 1.51 CAP−1 − .05 GDP (2.4)

(−2.2)

R = 90.2% 2

D.W. = 2.0

(1.2)

MSE = 28.20

(−0.7)

(Eq. 11.10B)

Average effects for this model using the 6 sample periods cited above were: Unmodified deficit model Tax deficit coefficient

(t-statistic) = −.28 (2.1); R 2 /Adj.R 2 = 88.3%/85.2%

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

595

Spending deficit coefficient (t-stat.) = −.36 (5.0); (Table 11.11)

Modified deficit model Tax deficit coefficient

(t-statistic) = −.13 (1.7); R 2 /Adj.R 2 = 90.5%/88.5% Spending deficit coefficient (t-stat.) = −.12 (2.1) (Table 11.11)

30.5 Do Endogenous or Exogenous Increases in Loanable Funds Have the Most Success in Reducing Crowd Out? 30.5.1

Comparing Endogenous and Exogenous Loanable Funds Effects on Consumption—Initial Model

The model below illustrates the full model from which consumption results were obtained, but only for one sample period, 1960–2010. This initial model tests the two types of growth in loanable funds by including both as additional separate variables in the standard consumption and investment. Further below, an alternative model directly modifies the deficit variables by exogenous growth in loanable funds, while using a separate variable to control for any endogenous changes that may be occurring during the same period. Consumption (1960–2010 Sample Results; Full Standard One-Variable Deficit Model): CD (t=)

= .31(Y − TT ) + .19((T − G) + (S + FB) − (Tr + A)) (7.3)

(5.1)

+ .17((T − G) + (Tr + A)) − .37 (S + FB) − 4.84PR (3.8)

(−2.8)

(−2.0)

+ .43DJ−2 − .571.32 POP16/65 +.023POP (5.5)

+ 44.96 M2AV + .11 C B2 (5.7)

Adj.R 2 = 85.4%

(5.6)

(3.1)

(3.1)

R = 88.0%

D.W. = 2.0

2

MSE = 24.98

(Eq. 10.7)

The model was retested in 5 additional different, though overlapping, sample periods. The total 6 periods sampled were 1960–1980, 1990,

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J. J. HEIM

2000, 2007, 2008, and 2010. Results for the six periods, when averaged, were as follows: regression coefficient (t-statistic) = +.33 (4.0); R 2 /Adj.R 2 = 88.2%/83.8%. regression coefficient (t-statistic) = +.10 (1.2) (Table 10.5)

Endogenous LF variable: Exogenous LF variable:

Notice that on average, marginal effects on consumption of an exogenous increase (FR security purchases) are less than a third of the endogenous increase effect. R 2 is 6 percent higher than for the baseline model without any loanable funds variable. The 1960–2010 sample shown above showed higher than average effects for exogenous increases in loanable funds because of the unusually large increases occurring during the early QE years. Investment (1960–2010 Sample Results; Full Standard One-Variable Deficit Model): I D = + .23(ACC) + .11((TT − G T &I ) + (S + FB − Tr − A) ) (t=)

(7.1)

(6.4)

+ .14((TT − G T &I ) + ( Tr + A) ) (4.2)

+ .008POP − 3.20PR−2 + 7.78XRAV + 2.40 CAP−1 (5.8)

R = 90.7% 2

(−1.7)

Adj.R = 89.4% 2

(2.9)

D.W. = 1.8

(1.5)

MSE = 26.85 (Eq. 10.8)

For the same six periods tested earlier, we have the following average results: Endogenous LF variable: Exogenous LF variable:

regression coefficient (t-statistic) = +.20 (3.7); R 2 /Adj.R 2 = 90.5%/88.2%. regression coefficient (t-statistic) = +.04 (19) (Table 10.6)

For use as engineering coefficients, average results are generally better estimates of underlying effects than any single sample results’.

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

597

An increase in R 2 /Adj.R 2 of 2.7%/4.0% over the baseline model with no modifier. Notice an exogenous increase in LF has only 1/5 the positive effect on investment as an endogenous increase, and again, when the early QE years 2008–2010 are added to the sample, it strengthens significantly the estimated effect on investment of exogenous increases in loanable funds. Results for the Initial Model tested indicate endogenous growth in the pool has a much greater positive effect on both consumption and investment than does exogenous growth. 30.5.2

An Alternative Model Comparing Endogenous and Exogenous Effects

Results of the alternative model also generally showed the marginal impact of an increase in exogenous loanable funds to be greater than the marginal effect of an increase in endogenous loanable funds (Fed security purchases) for consumption; the exact opposite of our initial model average results. In the initial model tested immediately above, the standard consumption model had no modification of the deficit variables themselves, but did add two separate stand-alone variables to the model, endogenous and exogenous loanable funds. Below, we try a different approach: we evaluate the marginal impact of the deficit variable net of any offsetting same period increase in Fed security purchases, i.e., (T − G) + (Tr + A). We estimate that effect controlling for any changes in consumption resulting from a change in endogenous loanable funds. This is done by adding it as a separate control variable in the model. Results for the one-variable deficit model are as follows: C D = .22(Y − TT ) + .11(T − G)m + 16(S + FB − (Tr + A)) (t=)

(5.3)

(8.3)

(3.8)

− 5.26PR + .59DJ−2 − .546.98POP16/65 + .021POP (−2.2)

(6.3)

(−2.7)

+ 48.90M2AV + .09 C B2 (6.3)

R = 83.0% 2

MSE = 30.08 (14.2)

(2.5)

Adj.R = 78.8% 2

AR(1) used

D.W. = 2.0

(10.3)

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For this model, a dollar’s increase in endogenous loanable funds increases consumption spending by $0.16; an dollar’s increase in exogenous loanable funds by $0.11. The endogenous increase clearly has the larger marginal effect. In this sample, but average results for six samples shows just the opposite For the same six periods tested earlier, we have the following average consumption results: regression coefficient (t-statistic) = +.24 (3.0) (Table 14.1) regression coefficient (t-statistic) = −.03 (0.9)

Exogenous variable: Endogenous LF variable:

For the two variable deficit model, we have two tests of the same model, the two models are exactly the same except they use different (but Waldstrong and Sargan tested) instruments for the endogenous variables. We get different results because one instrument is a closer approximation of the variable being replaced than the other. The two variants yielded the following results: C D = .27(Y − TT ) + .27(TT )m + .20(G T &I )m (t=)

(3.0)

(3.0)

(1.5)

+ .10(ST + FB − (Tr + A)) − 6 .11PR + .42DJ−2 (−2.1)

(1.7)

(3.2)

− 295.42 POP16/65 + .01POP + 39.44 M2AV (1.4)

(−1.0)

+.08 C B2 (15.2)

D.W. = 2.2

R = 83.8% 2

(2.9)

Adj.R = 80.1% 2

MSE = 29.11

(2.0) The results indicate a one dollar increase in FR security purchases leads to a net $ + 0.07 change in consumption ($0.07 = + 0.27 – 0.20) marginal effects of the dollar increase in FR purchases on the modified taxes and spending variables. This is less than the $ + 0.10 change in consumption resulting from a one dollar increase in the endogenous part of the loanable funds pool. Six sample average results were as follows:

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

T + Exogenous variable:

599

regression coefficient (t-statistic) = +.28 (2.2) (Table 15.1) regression coefficient (t-statistic) = +.13 (0.6) regression coefficient (t-statistic) = −.03 (0.8)

G − Exogenous variable: Endogenous LF variable:

Average results indicate a net positive effect of $0.15 for a one dollar increase in FR security purchases, an essentially a zero average impact on consumption for an increase in endogenous loanable funds. Same model, tested on the same time period, but with different instrument reevaluated in Cptr 18: C D = .14(Y − TT ) + .13(TT ) + .01(G T &I ) (t=)

(2.6)

(1.7)

(0.1)

+ .12(ST + FB − Tr − A) − 4.89PR + .66DJ−2 (−1.8)

(2.6)

(4.4)

− 549.84POP16/65 + .023POP + 54.52 M2AV (4.9)

(−2.8)

+.15 C B2 (11.1)

R = 81.5% 2

(5.1)

Adj.R = 77.2% 2

D.W. = 2.5 MSE = 30.86 (4.1)

The results indicate a one dollar increase in FR security purchases leads to a net $ + 0.07 change in consumption ($0.12 = +0.13–0.01) marginal effects of the dollar increase in FR purchases on the modified taxes and spending variables. This is the same as the $ + 0.12 change in consumption resulting from a one dollar increase in the endogenous part of the loanable funds pool, so this sample indicated they have equal results. Six sample period averages were as follows: T + Exogenous variable: G-Exogenous variable: Endogenous LF variable:

regression coefficient (t-statistic) = +.20 (2.3) (Table 11.1) regression coefficient (t-statistic) = +.01 (1.1) regression coefficient (t-statistic) = +.05 (1.1)

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Average results indicate a net positive effect of $0.15 for a one dollar increase in FR security purchases, an essentially a zero average impact on consumption for an increase in endogenous loanable funds. Consumption conclusions: The initial and alternate models, both of which are reasonable models, tested produced contradictory results, so we must conclude that it is ambiguous whether increases in endogenous or exogenous loanable funds have a greater impact on consumption. The alternate model below illustrates the full one-variable deficit alternative model from which investment results were obtained, but only for one sample period, 1962–2009: I D = + .23(ACC) + .22(TT − G T &I )m (t=)

(5.1)

(5.1)

+ .18( (S + FB) − (Tr + A) ) + 2.47 CAP−1 (6.4)

(1.2)

− 2.34PR−2 + 8.30XRAV + .010POP − .04GDP (−1.1)

R = 89.4% 2

MSE = 28.66

(2.6)

Adj.R = 86.7% 2

(2.2)

(−0.8)

D.W. = 1.7 (Eq. 14.4)

For the same six periods tested earlier, we have the following average results: Exogenous variable: Endogenous LF variable:

regression coefficient (t-statistic) = +.16 (2.9) (Table 14.1) regression coefficient (t-statistic) = +.27 (4.8)

Clearly, for the six samples, the average effect of endogenous increases in loanable funds has a greater positive impact on investment than an exogenous increase in loanable funds. This is the same result obtained with the initial model tested in Sect. 5.1 above. For the two variable deficit model, we have two tests of the same model, the two models are the same except they use different (but Waldstrong and Sargan tested) instruments for the endogenous variables. We get different results because one instrument is a closer approximation of the variable being replaced than the other. The two variants yielded the following average results for the same 6-test periods as used in earlier endogenous/exogenous tests:

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

T + Exogenous variable:

601

regression coefficient (t-statistic) = +.13 (1.9) (Table 15.3) regression coefficient (t-statistic) = −.16 (1.3) regression coefficient (t-statistic) = +.29 (4.4)

G-Exogenous variable: Endogenous LF variable:

The net effect of a one dollar increase in exogenous loanable funds is + 13−(−.16*−1) = −.03, whereas the net increase resulting from a dollar growth in endogenous loanable funds is $ + 0.29. Clearly endogenous growth has the greater positive impact on investment. Same model, tested on the same time period, but using a different strong instrument, was reevaluated in Cptr 18: Sample Period: 1960–2010; I D = + .17(ACC) + .13Tm − .16G m + .26( (S + FB) − (Tr + A)) (t=)

(2.3)

(5.0)

(−1.9)

(6.3)

+ .005POP − 1.47PR−2 + 5.06XRAV + 2.02 CAP−1 (1.7)

R = 90.0% 2

(−0.7)

D.W. = 1.9

(2.6)

MSE = 27.97

(1.5)

(Eq. 18.4)

Six Sample Period Averages: T+Exogenous variable: G-Exogenous variable: Endogenous LF variable:

regression coefficient (t-statistic) = +.13 (2.3) (Table 18.3) regression coefficient (t-statistic) = −.15 (1.6) regression coefficient (t-statistic) = +.30 (5.5)

Average results are very similar to those obtained using the same model, but a different instrument, and again clearly indicate the net effect of a dollar increase in exogenous loanable funds (+.13−[1.15*−1]) = −.02, i.e., essentially zero, while a dollar increase in endogenous loanable funds yields a positive increase in investment of $0.30. Here again, endogenous increases in loanable funds seem to have a much larger and more positive impact on investment than do exogenous increases. Investment conclusion: The alternative investment model, like the original model, indicate clearly that endogenous growth in loanable

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J. J. HEIM

funds has a larger positive impact on investment than exogenous growth brought about by FR security purchases.

30.6 Do Increases in Loanable Funds Increase Consumer and Business Borrowing? Does Increased Business Borrowing Decrease Consumer Borrowing? (Results Taken from Heim 2021; Equation Numbers are from that Book) Effect off Increases in Loanable Funds on Consumer Borrowing: C B2 = .49(Y − TT ) + 68(TT ) − .70(G T &I ) − 21.79PR − 2.54 DJ−1 (t=)

(3.0)

(2.7)

(−4.8)

(−2.4)

(−4.1)

+ 20.25XRAV − .09 (PerSav0−9Tot + M2 − M10−3Tot ) (3.9)

(−1.7)

+.25 (S + FB) E (2.6)

R 2 = 70.7%

D.W. = 2.1 MSE = 88.85

(Eq. 22.4)

Effect off Increases in Loanable Funds on Business Borrowing: I B = .55(ACC+1 ) + .35(TT ) − .36(G T &I ) (t=)

(1.6)

(7.2)

(−3.4)

− 3.32CAP−1 − 1.57DJ−1 + 1.03 (S + FB) (−0.9)

R = 71.0% 2

(5.8)

(−3.7)

D.W. = 2.4

MSE = 103.88

(Eq. 22.1)

Results indicate A dollar increase in loanable funds increases borrowing by $0.25 and business borrowing by $1.03. Does Business Borrowing Affect Consumer Borrowing? C B2 = .49(Y − TT ) + 54(TT ) − .70(G T &I ) − 15.74PR − 1.86 DJ−1 (t=)

(2.9)

(2.4)

(−2.6)

(−2.3)

(−3.7)

+ 21.40XRAV − .09 (PerSav0−9Tot + M2 − M10−3Tot ) (5.1)

(−3.3)

+.57 (S + FB) E + .08 (Tr + A) X − .51 (IBOR−2 ) (5.5)

D.W. = 2.4

(0.3)

MSE = 77.97

(−5.0)

R 2 = 77.1% (Eq. 22.6)

30

SUMMARY OF ENGINEERING QUALITY EQUATIONS IN THIS BOOK

603

Results indicate a dollar increase in business borrowing is associated with a $0.51 decrease in consumer borrowing. This is consistent with other findings in this book that increases in loanable funds seem skewed toward reducing business crowd out, not consumer crowd out.

Index

A Academic/professional press, 559 Accommodative monetary policy, 4, 5, 7, 10, 13, 22, 25, 28, 29, 41, 42, 49, 65, 82, 83, 87, 88, 90, 93, 117, 120, 122, 126, 128, 151, 196, 200, 202, 203, 321, 322, 333, 345, 352, 397, 420, 442, 449, 450, 471, 558, 561, 563, 565, 567, 571 Accommodative monetary theory, 105, 557 underlying science, 34 B Bond market effects, 17, 21 Bond markets, 13, 86, 115 Business press, 6, 13–15, 21, 33, 34, 115, 559 C Commercial banks, 86 Consumption, 6–11, 23, 27–30, 33, 34, 36, 37, 42, 43, 45,

46, 48–51, 54, 57, 58, 60, 62, 63, 65, 66, 68, 69, 71–76, 82, 83, 87, 89, 90, 94–104, 116, 125, 137–148, 151–157, 159, 160, 166–172, 174, 175, 177, 179–184, 186, 188–191, 193, 195, 200, 201, 203–205, 207, 208, 211–215, 217, 218, 222, 224, 227, 230, 234, 236, 237, 239–242, 244–250, 252–254, 256–260, 262–268, 270, 273, 274, 276, 277, 281, 285–288, 291, 292, 294, 295, 303, 310–316, 324, 326–328, 330–332, 334, 336, 338–342, 345, 354, 355, 357–359, 362, 371, 373, 375–377, 379, 380, 383–385, 390, 392, 400, 403, 405, 407, 409–412, 421, 425, 426, 428, 431–433, 439, 440, 445, 447, 448, 453, 454, 457, 460, 462–464, 471, 475, 479, 480, 482–484, 486–491, 493, 495–498, 500, 503, 513, 514,

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 J. J. Heim, Why Fiscal Stimulus Programs Fail, Volume 2, https://doi.org/10.1007/978-3-030-64727-8

605

606

INDEX

517–523, 525, 527, 529, 530, 533, 535, 536, 538, 539, 542, 547, 552, 559, 565, 568–572, 577, 578, 585–587, 595–600 crowd out effects, 6, 7, 42, 49, 51, 57, 62, 65, 66, 71, 75, 82, 89, 95, 96, 99–101, 103, 125, 137, 140–142, 144–147, 152–154, 156, 157, 159, 160, 185–188, 191, 193, 195, 199–201, 204, 205, 208, 211–213, 215, 217–220, 222, 224, 230, 231, 235, 237, 240, 242, 245, 246, 249, 258, 259, 262, 264, 266, 267, 273, 274, 277, 281, 286, 287, 292–295, 311, 313, 316, 324, 327, 328, 331, 335, 336, 338–343, 345, 355, 357, 362, 371, 377, 380, 392, 408, 412, 421, 433, 440, 445, 453, 463, 475, 489, 495, 517, 518, 522, 523 loanable funds effects, 43, 97, 99, 100, 153, 212, 277, 294, 339, 340, 377, 552, 559 M1 effects, 6, 29, 70, 285, 287, 288, 291, 292, 294, 312, 565 Cowles methodology, 34 Crowd in, 7, 56–59, 61, 63, 65, 67, 72, 102, 103, 147, 148, 156, 160, 184, 193, 195, 201, 204, 206, 208, 209, 216, 218, 224, 237, 239–243, 245–252, 254, 255, 264, 276, 277, 279, 280, 294, 311, 313, 314, 316, 342, 345, 353, 355, 391, 393, 400, 407, 411, 412, 432, 445, 446, 460, 482, 483, 514, 516, 523, 524, 551, 552, 561, 567 Crowd out, 4–12, 28, 29, 41–45, 49–52, 54–58, 60–63, 65–67, 69–77, 81–83, 88–105, 110,

116, 121, 122, 124–126, 128, 137–142, 144–148, 151–161, 163–177, 179–184, 186, 188, 189, 191, 193, 195, 196, 198–206, 208–218, 222, 224, 230, 234, 236–262, 264–268, 270, 273, 274, 276, 277, 280, 281, 285–288, 291, 292, 294, 295, 297, 298, 302–306, 308– 313, 315–317, 321–334, 336, 338, 339, 341, 342, 345, 346, 349–352, 354, 355, 357–360, 362, 364, 368–372, 375–380, 383–387, 390, 392, 394, 398, 400, 403–407, 409–412, 416, 418, 419, 421–423, 426–428, 431–433, 436, 439–443, 445– 450, 453–457, 460, 462, 463, 465, 466, 470–473, 475, 477, 479–487, 489, 490, 493, 495, 497, 498, 500, 501, 503–505, 507, 508, 510, 512, 513, 515, 517–519, 521–525, 527, 529– 533, 535, 536, 538, 539, 541, 542, 545–547, 549–553, 557, 559–561, 563–566, 569–574, 577, 579, 586, 587, 591, 593, 603 Crowd out modifiers, 45, 74, 334 loanable funds, 8 M1, 566 Crowd out theory, 66, 89, 141, 148, 328, 333 mathematical exposition, 81 money multiplier exposition, 52, 288 underlying science, 34 Currency in circulation, 117 D Data, 7, 20–22, 27, 30–33, 35, 36, 45, 46, 49, 51, 53, 55, 56, 59,

INDEX

60, 62–64, 66–72, 74, 92, 96, 100, 102, 103, 112, 114, 121, 124, 128, 139, 141, 147, 152, 154, 158, 159, 166, 168, 169, 173, 174, 176, 180–182, 184, 186, 189–191, 193, 196, 198, 201, 207, 210, 215–218, 222, 230, 239, 241–243, 245–256, 260–263, 265, 277, 286, 295–298, 306, 313, 316, 323, 324, 327, 332, 337, 340–342, 345, 346, 349, 351, 359, 362, 367, 368, 375, 377, 384, 386, 387, 390, 396, 406, 407, 411, 412, 414, 418–420, 423, 425, 426, 432, 433, 436, 440, 442, 449, 454, 463–466, 470, 471, 473, 475, 480, 482–487, 489–491, 494, 496, 499, 500, 502–512, 531, 532, 535, 539, 541, 559, 567, 569, 570, 585, 587, 590–594 insufficient sample size, 52, 72, 560 lack of variation, 52, 67, 559 multicollinearity, 169, 174, 215, 217 spurious results, 52, 560 Deficit modifiers, 8, 9, 52, 72, 172, 190, 204, 205, 207, 208, 210, 257, 262, 267, 277, 280, 287, 297, 309–311, 313, 314, 316, 317, 337, 344, 346, 348, 353– 355, 369, 371, 373, 386, 388, 389, 391, 392, 394, 420–422, 431, 439, 441, 445–447, 453, 455, 458–460, 462, 463, 471, 472, 475, 477, 479, 493, 503, 517, 529, 533, 536, 538–540, 546, 549, 552, 553, 568, 573, 589, 593 Deficits, 4, 5, 7, 8, 12, 34, 41–44, 50, 51, 57–63, 66, 73–77, 81–83,

607

88, 90, 92–94, 98, 100–105, 110, 121–125, 128, 138–144, 146–148, 151, 154, 155, 159, 160, 163–165, 167–169, 172–175, 177, 179, 181, 184, 186, 188, 191, 193, 196, 198, 200, 202, 204–206, 208, 214–216, 218, 222, 230, 234, 237, 239–242, 244–247, 249, 250, 252–254, 258, 261, 262, 264–266, 268, 270, 273, 274, 276, 277, 280, 281, 294, 302, 303, 305, 308, 310–313, 315, 317, 321, 324, 325, 327–329, 331, 334, 338, 345, 346, 350, 354, 355, 357, 369, 371–373, 375, 380, 383–387, 390, 392, 394, 396–399, 403–405, 407, 410, 411, 420–422, 426, 427, 433, 439, 440, 442, 445, 447, 449, 460, 462, 463, 471, 473, 475, 477, 480, 482, 485, 487, 489–491, 493, 495, 497, 501, 503, 516, 517, 521–524, 529, 535, 536, 539, 546, 547, 550, 552, 553, 557, 558, 560, 561, 563, 565, 567, 570, 571, 579, 587, 591 spending, 62, 63, 73, 76, 82, 90, 94, 96, 100, 102, 139, 147, 167, 170, 173, 175, 211, 224, 230, 234, 237, 241, 245, 248, 259, 261, 264–267, 273, 276, 291, 292, 294, 295, 302, 303, 305, 306, 308–310, 312, 324, 327–329, 331, 332, 334, 346, 359, 362, 364, 369, 370, 386, 405, 407, 410–412, 419, 432, 439–442, 457, 460, 462, 463, 470–473, 485, 487, 489, 490, 493, 495, 497, 501, 503, 508, 516, 519, 529, 535, 538,

608

INDEX

539, 545–547, 549, 550, 561, 588–590 tax cut, 66, 90, 94, 95, 98, 139, 144, 147, 170, 173, 230, 234, 237, 238, 245, 248, 254, 259, 265–267, 274, 276, 291, 295, 302–306, 308, 309, 327, 331, 359, 362, 405, 407, 409–411, 440, 441, 457, 460, 462, 463, 470–472, 535, 539, 545, 546, 549, 587–591 DSGE methodology, 35 DSGE models, 36, 189 E Endogeneity, 7, 35, 43, 45–47, 145, 152, 181, 215, 217, 218, 258, 261, 287, 292, 297, 304, 330, 364, 414, 428, 431, 434, 454, 462, 465, 470, 472, 484, 489, 491, 493, 498, 502, 503, 506, 508, 511, 530, 536, 540, 546, 559, 567 Endogenous loanable funds, 9, 11, 77, 207, 295, 340–342, 349–351, 354, 355, 362, 368–372, 407, 427, 428, 431, 436, 439–441, 445, 447, 457, 462, 471–473, 475, 477, 479, 483, 497, 511, 520–524, 535, 536, 538, 539, 541, 542, 545, 546, 549, 550, 553, 570, 573, 577, 597–601 Excess reserves, 18, 57, 61, 73, 76, 82, 84, 86, 91, 92, 96, 120–122, 124, 126–128, 140, 321, 323, 399, 420, 564 Exogenous loanable funds, 9, 207, 208, 210, 338, 351, 369, 439, 479, 483, 521, 535, 547, 569, 573, 595, 597, 598, 600, 601 Explained variance (R2 ), 48, 153, 159, 181, 191, 215, 217, 262,

270, 276, 292, 309, 354, 369, 390, 421, 431, 440, 532, 533, 535, 550, 566 adjusted (Adj. R2 ), 42, 184, 186, 193, 198–200, 202, 204, 236, 258, 266, 270, 288, 306, 390, 409, 418, 431, 432, 498, 515, 521, 535, 536, 542, 549

F Failures of accommodating monetary policy, 117, 120, 126, 450, 565 Federal Reserve, 4, 5, 7, 11, 12, 15, 16, 19, 22, 25–28, 30–33, 41, 44, 45, 51, 52, 57, 82–84, 88, 109–112, 114, 116, 123, 126–128, 141, 164, 321, 385, 449, 558, 577–579 Federal Reserve security purchases, 5–8, 11, 12, 14, 15, 34, 44, 51, 76, 81, 85, 116, 119, 123, 124, 147, 209, 322, 326, 327, 330, 336, 341, 346, 349, 369, 370, 376, 380, 384, 387, 390, 394, 395, 399, 409, 412, 419, 420, 426, 428, 434, 441, 442, 470, 471, 502, 504, 506–509, 511, 514, 522, 551, 558, 559, 563, 571, 573, 577, 578, 598–600, 602 effect on bond markets, 17, 21 effect on stock markets, 14, 16 Fiscal stimulus, 3–6, 10, 12, 29, 81, 89, 92, 116, 117, 124–126, 139, 142, 143, 151, 253, 266, 281, 321–323, 383, 394, 397, 449, 557, 558, 577, 579 Foreign banks, 5–7, 12, 117, 119, 120, 342, 345, 352, 371, 383, 400, 480, 529, 558, 579 Foreign dealers, 562

INDEX

G GDP effects, 17, 23 H Hausman test, 180, 215, 287, 339, 377, 428, 454, 530 I Inequality, 13, 15, 18, 33, 34 Inequality effects, 18 Instruments, 27, 46–48, 111, 141, 169, 181, 190, 203, 258, 261, 292, 306, 330, 341, 346, 349, 362, 364, 407, 408, 416, 425, 428, 431, 432, 454, 472, 484, 487, 489, 496, 498, 502, 504, 506, 509, 511, 532, 536, 542, 545, 546, 559, 567, 598, 600, 601 Investment, 5, 6, 8–12, 18–20, 22, 25, 27–31, 34, 36, 37, 42, 43, 45, 46, 49–51, 54, 57, 58, 62, 63, 73, 75, 76, 82–84, 86, 87, 89–91, 94–96, 100–104, 109, 112, 116, 125, 137–147, 151–153, 158–160, 164, 166, 168, 172–177, 183, 189, 191, 193, 195, 197, 198, 201–204, 206, 207, 209–211, 215, 224, 227, 230, 234, 236, 253, 256, 260–262, 264–268, 270, 273, 274, 280, 281, 285, 287, 296, 302–306, 308–311, 315, 317, 323, 327, 330, 345, 350, 351, 355, 357, 358, 364, 369, 372, 373, 375–377, 385–387, 390, 394, 400, 403, 404, 419, 420, 422, 433, 434, 436, 439–442, 447, 453, 454, 464, 471–473, 477, 479, 480, 482, 483, 498, 499, 501, 503, 505–508, 510,

609

512–515, 517, 519–525, 527, 529, 530, 542, 547, 549–551, 553, 559, 563, 565, 566, 568–572, 577–579, 585–587, 590, 595, 597, 600–602 crowd out effects, 6, 7, 12, 42, 49, 50, 57, 76, 94, 96, 102, 140–142, 152, 160, 168, 172, 174, 175, 193, 198, 203, 206, 209, 211, 230, 234, 260, 264–267, 273, 280, 303, 305, 308, 327, 346, 351, 355, 357, 371–373, 376, 377, 386, 387, 390, 394, 422, 440–442, 447, 453, 477, 482, 501, 505, 508, 510, 515, 522, 524, 547, 549, 579 loanable funds effects, 43, 100, 501, 559 M1 effects, 6, 29, 85, 285, 302–304, 306, 308–310, 317, 565, 590 Investment banks, 5, 7, 11, 12, 83–85, 87, 111, 112, 115–117, 342, 352, 371, 380, 400, 529, 558, 562, 578 K Keynesian, 4, 29, 30, 50, 73, 117, 128, 138, 139, 141, 151, 156, 157, 200, 202, 323, 397, 410 Keynes, John Maynard, 3, 4, 322, 397, 557 L Loanable funds endogenous, 5, 9–11, 42, 52, 65, 75, 77, 92, 94, 116, 147, 161, 164, 181, 195, 199–202, 207, 208, 210, 285, 295, 327, 330, 340–342, 349–351, 354, 355,

610

INDEX

358, 362, 364, 368–372, 407, 427, 428, 431, 436, 439–441, 445, 447, 457, 462, 471–473, 475, 477, 479, 483, 497, 511, 520–524, 535, 536, 538, 539, 541, 542, 545, 546, 549, 550, 553, 570, 573, 577, 597–601 exogenous, 9, 207, 208, 210, 338, 351, 369, 439, 479, 483, 521, 535, 547, 569, 573, 595, 597, 598, 600, 601 total, 6, 8–11, 44, 51, 75, 146, 147, 152, 175, 179, 180, 182, 183, 198–201, 204–208, 210, 254, 266, 270, 285, 288, 291, 292, 294, 302–304, 306, 308–310, 312, 315, 317, 325–328, 330, 332, 334, 336, 346, 350, 354, 355, 358, 364, 372, 375–377, 379, 383, 384, 386, 390, 392, 394, 398, 404, 405, 411, 412, 414, 419, 421, 422, 426, 431, 445–447, 453, 455, 460, 462, 463, 470–473, 475, 477, 479, 480, 483, 484, 486–489, 491–493, 495, 497, 498, 503, 505–508, 510, 512, 513, 515–517, 519–523, 525, 529–533, 535, 536, 538, 539, 542, 545, 546, 549–553, 564–566, 568–573, 577, 578, 590 M M1, 6–8, 11, 28, 29, 54, 68, 70, 76, 77, 85, 88, 126, 128, 285, 288, 291, 292, 294, 295, 302–304, 309, 317, 566, 571, 574, 578 effects on crowd out, 6–8, 11, 29, 54, 285, 295 Methodological issues GDP deflator, 53

general, 44 other, 50 Modeling Crowd Out Effects, 96 Monetary policy, 5, 13–15, 17–20, 22, 23, 25–31, 33–35, 37, 82, 89, 91, 92, 94, 109, 111, 124, 126, 128, 164, 322, 323, 383, 394, 396, 397 Money multiplier, 52, 85, 92, 111, 288

O Ordinary Least Squares (OLS), 46, 48, 169, 174, 181, 217, 236, 243, 258, 292, 412, 431, 462, 485, 536, 541, 545, 546, 553

P Primary dealers, 84, 109–111, 114, 116, 117, 562 Pushing on a string, 14, 92, 94, 120, 124, 128, 243, 420, 450, 563, 564

Q Quantitative Easing (QE), 5, 6, 10, 13–23, 25, 27, 29, 32–34, 57, 66, 75, 85, 91, 92, 96, 112, 114, 115, 117, 120, 141, 161, 200–203, 208–210, 243, 244, 246, 305, 330, 351, 380, 383, 396, 397, 419, 420, 423, 432, 439, 449, 450, 456, 463, 472, 473, 477, 488, 489, 512, 513, 515, 525, 527, 547, 550, 558, 559, 565, 569–571, 577, 596, 597

INDEX

R Reconciling, differences, sign and significance levels, 54, 244 Regression coefficient, 10, 49, 55–58, 60, 63, 66, 69, 153, 156, 157, 160, 166, 172, 241, 242, 247, 248, 254, 294, 350, 396, 398, 411, 439, 481–483, 521, 588–590, 592, 594, 596, 598–601 Replication, 6, 50, 138, 375, 428 Replication of results, 6, 50, 138, 375, 428

S Sargan test, 169, 203, 258, 261, 292, 346, 364, 416, 425, 428, 432, 454, 472, 484, 487, 489, 498, 502, 504, 506, 509, 511, 532, 536, 546, 598, 600 Savings banks, 5–7, 12, 83, 84, 110–112, 114–116, 322, 558, 562, 578 Stationarity, 7, 43, 45, 47, 145, 152, 169, 174, 180, 215, 217, 218, 258, 287, 292, 306, 330, 362, 364, 407, 416, 428, 431, 454, 462, 484, 491, 493, 496, 498, 502, 503, 506, 508, 511, 530, 532, 536, 545, 559 Stimulus, 3, 4, 12, 15, 28–30, 34, 50, 73, 81, 82, 89, 90, 92–94, 104, 112, 114, 122, 124, 138–142, 151, 156, 157, 163, 164, 245, 281, 316, 322, 327, 404, 410, 513, 557, 579 Stock market effects, 14

611

Stock markets, 6, 33, 559 Structural models, 4, 6, 34, 36, 74, 143, 166, 587, 589 T T-statistic, 10, 43, 51, 54, 59, 66, 67, 69, 71, 72, 74, 140, 160, 169, 183, 193, 198, 200, 202, 222, 224, 225, 236, 238, 241, 245, 246, 256, 257, 260, 263, 302, 304, 310, 311, 315, 328, 332, 334, 335, 341, 345, 349, 369, 379, 380, 387, 400, 407, 411, 485, 486, 488, 491, 492, 494, 496, 499, 502, 504–509, 511, 513, 519, 521, 522, 542, 569, 585, 587–590, 592–596, 598–601 Two Stage Least Squares (2SLS), 4, 28, 29, 46, 48, 139, 141, 169, 181, 190, 196, 261, 340, 349, 408, 553 V VAR methodology, 35 VAR models, 36, 37 W Wald test, 46, 47, 169, 203, 258, 261, 292, 306, 330, 346, 362, 364, 407, 408, 416, 425, 428, 431, 432, 454, 472, 484, 487, 489, 496, 498, 502, 504, 506, 509, 511, 532, 536, 542, 545, 546, 553, 559, 567, 598, 600 Watson, Durbin, 49, 255, 408