Wage-Price-Productivity Nexus [Reprint 2016 ed.] 9781512800401

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The Wage-Price-Productivity Nexus

The Wage-PriceProductivity Nexus By Ronald G. Bodkin

Philadelphia

University of Pennsylvania Press

(g) 1966 by the Trustees of the University of Pennsylvania Published in Great Britain, India, and Pakistan by the Oxford University Press London, Bombay, and Karachi

Library of Congress Catalog Card Number: 64-24502

7470 Printed in the United States of America

To the Memory of JOHN FITZGERALD KENNEDY

Prefacc

In this work I have attempted to analyze the wage and price structure of an important segment of the American economy. A strong motivating force has been a concern with basic economic goals; the compatibility or incompatibility of the goals of full employment and price level stability is, in my view, a fundamental issue. Although problems of structure occupy most of the discussion, the question of what a free community can do to defend itself against inflation is discussed, albeit briefly. T w o important related issues are not discussed, so it is perhaps well to call attention to them at this point. W h e n policy issues are discussed, it is assumed that inflation is undesirable. Even if one were completely agnostic about distributional

effects, he

would have to admit that inflation aggravates balance of payments difficulties, a problem facing the American economy at the present time. Furthermore, there is some presumption that inflation tends to induce less than maximum production, for any given level of resource utilization, through making rational calculation of future conditions more difficult and through encouraging speculative activities. T h i s effect will depend on the

degree

of inflation and is likely to be quite small, if not negligible, for the "creeping inflation" of post-war experience. A second issue is the reliability of the statistical materials used. In general, as a data-user, I have been content to accept passively the output of data-producers. Even when duly warned that data 7

8

The

Wage-Price-Productivity

Nexus

may contain imperfections, I have taken the view that half a loaf is better than none. If theoretical relationships shine through imperfect data, this seems, in my view, to testify to the strength of these relationships. Some have argued that price indices are virtually worthless, because of well-known shortcomings. For instance, it has been argued that all or nearly all of the apparent rises in prices since 1950 are fictitious and would disappear if quality changes were properly taken into account. I cannot subscribe to this view. As my reservations are indicated in an earlier piece of work (Lawrence R. Klein, senior author, "Empirical Aspects of the Trade-offs among Three Goals: High Level Employment, Price Stability, and Economic Growth," Research Study Seven in Inflation, Growth, and Employment—a forthcoming volume of research studies prepared for the Commission on Money and Credit), I shall not repeat this earlier discussion. This book is a revision of my doctoral dissertation, which was accepted by the economics department of the University of Pennsylvania in the fall of 1962. The dissertation, which had the same title as this work, was also circulated privately as Cowles Foundation Discussion Paper 147. Chapters V, VI, and VIII are the ones which have undergone major reworking, but some substantive changes have been made in every chapter. In addition, I have taken advantage of the rewriting to correct as many typographical mistakes as I could, to make some stylistic improvements, and to refer to some additional researches of other writers. Some of these new references are works that I overlooked in the previous version, while others have appeared (in print or in preliminary form) since that earlier date. It is a pleasure to express my thanks to those who have contributed so much to the preparation of this book. T h e generous and sympathetic support I have received has enabled me to carry this work through to completion. It is literally true that without this aid, this work could not have been started, much less finished.

9

Preface

Lawrence R . Klein served as dissertation supervisor; my debt to him is enormous. T h e references in the text to his published works are only a small measure of his contribution to my thinking. Professor Klein was most generous with his time, his ideas, and his data. His kindnesses and his firm but gentle guidance will be forever remembered by this student of his. Paul Davidson, Miles Fleming, Robert Summers, and Sidney Weintraub served as the examining committee for this work when it was in final form as a dissertation. Every member of this committee made a number of helpful suggestions, which I drew upon in the rewriting process. In addition, Paul Davidson had made some stimulating comments at an earlier stage of my work. A m o n g my former teachers, William H . Brown, of Swarthmore College, Irwin Friend, and Sidney Weintraub must be named. A student always owes much to those who have taught him previously, and this is no less true for me personally. R . James Ball is the co-author of Chapter II, which was first, written during the summer of 1960 when we were both at the University of Pennsylvania. His stimulus to my thinking on these subjects has been much appreciated. W e have also benefited from the comments of Frank

Brechling, George Green,

Franklyn

Holzman, and Sidney Weintraub on earlier drafts of this chapter. Chapter II will also appear as a separate article in mica

Metroecono-

(Volume X V , No. 2 ) , and we gratefully acknowledge the

kindness of the editor-in-chief, Manlio Resta, in permitting us to republish this article. T h e opportunity provided by the reprinting allowed us to make some minor modifications in the text of Chapter II. In the course of working on the dissertation, the author received generous

financial

support. T h e Samuel S. Fels Fund

provided a dissertation fellowship during the 1960-1961 academic year. I was also the recipient of a Wharton School supplementary grant during that period. During the summer of 1961, the

The

10

Wage-Price-Productivity

Nexus

N a t i o n a l S c i e n c e Foundation provided a s u m m e r fellowship for a g r a d u a t e t e a c h i n g assistant. T h i s dissertation g r e w out o f an earlier

study

prepared

for

the

Commission

on

Money

and

Credit, d u r i n g the s u m m e r of 1960, which led to the published w o r k cited above. In connection with that paper, the

helpful

c o m m e n t s and assistance of Joseph W . C o n a r d , w h o represented t h e C o m m i s s i o n , and M o t o o Abe, w h o worked with Professor K l e i n a n d m e , m u s t be acknowledged. T h e dissertation was finished and the manuscript was revised d u r i n g the past eighteen months, while the author was a m e m b e r of the research staff of the Cowles F o u n d a t i o n . In addition, the C o w l e s F o u n d a t i o n provided a stimulating atmosphere in w h i c h to rework the earlier draft. T w o m e m b e r s of the staff were particularly helpful. A r t h u r M . O k u n read the entire manuscript, in its earlier f o r m , and made several valuable c o m m e n t s .

James

T o b i n offered a n u m b e r of helpful suggestions. T h e c o m p u t a t i o n s in this book were largely done on electronic c o m p u t e r s . A debt of thanks is due the University o f Pennsylvania C o m p u t e r Center, where the bulk of this w o r k was done. It would be tedious to n a m e the entire staff, but the k i n d efforts o f J a m e s G u e r t i n ( t h e director), D a v i d M a c G o n a g l e

(program-

m e r ) , W i l l i a m Castro, and Dolores M o n z o must be m e n t i o n e d . David

MacGonagle's

help was invaluable,

and

without

it

I

would still be g r i n d i n g out the statistical results. T h e t w o stage least squares calculations and the computations for the revisions were done at the Y a l e C o m p u t e r C e n t e r . James W .

Friedman

served as p r o g r a m m e r and G e o r g e Sadowsky as general adviser for these computations. W i l l i a m G . B o w e n also read the entire manuscript liminary

form.

Professor

Bowen's

comments

were

in pre-

extremely

valuable, a n d I had many occasions to consult them d u r i n g t h e course of m y rewriting. T h e helpful c o m m e n t s of Joel

Popkin

a n d of the publisher's anonymous referee are gratefully a c k n o w l edged.

11

Preface

D a t a sources are indicated in the text. However, my debt is so great in several cases that an explicit acknowledgment at this point seems in order. Albert Rees's careful

reconstruction

money wages in manufacturing over this past century

of

proved

invaluable in this study. John W . Kendrick's work on production and productivity figures were made available months in advance of

publication.

Professor

Kendrick's

assistant

in

his

labors,

M a u d e R. Pech, was most helpful in extending the published series up to 1957 (and, in one case, up to 1959). Stanley Lebergott's revised figures of unemployment since 1900 were made available to me far in advance of publication. Assistance with data used in Professor Klein's quarterly model of the American economy, which is described in his recent paper, " A Quarterly

Model:

Description

and

Applications"

Postwar (National

Bureau of Economic Research, mimeographed), was provided by Kanta Marwah, Professor Klein's research assistant. Finally, some series and the results of several

unpublished

statistical

series were made available to me from the files of the National Bureau of Economic Research. For these kindnesses, my thanks go out to Geoffrey Moore (the director), T h o r Hultgren, and Jane Kennedy. T h e bulk of the typing was done by A m a n d a Slowen of the Cowles Foundation. Mrs. Slowen's suggestions format of preliminary

versions of this work

regarding were

the

especially

valuable. At various times, Gladys Decker and Lydia Kovi also typed parts of the manuscript. T h e full page charts were drawn by Rose Gallagher. T h e responsibility for any errors of f o r m or content which may have survived the excellent aid which I have received remains, of course, my own. T h i s is particularly true with regard to the many substantive comments given me, as I have not taken all of these helpful suggestions. But the reader is better off because of those suggestions which I did accept. I owe a debt of gratitude to my wife, Susann R . Bodkin. H e r aid goes far beyond the proofreading and checking labors to

12

The Wage-Price-Productivity Nexus

which I have subjected her. W o r d s are forever inadequate to express thanks, and this is especially true in her case. W i t h o u t her enthusiasm and w a r m support, this work could not have been completed. N o t the least of her staunch encouragement was her ready assent to the idea of changing the dedication page of this book, so that we two might honor, in some small way, one of this nation's greatest presidents.

December, 1963

Contents Preface

7

CHAPTER

I.

INTRODUCTION

AND P R E V I O U S RESEARCHES

23

1. Wage A d j u s t m e n t Relationships 2. Relationships between the Price Level a n d the Level of Costs 3. F u r t h e r R e m a r k s

C H A P T E R II.

I N C O M E , T H E P R I C E L E V E L , AND G E N E R A L I Z E D

P L I E R S IN KEYNESIAN E C O N O M I C S

E M P I R I C A L RELATIONSHIPS BETWEEN WAGE CHANGES, 95

1. Some Preliminary Results 2. T h e Possible Lag of W a g e Changes b e h i n d Price Level Changes 3. Preliminary Estimates of U n e m p l o y m e n t Levels "Req u i r e d " for Price Level Stability Appendix A Appendix Β

IV.

A

FURTHER

EXAMINATION

OK

THE

WAGE

97 107 113 121 123

ADJUST-

MENT EQUATION

1. 2. 3. 4.

63

65 71 82 89

U N E M P L O Y M E N T , AND P R I C E LEVEL C H A N G E S

CHAPTER

46 61

MULTI-

(R. J . B A L L , C O - A U T H O R )

1. A Static Model 2. Generalized M u l t i p l i e r Analysis 3. A G r a p h i c R e p r e s e n t a t i o n Appendix

C H A P T E R III.

25

T h e Possible Role of Profits T h e Possible Role of Changes in U n e m p l o y m e n t T h e Possible Role of Productivity Changes T h e Question of Irreversibility Appendix A Appendix Β

1 28

128 140 143 151 156 160

CHAPTER

V. T H E

INFLUENCE

OF

COSTS AND O T H E R

F A C T O R S ON

P R I C E LEVELS

1. 2. 3. 4. 5. 6.

'

Some Preliminary Price Level Relationships T h e Role of Raw Materials Prices An Examination of T w o "Abnormal" Periods T h e Role of T w o Proxies for Excess Demand T h e Question of Irreversibility Further Discussion Appendix A Appendix Β

163 169 172 174 177 185 196 200

C H A P T E R VI. T I M E P A T T E R N S O F T H E AVERAGE P R O D U C T O F LABOR AND S O M E F U L L SYSTEM P A R A M E T E R E S T I M A T E S

1. 2. 3. 4.

201

T w o Empirical Equations of Productivity Growth T h e Influence of the Degree of Labor Force Utilization Further Discussion of the Productivity Relationships Estimates of the Parameters of the Wage, Price, and Productivity Equations by the Method of T w o Stage Least Squares

205 206 212

Appendix Appendix Appendix Appendix

224 226 227 228

CHAPTER

A Β C D

VII. S O M E

LIMITATIONS

OF

AGGREGATIVE

ANALYSES

216

OF

WAGES AND P R I C E S

1. Bent Hansen's Λ Study in the Theory of Inflation 2. Interaction of Competitive Agriculture and NonCompetitive Industry: T h e Explanations of Duesenberry and Ackley 3. Charles L. Schultze's "Recent Inflation in the United States" 4. Structural Pressures on the General Price Level: T h e Discussions of Bowen, Moulton, and T h o r p and Quandt 5. Sectoral Analyses of Wages and Price: T h r e e Joint Economic Committee Studies 6. Richard G. Lipsey's " T h e Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom 1862-1957: A Further Analysis": T h e Functioning of the Individual Labor Markets 7. Summary and Implications for Research and Policy

230

232

238 241

249 253

259 268

C H A P T E R VIII.

CONCLUDING R E F L E C T I O N S

1. A F u r t h e r E x a m i n a t i o n of the Trade-Off between Une m p l o y m e n t a n d Inflation 2. Some Conclusions

274

274 281

Bibliography

285

Index

297

Tables, Graphs, and Charts

Figure 1. Functions

The

Aggregate

Supply

and

Aggregate

Demand 87

Figure 2. T i m e Diagram of the Money Wage Change ( i m ) , the Consumer Price Level C h a n g e (ΔΡ) . a n d U n e m p l o y m e n t (U) , U.S.A., 1900-1957 101 Figure 3. Gross Scatter Diagram of Money Wage { \ w t ) ancl U n e m p l o y m e n t ( U t ) , U.S.A., 1900-1957

Changes 103

Figure 4. Gross Scatter Diagram of Money Wage Changes ( \ w ) and Consumer Price Level Changes (ΔΡ) , U.S.A., 19001957

106

T a b l e I. Summary of the National Bureau's T i m i n g Measures, Cost of Living Index and Average Hourly Earnings of 25 M a n u facturing Industries, U.S.A., 1922-1939 108 T a b l e II. Correlation Coefficients (r) for and Price Level Changes, U.S.A., 1947-1958 T a b l e III. Correlation Coefficients for Wage Price Level Changes, U.S.A., 1921-1940 T a b i c IV.

Level 1957

Average Hourly Earnings

(Ρ) , and

Wage

Changes 110

Changes

(w) , t h e C o n s u m e r

Residuals of Equation

(3.4) , U.S.A.,

and 111 Pricc

1898123

T a b l e V. Quarterly Values of the Average Wage at an A n n u a l R a t e (w) and of the Implicit Deflator of Personal C o n s u m p t i o n E x p e n d i t u r e s (Ρ) , U.S.A., 1945-1958 126 Figure 5. T i m e Diagram of the Money Wage Change (Δ 1 "), the R a t i o of T o t a l Corporate Profits to Corporate Net W o r t h

m« (A-4),

i n d Changes of the Average Productivity of

Labor

U.S.A., 1900-1957

T a b l e VI. T o t a l C o r p o r a t e Profits ( Π Γ ) , Corporate N e t W o r t h ( N W T ) , M a n u f a c t u r i n g C o r p o r a t e Profits ( I l j f ) . M a n u -

133

facturing Employees U.S.A., 1898-1959

( N u ) , and Average Productivity

(A),

156

Figure 6. T i m e Diagram of the Wholesale Price Index for Finished Goods (P>) , Average Hourly Compensation in Manufacturing (u>), Manufacturing Output per Man-Hour (Am), and Manufacturing Wage Costs Figure 7.

U.S.A., 1913-1957

165

Scatter Diagram of the Wholesale Price Index of

Finished Goods

(ΡΓ)

and Manufacturing Wage Cost ( — J, \Am) with T w o Fitted Relationships, U.S.A., 1913-1957 167 Figure 8. T i m e Diagram of the Wholesale Price Index of Finished Goods (P0 is

taken as e x o g e n o u s ; it is f u r t h e r assumed that the e n d o g e n o u s c o m p o n e n t of the w a g e d e t e r m i n a t i o n m e c h a n i s m

G(N,

P)

is

i n d e p e n d e n t of the exogenous c o m p o n e n t . T h u s w e m a y w r i t e : (2.6a)

w = g(N,

where g(N,

P) +

P) sS 0 so that w ^ w0.

wo, It is f u r t h e r assumed that

the " w i t h i n - s y s t e m " response of a c h a n g e in m o n e y wages to a change

in the price level is less than

proportionate,

when

under-employment conditions exist. I n symbols, w e w o u l d have 0


, and

E q u a t i o n - c o u n t i n g conditions are thus satisfied. O u r variables are Μ, general

Π, a, and w0.

P).

exogenous

W e shall assume that

certain

conditions are satisfied, so that a u n i q u e solution

of

economically meaningful variable values exists, and so we are ready to discuss the response of the system exogenous

parameters.

We

may

call

this

to shifts in

type

of

the

discussion

" g e n e r a l i z e d multiplier analysis."

2 . GENERALIZED M U L T I P L I E R

For

convenience,

the

system

of

ANALYSIS

seven

equations

in

seven

u n k n o w n s is reduced to one of three equations in three

un-

k n o w n s . W e have, after some manipulation, (2.8)

f(N)

-C^f(N),

(2.9) (2.10)

,'

n l - I {,, f(N),

(1 -

„

χ") = Μ

L(Pf(N), Pf (Ν)

Π} =

Π) -

g(N,

Ρ)

=

wo.

12 In an application of inventory theory, William J . Baumol ( " T h e Transactions Demand for Cash: An Inventory Theoretic Approach," Quarterly Journal of Economics, Volume L X V I , No. 4 [November 1952], pp. 545-556) has shown that the interest rate will govern the allocation of working capital between cash and liquid assets of short maturity. Hence even the transactions demand for money will be sensitive to variations in the interest rate. James Tobin ( " T h e Interest-Elasticity of Transactions Demand for Cash," The Review of Economics and Statistics, Volume X X X V I I I , No. 3 [August, 1956], pp. 241-247) has extended Baumol's treatment and reached similar conclusions.

72

The

Wage-Price-Productivity

Nexus

First, we obtain the traditional expenditure multipliers. Total differentiation of the system with respect to a yields, after some manipulation,

(2.11) dN f ( N ) ( l - C r - I r ) —

(2.12)

f(N)PLrm

-(Ci

+ Li ~

+

I

di i ) T a +

+ Lrm f(N)

Μ dP C ^ T Q =

^

l

= 0

(2.13) (1 - Π ) -

[Pf"(N)

gll]

As indicated above, Cr

^ L

+ 0 •

+ [ f ' ( N ) (1 - Π ) -

gP

]

denotes the partial derivative of con-

sumption with respect to real income, and similar symbols have analogous interpretations. Since Ym =

PY,

denotes

Lym

the

partial derivative of L with respect to money income. dN Using Cramer's rule, we can solve for — — and da

dP —. da

This

gives:

(2.14)

, dN da

_

Li [f'(N)

( w

dut \

^ Ύ ' Ί ρ )

(1 — Π ) — £p] D

D

where

(2.15) D

-

(1 - C r - Iy)f(N) f\N)PLym [Pf'(N)(

- ( a + //) Li

1 - Π ) - * , ]

0

Μ £ Ch Ρ2 Ρ f(N)Lym ( f - - ^ - )

Income, the Price Level, and Generalized =

(1 -Cr~

h ) f(N)L>

(C
0 and

dM

obtain:

, and

Kl p

> 0, as both n u m e r a t o r s are negative

and D is negative. T h u s an expansion of the m o n e y supply both stimulates real i n c o m e and raises prices, in the typical case. T h e r e fore, on a broad level of generality, the direction of the effect on the price level is the same for this theoretical f r a m e w o r k as for the quantity theory. T h r e e special cases r e m a i n to be considered. (1.)

Suppose

exists. T h e n , gK

that

"severe"

—> 0 and f"(N)

viously. I n this case

dM

underemployment

equilibrium

—* 0, as was pointed out pre

—» 0, a n d the quantity theory breaks

"severe" underemployment equilibrium, f " ( N ) ~ * 0—, i.e. , /"(N). which is always negative, can be made arbitrarily close to zero. T h u s the quantitative importance of diminishing returns becomes negligible in "severe" underemployment equilibrium while the sufficient condition for profit maximization continues to hold. Similarly, the wage unit may be taken to l>e unresponsive to changes in the level of employment if the employment level is low enough. dP is also negligible if the demand for money is independent of the 1β da rate of interest. T h i s is the somewhat unusual case discussed in footnote 14.

76

The

Wage-Price-Productivity

Nexus

down: changes in the money supply have no effect on the price level. This is not because changes in money have no significance, but merely because all expansionary forces, additions to the money stock included, result in increased output and employment with negligible price level increases. Under these circumstances, a "quantity theory" of output and employment would be valid, if in addition the demand for money were independent of the rate of interest and were related to money income in a particularly simple manner.17 (2.) Suppose the real balance effect is totally absent (i.e., CM — 0); it may be argued that this was the view espoused by Keynes. If, in addition, expenditures are perfectly interest in17 Suppose L = kPY

so that

= 0 and LTm

ff"

=

d (™Y)

becomes

ui

(

(2.17a)

(2.17) then

dw\

~p-Jp)( D

dM

= k.

C

'

+ I·>

W i t h "severe" underemployment conditions,

w

(

dM

dui \

(C/' w + / Qw \' ~P~~Jp) (C, + lt)r(N)PLrmy---— j

as an examination of (2.15) will substantiate. Therefore, so that V (AO

But

dY dM

=

dN m

_

dN dM

1 r (N)Pk

1

— .

3nd

Pk

Μ ~ ~Y~' S'"CC

M

=

L

sequently, these assumptions lead to the result that

dY

dN dM

e

( , m

Ητ~ «

-

~

— gy]

—

£λγ]

>0,

[ P ( l — Π ) / " ( N ) — gft]

Ηγ

Π ) /"(TV)

r m [Ρ(1-Π)/

(N)-gn]

where Ν = /

'(Υ).

U n d e r "severe" underemployment conditions, the denominator approaches zero f r o m a negative direction, so t h a t : ψ,. —• + oc φ„ —* - » φ«·„ -> - oo. W i t h full employment, ^

—*• ~

and consequently ψρ —> 0.

T h e aggregate d e m a n d curve is derived f r o m the following set of equations:

92

The Wage-Price-Productivity

Nexus

(a.18)

C =

(a.19)

/ = /(;, Υ, Π ) + α

C(Y,i.~,n)

(a20)

Y = C + /

(a21)

Μ = L ( P Y , /).

Substituting (a.18) and (a.19) into ( a 2 0 ) , wc may reduce the above set down to a pair of simultaneous equations: (a22)

C ( Y , «,

Π ) + /(,, Υ, Π ) + α - Y = 0 L(PY,

= 0.

t)~M

Schematically, the set ( a 2 2 ) may be written: (a23)

F ( Y , «', Ρ ;

Μ,

α,

Π) = 0

G ( Y , i, Ρ; Μ, α, Π ) = 0. It is assumed the C, I, and L functions all have continuous partial derivatives. T h e n F and G will have continuous partial derivatives also. Suppose that

/:

(a24)

FT

Ft

Gy

Gi

^

0.

In this case, the set ( a 2 3 ) will yield a solution "in the small": (a25)

Υ = φ ( Ρ ; Μ, α, Π ; .

( W e could also solve for i as an explicit function of Ρ, M, a, and Π under these circumstances; but this expression is of little interest and is consequently neglected.) T h e expression for / is: (a26)

J

Ft

F(

GY

Gi

= Li(Cy

{CY

+

I Y -

p Ly m

+ h - l ) - ( C i +

1)

(Ci + Ii) U I

0, and ( C , + / , )

0, 0.

Consequently / is non-negative. It will be assumed that / is strictly positive; this entails the condition that Li and (Ct + /)LYmP

(a.29) ψ. =

~

Fa

Fi

Ga

Gi

/

(C, + h)Lrm

Ρ

(a 3 0 ) ψΜ

=

Fm

Fi

Gm

Gi

—

- [ L i C u ± ρ ' Li ( C r + /y

I

+ (Ci + L) 1

1) -

(Ci +

li)LYmP

(a31)

ψη

=

—

Fn

F( I

Gn

Gi I

~ 7

- Li (Cn + Li (Cr

+ lr -

1) -

In)

(Ci + U)Lrm

Ρ

^0.
( is the absolute difference between the current level of the consumer price index and that of the previous year; the consumer price index is measured on a 1926 base. Empirical counterparts of this relationship were estimated f r o m A m e r i c a n data, f r o m 1899 to 1957. For wages, the concept used is average hourly compensation in m a n u f a c t u r i n g , as developed by Albert Rees. 2 Rees' data include wages but exclude salaries; the concept used includes wage supplements. T h e hours divisor is hours at work (e.g., excludes paid holidays), rather than hours paid. A consumer price index was pieced together f r o m two sources. Rees' book gives a consumer price index f r o m 1898 to 1914,3 while the Bureau of Labor Statistics' cost of living index, as recorded in the files of the National Bureau of Economic Research a n d Historical Statistics,* was used for 1913 to 1957. ( T h e overlapping years were used for the purpose of linking the t w o series.) A homogeneous series on unemployment was obtained by using figures for the years 1900 to 1940, developed by Stanley Lebergott in a forthcoming work 5 and made 2 Albert Rees (assisted by Donald P. Jacobs), Real Wages in Manufacturing 1890-1914 (Princeton: Princeton University Press, 1961), p. 4; Albert Rees, "New Measures of Wage-Earner Compensation in Manufacturing, 1914-1957," Occasional Paper 75, National Bureau of Economic Research, 1960, p. 3. ( T h e National Bureau of Economic Research is occasionally abbreviated NBER in the remainder of this work.) 3 Albert Rees (assisted by Donald P. Jacobs), op. cit., p. 4. < U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1957 (Washington: U.S. Government Printing Office; 1960), T a b l e Ε 113, p. 125. (This work is hereafter called by the short title, Historical Statistics.) 5 Stanley Lebergott, Manpower in Economic Growth: The United States Record since 1800 (New York: McGraw-Hill Book Company, Inc., forthcoming). T h e s e estimates are a revision of Lebergoti's earlier figures, which appeared in his "Annual Estimates of Unemployment in the United States, 1900-1954," The Measurement and Behavior of Unemployment (Princeton, N.J.: Princeton University Press [for T h e UniversitiesNational Bureau Committee for Economical Research], 1957), pp. 213239. T h e a u t h o r ' s immediate source was a letter from Professor Leber-

Empirical

Relationships

97

a v a i l a b l e to the author in advance of publication. Department of C o m m e r c e figures 6 on u n e m p l o y m e n t are used for the years 1941 to 1957. ( T h e former definition of u n e m p l o y m e n t is the one e m p l o y e d here—thus the temporarily laid-off a r e counted as e m p l o y e d . ) F o r a tabular presentation of these data (except the u n e m p l o y m e n t figures), see A p p e n d i x B.

1 . SOME P R E L I M I N A R Y

RESULTS

T h e m e t h o d of parameter estimation used in this chapter is single e q u a t i o n least squares. A l t h o u g h this method is subject to w e l l - k n o w n biases, it offers certain c o m p u t i n g economies w h i c h m a k e it attractive for p r e l i m i n a r y experimentation in comparison w i t h a consistent method of p a r a m e t e r estimation. Perhaps the most serious short-coming of this t e c h n i q u e is related to the p r o b l e m of identification. Price level changes in fluence w a g e d e m a n d s ; but w a g e increases influence the price level, because of cost pressures. S o m e of this problem is ameliorated by the use of a consumer price index a n d of w a g e s in m a n u f a c t u r i n g . ( T h e i m m e d i a t e impact of a w a g e increase in m a n u f a c t u r i n g w o u l d be on certain selected wholesale prices.) In Chapter V I below, the parameters of the final w a g e adjustment relationships are re-estimated by the method of t w o stage least squares. H e n c e the estimates of these parameters are free of single e q u a t i o n bias. S o m e p r e l i m i n a r y experimentation w a s u n d e r t a k e n to determ i n e the most appropriate form of the w a g e a d j u s t m e n t equation. W h e t h e r variables should be expressed in absolute or percentage f o r m a n d w h e t h e r a t i m e trend should be included as gott, dated J a n u a r y 22, 1962. In this letter, Lebergott requested that the author not present these estimates in advance of the p u b l i c a t i o n of his (Lebergott's) latest book, and consequently this series does not a p p e a r in A p p e n d i x Β of this Chapter, β Historical Statistics, T a b l e D 46, p. 73.

The

98

Wage-Prtce-Productivity

Nexus

an explanatory variable were investigated. A f t e r this preliminary study, it was decided to use the absolute w a g e change, the absolute u n e m p l o y m e n t

level, and the absolute price level

instead o f percentage w a g e a n d

change

price level changes and

un-

e m p l o y m e n t as a percentage of t h e labor force. 7 T h e coefficient on u n e m p l o y m e n t becomes significantly negative only with the absolute variables, after a t i m e trend is included as an explanatory

variable. A s

was

pointed

out

in

Chapter

I

above,

our

theory w o u l d lead us to expect a negative sign on u n e m p l o y m e n t , f o r u n e m p l o y m e n t w o u l d constitute excess supply and as such w o u l d exert a restraining force on the increase in m o n e y wages. H e n c e r e q u i r i n g this coefficient to be negative seems a reasonable e c o n o m i c criterion. T h e t i m e trend variable permitted the negative influence of u n e m p l o y m e n t on t h e w a g e c h a n g e to app e a r ; f u r t h e r m o r e , this variable was highly

significant

in

its

o w n right and so it was included. T h i s t i m e t r e n d m a y be given several interpretations. I n o n e view, it m i g h t represent increasing power or pushfulness f r o m the supply side of the labor m a r k e t , as could occur f r o m a g r o w t h in the m e m b e r s h i p or the power o f the trade unions. 8 O n another view, its significance might be an

artifact

resulting

from

stating

the

dependent

variable

in

absolute, not percentage, t e r m s ; a given absolute wage increase means less to the participants w h e n the base is large than when it is small. In A p p e n d i x A , the regression equations which were e x a m i n e d and then

rejected as candidates for the

final

wage

a d j u s t m e n t equation are listed. 7 T h i s series (unemployment as a percentage of the labor force) was obtained from Lebergott, letter of January 22, 1962 (values for 19001940) and Historical Statistics, T a b l e D 47, p. 73 (values for 1941-1957). 8 In the "wage bargain" equation of Valavanis-Vail's model (which is analogous to the author's wage adjustment equation), there is no time trend, but one of the explanatory variables is the percentage of wage earners who are unionized. Since Valavanis-Vail effectively has the author's other two explanatory variables in his relation, the fact that he obtains a highly significant coefficient on his percentage unionized variable strengthens this interpretation of the present results. See Stefan Valavanis-Vail, op. cit.

Empirical

Relationships

99

T h e equations accepted for f u r t h e r examination w e r e :

(3.2) Aw, = -

.00619 - 0.5238 x 10"'°U, + 0.1955 x 10~2 ΔΡ,_, (.01012) (0.1673 x 10"5) (0.0995 x 10"2) 2 + 0.2005 X 10- /, Su = 0.0365, R2 = 0.5394, (0.0306 X 10- 2 )

(33) AWt

= -

.01374 -

0.2463 x 10- 5 Z7, + (0.1403 x 10~ 5 )

(.00817) +

0.1677 X I0~2t,

0.5845 x 1 0 " 2 Δ Ρ , _

1/2

(0.0967 x 10~ 2 ) Su = 0.0292. R- = 0.7055,

(0.0250 Χ 1 0 " 2 ) (APt-i/2

= - y ( Δ Ρ , + Δ Ρ , . , ) , by definition.)

(3.4)

Aw, = -

.01492 - 0.1987 x 10"5ί7< + 0.6200 X 10 " 2 AP, (.00628) (0.1056 x 10" s ) (0.0627 x ΙΟ"2) _2 + 0.1628 X 10 i, S„ = 0.0225, R2 = 0.8243. (0.0190 Χ 10"2)

t, the time trend, is equal to zero in 1900 a n d is in a n n u a l units. ( H e n c e A P t - i , t h e change in the consumer price level, lagged one time period, is equal to last year's consumer price level minus that of t w o years ago.) T h e n u m b e r s in parentheses are standard errors, while R~ is the coefficient of multiple determination and Su is the estimated standard deviation of the residuals. (5„, but not R~, is corrected for degrees of f r e e d o m . ) In each of these regressions, there were 58 a n n u a l observations, as the period ran f r o m 1900 to 1957. Some c o m m e n t s may be proffered on these equations. All of t h e m indicate that an increase in the consumer price level is associated with an increase in the money wage. T h i s is hardly surprising, for labor m i g h t be expected to exert pressure for higher wages ( a n d business more ready to give t h e m )

when

100

The

Wage-Prtce-Productivity

Nexus

prices rise. (Even if a wage push were responsible for the price level rise, this should make no difference to the argument. In the labor market, which this equation purports to describe, a price level increase is likely to result in a higher money wage. This is so because workers desire more strongly wage advances to offset higher living costs and employers are more willing to grant these, as value productivity is now higher.) Over the period 1900-1957, the mean money wage was $0.7102 and the mean value of the consumer price level, in 1926 index points, was 89.8. Thus, if a rise in prices one per cent of the period's average level were associated with a rise in wages one per cent of the average money wage of this period, the coefficient on the price level change would be 0.0079. It is to be noted that the observed regression coefficients differ significantly from this hypothetical value, if one accepts the accompanying standard errors. Another question that arises is that of the appropriate time lag of the price level change variable. T h e time diagram of the money wage change, the consumer price level change, and unemployment (Figure 2) 9 suggests that the influence of the price level change on the wage change is principally a simultaneous one, rather than one involving a time lag. This impression is confirmed by equations (3.2), ( 3 3 ) , and (3.4); the shorter the time lag in the price level change variable, the higher the coefficient of multiple determination, R~. Hence, for the moment, the hypothesis that the unlagged form of this variable is best will be tentatively accepted. This question is further pursued in Section 2 below. These regression equations all show a significant relationship (at the 5 per cent level, with a one-tailed test, or at the 10 per cent level, with a two-tailed test) between unemployment and the β T h e unemployment series in this time diagram is taken (for the years 1900-1940) from Lebergott's published paper, "Annual Estimates of Unemployment in the United States, 1900-1954," and so it differs somewhat from the unemployment series from which the regression equations were calculated.

Empirical

Relationships

101

FIGURE 2. T i m e Diagram of the Money Wage Change (AW), the C o n s u m e r P r i c e Level Change ( i P ) , and Unemployment (U), U.S.A., 1900 - 1957.

Calendar Time

The

102

Wage-Price-Productivity

Nexus

m o n e y wage change. T h e negative sign of the coefficient of une m p l o y m e n t is in accord with standard e c o n o m i c theory, as has been pointed out. T h e relationship between u n e m p l o y m e n t and t h e money wage change is, however, very loose. O v e r the period 1900-1957, the mean level of the labor force was, in thousands of m e n , 47,679. T h e r e f o r e , if an increase in the level of unemploym e n t which was 1 per cent of this mean labor force w e r e associated with a wage decrease 1 per cent of the period mean money wage, the coefficient of the Ui variable would be

—

1.49 X 1 0 ~ 5 .

S i n c e all coefficients of unemployment are m u c h lower, this suggests that the wage change is not very sensitive to the level of u n e m p l o y m e n t . T h e same impression is obtained from looking at the gross scatter diagram between the w a g e c h a n g e and une m p l o y m e n t ( F i g u r e 3 ) . 1 0 T h e r e is m u c h dispersion about the negative relationship between wage changes and u n e m p l o y m e n t . F i g u r e 2 ( t h e time d i a g r a m ) suggests no obvious lag in the influence

of unemployment on the money w a g e c h a n g e . T h i s pos-

sibility may be further tested by introducing lagged values of the unemployment

variable into the wage adjustment

regres-

sions. U s i n g a time lag of one year for the first regression, a time lag of half a year for the second, and the sample period 19011957 for both

regressions, the author obtained

the

following

modifications of equation ( 3 . 4 ) : (3.5) Δ«/, = -

.01916 -

(0.1019 x 10~ 5 )

(.00656) +

0.6606 X 10 " 2 AP,

0.0662 x 1 0 - 5 i 7 r - i +

(0.0603 Χ 1 0 " 2 )

0.1578 x 10"-r, S„ = 0.0232, R* = 0.8152, (0.0199 Χ 1 0 " 2 )

(3.6) Δ«/, = -

.01768 (.00657)

0.1337 x i 0 - 5 l / ( - i / 2 + (0.1068 x Ι Ο " " )

+

0.6433 x 1 0 " : 2 A P , (0.0617 X 1 0 ~ 2 )

0.1619 X 1 0 ~ h , S„ = 0.0230, R2 = 0.8191. (0.0198 X 1 0 - 2 )

10 The unemployment series used in Figure 3 is that of Figure 2 and hence differs somewhat from Lebergott's latest unemployment series.

Empirical

Relationships

103

FIGURE 3. G r o s s S c a t t e r D i a g r a m of

Aw t .18 -τ—

Money Wage Changes ( A w t ) and Unemployment (U t ), U.S.A., 1900 - 1957.

(1951) «

.16-.14 - .12

.10 •

*

*

(1934) *

*

.08· .06

.04 *

.02

χ

(1945) , , » ' «

U ·

< *

1000

X

;« «

* *

χ 4000

6000

.02-

.04.06-

.08-*-

(1921) χ

Τ 8000

χ 10,000

jr *

.. ^

12,000

104

The

Wage-Price-Productivity

Nexus

A c o m p a r i s o n w i t h e q u a t i o n ( 3 . 4 ) suggests t h a t this m o d i f i c a t i o n p r o d u c e s inferior results. T h e coefficient of m u l t i p l e

determina-

tion falls slightly; m o r e o v e r , the coefficient of t h e u n e m p l o y m e n t variable fails to retain formulation. T h e

statistical

significance

in

either

statistical e v i d e n c e suggests that

lagged

current

un-

e m p l o y m e n t is preferable to a l a g g e d v a l u e of u n e m p l o y m e n t as a n e x p l a n a t o r y variable in a w a g e a d j u s t m e n t

relationship. 1 1

F i g u r e 3 ( t h e gross scatter d i a g r a m ) s u g g e s t s n o o b v i o u s nonlinearity

in

the

relationship

between

wage

changes

and

un-

e m p l o y m e n t . T h i s is in contrast w i t h t h e w o r k of Phillips a n d Lipsey,

who,

using

British

data

from

1861

to

1957,

found

a

p r o n o u n c e d non-linearity in this relationship. 1 2 H o w e v e r , S a m u e l son a n d S o l o w , w o r k i n g w i t h A m e r i c a n d a t a , o b s e r v e d that nonlinearity

in

the

relationship

between

unemployment

and

the

n Equation (3.6), in which the unemployment level is the arithmetic mean of the current level of unemployment and that of the previous year, corresponds most closely to the regressions fitted by Bowen and Berry. They believe that this is a better method of aligning wage changes and the level of unemployment. See Bowen and Berry, op. cit., especially pp. 171-172, for a discussion of this issue. T h e present author prefers, however, to regard the wage change as located at the point in time corresponding to the current level of money wages (the first term of &ur,); on this view, the previous level of money wages ) is merely an implicit explanatory variable for the current level of money wages (u>,). With this outlook, the manner in which the wage change and unemployment variables are related in the text is an appropriate one. 12A. W. Phillips, op. cit.; Richard G. Lipsey, op. cit. Recently R. J . Ball has studied the forecasting accuracy of two post-war British wage adjustment relationships, beyond the period for which they were fitted. (See R. J . Ball, " T h e Prediction of Wage-Rate Changes in the United Kingdom Economy 1957-60," Economic Journal, Volume L X X I I , No. 285 [March, 1962], pp. 27-44. T h e two wage adjustment relationships are taken from L. R . Klein and R. J . Ball, op. cit., and L. A. Dicks-Mireaux and J . C. R. Dow, op. cit.) Ball found that both wage adjustment relationships predicted most poorly during the period between the third quarter of 195H and the third quarter of 1959, a period of recession in business activity. One possible explanation of these results is a non-linearity in the relationship between unemployment and wage rate changes. Such a non-linearity, if present, would probably not have been apparent during the period for which these wage adjustment relationships were fitted because of the low level of unemployment (high level of labor demand) which existed over that entire earlier period.

Empirical money

Relationships

w a g e c h a n g e w a s not so e v i d e n t

105 in t h e i r d a t a .

Bhatia

also c o n c l u d e d t h a t t h e r e l a t i o n s h i p b e t w e e n u n e m p l o y m e n t w a g e changes was approximately linear, for the A m e r i c a n

and econ-

o m y . A n d F r a n c e a c t u a l l y i n t r o d u c e d t h e u n e m p l o y m e n t level in a n o n - l i n e a r f a s h i o n i n t o his w a g e a d j u s t m e n t r e g r e s s i o n s b e f o r e deciding

that

a

linear

relationship

between

wage

a n d u n e m p l o y m e n t w a s a s u p e r i o r d e s c r i p t i o n of his

changes American

data. T h u s the author's impressions agree with those of other students of this relationship for the A m e r i c a n and the different

conclusions

(about

this

relationship

U n i t e d States a n d B r i t a i n ) may point up a g e n u i n e difference between the two

several

economy, for

the

institutional

economies.13

A f u r t h e r test o f n o n - l i n e a r i t y m a y be m a d e . W e m a y

intro-

duce the reciprocal of current u n e m p l o y m e n t , adjustment

regression

able).14 W h e n

(in

into the w a g e Ut p l a c e o f a l i n e a r f o r m o f t h i s vari-

t h i s is d o n e f o r t h e p e r i o d 1900-1957, t h e

results

are: (3.7) Δ^,

=

-

.02422

+

(.00879)

(ο.ΐΐυ^ +

^L/ΛΛΤΤΙ ^ IV

0 . 1 5 6 7 Χ 1 0 " 2 / , .„ =

)

0.0231, R 1 =

0.8149.

(0.0200 X 10"'-) 13 See Samuclson and Solow, op. cit.; Bhatia, op. cit.; and France, op. cit. As Bowen and Berry have pointed out (op. cit., p. 169), however, comparisons between the U.S. and U.K. of the wage change-unemployment relationship are hindered by the almost complete absence from American data of very low levels of unemployment (say, unemployment below 3 per cent of the labor force). It is possible that the American relationships would display non-linearity over the full range of unemployment, similar to that observed in the British studies, if such observations were available. 1Ί Richard G. Lipsey and M. D. Steuer ( " T h e Relation between Profits and Wage Rates," Economica, N.S., Volume X X V I I I , No. 110 [May, 1961], pp. 137-155) use this form of the unemployment variable in their regression analysis. T h i s article is discussed more fully in Chapter IV below.

106

The

Wage-Price-Productivity

Nexus

FIGURE 4. Gross Scatter Diagram of Money Wage Changes (Aw) and Consumer Price Level Changes (ΔΡ), U.S.A., 1900-1957.

Aw .18

- -

.16

- -

χ (1951)

.14 - .12

- -

.10 —I— * x X * » (1934) *

.06 -+χ .04 .02

^ -12

-10

1 -6

l· -4

_iL

*

- -

: ο -.02

2 - -

-.04 - Χ (1921)

-.06

-.08

ΔΡ

Λ (1945) iV" I I 4

6

10

12

14

16

Empirical

107

Relationships

O n c e a g a i n , the m o d i f i c a t i o n

p r o v e s to be statistically

T h e coefficient o f m u l t i p l e d e t e r m i n a t i o n

inferior.

is l o w e r t h a n t h a t o f

e q u a t i o n ( 3 . 4 ) , a n d t h e coefficient o f t h e r e c i p r o c a l o f u n e m p l o y m e n t d o e s not retain statistical s i g n i f i c a n c e . H e n c e this d o e s not s e e m to be a f r u i t f u l

modification,

and

non-linearity

(of

this

t y p e ) b e t w e e n u n e m p l o y m e n t a n d w a g e c h a n g e s d o e s not a p p e a r to b e p r e s e n t , f o r t h e A m e r i c a n

economy.

T h e g r o s s scatter d i a g r a m o f m o n e y w a g e c h a n g e s a n d s u m e r p r i c e level c h a n g e s is p r e s e n t e d in F i g u r e 4 . A n

con-

examina-

t i o n o f this d i a g r a m s u g g e s t s n o p r o n o u n c e d n o n - l i n e a r i t y in t h e relationship

between

wage

changes

and

price

changes.

d i a g r a m also s u g g e s t s t h a t t h e p r i c e level c h a n g e v a r i a b l e

This does

m o r e o f t h e w o r k o f e x p l a i n i n g w a g e c h a n g e s t h a n d o e s t h e level o f u n e m p l o y m e n t . T h i s i m p r e s s i o n is c o n f i r m e d by an e x a m i n a t i o n o f e q u a t i o n ( 3 . 4 ) : t h e r a t i o o f coefficient to s t a n d a r d ( t h e t r a t i o ) is m u c h h i g h e r f o r t h e p r i c e level c h a n g e t h a n f o r t h e level o f

2. THE

POSSIBLE

error

variable

unemployment.15

LAG OF

WAGE CHANGES

BEHIND

PRICE

LEVEL CHANCES

L e t us p u r s u e f u r t h e r t h e q u e s t i o n o f t h e a p p r o p r i a t e l a g for t h e p r i c e level c h a n g c v a r i a b l e . I n t h e p r e v i o u s s c c t i o n , w e saw t h a t t h e h i g h e s t coefficient

of multiple

correlation

is

obtained

w h e n this v a r i a b l e is u n l a g g e d . 1 6 T h u s it m i g h t be a s s u m e d t h a t 15 Robert L. Gustafson has shown ("Partial Correlations in Regression Computations," Journal of the American Statistical Association, Volume LVI, No. 294 [June, 1961], pp. 363-367) that the relevant partial correlation coefficients can be computed from the t ratios and the number of observations. Furthermore, for a given number of observations, the relevant partial correlation coefficient varies monotonically (in a positive sense) with the / ratio. ιβ It is also interesting to note that the effect of unemployment on the wage change is diminished as the length of the price level change lag is reduced—see equations (3.2), (3.3), and (3.4). L. R. Klein and R. J . Ball (op. cit., p. 474) come to a similar conclusion.

108

The Wage-Price-Productivity

Nexus

the untagged f o r m is best. However, there is one consideration that m i g h t m a k e us hesitant to accept this result at face value. In C h a p t e r II, the existence of another relationship between wages a n d prices—a marginal productivity equation or a m a r k - u p equation—was pointed up. H e n c e it is desirable to investigate this problem further, by seeing what additional evidence is available on this matter. T h e National Bureau of Economic Research has completed m a n y cyclical analyses of various economic time series. A m o n g the series analyzed were average hourly earnings of 25 m a n u facturing industries (a series published by the National Industrial Conference Board) and the Bureau of Labor Statistics' cost of living index. Both were analyzed for the period 1922-1939. T h e following table is a summary of processed data, taken f r o m the National Bureau files in N e w Y o r k : Table I Summary of the National Bureau's Timing Measures, Cost of Living Index and Average Hourly Earnings of 25 Manufacturing Industries, U.S.A., 1922-1939Lead ( — ) or Lag ( + ) at: Reference Peak ( N o . of Months) (1.) Cost of Living Index Average Hourly Earnings, 25 Manufacturing Industries

Reference Trough (No. of Months) (2.)

Unweighted Average of (1·) and (2.) (3.)

+

2.2

+

9-0

+

5.6

+

12.0

+

7.6

+

9.8

T h u s average hourly earnings lag consumer prices by 4.2 months over the cycle, on the average for the period 1922-39. If this lag is the appropriate one for our regression equation, the

Empirical

Relationships

109

annual data would tend to conceal this lag. This piece of evidence would lead us to accept equation ( 3 3 ) as the closest statistical counterpart of the underlying economic structure. Before this conclusion is accepted as a working hypothesis, some further evidence may be examined. Quarterly data on wages and consumer prices exist for the United States in the post-war period. T h e wage data, which are average earnings at an annual rate, were taken from the worksheets of the Unit for Econometric Research on the Structure of the American Economy at the University of Pennsylvania. 17 Unlike the annual data, this series includes the salaries of nonproduction workers. T h e consumer price index used is the implicit deflator of personal consumption expenditures, from the G.N.P. accounts. 18 ( T h e data used are given in Appendix B.) T h e change between the average earnings (at an annual rate) in a given quarter and the average earnings in the same quarter a year earlier was correlated with the price level change, which was lagged zero, one, two, three, and four quarters, successively. ( T h e price level change was defined as the difference between the consumer price level in a particular quarter and the consumer price level of the corresponding quarter one year earlier.) If the time unit t represents quarters of a year and α, β, and θ are parameters, then the correlations computed are symbolically described by the following equation: (3.8) wt-wt-«

= « + β

( P t - e -

P,-4

.),

θ = 0, 1, 2, 3, and 4.

17 T h i s series is a constructed series. For a fuller description, see L. R. Klein, "A Postwar Quarterly Model." T h e author's special thanks go to Miss Kanta Marwah, for her time and cooperation. 18 T h e figures for 1945 and 1946 were estimated from the monthly values of the B.L.S.'s cost of living index for those years. T h e author's immediate source was the NBER files.) T h e figures for 1947-1955 were taken from the U.S. Department of Commerce, Office of Business Economics, U.S. Income and Output (Washington: U.S. Government Printing Office, 1958), p. 222. T h e figures for 1956-1958 were taken from the Survey of Current Business, Volume XL, No. 7 (July, 1960), p. 10.

110

The

Wage-Price-Productivity

Nexus

T h e s e correlations were run for the period 1947-1958. Since the principal interest is the question of the most appropriate time lag, no other explanatory variables were included. T h e size of the gross correlation coefficient is the criterion for the appropriate lag. W h i l e this is somewhat crude, it does appear to be a reasonably effective method which does not involve undue effort. T h e results of these computations are given in T a b l e I I . Table II Correlation Coefficients ( r ) for W a g e Changes and Price Level Changes, U.S.A., 1947-1958.

0 Quarter lag

1 Quarter lag

2 Quarter lag

3 Quarter lag

4 Quarter lag

.6402·

.5446·

.3669·

.1565

—.0360

Correlation Coefficient

(f)

• indicates that the correlation coefficient is statistically significant (at least two times the sampling error of

r).

Similar computations have been made for the American econo m y during the period 1921-1940. T h e wage concept is average hourly earnings of 25 manufacturing industries, data originally collected

by the National

Industrial

Conference

Board.

The

price index is the Bureau of L a b o r Statistics' cost of living index. T h e author took both of these series from the files of the National Bureau in N e w Y o r k . Since these series are available on a monthly basis, the author tabulated regressions of the f o r m : (3.9) Wt-Wt-12

= c' + ß' (Pt-r-Pt-r-Vi),

# = o, 1, 2 , . . . , 7, 8.

H e r e t, the time unit, is in months of the year. T h e results are presented in T a b l e III.

Empirical

Relationships

111

Table III Correlation Coefficients for W a g e Changes and Price Level Changes, U.S.A., 1921-1940.

Time lag

Coefficient of Correlation

0 months 1 month

.8031 .8243 .8202 .7911 .7398 .6707 .5814 .4816 .3803

2 months 3 months 4 months 5 months 6 months 7 months 8 months

Note: All the r s are statistically significant, using standard tests. It can be seen that T a b l e s II and III tell a consistent story. T h e lag of the wage change behind the price level change is very short—so short in fact that even quarterly data conceal it. T h e monthly data, together with the previously stated criterion, suggest that the lengh of this lag is roughly one month—or slightly longer if the correlation coefficient associated with a lag of two months is considered to be equivalent to that associated with a one month lag. T h e limitations of this technique should be emphasized. W e have merely studied the appropriate lag with only one explanatory variable used in the wage adjustment equation. It is quite possible that if several explanatory variables were used, a different answer for the appropriate time lag might be obtained even with the same criterion ( m a x i m u m correlation). T h e r e is also the question of the criterion. O t h e r criteria could have been used, such as the absence of autocorrelation in the residuals or appropriate

economic

structure.

Moreover,

autocorrelated

re-

siduals, if present, could affect the reliability of the comparisons made in T a b l e s II and I I I . Furthermore, despite the fact that the

112

The

Wage-Price-Productivity

Nexus

price level changes precede the wage changes, there might still be a causal influence of these wage changes on these

price

changes, if the wage changes were anticipated before their occurrence and prices responded to such anticipated wage increases before they actually occurred. ( T h i s difficulty is the identification problem once again.) T h e problem of single equation bias, however, is not strictly present (except for the correlations with a zero time l a g ) . T h i s is so because the lagged value of a systemdetermined variable is effectively an exogenous variable; there can

be no " f e e d b a c k "

effects on

variables

whose values

are

already a matter of record. R e t u r n i n g to the annual data, the author decided to accept the tentative conclusion

that the price level change

variable

should be included without a lag in the wage adjustment relationship. ( A time lag of one or one and a half months is much too short to capture with annual data.) Accordingly, equation ( 3 . 4 ) was accepted as the tentative w o r k i n g relationship. A discussion of the estimated parameters of equation

(3.4)

may be useful. T h e coefficient on unemployment is 1.88 times its estimated standard error; hence it is statistically significant at the 5 per cent level, using a one-tailed test ( o r at the 10 per cent level, using a two-tailed test), but not at the more restrictive level (5 per cent) with a two-tailed test. 1 9 Using the period mean values cited earlier, one can calculate that an increase in the level of unemployment 1 per cent of the mean labor force is associated with a decline in average hourly earnings equal to 0.13 per cent of the period's mean average hourly wage. Both the coefficient of the price level change and the coefficient of the time trend are highly significant. A g a i n using period averages, o n e can obtain the result that a 1 per cent increase in consumer 19 When certain outlier years are excluded from the regression calculations, the statistical significance of the unemployment variable increases. Sec equations (3.14) and (3.15), together with surrounding discussion, in Section 3 below.

Empirical

113

Relationships

prices is associated with a 0.78 per cent

increase

in

wages.20

T h e author tested for serial correlation in the residuals o f equation

( 3 . 4 ) , using t h e D u r b i n - W a t s o n

statistic. 2 1

The

ratio

of

the s u m of the squared successive differences of the residuals to the s u m of the residuals squared

(i.e., d,

the

Durbin-Watson

statistic) was 1.618. F o r a sample of the size actually employed, the residuals are significantly non-autocorrelated at the 2.5 and the 1 per cent levels, while the test is indecisive at the 5 per cent level. H e n c e the hypothsis of non-autocorrelation of the residuals o f this equation

can

be accepted. A c c o r d i n g l y ,

errors of the regression

coefficients may

the

standard

be considered

to

be

reliable. O n e reason why the wage a d j u s t m e n t regression (3-4) is considered only a tentative o n e is the possibility that other variables play an important role in e x p l a i n i n g w a g e changes. Inclusion of these additional variables may c h a n g e the estimates of the m a g n i tude o f effect of the currently included variables. F u r t h e r m o r e , it is q u i t e possible that o n e or m o r e currently included variables will no longer play a statistically significant role. T h e s e questions are

examined

changes

in

Chapter

IV,

of s o m e

possible

alternative

where

the

influence

variables

on

wage

is studied.

present, an application of these results with public policy

At im-

plications may he e x a m i n e d .

PRELIMINARY

ESTIMATES

OF

UNEMPLOYMENT

FOR PRICE L E V E L

LEVELS

"REQUIRED"

STABILITY

T h e s e results have certain implications for the trade-off between

unemployment

and

price

level

stability.

G)nsider

the

following sub-system of e q u a t i o n s : "'•'Two stage least squares estimates of the parameters of a wage adjustment relationship corresponding to equation (3.4) are presented in Chapter VI. 21 J. Durbin and G. S. Watson, "Testing for Serial Correlation in Least Squares Regression: II," Biometrika, Volume 38 (1951), pp. 159-178.

114

The

Wage-Price-Productivity

Nexus

(3.4) Wt ~ wt-1

= - .01492 - 0.1987 x

lO~6Ut

+ 0.6200 x 1 0 - a ( P , — P f _ i ) + 0.1628 x 1 0 - 2 < (/ — 0 in 1900 and is in annual units.) (3.10)

Pt =

(3.11)

At = 1.025

K^ Λ,-i.

In this system, At is output per man-hour (at time t) and is interpreted as the average productivity of labor. Equation (3.4) is our working wage adjustment relationship; it plays the same role in a dynamic system that a labor supply function, such as (2.6) of Chapter II, plays in a static system. Equation (3.10) is the W e i n t r a u b wage-cost-mark-up equation. T h i s relationship has already been derived from equation (2.5) of the previous chapter; its role in this system is considered to be the direct determination of the price level. Equation (3.11) states that output per man-hour grows at the rate of 2.5 per cent per annum. T h i s relationship can be interpreted as a special type of production function; it implies that, as of one moment of time, output varies proportionately with man-hour inputs. T h i s is admittedly an oversimplification, which will be discussed further in Chapter V I . Also in Chapter V I the empirical estimate of the rate of growth of labor's average productivity will be sharpened. F o r the moment, let us accept this model and examine its implications. If the average product of labor grows at the rate of 21/·» per cent per annum, equation (3.10) implies that the money wage must grow at only the same rate in order to maintain

price

level stability. F r o m equation (3.4), we can obtain the level of unemployment "required"

(in this sense) for price level sta-

bility. If unemployment is greater than this level, wages will

Empirical

Relationships

115

rise less rapidly t h a n a v e r a g e productivity a n d t h e price level will, a c c o r d i n g to this m o d e l , fall. If u n e m p l o y m e n t is less t h a n this critical level, w a g e s will rise m o r e rapidly t h a n

average

p r o d u c t i v i t y a n d prices w o u l d be expected to rise. It is to be noted t h a t the system is o p e n w i t h respect to presumably

demand

conditions, taken

unemployment;

into account

in a full

m o d e l , c o m p l e t e the sub-system. A

solution

of this p r o b l e m

may

now

be o b t a i n e d .

Extra-

p o l a t i n g the Rees data, the a u t h o r f o u n d that the m o n e y w a g e was a p p r o x i m a t e l y e q u a l to $2.50 in 1959. H e n c e for t h e year 1960, t h e r e q u i r e d c h a n g e in m o n e y wages is given b y : (3.12)

r e q u i r e d Atv> = 0.025 ^1959 = $0.0625.

Also, / = 60 in 1960 since t = 0 in 1900. F o r i n t e r n a l consistency, Pt~Pt

ι = 0. S u b s t i t u t i o n in (3.4) yields

(3.13) 0.0625 =

- 0.01492 - 0.1987 X 1 0 " 5 t / , + 0 . 1 6 2 8 x 1 0 " 2 ( 6 0 ) .

T h e solution is Ut — 10,200 t h o u s a n d w o r k e r s or 10,200,000— slightly m o r e t h a n Yr of a labor force of over 70 million. 2 2 T h i s is a r a t h e r s u r p r i s i n g — a n d , if true, d i s t u r b i n g — r e s u l t . Before p r o c e e d i n g to q u a l i f y it, w e m a y e x a m i n e e q u a t i o n s (3.2) a n d (3.3) to see w h e t h e r they tell a similar story. T h e answer is in the affirmative. A c c o r d i n g to e q u a t i o n (3.2), u n e m p l o y m e n t " r e q u i r e d " for price level stability is 9,853,000. Accords ' Samuelson and Solow, op. cit., present a similar discussion of a numerical trade-off between full employment and price level stability. They conclude that price level stability requires unemployment of 5 to 6 per cent of the labor force. Since they also use Rees's wage series (fringe benefit concept), the discrepancy in results is not due to this source. They also use only "recent years" (1946-1958). Since two of the present author's outliers occur in 1934 and 1945, one may seek an explanation of part of the divergence in results in these facts. (See the discussion in the text below.) Samuelson and Solow also consider only the gross relationship between the wage change and unemployment, without considering other explanatory variables, such as the price level change.

116

The

Wage-Pf ice-Productivity

Nexus

ing to equation ( 3 3 ) , this figure is 9,898,000. W h i l e lower, these figures

are hardly cause for imptimism. If true, the conflict

between low unemployment

and price level stability is even

more severe than currently believed. It must be pointed out that this result is premised on given institutional

conditions,

and

if

these

institutional conditions

change, the results will change also. T h e wage adjustment relationship was estimated by single equation

rather than

full

system methods; some estimation biases have doubtlessly crept in as a consequence. Also, the statistics indicate that the relationship between the money wage change and unemployment is not very tight. In the gross scatter diagram

( F i g u r e 3 ) , the

points are widely distributed, and the negative relationship between the wage change and unemployment is barely discernible. Even when the other explanatory variables are taken into account, the large estimated standard deviation of the residuals ( m o r e than 3 per cent of the mean level of average hourly earnings over the period, and nearly % of the mean change in average hourly earnings) implies that this relation is still quite loose. In terms of our problem, this imparts a substantial measure of indeterminacy to the results; low levels of unemployment may accompany small money wage changes, or high levels of unemployment may accompany large money wage increases. It should also be noted that the author has extrapolated a time trend, which is always a questionable procedure, even for a short period beyond the time horizon of the sample. 2 3 23 T h e s e statistical reservations may be summed up in the point that a range estimate with an associated probability of error, rather than a point estimate, would be desirable. Unfortunately, the author does not know how to construct such an interval estimate of the " r e q u i r e d " level of unemployment. As we are extrapolating beyond the sample period, something analogous to a standard error of forecast is necessitated; but it must refer to an implied value of an explanatory variable, not to the dependent variable. T h e discussion of the text suggests that this interval estimate would be fairly wide for conventionally low probabilities of error (e.g., 5 or 1 per cent).

Empirical

Relationships

117

Most of the above statistical qualifications generate additional uncertainty but do not lead us to suspect a bias in the results. T h e r e are several economic considerations which must also be stated as qualifications to the above analysis. These qualifications would lead to an upward bias in the stated results. Lipsey, in his recent comment upon and elaboration of Phillips' work," 4 has presented an argument showing that the aggregative w a g e adjustment relationship has an upward bias. If this is so, the level of unemployment "required" for price level stability, even under the above assumptions, will be smaller than the previous computations suggest. Schultze has suggested 25 that inflation cannot be properly analyzed in an aggregative framework and that a sharp shift in demand can produce inflation even though no excess demand is present. H e argues that wages tend to rise more or less uniformly throughout the economy, the pace being set by the demand-in-excess sectors. If this is true, the above conclusions are too pessimistic, provided structural maladjustments can be prevented. Both the Lipsey work and the Schultze thesis will be discussed in much greater detail in Chapter VII. Here our principal concern is with the implications of these hypotheses for the accuracy of the above calculations. W e have assumed that average productivity rises at the rate of 2 U per cent per a n n u m . W h i l e an approximation, this figure is of the right order of magnitude. Recently two writers 2 8 have argued that productivity is higher and rises more rapidly in boom periods than in periods of slack demand. Counter-balanced against this argument would be the classical principle of diminishing returns. If productivity does grow less rapidly under Richard G. Lipsey, op. cit. Parts of this article have already been discussed in some detail in Chapter I. 2S Charles L. Schultze, "Recent Inflation in the United States," Study Paper No. 1, prepared for the Joint Economic Committee of the United States Congress, Study of Employment, Growth, and Price Levels (Washington: U.S. Government Printing Office, 1959). 2« Charles L. Schultze, op. cit.; H. F. Lydall, op. cit.

The

118

Wage-Price-Prodvctivity

Nexus

conditions of slack demand, this will work in the opposite direction from the above considerations: more

unemployment

will be required for price level stability than if productivity always grows at the same rate regardless of demand conditions. These questions are examined further in Chapter V I . Finally, one may question whether increased labor costs are always proportionately

marked

up into higher

1913, the capital-output ratio has declined like

rising labor

productivity, of

prices.

Since

slightly 2 7 —evidence,

technological

progress

and

greater efficiency on the part of the labor force. T h u s , if the rate of return on capital were to stay constant, wages could rise slightly faster than labor's average productivity, or the price level could drop somewhat. T h a t real wages have in fact risen somewhat more rapidly than the average productivity of labor is indicated by the gradual increase in the wage share over the recent past. 28

Because

the

movements

involved

are

small,

this is not a major qualification to the above computations. In periods of slack demand, one might expect prices to fall— or at least not to rise proportionately with labor costs. T h i s is a possibility. However, even if prices are sensitive to demand conditions, it may be that a period of slack demand reduces prices and profits margins in a once-and-for-all event, rather than putting them under continuing pressure. If this is true, the principal effect of slack demand is on the level

of prices in the

period of demand reduction, rather than on the continuing rate of growth of the price level. T h e empirical results of Chapter V are consistent with this supposition. 27 L. R. Klein and R. F. Kosobud, "Some Econometrics of Growth: Great Ratios of Economics," Quarterly Journal of Economics, Volume LXXV, No. 2 (May, 1961), pp. 173-198. Klein and Kosobud conclude (p. 180) that the downward trend alluded to in the text is statistically significant. 28 Irving B. Kravis, "Relative Shares in Fact and Theory," American Economic Review, Volume X L I X , No. 5 (December, 1959), pp. 917-949; Sidney Weintraub, A General Theory. As pointed out in Chapter I, Weintraub is skeptical, or at least agnostic, concerning this explanation of the downward trend in his mark-up factor k. (A downward trend in the mark-up factor implies, of course, a rising trend in the wage share.)

Empirical

Relationships

119

As an indication of the uncertainties and upward biases involved, the author has computed truncated regressions, which omit outlier years. An examination of the residuals of equation (3.4) indicates positive outliers in 1934 and 1951. ( T h e residuals of equation

(3.4) are tabulated in Appendix

B ; an outlier is

defined as an observation for which the numerical value of the associated residual is more than twice the estimated standard deviation of the residuals.) Both of these years could have been excluded from the sample period on other grounds, also. T h e year 1934, in which unemployment was over 11 million

and

the wage increase was $0,086, is at least partially explained by N R A codes and governmental wage-push pressures. 29 Similarly, 1951 was a year of wartime inflationary pressures without effective wartime direct controls over wages.'* 0 T h e regression of the same form as (3.4), in which the years 1934 and 1951 are excluded from the sample period, is: (3.14) \wt

=

-

.01193 (.00573)

0.2974 X 10-δί/< + (0.1027 x 1 0 " 5 )

+

0 . 5 6 6 4 Χ Ι Ο " 2 Δ/>, (0.0585 x

10"2)

0 . 1 6 0 8 x 1 0 - * / , S„ = 0 . 0 2 0 4 , R2 (0.0175 x

=

0.8369.

10"-')

It is to be noted that excluding these outliers increases the sensitivity of the money wage change to unemployment and increases the coefficient of multiple determination. Both of these changes were to be expected. Substitution into ( 3 . 1 4 ) , in order to find the level of unemployment "required" for price level stability, according to the model of this section, yields: (3.14a) 0.0625 =

-

.01193 -

0.2974 x 1 0 - * Ϊ Λ + 0 +

60(0.001608).

2» Samuelson and Solow (op. cit., pp. 188-189) come to a similar conclusion. From Figure 3 it can be seen (hat, aside from 1934, a wage increase of this magnitude or larger was experienced only in years when unemployment was 3.2 million or lower. 30 On this point, see Harold G. Moulton, op. cit., p. 147.

The

120

Wage-Price-Productivity

Nexus

Solving, the author obtained 7414 thousand men, or 7,414,000. This

is considerably

lower than

the previous estimates

and

serves to confirm our suspicions that these previous estimates may be too high. An examination of the residuals of equation covers

a negative outlier

in

1945. T h i s

(3.4) also un-

outlier can also be

rationalized. O n e plausible explanation of the 1945 wage experience is that reconversion from wartime conditions disrupted the normal relationship. T h u s Moulton points o u t 3 1 that although wage earnings

rose very little from 1944 to 1945 (and

actually declined during the second half of 1945), because of fewer hours worked at overtime rates of pay, standard money wage rates

continued to rise throughout 1945. Excluding the

years 1934, 1945, and 1951 from the sample period and computing a regression of the same form as (3.4), the author obtained:

(3.15) C^wt = -

.01166 - 03488 Χ 10"5ίΛ + 0.5527 Χ ΚΤ 2 ΔΡ, (.00524) (0.0952 x 10" 5 ) (0.0536 x 10~-) + 0.1708 x 10 5„ = 0.01863, R2 = 0.8657. (0.0163 x KT 2 )

As before, excluding these years increases both the sensitivity of the wage change to unemployment

and the coefficient of

multiple determination. Similar calculations

indicate that

un-

employment "required" for price level stability, according

to

this equation, is 8,119,000 workers. T h i s is moderately close to the estimate from the earlier truncated regression, from which only the 1934 and 1951 outliers were excluded. After all these qualifications, where do we end up?

The

author believes that it may safely be said that with American institutional conditions, the goals of reasonably full employment and price level stability are incompatible—unless "reasonably" is 31 Op. cit., pp. 139 143, especially p. 143.

Empirical Relationships

121

given an unreasonable interpretation. 3 2 Furthermore, he would argue that the quantitative estimates are of the right order of magnitude, even though they may be of? by as much as 25 or 50 per cent. E a c h of the underlying relationships, though in part an oversimplification, is a generalization with theoretical as well as empirical underpinning. Hence one might expect these relations to possess a definitive amount of validity and stability. These qualifications, while they point to the "first approximation" character of the model and of the derived

results, do

not destroy the usefulness of the conclusions. If one is to judge by recent experience, the recession of 1960-1961 suggests that even when unemployment reaches 5 to 554 million (7-8 per cent of a labor force of approximately 70 million), prices do not cease rising. T h e incompatibility exists in fact as well as in the author's "theory."

33

APPENDIX

Λ

In this appendix, all symbols which have appeared in the text have the meaning assigned there to them. T h e symbol

LFt

32 In Chapter V I I I , however, we shall see that the author's computed relationships imply a q u i t e moderate expected rate of rise of prices at "full employment" (3 per cent unemployment). T h i s suggests in turn that, as a policy to combat inflation, dampened demand will evoke a rather large increase on the unemployment percentage per percentage {joint decrease of the rate of rise of prices, in the absence of economywide excess demand. 33 Empirical evidence leads the authors of Employment, C,rowth, and Price Levels (the Staff Report prepared for the J o i n t Economic Committee, 86th United States Congress, 1st session; Otto Eckstein, Technical Director; Washington: U.S. Government Printing Office, 1959) to be almost as pessimistic. T h e y state: "Past evidence suggests, therefore, that unemployment would have to average at least 6 per cent to keep the rate of wage advance no greater than the rate of increase in productivity." (Page 144; italics in original.) Consequently, " I t is doubtful that a secular uptrend in wages and prices can be avoided with an average level of unemployment which is considered socially acceptable, given our present types of anti-inflation weapons." (Page 144; entire passage italicized in original.)

The

122

Wage-Price-Productivity

Nexus

denotes the labor force at time /; this variable, like unemployment, is measured in thousands of workers. ( T h e sources of the ratio of unemployment to labor force are Lebergott's forthcoming book, Manpower

in Economic

Growth: The United States Re-

cord since 1800, for the years 1900-1940, and Historical Statistics, Table D 47, p. 73, for 1941-1957.) The six equations of the preliminary study alluded to in the text are listed below. T h e method of parameter estimation is single equation least squares. It might also be noted that equations ( a 3 ) and (a.4) appeared to have strongly autocorrelated residuals, although no formal test was made. (a.l) ( ^ L

x 1(χΛ = )

0.4968 (0.1679)

5325 ( 1 5 9 9 )

( ^ f ' ' x 100 Υ ^ Pt~2 '

(j^i.xi0(A= '

(a

1.193 (-jr^(0.0925)

0.1882 (0.1617)^

χ 1(χΛ + ' '

Su = 6.881, R2 = 0.2124.

1.511 + 0.1253 x loo) + L F i (0.884) (0.08900)^ ' x

100Y '

Su = 3.692, R2 = 0.7733.

(a.3) Aw ι =

.03558 -

0.1647 X 10 ~sUt

(.01043)

+

(02098 x 1 0 " 5 )

03639 Χ 10~ 2 ΔΡ, (0.1276 x 10~ 2 )

5« = 0.0484, R2 = 0.1737. (a.4) &wt = -

.01795 + (.00753)

0.1110 x 1 0 " 5 t / t + (0.1507 x 1 0 " ) 5

0.7716 x 10~ 2 Δ / y (0.0914 x 1 0 ~ 2 )

Sn = 0.0342, R = 0.5868. 2

123

Empirical Relationships (a.5)

(-^L x 10(Λ = \ie.-i )

4.139 ( 2 1 B )

0.2062

((U634)\LF*

x 1(χΛ }

+ 0.4841 ( ^ ^ x Κ » ) + 0.04703 t, (0.1690)^ P t ~ 2 ' (0.05459) Su = 6.897, R2 = 0.2231 (a.6)

( - ^ L X loo) = / +

0.8328 + 0.1143 (0.0899) ^

( 1 H 8 )

x 1(χΛ '

x 100^ + 0.02712 t, 1.186 (0.0930)^ ' (0.02927) 5„ = 3.696, = 0.7768.

APPENDIX

Β

The annual data (except the unemployment figures) used in calculating wage adjustment regressions are given in the table below. For definitions and sources, see the text. The residuals of equation (3.4) of the text are also included. Table IV Average Hourly Earnings (w), the Consumer Price Level ( Ρ ) , and Residuals of Equation (3.4), U.S.A., 1898-1957.

Year 1898 1899 1900 1901 1902 1903

Residuals of equation (3.4) (t/hour)

$.146

Consumer price index (1926— 100) 47 47

.151 .158 .165 .170

48 48 49 50

$.0165 .0227 .0146 .0112

Average hourly earnings (t/hour)

124

The

Wage-Price-Productivity

Nexus

Table IV (Continued) Average ly Year

hour-

earnings

(•t/hour)

Consumer price (1926

—

1904 1905 1906 1907 1908 1909

.169 .172 .184 .191 .184 .186

51 50 51 53 52 52

1910 1911

.198 .202 .207

54 54 55 56 57 57.4

1912

1913 1914 1915 1916 1917 1918 1919

.221

.220 .226 .262

61.6

.417 .477

72.5 85.0 97.9

.316

113.4

1922 1923 1924 1925 1926 1927 1928 1929

.553 .488 .451 .499 .516 .513 .517 .522 .522 .534

1930 1931

.530 .506

94.5

1920 1921

Residuals

index

101.0

94.7 96.4 96.7 99.2 100.0 98.1

97.0 97.0

86.0

100)

equation (%/hour)

.0046 .0187 .0121 .0000

.0066 .0059 .0025 .0060

-.0023 .0049 -.0089 .0007 .0029 -.0227 .0102 -.0349 -.0335 .0024 -.0132 .0170 -.0047 -.0414 -.0268

-.0092 -.0199 -.0172 .0138 .0091

of (3.4)

Empirical

125

Relationships

1932 1933 1934 1935 1936 1937 1938 1939

.446 .441 .527 .542 .553 .633 .639 .638

77.2 73.1 75.7 77.6 78.4 81.3 79.7 78.6

—.0187 .0071 .0520 — .0178 —.0197 .0320 —.0104 -.0239

1940 1941 1942 1943 1944 1945 1946 1947 1948 1949

.670 .737 .864 .975 1.05 1.06 1.13 1.30 1.41 1.46

79.3

97.8 99.3 101.6

—.0064 .0020 .0230 .0233 .0103 —.0605

110.2

—.0388

1950 1951 1952 1953 1954 1955 1956 1957

1.55 1.73 1.83 1.94 1.97 2.05 2.15 2.27

83.2 92.2

126.2

.0135

135.8 134.5

— .0086

135.8 146.7 150.0 151.1 151.7 151.3 153.5 158.8

.0217 .0481 .0131 .0350 —.0403 .0131 .0152 .0151

.0000

The quarterly wage and price level data used in calculating the correlation coefficients listed in Table II of the text appear below. The sources are outlined in the text.

126

The Wage-Price-Productivity

Nexus

Table V Quarterly Values of the Average Wage at an Annual Rate (w) and of the Implicit Deflator of Personal Consumption Expenditures ( P ) , U.S.A., 1945-1958. Average Wage at an Annual Rate it/year)

Period

Implicit Deflator of Personal Consumption Expenditures (1954=100)

1945

I II III IV

67.3 67.9 68.5 68.6

1946

I Π III IV

$2100 2220 2314 2328

68.9 70.0 76.2 80.3

1947

I II III IV

2438 2488 2503 2541

82.8 83.6 84.9 86.9

1948

I II III IV

2601 2651 2715 2742

88.2 89.2 90.4 90.2

1949

I II III IV

2767 2830 2765 2724

89.5 88.9 88.1 88.1

1950

I II III IV

2798 2864 2983 3041

88.1 88.7 90.6 92.2

Empirical Relationships

127

1951

I II III IV

3057 3170 3201 3232

95.2 95.8 96.0 97.1

1952

I II III IV

3286 3373 3400 3424

97.5 97.8 98.1 98.7

1953

I II III IV

3466 3582 3670 3656

98.7 98.7 99.2 99.2

1954

I II III IV

3639 3721 3712 3700

100.1

1955

I II III IV

3738 3800 3825 3794

100.3 100.2 100.4 100.6

1956

I II III IV

3906 4005 4019 4051

100.9 101.7 102.6

1957

I II III IV

4154 4245 4289 4234

104.1 104.8 105.6 106.1

1958

I II III IV

4347 4407 4412 4386

107.0 107.4 107.3 107.5

100.0 99.9 100.0

103.2

CHAPTER IV.

A Further Examination of the Wage Adjustment Equation I n C h a p t e r I I I the author f o u n d , using empirical methods, a w o r k i n g relationship between m o n e y w a g e changes and u n e m p l o y m e n t , a c o n s u m e r price level c h a n g e , and a time trend. I n this chapter some f u r t h e r possible modifications of this relation will b e e x a m i n e d in order to d e t e r m i n e w h e t h e r such

refine-

m e n t s w o u l d i m p r o v e the relationship. S o m e evidence concerni n g the question of irreversibility o f m o n e y wages will also be presented.

1. THE

POSSIBLE

ROLE

OF

PROFITS

T h e possible role of profits in the w a g e adjustment relationship m a y be investigated. O n e a r g u m e n t often heard at bargaining tables is that profits are high and that therefore a large wage increase is feasible. In J o h n T . D u n l o p ' s w a g e adjustment regression, 1 the previous year's ratio of corporate profits

(before

t a x e s ) to corporate sales is included a l o n g with last year's percentage

unemployment

of

the labor

force as an

explanatory

variable. W i l l i a m G . B o w e n has a r g u e d that once it is recognized that

firms

have goals other than m a x i m u m profits, profits

(in

ι John T . Dunlop, op. cit., pp. 23-24. This article has already been discussed above in Section 1 of Chapter I. 128

A Further Examination

of the Wage Adjustment

Equation

129

the sense of expected profitability) become a determinant of the wage increase. 2 Nicholas Kaldor, in his comment on Phillips' work,* suggested that the basic structural relationship was between money wage changes and profits and that the observed results merely reflect the intercorrelation between unemployment and profits. It is interesting to see, therefore, whether the profits variable is significant in the wage adjustment relation or can become significant if the relationship is reformulated slightly. Because we are dealing with such a long time period, any profits variable in an absolute form would show a pronounced time trend. Also, a variable like corporate profits would show variability because of changing economic organization as well as changing economic conditions—variations in the extent of incorporation could easily affect the recorded level of corporate profits. F o r these reasons, it seemed reasonable to deflate the level of profits by a scaling variable. T w o scaling variables were chosen: corporate net worth and the number of employees (in manufacturing). Consequently, two types of profits explantory variables were used. T h e first was total corporate profits

(Πτ)

divided by corporate net worth ( N W t ) , which can be interpreted as a type of rate of return on corporate capital. T h e second was manufacturing corporations' profits ( Π Μ ) divided by the number o£ employees in manufacturing establishments ( N m ) , which is (roughly) profits per man in the manufacturing sector. ( T h i s measure was restricted to the manufacturing sector because of the unavailability of data on the number of employees in the corporate sector, at least for the earlier years.) T h e first task was to gather data. T h i s has been done, and the

author's

series

of

total

corporate

profits,

corporate

net

2 William G. Bowen, The Wage-Price Issue, pp. 113-124. See the discussion in Section 1 of Chapter I above. 3 Nicholas Kaldor, op. cit., especially pp. 292-297. It should be noted that Kaldor argues that the money wage change is associated with the rate of change of profits and not their absolute level, which is the explanatory variable used (with modifications) below.

130

The

V/age-Price-Productivity

Nexus

worth, profits of manufacturing corporations, and employees of manufacturing establishments are presented in Appendix A of this chapter. T h e data on total corporate profits come from two sources. For the years 1900-1922 the estimates are Goldsmith's, 4 while the estimates from 1923 to 1956 are based on those of the Internal Revenue Service, as published in the various issues of Statistics

of Income,5

These are net profits after taxes; hence

not only corporate income taxes are deducted but also depreciation, amortization, and depletion. While Department of Commerce figures on corporate profits, corrected for underreporting and inappropriate conceptual treatments, exist, these were not used because the author thought that the reported figures were more relevant in the actual wage negotiations. A continuous series on corporate net worth was much harder to obtain. In the end, the author settled for a series of his own (rather crude) construction. T h e starting point was Goldsmith's estimates β of the total equity of corporations, for the benchmarks years 1900, 1912, 1922, 1929, 1933, 1939, 1945, and 1949. T h e non-bench-mark years between 1900 and 1949 were estimated with the help of Goldsmith's series on total national * Raymond W . Goldsmith, A Study of Saving in the United States, Volume I (Princeton, N.J.: Princeton University Press, 1955). T h e observations for 1900-1915 come from T a b l e C-5 on p. 917; those for 1916-1922 from T a b l e C-28, p. 939. T h e observation for 1922 is the same as the corresponding figure in that year's issue of Statistics of Income. 5 U.S. Treasury Department, Internal Revenue Service [formerly, Division o f Internal Revenue], Statistics of Income (Washington: U.S. Government Printing Office), various issues. After 1954, corporate earnings were reported on a fiscal year basis, rather than for a calendar year. Consequently, the net corporate profits (after taxes) of all corporations for the calendar years 1955 and 1956, are computed from the 1955-1956 and 1956-1957 fiscal year figures, using linear interpolation and extrapolation. T h e interpolator is the quarterly values of corporate profits after taxes for the years 1954-1957, as reported in U.S. Income and Output, Table VI I-18. pp. 230-231. β Raymond W . Goldsmith, "National Balance Sheets and National Wealth Statements, 1896 to 1949," Part I of Raymond W. Goldsmith, Dorothy S. Brady and Horst Mendershausen, A Study of Saving in the United States, Volume I I I (Princeton, N.J.: Princeton University Press, 1956), pp. 3-135. T h e series cited is taken from T a b l e W - 3 0 on p. 79.

A Further Examination

of the Wage Adjustment

Equation

131

wealth in current values; ' it was assumed that the change from the bench-mark date in both series, for an intervening year, was proportional to the change in both series, between two contiguous bench-mark years. 8 T h e n , to extend the estimates of corporate net worth beyond 1949, the following procedure was employed. A regression of corporate net worth on total national wealth was run for the bench-mark

years. Substituting Goldsmith's

mate9

wealth

of total

equation,

the

national author

obtained

in an

1956 into the estimate

esti-

estimating

of corporate

net

worth for the year 1956. Estimates of corporate net worth for the years 1950-1955 were then obtained by linear interpolation. If these techniques seem crude, the purpose for which

they

were employed must be kept in mind. Corporate net worth, the denominator of the ratio which represents the rate of return on corporate capital, is large relative to the numerator, corporate profits. Hence even moderate errors in the denominator

will

produce only small distortions in the ratio. T h e figures on the profits of manufacturing corporations come from similar sources. T h e figures for the years 1919-1922 were compiled by Goldsmith. 1 0 T h e figures for 1923-1957 are taken from or based on various issues of Statistic

of Income.11

The

7 Ibid., T a b l e W - I , p. 14. I-ct y be corporate net worth and χ total national wealth. Basically, we know x o , * , . . . , x n and yo and yn. Our problem is to estimate yr j = 1, 2 , . . . η — 1, from this information. T o do this, we assume

T h u s our estimate of yt is given by (ii) est. of y, = y„ + (x, - χ J -f*" _ a Historical

Statistics,

^

T a b l e F 197, p. 151.

10 Raymond W . Goldsmith, A Study of Saving in the United States, Volume I, T a b l e C-28, p. 939. 11 T h e profits of manufacturing corporations for the years 1923-1954 were taken directly from this source. T h e 1955, 1956, and 1957 values were estimated by the author, using the method of interpolation that was employed for total corporate profits.

The

132

Wage-Price-Productivity

Nexus

series of employees in manufacturing establishments comes directly from Historical

Statistics,12

Next, we may turn to the time diagram of the money wage change and of total corporate profits divided by corporate net worth. (See Figure 5; the productivity change series is not under discussion until Section 3 below.) T h e mean value of the ratio of total corporate profits to corporate net worth, over the period 1900-1956, is 0.06195. T h e time diagram suggests that current profits are a slightly superior explanatory variable, although the relationship between money wage changes and profits appears to be a loose one. I S Hence the current profits variable was tried first;

but the parameters of a formulation employing lagged

values of the better variant of scaled profits have also been estimated. W e now seek to determine whether the addition of a profits variable will improve the tentative wage adjustment

relation-

ship. Hence a regression of the form: (4.1)

Δ«/( =

, are included in the regressions for the entire

period

1913-1957,

the coefficients of both

demand-

proxy variables are slightly larger than those appearing in the corresponding regressions f r o m which the " a b n o r m a l " year observations have been excluded. T h i s suggests that, after allowance is m a d e for the unusual circumstances (price c o n t r o l s )

of

the w a r t i m e subperiods, d e m a n d influences did exert some upward

pull on

prices, w h i c h

was

possibly even stronger

than

d u r i n g other, m o r e n o r m a l years of the total period.

5. THE

QUESTION

OF

IRREVERSIBILITY

A n o t h e r subject of interest is the possible presence of irreversibility in these relations. Is there any evidence that prices m o v e

178

The Wage-Price-Productivity

Nexus

upward more easily than downward? One possible type of irreversibility is a greater responsiveness to high demand than to low demand. This can be tested by partitioning the demand. * ι Xm MA ι· proxy variable —— as follows: MA e

(5.14) Xm — MA \

(

—— MA

Xm — MA

1= /1

(5.15) ( Xm — MA \ { ΜΑ Λ"

,

,

.

—— when the latter is positive, MA = 0 otherwise; |X„, - MA\ , Xm- MA n s f i Whcn MÄ — 0 otherwise.

. negatlVe'

,s

ι ./... • (Xm Xm \ ι (Xm Xm \ Analogous dehnitions apply to I — - — I and ι — — I. \ Xm /l \ Xm /2 When these split variables are substituted for the regular demand-proxy variables, the regression results become:

(5.16) P< =

7.057 + 6 2 2 7 ( — ) (1.940) ( 5 . 5 4 8 ) ^ A m '

+ 03515 P r - 0.1548/ (0.05258) (0.04893)

- 1 0 . 9 3 * 1 - 3.919*2 + 5.711 (1370) (1.583) (2.000)^ + 3.567 ( X m ~ M \ MA (6.758)

A

\ Su = 2.291, /·.

''

M A

I P = 0.9913,

(5.17) P> = 10.08 + 63.60 ( - ^ Λ (2.074) (6.096)^ ' -

+ 0 3 0 8 5 P · - 0.1297/ (0.05963) (0.04988)

9.433 2ι - 3.606 22 + 5.990 ( X (1339) (1.662) (5.678)^ 6.958 ( X m ~ (6.578)^

Xm

m

~ Xm

Xm

\ >x

Y S„ = 2.408, R 2 = 0.9904. '2

The Influence

of Costs and Other Factors on Price Levels

179

If there is symmetry of response (i.e., no irreversibility), then the sum of the coefficients of the

partitioned

demand-proxy

variables should not be significantly different from zero.

(The

coefficient of the negative deviations of output from the moving geometric mean

is expected

to have a negative sign, as this

variable has been defined so that it takes on only non-negative values.)

Equation

irreversibility

(5.16)

suggests, on

the surface, that

such

was present. T h u s the influence of the positive

deviations of output from the moving average is stronger than the influence of the entire group of values of this

demand-

proxy vriable. F u r t h e r m o r e , the negative deviations have a perverse influence on Pf,

although the positive coefficient of this

variable is not statistically significant. In addition, partitioning this demand-proxy in this manner raises the coefficient of multiple determination slightly. However, the standard error of the sum of these two coefficients, if the estimated covariance term 9 278 into account, is 7.766. T h e t ratio is — or 1.19. 7.766 T h i s discrepancy is far from being statistically significant, even is taken

at the 5 per cent level with a one-tailed test. Hence,

while

intriguing, this apparent asymmetry is not conclusive evidence that these prices moved upward more easily under the pressure of high demand than they moved downward when demand was low. T h e same conclusion easily falls out of equation ( 5 . 1 7 ) . H e r e the modification worsens the fit after a correction for degrees of freedom is made. (5 K is lower for equation (5.13) than for this equation.) T h e t ratio of the sum of these two coefficients to the estimated standard error of this sum is 0.09. T h i s corroborates the apparent symmetry of movement and is consistent with the final conclusion about equation

(5.16).

Another possible irreversibility is that high past levels of costs may have a persisting influence. A plausible hypothesis is that o n e determinant of current prices is the previous peak level of costs, as this high structure of costs may become

embedded

The Wage-Price-Productivity

180

Nexus

in particular prices, which are slow to readjust downwards. T o test one variant of this thesis, we may define w fe ak as the highest value of the money wage in manufacturing, w, from the beginning of the period of the current date. In symbols, this variable is defined by the expression: (5.18)

Wpeak at time t =

Max. (wi,w*,...

,wt),

where wι is the value of w in 1913, w-i is the 1914 value of w, and so on up to the current value (the value at time / ) of this variable. ( T h e symbol Max. denotes the m a x i m u m value of the numbers enclosed by the succeeding parentheses.) An analogous

A method of testing for this type of irreversibility is to introduce both of these variables, one at a time, into the

finished

goods wholesale price regressions. T h e relations then become: (5.19) P' =

8513 + 5353 (1590) (7.954)

9.883 ζ ι (1.423)

0 3 6 3 3 PT (0.05279)

0.23681 (0.07317)

3.975 22 (1.554) Su = 2.249,

R2 =

0.9916,

(520) P' =

-

9.886 + 52.97 (1.510) (8332)

8.746 a ι (1331)

0 3 4 8 1 Pr (0.05970)

3.887 2 2 (1.597) Su = 2 3 1 1 ,

02337/ (0.07525)

- ) + 5.606 ' (3316) R' =

0.9912,

Wfeak,

The Influence of Costs and Other Factors on Price Levels

181

(521)

P> -

6.011 +61.13 ( - ^ A + 03442 Γ - 0.1733/ (3.190) (5.973)^Am ' (0.05262) (0.05796)

-10.45«, - 3.783ζ2 + 4.531 ( X m ~ ^ A ) (1.402) (1.595) (1.646)V M A ' + 3.024 ( - f - Y 5« = 2317, K 1 = 0.9911, (3.560)^ A m ' pe"k (522) P' = 11.24 +65.26 ( — ' ) + 0.2962 F ~ 0.11731 (3273) (7.151) ^ A m ' (0.06541) (0.05718) - 9.647 z, - 3.602 ζ·< + 6.956 ( X m ~ ? m " ) (1394) (1.655) (3.280)V X m ' -

1.739 ( - ^ - Y 5U = 2.405, R 2 = 0.9904. (3 897)^ ' ' v'"k

T h e coefficient of the I —— ) variable is less t h a n its associated \ Am / peak s t a n d a r d error, in b o t h e q u a t i o n s (5.21) a n d (5.22). H e n c e this variable does not have a statistically significant influence. O n t h e other h a n d , the t ratio for wveak

is 1.62 in e q u a t i o n (5.19) a n d

1.79 in e q u a t i o n (5.20). U s i n g t h e 5 per cent level w i t h a onetailed test ( o r t h e 10 per cent level w i t h a two-tailed t e s t ) , o n e w o u l d c o n c l u d e that this variable plays a statistically significant role in e q u a t i o n

(5.20), but not in (5.19). T h u s this

variable

seems i n t e r e s t i n g e n o u g h to w a r r a n t f u r t h e r study, especially in view of t h e low values of the D u r b i n - W a t s o n statistic, 1.27 a n d 1.15, associated w i t h e q u a t i o n s (5.19) a n d (5.20) respectively. In Section 6 below, t h e role of the tvv,nk

variable is reconsidered

a f t e r autoregressive t r a n s f o r m a t i o n s are p e r f o r m e d o n all

the

variables of these relations so that the p r o b l e m of a u t o c o r r e l a t e d residuals m a y be m i t i g a t e d . In that section, it is f o u n d t h a t the

182

The

Wage-Price-Productivity

Nexus

suspicion that past levels of wages may have a persisting influence

on prices is strengthened.

( S e e T a b l e s V I I and

VIII

below.) It should be noted, however, that these tests do not constitute conclusive evidence of the presence of irreversibility. It is possible to give different interpretations of the variables used in the attempt to test for irreversibility. T h u s one possibility, suggested by the poorer performance of the

( ——-) variable, is that the \ Am / peak

u>p,:„k variable represents some additional influence of

money

wages beyond their role as the numerator of the labor cost ratio. ( I n Section 1, however, it was seen that money wages and labor productivity appeared to have an influence on

finished

goods

prices that was symmetric though opposite in sign.) Also, different methods of asking these questions may yield different conclusions, as we shall note below in connection with the Y a n c e study. Furthermore, it is quite possible that reversibility characterized some subperiods of this era, but not the entire period. T h u s the conclusion of some irreversibility in these relations, over the period studied, is a tentative one. T w o recent studies, in part directed toward these same questions, may be briefly e x a m i n e d . ' " Joseph V . Y a n c e fits a distributed delay model, in order to explain product prices in the U . S . shoe manufacturing and leather tanning industries, over the period 1947-1956. In his model, the equilibrium product price (in the empirical work, a price index) is a linear function of the industry wage and the price ( i n d e x ) of a principal raw ma12 Joseph V. Yance, " A Model of Price Flexibility," American Economic Review, Volume L, No. 3, (June, 1960), pp. 401-418; Wesley J . Yordon, J r . . "Industrial Concentration and Price Flexibility in Inflation: Price Response Rates in Fourteen Industries, 1947-1958," Review of Economics and Statistics, Volume X L I I I , No. 3 (August, 1961), pp. 287-294. See also the discussion between Yordon and Yance, which appears in the American Economic Review, Volume L I , No. 3 (June, 1961), pp. 390-394.

The Influence

of Costs and Other Factors on Price Levels

183

terial. T h e actual current price is related to the normal current price by a distributed delay adjustment equation, which states that the change in the product price, f r o m the previous to the current period, is a constant proportion of the discrepancy between the current equilibrium price and the actual price of the previous period. After estimating the parameters of this model, Y a n c e asks whether the introduction of two reaction coefficients, one for non-negative discrepancies (between the current equilibrium price and the lagged actual price) and one for negative discrepancies, would significantly improve the model. In both tanning

and shoe manufacturing,

however, this

modification

leaves the response parameters close to those estimated previously. Moreover,

in

both

cases, the

partitioned

reaction

coefficients

do not differ significantly from each other. Somewhat different results were obtained by Wesley J. Yordon, who fitted a more conventional regression model to fourteen U.S. manufacturing industries over the period

1947-1958.

His dependent variable was the change in an industry's product price index, and his explanatory variables, which related to the individual industry, were changes in labor cost, positive changes in materials costs, negative changes in materials costs, positive changes in the demand pressures variable, and negative changes o£ this demand variable. 1 3 T h u s the form of Yordon's regressions allows one to test possible asymmetries of response, both for the influence on final price of the demand variable and for that of materials costs. In this case of the split demand variables, the regression coefficients suggest some asymmetry, but the standard errors are too large to allow one to draw this conclusion. T h e r e is, however, definite evidence that materials costs increases had a stronger impact on prices than materials costs decreases; morei s Yordon's demand variables, which are discussed more fully in Section 6 below, were used only in the regressions calculated from quarterly data, but not in those calculated from monthly data.

184

The

Wage-Price-Productivity

Nexus

over, the difference in these response rates was statistically significant. 1 4 T h i s type of irreversibility appeared in both

Yordon's

concentrated ( " m a r k e t power") group of industries and in his unconcentrated ("competitive")

group.

T h u s Yordon's findings lend support to the present author's tentatively final conclusions concerning irreversibility in the price formation equations, while Yance's results tend to cast doubt upon the existence of irreversibility. As the techniques employed in this section resemble more closely those used by Yordon, it is not surprising that the results of this section are supported by Yordon's findings, but not by those of Yance. In that Yordon made a partial allowance for changing input coefficients (i.e., changing factor productivity), his study would appear to be slightly superior on these grounds. O n the other hand, Yance's study suggests that if the model is formulated differently, the analysis of similar data may yield different conclusions regarding irreversibility of the price formation relationships. Moreover, as Y a n c e has pointed out in the already cited dialogue between the two, regression analysis is a blunt tool for analyzing small, longdelayed responses of product prices to cost changes. 1 '' T h i s difficulty

is a possible source of their differing conclusions about

price formation asymmetries in American manufacturing industries, which both of them studied over roughlv the same postwar κ William G. Bowen has argued that business firms may be expected to be more responsive, in their pricing policy, to increases in costs than to cost decreases, when account is taken of the actual uncertainty which pervades all real world business decisions. See The Wage-Price Issue, pp.

294-295.

i s L. A. Dicks-Mireaux (op. cit.,) makes a similar point and actually attempts, by trial and error, to estimate parameters of price change and wage change relationships in which the explanatory variables work out their impact on the dependent variable over the current and the four preceding years. T h e results, for the equation in which changes in the price level are the dependent variable, allow him to interpret the significant constant term in his earlier regressions as the average value of delayed responses to the explanatory variables, which of course are not captured in the straight regression equations.

The Influence vears. In

this

185

of Costs and Other Factors on Price Levels

respect,

Yance's

study

would

appear to

yield

somewhat more relevant conclusions.

6 . F U R T H E R DISCUSSION

In this section, equations (5.12) and (5.13) are examined more closely. T h e author's results for his demand-proxy variables are compared to several other studies which attempt to gauge the influence of demand on the price level of final output, with particular attention Edwin K u h .

being

paid

to the study

undertaken

by

T h e problem of autocorrelated residuals is dis-

cussed and autoregressive

transformations of the variables of

several of the most interesting regressions presented above are introduced, in an attempt to circumvent this problem. Finally, the section concludes with a brief discussion of possible single equation biases in the estimates of these regression parameters. Using mean values over the period studied, one may further examine the impact of the various explanatory variables of equation (5.12) on the wholesale price index of finished goods. T h e constant term of this regression, which on one interpretation is a measure of the importance of fixed costs in the manufacturing sector in general, is 8.3 index points, or 11.2 per cent of the period mean

value of P ' . Over the period studied, a 1 per

cent rise in — i s associated, on the average, with a 0.595 per Sim cent increase in P ' . Similarly, from equation (5.12), the partial elasticity of P' with respect to Pr, at the means of these variables, is 0.297. Ceteris

paribus,

P' falls by 0.15 index points a year,

which is approximately 0.20 per cent of the mean value of the wholesale price level of finished goods. D u r i n g the period 19431946, P ' was 10.7 index points lower than it would have been in the absence of the extraordinary forces (principally price controls) operative at that t i m e ; this magnitude represents 14.4 per cent of the mean value of P ' . Likewise, during the period 1951-1953,

The

186 the

finished

Wage-Price-Productivity

Nexus

goods wholesale price index was 3.8 index

points

lower t h a n it otherwise w o u l d have b e e n ; this figure is 5.1 per cent of its m e a n value. Also f r o m equation ( 5 . 1 2 ) , one may calculate that a 1 per cent rise in m a n u f a c t u r i n g output, Xm, relative to its " n o r m a l " value, M A , was associated with a rise in P r w h i c h was 0.06 per cent of the mean value of this price level variable. 1 6 T h u s , a l t h o u g h the demand-proxy variable ( t h e relative discrepancy o f m a n u f a c t u r i n g output f r o m its logarithmic m o v i n g a v e r a g e ) was f o u n d to have a statistically significant influence

( b y ordinary tests), its i m p o r t a n c e would appear to be

decidedly secondary. E d w i n K u h , in his Joint E c o n o m i c C o m m i t t e e S t u d y Paper, 1 7 also introduced a d e m a n d variable into his price level equation. As summarized

in C h a p t e r I above, this variable is the ratio

of current output to "capacity o u t p u t , " w h e r e "capacity o u t p u t " is defined as previous peak output adjusted, in certain cases, for the g r o w t h o f capacity in the corporate sector. K u h also f o u n d that this d e m a n d - p r o x y

variable had a statistically

significant

influence, t h o u g h it was of lesser i m p o r t a n c e than his t w o labor cost

variables. T h e

sensitivity

of the

corporate

product

price

index to variations in K u h ' s demand-proxy variable is s o m e w h a t greater than that of P ' to t h e present author's variables,

as

measured

by

equations

(5.12)

demand-proxy

and

(5.13).

The

elasticity of K u h ' s price index with respect to his d e m a n d - p r o x y variable is 0.22. T h i s elasticity corresponds closely ( a s a c o n c e p t ) to the present because

the

author's

mean

of

measure in Kuh's

the preceding

demand-proxy

paragraph,

variable

is

very

close to unity. ιβ For equation (5.13), the numerical analysis yields similar conclusions, as one might expect. The constant term is 13.4 per cent of the mean w

value of PI. T h e elasticity of P! with respect to — - is 0.602, while with respect to Pr it is 0.278. From this equation, one may calculate that a 1 per cent rise in X m (relative to X* m ) leads to a rise in PI which is 0.09 per ccnt of the period mean value of this price level variable. 17 Edwin Kuh, op. cit.

The Influence

of Costs and Other Factors on Price Levels

T h e view that demand factors are of secondary

187

importance

in the determination of the level of final prices has also been supported

in

Mireaux. 1 8

studies

J. C .

R.

by

Dow,

Dow,

Yordon,

examining

Yance,

postwar

and and

Dicksinterwar

British data, found that profit margins showed some tendency to vary in a positive direction with the level of demand, but he concluded that the quantitative importance of this effect was small. In the study discussed in the previous section, Wesley J . Yordon used, as a measure of demand pressures in the fourteen U.S. manufacturing industries studied, the deviation of average weekly hours over the preceding quarter of a year from

the

grand average of weekly hours worked during that quarter over the full period ( 1 9 4 7 - 1 9 5 8 ) . Yordon employed both positive and negative changes in this variable as explanatory variables in his regressions, in which the dependent variable was the change in the price index of the industry's final product. Yordon found that the influence of both increases and decreases in this measure of demand

was quite weak, although

he did

find

one or

two

significant coefficients of these demand variables out of the six calculated. 1 9 Also, from his examination of the gross profit margins of the fourteen industries, it appeared that, in both

the

concentrated and unconcentrated industries, demand had little influcncc on profit margins, while for both sets of industries, responsiveness to cost influences seemed sufficient, as a general rule, to maintain gross percentage margins. Joseph V .

Yance,

18 J . C. R . Dow. "Analysis of the Generation of Price Inflation: A Study of Cost and Price Changes in the United Kingdom, 1946-54"; Yordon, op. cit.; Yance, op. cit.; L. A. Dicks- Mireaux, " T h e Interrelationship between Cost and Price Changes 1946-1959: A Study of Inflation in Post-War Hritain." ιβ Yordon presents three sets of regression results: one for the concentrated industries, one for the unconcentrated industries, and a final set for both industry groups together. From these regressions, he also found some evidence that the influence of demand (especially demand increases) was slightly greater in his unconcentrated industries than in the "market power" group. T h i s hypothesis did not, however, appear to be confirmed by his analysis of the gross profit margins of the various industries.

The

188

Wage-Price-Productivity

Ν ex/is

whose study is also briefly summarized in the preceding section, did not explicitly incorporate into his model a possible influence of demand on the actual price of the product. However, he points out that the presence of autocorrelated residuals in his estimated price change regressions suggests the possibility that an excluded variable, such as a demand variable, may be relevant. T h e same conclusion may be inferred more directly from Yance's simulation of the price index of shoes, over the period 1950-1952. T h e model-generated price reproduces the actual shoe price index very closely, except for the subperiod from September, 1950 to April, 1951, when the actual price was above that generated by the model. As these were the months after the outbreak of the hostilities in Korea and were presumably a period of high demand, this suggests that demand has some positive influence on price formation in the shoe industry. However, the fact that Yance obtained a good fit without explicitly considering a demand-proxy variable also suggests the secondary importance of the role of demand. Finally, glancing again at the economy of the United Kingdom, we may observe that L . A. Dicks-Mireaux experimented with his and J. C. R . Dow's index of the excess demand for labor as a proxy for the influence

of

ex

ante

demand

for

goods and

services.

Dicks-

Mireaux found, however, that this variable did not contribute very much to his explanation of the index of final prices at factor cost. Scanning the residuals of equations

(5.12) and (5.13), the

author was led to suspect autocorrelation. Calculation of the Durbin-Watson statistic ( d ) yielded the value 1.29 for equation (5.12) and 1.15 for equation

(5.13). For samples of the size

employed (45 observations), the hypothesis of positively autocorrelated residuals must be accepted at the 5 per cent level for (5.12) and at the 2.5 per cent level for (5.13). 2 0 T h u s the results 20 T h e s e levels of significance strictly apply to a regression with five explanateory variables, not one which has six, as do (5.12) and (5.13). How·

The

Influence

of Costs and Other

Factors

on Price

Levels

a r e less c e r t a i n a n d t h e statistical tests i n v o l v i n g errors less v a l i d , b e c a u s e o f t h e p r e s e n c e o f this By

recomputing

the

working

price

level

the

189

standard

phenomenon.

relationships

in

a

slightly d i f f e r e n t f o r m , o n e m a y a t t e m p t to o b v i a t e t h e p r o b l e m of

autocorrelated

transformation

residuals.

If

we

perform

an

autoregressive

on t h e v a r i a b l e s a n d o n t h e e r r o r t e r m ( i n )

of

equation (5.12), we obtain: (5.12a)

+ aS(P,r

-

ρ P-t-i)

+ β» [ t - p ( t - 1 ) ] + « 4 ( * . . -

, +, 2 53. 2 56, 257, 267, 269

Index

302

Winsten, C. B., 36, 37 World W a r I, 23, 3 1 , 35, 37, 38, 172, 2 5 1 , 252, 260, 268 World W a r II, 32, 35, 38, 49, 120, •72, 173. ' 7 7 . 283

2l

5>

22

3'

2

59.

2

7°.

Yance, Joseph V., 1 8 2 - 1 8 5 , 187, 188, 241 Y o r d o n , Wesley J., Jr., 1 8 2 - 1 8 4 , 187