Strong Money Demand in Financing War and Peace: The Cases of Wartime and Contemporary Japan (Advances in Japanese Business and Economics, 28) 9811624453, 9789811624452

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Advances in Japanese Business and Economics 28

Makoto Saito

Strong Money Demand in Financing War and Peace The Cases of Wartime and Contemporary Japan

Advances in Japanese Business and Economics Volume 28 Editor-in-Chief Ryuzo Sato, C.V. Starr Professor Emeritus of Economics, Stern School of Business, New York University, New York, NY, USA Senior Editor KAZUO MINO Professor Emeritus, Kyoto University; Professor of Economics, Doshisha University Managing Editors HAJIME HORI Professor Emeritus, Tohoku University HIROSHI YOSHIKAWA Professor Emeritus, The University of Tokyo; President, Rissho University TOSHIHIRO IHORI Professor Emeritus, The University of Tokyo; Professor, GRIPS Editorial Board YUZO HONDA Professor Emeritus, Osaka University; Professor, Osaka Gakuin University JOTA ISHIKAWA Professor, Hitotsubashi University KUNIO ITO Professor Emeritus, Hitotsubashi University KATSUHITO IWAI Professor Emeritus, The University of Tokyo; Visiting Professor, International Christian University TAKASHI NEGISHI Professor Emeritus, The University of Tokyo; Fellow, The Japan Academy KIYOHIKO NISHIMURA Professor Emeritus, The University of Tokyo; Professor, GRIPS TETSUJI OKAZAKI Professor, The University of Tokyo YOSHIYASU ONO Professor, Osaka University JUNJIRO SHINTAKU Professor, The University of Tokyo MEGUMI SUTO Professor Emeritus, Waseda University EIICHI TOMIURA Professor, Hitotsubashi University KAZUO YAMAGUCHI Ralph Lewis Professor of Sociology, University of Chicago

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Makoto Saito

Strong Money Demand in Financing War and Peace The Cases of Wartime and Contemporary Japan

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Makoto Saito Graduate School of Economics Nagoya University Nagoya, Aichi, Japan

ISSN 2197-8859 ISSN 2197-8867 (electronic) Advances in Japanese Business and Economics ISBN 978-981-16-2445-2 ISBN 978-981-16-2446-9 (eBook) https://doi.org/10.1007/978-981-16-2446-9 © Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

As I ventured to point out to Sergeant Rogers this morning, its importance for our purposes lies precisely in an event which did not happen. Because it did not happen, it has been forgotten, except by historians, who unfortunately are not permitted to exercise much influence in current English politics. Cyril Hare, An English Murder (1951).

Preface

The “strong money demand” in the title of this book is the situation where money demand exceeds normal transaction demand. Such strong money demand has appeared twice in the modern Japanese economy. It first appeared during World War II and then, more recently, after the mid-1990s. By analyzing these two occasions, I resolve one important policy question, as posed below, and propose one new theory, being a monetary and fiscal theory of the price level. For its part, my policy question is straightforward: Are the fiscal conditions of the contemporary Japanese economy sustainable? This question has been raised repeatedly by contemporaries in various positions inside and outside Japan around the beginning of the twenty-first century. The Japanese government has accumulated enormous debt since the early 1990s, while the Bank of Japan (BOJ) has guided interest rates at near-zero levels since late 1995. Given this sizeable fiscal and monetary policy mix, I have become fearful of sharp inflation, a crash in the market for public bonds, and even fiscal collapse. It was by this same policy mix that Japanese society has overcome one crisis after another, including the collapse of the asset price bubbles in the early 1990s, the Great Hanshin–Awaji Earthquake in January 1995, the 1997–1998 national financial and 2007–2008 global financial crises, the Great East Japan Earthquake in March 2011, and the present coronavirus crisis starting in early 2020. Nevertheless, there has yet been no sign of sharp inflation increases, hikes in long-term bond yields, or fiscal catastrophe. Instead, the nominal rate of interest has remained near zero, while the price level has been almost constant. Behind these near-zero nominal interest rates and stable prices, the real rate of interest has also been stagnant at around zero, reflecting the low productivity of the Japanese economy. The combination of zero nominal interest rates, zero inflation rates, and zero real interest rates, which I refer to as the Triple Zero for the moment, has now been present in Japan for a quarter of a century. But a more popular term is the Lost Decades, to which negative images of mild deflation and low productivity have become attached.

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A strange policy recommendation has come to the fore as the Triple Zero continued in Japan over this prolonged period, with many policy commentators beginning to argue, “Don’t worry about public debt expansion as long as zero interest continues.” This view seems quite strange, at least to me. The same commentators formerly recommended expansionary macroeconomic policies to overcome the Triple Zero, made up of around 2% inflation through monetary expansion, a higher-than-0% positive real interest from improvements in productivity and, lastly, an above-zero nominal interest with monetary policy normalization. However, we cannot separate zero interest from the other two zeros. Thus, these same commentators now propose the Triple Zero as a major assumption of their policy framework but with overcoming the Triple Zero replaced by appreciating it. The target of aggressive macroeconomic policies thus shifts subtly toward using the Triple Zero to help sustain Japan’s large and growing public debt. Nonetheless, this policy view is quite troublesome to macroeconomists like us exposed to the rational expectations revolution. In their view, the Triple Zero is self-fulfilling. Thus, to the extent that the Triple Zero continues, Japan’s huge public debt may be sustainable. But for what purpose? Does anyone want the Triple Zero to continue forever, and is it even sustainable in the first instance? I hesitate to accept this view, and in this book, I present a theoretical, empirical, and historical argument against it. When I had almost finished my research project on the social and economic impacts of the Great East Japan Earthquake in late 2014, I tried to begin macroeconomic research on Japanese fiscal conditions. My conscience even urged me to study it after seeing that the reconstruction budget swelled enormously through many outrageous political processes. However, the earthquake project had exhausted me, and I wished that I had tackled another ongoing problem of Japanese society. I simply could not. Instead, I tried to put my work in a historical context, one different from the current economy, and to reflect casually about fiscal and monetary problems. A past historical incidence, which I tried to separate from the present, was Japan’s controlled-economy period, running between the Second Sino-Japanese War that began in July 1937 and the occupation of Japan by the Allies after World War II, which ended in April 1952. During and after the war, the Japanese economy was subject to strict price controls and rationing. Two fascinating books by Nakamura (1974) and Tatai (2002) on the controlled economy influenced this choice. I also appreciated that the industrial policy of postwar Japan took over that of the controlled economy by reading Noguchi (1998) and Okazaki and Okuno-Fujiwara (1999). But their argument concerned the microeconomic aspects of the controlled economy, and I thought that the macroeconomy would be rather different. In my study at home, and in my university office, I lay down on a sofa much of the time, just read as many books and articles as I could, and perused as much data as possible. In late 2015, I suffered retinal detachment in both eyes through what might be considered masochism and almost lost sight in my right eye. However, through a forced slowdown, I found that I could read characters and figures even better than before.

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I had been surprised and even fascinated by my many discoveries, both large and small, only in my view, of the studies on the Japanese controlled economy. For example, some consider the sharp inflation immediately after the war as hyperinflation but, in fact, it was not. Iwamura (2010) compares the prices of postcard stamps before and after the war. In July 1937 when the Second Sino-Japanese War started, stamps were 2 sen (two hundredths of a yen), rose to 5 sen in April 1945 just before the end of the war, and increased to 5 yen in November 1951 by the end of the Allied occupation. According to this stamp price index, wartime inflation just increased by a factor of 2.5, while that during the occupation period was a hundredfold larger. Upon reading these prices, I asked myself, “Was inflation really that low?” I checked with more general price indexes, but the figures were the same and far too moderate to be hyperinflation. A question, more subtle to me at the time, was why the price surge stopped suddenly in the late 1940s, instead of descending into actual hyperinflation. In several respects, the Japanese macroeconomy after the controlled-economy period returned to the macroeconomy that came before. Of course, the nominal exchange rate between Japanese yen and the US dollar heavily depreciated from 4 yen 27 sen per dollar in 1940 to 360 yen per dollar in 1949. But this was not the case for the real yen–US exchange rate. Between 1940 and 1950, the retail price index rose by a factor of 140 in Japan (Tokyo) (Ohkawa et al. 1967), while the consumer price index increased by a factor of 1.7 in the USA (city average) (US Bureau of Labor Statistics, 2020). Thus, in real terms 4 yen 27 sen in 1940 was equivalent to 350 yen in 1950, which was not significantly different from 360 yen fixed in 1949. Similarly, the nominal balance of BOJ notes in circulation increased by a factor of 154 over the period 1937–1949. As shown in Chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, however, if it is standardized by nominal gross national expenditure (GNE), a completely different picture appears. The balance of BOJ notes in circulation was stable at about 10% of nominal GNE before the Second Sino-Japanese War began in 1937. But it expanded to just below 50% during the war and then declined quickly to its prewar level of 10% just five years after the war. By interpreting outstanding BOJ notes over nominal GNE as the strength of money demand, we can see that it was extremely strong during the war, but quickly returned to its prewar level after the war ended. I also found that I could precisely estimate the size of the black markets in place in Japan during the controlled-economy period in quite an unexpected manner (see Chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”). In the national income accounts between 1937 and 1949 (Economic Planning Agency, 1964), large discrepancies arose between aggregate expenditure and income in Japan. I initially thought that these were just measurement errors, but later found that they corresponded to the size of the income leakage from the formal to the underground economy. It is easy to prove that if goods trade in both official and black markets, then aggregate expenditure always exceeds aggregate income by this amount in the national accounts. What is more, black marketeers at the time held copious amounts

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of BOJ notes to mask this illicit income given the uninscribed nature of banknotes. These vast holdings of BOJ notes appeared as strong money demand in the wartime formal economy. However, as black marketeers rushed to exchange their BOJ notes for physical assets after the war, the strong money demand quickly disappeared. The Japanese wartime government financed war expenditures from not only its home (or interior) territory, but also its occupied territories, requiring reserve and central banks in the occupied territories to underwrite public debt directly (see Chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”). How successful the funding was through these reserve/central banks depended on how strong the demand for their issued notes was. The banknotes, accepted locally as convenient currencies, brought much purchasing power to the Japanese occupation forces, while those rejected as inconvenient did little. But this was not the end of the story. After the war, it costs the defeated Japanese government dearly to repay its liabilities owed to countries where the Japanese army acquired much purchasing power during the war. While I saw these fiscal and monetary phenomena of the controlled economy, I occasionally confused public debt with money. I even deluded myself that public debt and money were identical. In the interior territory, the Japanese consolidated government, consisting of the central government and the BOJ, replaced government bonds with BOJ notes through a direct deal between the two bodies. Money demand from both the formal and underground economies then absorbed the BOJ notes issued massively to the government. In the occupied territories, the government replaced its own debt by the notes issued locally by the local reserve/central banks. These massively issued banknotes sometimes circulated well, but sometimes did not. In this way, the public debt supply is substituted for the money supply, while money demand replaced public bond demand. In modern monetary economics, however, we treat money and public bond markets completely separately. According to the quantity theory of money (QTM), the supply–demand balance of money markets solely decides the price level. In the fiscal theory of the price level (FTPL), an especially influential alternative to the QTM, fiscal policy decides the price level. In the FTPL, we even sometimes totally ignore money markets. Formed by such modern macroeconomic theory, I found something refreshing in the Japanese controlled wartime economy where the borders between money and public debt were more ambiguous. As I had almost recovered from an illness by 2018, I returned to the concerns of the contemporary Japanese economy. In the current economy, money demand has been as strong as in the wartime economy. The demand for BOJ notes has expanded given that the holding costs of money became almost nothing at near-zero interest rates in late 1995. The balance of BOJ notes in circulation was stable at around 8% of nominal gross domestic product (GDP) up to 1995, but it reached 20% in 2018. The balance of the monetary base, which consisted of BOJ notes and reserves, was steady at around 9% of nominal GDP up to 1995 but moved above 90% in 2018. When I started to examine this contemporary strong money demand,

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I was not obsessed too much with the conventions of modern macroeconomics. Instead, I found myself enticed to treat money and public debt as a harmonious whole, even in the contemporary context. The “disequilibrium analysis” in the title of Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” is already passé in modern macroeconomics. Nevertheless, employing this dated analytical tool, I described money and public debt as a single unit. When the nominal rate of interest is near zero, public debt is a close substitute for, or almost equivalent to, money. Then, in the terminology of disequilibrium analysis, excess demand in money markets can cancel out excess supply in public debt markets. The public bonds, which are issued beyond the present value of future fiscal surpluses, find themselves now not absorbed as public debt, but as money by strong money demand at near-zero interest rates. Again, this was not the end of the story. Still thinking as a modern macroeconomist, I urged myself to ask, “How can excess demand in money markets be characterized in equilibrium analysis?” In Chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, I employed one assumption prohibited in modern macroeconomics, that is, a temporary violation of the zero-terminal condition. To my surprise, the terminal condition, which converges to not zero, but finitely positive, corresponds to excess demand in money markets, such that we know it as an asset price bubble. Thus, we can interpret excess demand in money markets as the public bond price bubble. In this manner, I strolled between and around the past of the Japanese economy (Chapters “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II” and “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”) and travelled without restraint across its present (Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” and “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”). It was then time to venture into its future. In Chapter “Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?”, I asked myself, “Can strong money demand survive in the digital age when cryptocurrencies are issued by central banks?” Again, to my surprise, in the presence of interest-bearing central bank cryptocurrencies, a bitter conflict between the QTM and the FTPL can be sublated successfully. After my theoretical, empirical, and historical endeavors, I was convinced that I could discover a clue to a monetary and fiscal theory of the price level or MFTPL. At the same time, I believed that I could grasp the theoretical implications for the strange policy view described at the beginning of this preface. My first policy question finally linked with my theoretical investigation. When the terminal condition does not converge to zero in equilibrium analysis, public bonds degenerate to unbacked assets for the consolidated government, and they serve as net wealth for households. However, the terminal condition converges to zero in most cases, so public debt requires redemption through taxes on

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households. One of the rare cases in which the terminal condition does not converge to zero is where a combination of zero interest rates, mild deflation, and low real interest rates continues indefinitely. Such a case very much corresponds to the basic assumption of the hitherto described strange policy view of as long as zero interest continues. Once the Triple Zero breaks down, the public bond price bubble, corresponding to the nonzero-terminal condition, bursts, and public debt needs to be repaid. In fact, around 40% of the liabilities of the Japanese government have been replaced by BOJ excess reserves (those in excess of required reserves). As the nominal interest rate is zero, BOJ excess reserves display the same appearance as BOJ notes and, indeed, appear in the monetary base. However, once interest rates move up from zero, BOJ excess reserves abruptly transfigure to interest-bearing money or floating-rate public bonds, which need to be repaid with any future fiscal surpluses. In the near or far future, the Triple Zero may break down for any number of reasons, including a sudden economic recovery, private saving shortfalls, deteriorating trade balances, natural disasters, social disorder, the introduction of central cryptocurrencies (see Chapter “Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age? ”), and even sunspots. But even before any of these occur, people may consider that the Triple Zero will not continue forever. The Japanese economy would then experience immediate price surges and interest rate hikes. As predicted in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” and “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, the price level would then be several times higher than before. However, the predicted price surge would not be as serious as the immediate postwar inflation (about a hundredfold) and much milder than any of the large inflation in interwar Europe (e.g., by a factor of 88 billion between 1921 and 1923 in Germany). See Section “A Comparison with Four Big Inflations in Interwar Europe” for details. But it would still be massively destructive of the macroeconomy. What is worse, a price surge would fall into genuine hyperinflation if the Japanese government failed to commit to fiscal reforms to address the underlying problems. It is still too early to jump to the conclusion that the Triple Zero continues forever as some new normal. I believe that given the historical observations, empirical evidence, and theoretical predictions presented in this book, it is necessary to prudently consider an abrupt and rapid return of contemporary strong money demand to the long-run normal level (or the level prevailing before the mid-1990s). When such a return will be is necessarily difficult to predict. But how to prepare for price surges and interest hikes before the return to normal, how to respond to them during the return to normal, and how to calm them down after the return to normal are well specified and defined in this book. It is particularly crucially important to restore fiscal sustainability immediately after the return to normal, thereby preventing the resulting price surge from descending into hyperinflation. Using these concepts, I have written six short articles in English, thinking it better to collect them into a single unifying volume. My brief journey began in late 2014, and

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around six years have passed by early 2021 as it nears its completion. My small adventure is just preparation for more extensive explorations of monetary and fiscal theory. But it would be wise to receive any criticisms from readers before I start on another, much longer, venture into the unknown, which is why I have decided to publish this book. Nagoya, Japan

Makoto Saito

Acknowledgements

I thank the following colleagues for their criticisms, comments, and encouragements: Kosuke Aoki, R. Anton Braun, Raymond Fisman, Hiroshi Fujiki, Ippei Fujiwara, Kyoji Fukao, Ryo Horii, Daisuke Ikeda, Yasushi Iwamoto, Mitsuru Iwamura, Keiichiro Kobayashi, Ryoji Koike, So Kubota, Tsuyoshi Mihira, Tomoyuki Nakajima, Makoto Nirei, Tetsuji Okazaki, Itsuo Sakuma, Masaya Sakuragawa, Etsuro Shioji, Masaaki Shirakawa, Shigenori Shiratsuka, Tomoko Shiroyama, Masato Shizume, Yuta Takahashi, Haruto Takeda, Satoshi Tanaka, Juro Teranishi, Iichiro Uesugi, Kenji Wada, Yuichiro Waki, Eugene N. White, Kazuki Yokoyama, and Hiroshi Yoshikawa. I also thank seminar participants at the Bank of Japan, the Cabinet Office, the Canon Institute for Global Studies, Chuo University, Gakushuin University, Hitotsubashi University, Hosei University, Keio University, the Ministry of Finance, the Ministry of Economy, Trade and Industry, Nagoya University, the NBER Japan Project, Osaka University, Otaru University, the University of Tokyo, and Waseda University. I acknowledge comments from Ryuzo Sato, Editor in Chief, and two anonymous referees from Advances in Japanese Business and Economics, Springer. I deeply appreciate the Graduate School of Economics and the Institute of Economic Research at Hitotsubashi University, the Graduate School of Economics at Nagoya University, and the Institute for Monetary and Economic Studies at the Bank of Japan for supplying a wonderful research environment while I was writing articles for this book. I also acknowledge the generous financial support from Grants-in-Aid for Scientific Research, the Japan Society for the Promotion of Science (project number: 16K13350 and 18K01720), and the aid for the research frontier in banking and security markets, the Nomura Foundation (project number: N20-4F00-005). Finally, I thank Akiko, Hajime, and Akane for their warm encouragement and continuous support.

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Introduction: Toward a Monetary and Fiscal Theory of the Price Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 How Is Strong Money Demand Characterized? . . . . . . . . . . . . . . . . . 1.1 Two Occasions When Money Demand Was Strong in Modern Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Money Demand Expansion and Contraction During the Controlled-Economy Period . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Strong Money Demand at Near-Zero Interest Rates . . . . . . . . . 1.4 A Comparison with Four Big Inflations in Interwar Europe . . . . 2 Government Debt, Private Saving, and Money Demand . . . . . . . . . . 2.1 Fiscal Conditions When Money Demand Was Stable . . . . . . . . 2.2 Fiscal Conditions During the Controlled-Economy Period . . . . . 2.3 Fiscal Conditions in an Environment with Near-Zero Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Toward a Monetary and Fiscal Theory of the Price Level . . . . . . . . . 3.1 Two Standard Theories of the Price Level: QTM and FTPL . . . 3.2 Five Cases of a Monetary and Fiscal Theory of the Price Level: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A Brief History of the Controlled Economy in the Years 1937–1949 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Price Controls During and Immediately After the War . . . . . . . 2.2 Government Subsidies to Offset Price Differentials . . . . . . . . . . 2.3 Massive Issues of BOJ Notes During and Immediately After the War . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 A Possible Macroeconomic Interaction Between the Circulation of BOJ Notes and the Black Markets: A Descriptive Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 A Theoretical Relationship Between Black Markets and Money Demand Under Price Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 A Simple Model of Possible Effects of Price Controls on the National Accounts . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Income Leakages into Black Markets and Aggregate Demand for Central Banknotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Interpretations of Statistical Discrepancies and Marshallian k in the Years 1937 to 1949 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 On Constructions of the National Accounts . . . . . . . . . . . . . . 4.2 Approximation of Nominal GNE and Minimum Statistical Discrepancy in 1945 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Largely Positive Statistical Discrepancies . . . . . . . . . . . . . . . . 4.4 GNE and GNI Deflators and Official Prices . . . . . . . . . . . . . . 4.5 Marshallian k and Money Demand from the Black Markets . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Monetary Operations by the Reserve Banks and the Central Banks in the Occupied Territories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Military Scrip and the Reserve Banks on the Continent . . . . . . 2.2 Bilateral Depositing as Fiscal Instruments . . . . . . . . . . . . . . . . 3 Transfers to the Occupation Forces from the Viewpoint of the Occupier and the Occupied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Scale of the Transfers to the Occupation Forces at Face Value and at PPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Transfers to the Occupation Forces from the Viewpoint of the Occupied Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Redemption of Wartime Obligations at the End of the War . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A Simple Disequilibrium Analysis Framework . . . . . . . . . . . . . . . 2.1 Strong Money Demand Induced by Near-Zero Interest Rates 2.2 Excess Supply in Goods, Labor, and Public Bond Markets and Excess Demand in Money Markets . . . . . . . . . . . . . . . . 2.3 Excess Demand in Money Markets at Near-Zero Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 A Comparison of Disequilibrium and Equilibrium Analyses .

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3 The Past and Future of Japan’s Economy from the Viewpoint of Disequilibrium Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Excess Supply in Goods and Labor Markets and Massive Issues of Money and Public Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The BOJ’s Issues of Money and Its Purchases of Public Bonds in the Near-Zero Interest Rate Environment . . . . . . . . . . . . . . . 3.3 The Outlook for Demand for Money and Public Bonds . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: How Did the BOJ de facto Refinance Its Own JGBs at Maturity? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Three Features of Japan’s Long-Run Mild Deflation . . . . . . . . . . . . 3 Behavior of the Price Level in the Fiscally Sustainable and Unsustainable Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Sketching a Model of a Price Surge as a Trigger for a Regime Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 A Simple Monetary Model of the Exchange Economy . . . . . . 3.3 The QTM in the FS Regime . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Possible Deflationary Processes in the FU Regime . . . . . . . . . 3.5 On the Term Structures of Interest Rates During the FU Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Real Risk-Free and Real Growth Rates . . . . . . . . . . . . . . . . . 4 Calibration Exercises for Japan’s Long-Run Deflation . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: Price Behavior During the FS Regime with d [ 0 . . . . . . . . Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 An Overview of CBCCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 How Do Private Cryptocurrencies Work? . . . . . . . . . . . . . . . 2.2 How Do CBCCs Work? . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 CBCCs in a Competitive Equilibrium Environment . . . . . . . . . . . 3.1 How to Formulate CBCCs in Macroeconomic Models . . . . . 3.2 Basic Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Optimality Conditions, Interest Parity, and Purchasing Power Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Extended QTM Under Fixed Interest on Currencies . . . . . . .

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129 130 133 138

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Contents

3.5 Standard FTPL and MFTPL Given Equivalence Between Currencies and Public Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 3.6 Money Demand and Seigniorage Under Fixed Spreads . . . . . . . . . 187 4 Conclusion: Strong Money Demand or Immense Seigniorage in the Digital Age? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

About the Author

Makoto Saito is Professor at Graduate School of Economics, Nagoya University, where he has been on the faculty since 2019. He received his B.A. from Kyoto University and his Ph.D. from Massachusetts Institute of Technology. After he worked as Economist at the Sumitomo Trust Bank, he was on the faculty at the University of British Columbia, Kyoto University, Osaka University, and Hitotsubashi University. His long-run research agenda concerns dynamics of asset pricing in the presence of heterogeneous agents in both domestic and international contexts. Immediately after the Great East Japan Earthquake happened in March 2011, he conducted intensive research into the causes, effects, and consequences of the disaster, including the Fukushima Daiichi nuclear power accident. His recent research puts the Bank of Japan’s monetary policy in historical contexts and explores policy implications. He published many papers in professional journals, including Journal of Monetary Economics, Journal of International Economics, Journal of Mathematical Economics, and Review of Income and Wealth. He received Ishikawa Prize from the Japanese Economic Association in 2007 and was given Medal with Purple Ribbon from the Emperor in 2014. For his books published in Japanese, he receives Nikkei Prize for Excellent Books in Economic Science in 2002, Economist Prize in 2008, the Zengin Foundation Award in 2010, and Ishibashi Tanzan Prize in 2012.

xxi

Abbreviations

AML BOC BOI BOJ BOTh CAD CAs CB CBCC CBM CDF CGPI CPI CRBC DVP ECB EFM EOHPF EPA FILP FRBC FS FTPL FU GDP GHQ GIBC GNE GNI HSBC

Anti-Money Laundering Bank of Canada Bank of Indochina Bank of Japan Bank of Thailand Canadian dollar Current accounts Central bank Central bank cryptocurrency Central Bank of Manchuria Complementary Deposit Facility Corporate goods price index Consumer price index Central Reserve Bank of China Delivery versus payment European Central Bank Emergency Financial Measures Editorial Office of History of Public Finance in Showa Era Economic Planning Agency Fiscal Investment and Loan Program Federal Reserve Bank of China Fiscal sustainability Fiscal theory of the price level Fiscal unsustainability Gross domestic product General Headquarters of the Allied Powers Government’s intertemporal budget constraint Gross national expenditure Gross national income Hong Kong and Shanghai Banking Corporation

xxiii

xxiv

JGBs MAS MFTPL MMP MMT MOF MOS NIRP OFB PBFT PCO PPP QE QQE QTM RFB SDB SWIFT TF TFS TIEGML USSBS YSB ZIRP

Abbreviations

Japanese government bonds Monetary Authority of Singapore Monetary and fiscal theory of the price level Material Mobilization Plans Modern monetary theory Ministry of Finance Market Operations Statistics Negative interest rate policy Overseas Funds Bank Practical Byzantine Fault Tolerance Price Control Order Purchasing power parity Quantitative easing Quantitative and qualitative easing Quantity theory of money Reconstruction Finance Bank Southern Development Bank Society for Worldwide Interbank Financial Telecommunication Treasury fund Treasury Funds Statistics Temporary Import/Export Grading Measures Law United States Strategic Bombing Survey Yokohama Specie Bank Zero interest rate policy

Introduction: Toward a Monetary and Fiscal Theory of the Price Level

Abstract This chapter briefly provides empirical and theoretical motivations for research papers that are collected in this book. In the modern Japanese economy, strong money demand has appeared twice. It first appeared during World War II and then, more recently, after the mid-1990s. Such strong money demand enabled the Japanese government to finance large-scale military spending in the first occasion, while it has supported massive fiscal operations developed by the government in the second. For the former part, the economy was forced to implement strict fiscal reforms to prevent hyperinflations from happening once the strong money demand disappeared immediately after the war ended. For the latter, on the other hand, nearzero rates of interest and stable prices continue to coexist with affluent money and poor fiscal surpluses, while strong money demand survives. The observations associated with the emergence and disappearance of strong money demand are hard to explain by either the quantity theory of money or the fiscal theory of the price level. Here, a monetary and fiscal theory of the price level is proposed as their alternative. In particular, it can successfully identify additional sources of money demand. More concretely, the strong money demand appearing during the war was attributed to immense demand for BOJ notes from black markets, while the current one has been driven by extremely low interest rates, starting from 1995. Employing rich implications from this alternative theory, I fully elucidate the extent to which the current monetary and fiscal situation of the Japanese economy is sustainable, and how it will break down in the near or far future.

1 How Is Strong Money Demand Characterized? 1.1 Two Occasions When Money Demand Was Strong in Modern Japan Let me first define ‘strong money demand’, which is the subject of the analysis in this book. What is implied by ‘money demand is strong’ is the situation where the scale of

© Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9_1

1

2

Introduction: Toward a Monetary and Fiscal Theory … 10%

60%

9% 50%

8% 7%

40%

6% 30%

5% 4%

20%

3% 2%

10%

1% 0%

0%

BOJ notes/Nominal GNE (GDP)

Official discount rate (right scale)

Fig. 1 BOJ notes/nominal GNE (GDP) and the official discount rate, 1885–2019. Notes (1) In terms of BOJ notes in circulation (measured at the end of each calendar year), Statistics Department, BOJ (1966) for the period 1885–1969, and Money and Deposits → Currency in Circulation in BOJ (2020) for the period 1970–2019. (2) In terms of nominal GNE (GDP), Ohkawa et al. (1974) for the period 1885–1929, EPA (1964) for the period 1930–1954, except for 1945, ESRI (1998) for the period 1955–1979, ESRI (2009) for the period 1980–1993, and ESRI (2019) for the period 1994– 2019. Section 4.2 in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II” describes the approximation of the 1945 value of nominal GNE. (3) GNE (1885–1944, and 1952–1954) and GDP (1955–2019) are for calendar years, while GNE (1946–1951) are for fiscal years. (4) For the official discount rate (the calendar-year average of daily data), Interest Rates on Deposits and Loans → the Basic Discount Rates and Basic Loan Rates in BOJ (2020)

money demand exceeds that of money demand driven by normal transaction motives. It is well known that the ordinary transaction demand for money is approximately proportional to nominal gross domestic product (GDP) at a fixed coefficient. Thus, if the balance of money in circulation is well above such a fixed share of nominal GDP, then money demand is strong. A typical phenomenon, which appears when money demand is strong, is a very weak relationship between the price level and money quantity, such that the price level does not increase as much as the quantity of money. In the modern Japanese economy,1 ordinary transaction motives have mostly driven money demand. Figure 1 plots the time series of the ratio of Bank of Japan (BOJ) notes in circulation to nominal gross national expenditure (GNE) up to 1954

1 Historians

consider that the Japanese ‘modern’ period began in 1868 with a new government inaugurated by the Meiji Restoration.

1 How Is Strong Money Demand Characterized?

3

and to nominal GDP from 1955 through 2019.2 This ratio is known as the Marshallian k by convention. Founded in February 1882, the BOJ began to issue its own notes in May 1885, and these were well established about five years after the first issue. In the prewar period from the 1890s to 1937, k stayed at around 10% of nominal GNE. On the other hand, in the postwar period from 1952 to 1995, k remained at around 8% of nominal GDP (GNE).3 The long-run average of Marshallian k differs slightly between the prewar period (10%) and the postwar period (8%) because, in the latter period, high volume payments are made not by BOJ notes, but through the BOJ reserve requirement system, which was formally established in 1957. However, there were two occasions in which k deviated upward from its long-run trend. Thus, money demand was especially strong on these two occasions. First, k started to deviate upward in 1937 when the Second Sino-Japanese War began and reached just below 50% in 1945 when World War II ended.4 It then declined quickly toward 10%, its prewar long-run level, in 1949 just before the Allied occupation of Japan ended. The period in which the Marshallian k displayed such a large upward swing almost overlaps with the period in which the Japanese economy was subject to strict economic controls in terms of prices and quantities. More precisely, control of the Japanese economy started in July 1937 with the outbreak of the Second SinoJapanese War and ended in April 1952 when the Allied occupation closed, but with most economic controls effectively lifted by the late 1940s. Second, the Marshallian k started to deviate upward in 1995 when the short-term interest rate was historically low, as shown in Fig. 1. The BOJ then began to guide its official discount rate and overnight call rates (interbank rates) were below 0.5% in September 1995. The k then increased gradually from 8% in 1994 to above 15% in 2004 and exceeded 20% in 2018. As of late 2020, this upward trend in k from its long-run level continued, with the above two occasions examined in more detail below.

1.2 Money Demand Expansion and Contraction During the Controlled-Economy Period Let me first make remarks on the wartime and immediate postwar price indexes, which are both employed in this analysis. As discussed in Sect. 2 in chapter “Central 2 The

nominal and real GNE and GNE deflator for 1945, not reported by the Economic Planning Agency (EPA, 1964), are estimated in Sect. 4.2 in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”. 3 Oi et al. (2004) provide rigorous statistical tests of the long-run stability of the Japanese money demand. 4 Most historians consider that World War II began in September 1939 when Germany invaded Poland and ended in August 1945 with the surrender of Japan. However, Japanese historians include the Second Sino-Japanese War, which started in July 1937, in World War II, even though, at its start, the then Japanese government referred to it not as a war, but an incident.

4

Introduction: Toward a Monetary and Fiscal Theory …

Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, the GNE deflator, as adopted for the national accounts by the Economic Planning Agency (EPA, 1964), reflected both heavily restricted official prices and excessive black market prices. Thus, the EPA did not underestimate nominal GNE but calculated it as properly as reasonably achievable. However, as the wholesale and retail price indexes were only based on official prices, both were heavily underestimated during the war, with a gradual correction as official prices approached market prices up until the late 1940s. If we were to calculate the real balance of BOJ notes in circulation using the wholesale/retail price indexes for the wartime period, then the real balance would be heavily overestimated. As mentioned, the Marshallian k displays an upward curve from 1937 to 1945. For this period, nominal GNE (the denominator of k) increased by a factor of 4.9, but outstanding BOJ notes (its numerator) expanded by a factor of 24.1. Accordingly, k rose from 10.1 to 48.4%. In contrast, k declined quickly from 1945 to 1949. Over that period, nominal GNE expanded by a factor of 29.5, but outstanding BOJ notes increased by a factor of 6.4. Consequently, k fell heavily from 48.4 to 10.5%. Behind the sharp upswing in the Marshallian k, the price level did not increase as much as outstanding BOJ notes did during the war, but surged despite relatively moderate monetary expansion after the war. By comparison, the GNE deflator increased by a factor of 6.8 from 1937 to 1945 and by a factor of 31.1 from 1945 to 1949. According to the wholesale and retail price indexes, which were based on official prices only, the immediate postwar inflation in Japan was even more remarkable. For the period 1945–1949, the wholesale price index increased by a factor of 59.6 (2.8 for the period 1937–1949), and the retail price index increased by a factor of 78.9 (2.7 for the period 1937–1949). The prevailing economic history of Japan, including Ito (2012), often affirms that the immediate postwar inflation was hyperinflation. Such a firm judgement is based on the behavior of the wholesale/retail price indexes. Including the years 1950 and 1951, the wholesale (retail) price index soared by a factor of 97.8 (100.4) for the period between 1945 and 1951. A substantial decline in the real balance of outstanding BOJ notes was also clear, being a typical phenomenon of hyperinflation. Because outstanding BOJ notes in circulation increased by just a factor of 9.1, the real balance reduced to less than one-tenth of its 1945 level by 1951. But it is difficult to judge that the immediate postwar inflation was hyperinflation for the following reasons. First, inflation based on either the wholesale or retail price index, in reflecting only official prices, underestimates the wartime price level. As discussed, the GNE deflator, reflecting both official and market prices, only recorded lower inflation, with a factor of 39.4 in the period 1945–1951. Second, money quantity and nominal GNE moved together for the entire period of the controlled economy. For the period between 1937 and 1949, the nominal balance of BOJ notes in circulation and nominal GNE increased by a factor of 154.1 and 144.1, respectively. That is, the value of the Marshallian k in 1937 and the value in 1949 were almost equal, at just above 10%. In the first half of the controlled-economy period, k changed from normal to extremely high and, in the second half, it changed from exceedingly high to normal. Third, price surges suddenly ceased in late 1949 when k returned to its prewar

1 How Is Strong Money Demand Characterized?

5

level, although the price level resumed increasing temporarily between mid-1950 and early 1951. During 1951–1960, the wholesale (retail) price index increased slightly by 0.3% (0.1%) per year. A more precise statement of immediate postwar inflation is that price surges came to a sudden halt before it fell into genuine hyperinflation, in which the Marshallian k would have declined from normal to extremely low. We can confirm this using monthly data of the real balance of BOJ notes in circulation calculated by the wholesale price index, even though the index was heavily underestimated during the war. As shown in Fig. 2, the real banknote balance began to increase in July 1937, when the so-called Marco Polo Bridge Incident (a trigger for the Second Sino-Japanese War) took place and peaked in August 1945 with Japan’s defeat. During the war, it increased by a factor of more than eight. Immediately after the war, the real banknote balance contracted quickly, and it reached its prewar level by the late 1940s. As discussed in Sect. 2.4.2 in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, the real banknote balance had a temporary but large fall in February 1946 because the BOJ collected old bills under the Emergency Financial Measures (EFM). According to Fig. 3, which plots the monthly time series of the wholesale and retail price indexes in common logarithms, price surges suddenly stopped after the real banknote balance returned to its prewar level in late 1949. The price level resumed increasing in June 1950 but was almost stable after April 1951. 1,000 900 800 700 600 500 400 300 200 100 0

Fig. 2 Real balance of BOJ notes in circulation, January 1930–December 1952 (January 1930 = 100). Notes (1) In terms of BOJ notes in circulation (measured at the end of each month), see Asakura and Nishiyama (1974) for the period 1930–1945, and Editorial Office of History of Public Finance in Showa Era (EPHPF), MOF (1976) for the period 1946–1952. (2) For the wholesale price index (monthly data), see Research and Statistics Department, BOJ (1987)

6

Introduction: Toward a Monetary and Fiscal Theory … 3.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

WPI in common logarithm

Tokyo retail price in common logarithm

Fig. 3 Wholesale and retail price indexes, January 1930–December 1960. Notes (1) For the wholesale price index, Research and Statistics Department, BOJ (1987). (2) For the Tokyo retail price indexes, Statistics Department, BOJ (1968)

Given the above observations, it may not be proper to consider that the immediate postwar inflation in Japan was indeed hyperinflation. Instead, the following questions are much more legitimate. Why did strong money demand appear during the war? Why did money demand shrink after the war? Why did the postwar price surge stop suddenly before sharp inflation fell into genuine hyperinflation? As discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, we can hold the behavior of black marketeers responsible for the rapid expansion and quick contraction of money demand during the controlled economy in Japan. During the war, black marketeers held massive amounts of BOJ notes to mask their illicit income given their uninscribed nature. But these black marketeers then shifted their asset portfolios from BOJ notes to real assets after the war for the reasons described in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”. Through strict tax reforms immediately after the war ended, the new Japanese government changed its fiscal surpluses from largely negative to nearly always positive from 1947 onward. Once money demand returned to its normal level, and sufficient fiscal surpluses fully backed the public debt, the upward pressure on the price level disappeared. Sharp inflation stopped abruptly in the late 1940s before it fell into genuine hyperinflation.

1 How Is Strong Money Demand Characterized?

7

1.3 Strong Money Demand at Near-Zero Interest Rates While it may be difficult to identify why strong money demand emerged during the war, it is much easier to understand why strong money demand appeared after late 1995. As mentioned, the BOJ began to control the official discount rate and overnight call rates below 0.5% in September 1995. As shown in Fig. 1, these near-zero interest rates were unparalleled in the modern Japanese economy. While the BOJ and the Ministry of Finance jointly developed a low interest rate policy during the war, the official discount rate was 3.3%. With the low interest rate policy of the second half of the 1980s, which might have been responsible for the asset price bubble at that time, the official discount rate was 2.5% between February 1987 and May 1989. Nearzero costs of money holding because of this historically low interest policy have been pointed at as a primary factor behind the recent appearance of strong money demand. We can confirm this argument using the quarterly data. Figure 4 plots the quarterly time series of the real balance of BOJ notes, calculated using the GDP deflator, together with those of real GDP. Up until the first quarter (Q1) of 1995, the real banknote balance moved in parallel with real GDP, which drove the transaction motive of money demand. Up until then, money demand moved above ordinary 700

600

500

400

300

200

100

0

Real GDP

Real BOJ notes

Fig. 4 Real balance of BOJ notes in circulation and real GDP, Q1 1980–Q3 2020. Notes (1) For BOJ notes in circulation (measured at the end of each quarter), Money and Deposits → Currency in Circulation in BOJ (2020). (2) For the corporate goods price index (seasonally adjusted quarterly data), Prices → Corporate Goods Price Index in BOJ (2020). (3) For real GDP (seasonally adjusted quarterly data), ESRI (2018, 2020)

8

Introduction: Toward a Monetary and Fiscal Theory … 6%

4%

2%

0%

-2%

-4%

-6%

GDP deflator Corporate goods price index Consumer price index (excluding housing rents and perishable foods)

Fig. 5 Inflation rates according to three price indexes, 1981–2019. Notes (1) For GDP deflator, ESRI (2018, 2020). (2) For the corporate goods price index (the fiscal year average of monthly data), Prices → Corporate Goods Price Index in BOJ (2020). (3) For the consumer price index, Statistics Bureau of Japan (2020a)

transaction demand. However, while real GDP was stagnant from 1995, the real banknote balance started to expand. With a value of 100 at Q1 1980, the real banknote balance surpassed 200 in Q1 1996, 300 in Q2 2001, 400 in Q1 2006, 500 in Q2 2015, and 600 in Q1 2020. These figures show that money demand exceeded transaction motives from late 1995 onward. Owing to this strong money demand, the price level was stable or mildly deflationary after late 1995.5 Figure 5 plots the time series of annual inflation rates using the GDP deflator, the corporate goods price index (CGPI), and the consumer price index (CPI, excluding housing rents and perishable foods) for the period between fiscal years 1981 and 2019. Of the three indexes, GDP deflator inflation is most representative of this mildly deflationary trend and spiked only with the raising of the consumption tax rate in Japan: from 3% since its introduction in April 1989 to 5% in April 1997, to 8% in April 2014, and to 10% in October 2019. The CPI inflation yields almost the same trend as that for the GDP deflator. But both differed substantially when primary commodity prices such as crude oil prices varied widely. A major reason for this is that an increase (decrease) in primary commodity prices works to raise (reduce) CPI but helps to reduce (raise) the GDP deflator through the deterioration (improvement) in the terms of trade. Thus, when 5 As discussed in Sect. 2 in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, if the price path is viewed in terms of the period starting not from 1980, but from 1955, the price level started to stagnate relative to the quantity of money from the mid-1980s.

1 How Is Strong Money Demand Characterized?

9

global crude oil prices surged from 2003 through 2008, CPI increased, but the GDP deflator decreased. Conversely, when crude oil prices declined from 2009 to 2010 and again from 2014 to 2016, CPI decreased, but the GDP deflator increased. CGPI moves together with CPI, but it is more influenced by crude oil prices than CPI. CGPI also decreases with the appreciation of the Japanese yen. When the yen appreciated after the second half of the 1980s to the first half of the 1990s and again from 2009 to 2012, CGPI declined much more than CPI.

1.4 A Comparison with Four Big Inflations in Interwar Europe In this subsection, I compare the price surge immediately after the war in Japan with the big inflations in interwar Europe intensively explored by Sargent (1982). Sargent raises two important points about big inflations. First, the big inflations in interwar Europe present a case against the quantity theory of money (QTM) in that in all of them the price level increased much faster than the quantity of money. Second, again in all of them, fiscal factors play an essential role in generating and stopping hyperinflation. These points are also quite suggestive of the generation and collapse of strong money demand in modern Japan. Let me briefly describe the argument used by Sargent (1982). After World War I, the governments in Austria, Hungary, Poland, and Germany unsuccessfully tried to finance their large fiscal deficits by issuing banknotes, not public bonds. But the banknotes, unbacked by future fiscal surpluses, depreciated quickly and majorly. With heavily depreciated currencies, price levels surged rapidly, while the exchange rate depreciated extraordinarily. The real banknote balance then shrank sharply because of the feeble demand for these now weak currencies. However, once their governments announced drastic fiscal and monetary reform, the big inflations stopped abruptly. The central governments committed to radical tax reforms and severe fiscal spending cuts, while the central banks became independent of the central governments, and never again underwrote public bonds directly from their governments, with the banknotes then backed by resulting fiscal surpluses. As money demand for the backed currencies recovered, the real banknote balance started to increase. Table 1 summarizes the analysis by Sargent (1982). In all of the countries, the price level surged much faster than the balance of banknotes in circulation expanded before the initiation of drastic fiscal and monetary reforms. Accordingly, the real banknote balance shrank quickly. But, immediately after the reforms were announced, price surges ceased, and the real banknote balance started to recover. Among the four countries, Germany is most representative of the above respects. As shown in Table 1, Germany experienced huge price surges prior to drastic fiscal and monetary reform. For the period between January 1921 and December 1923, the balance of banknotes increased by a factor of 7.5 billion, but the price level surged by a factor of 87.6 billion. Accordingly, the real banknote balance decreased substantially from 100 to 8.5.

10

Introduction: Toward a Monetary and Fiscal Theory …

Table 1 Price indexes, central banknotes, and real balances in four big inflations in interwar Europe Price index

Central bank notes

Real banknote balances

Month/year when a fiscal/monetary reform was initiated

January 1921–September 1922

201 times

66 times

100–32.8

August 1922

September 1922–June 1924

1.2 times

3.4 times

32.8–92.8

July 1921–March 1924

494 times

102 times

100–20.6

March 1924–September 1924

1.1 times

2.6 times

20.6–48.9

January 1922–January 1924

3,817 times

1,309 times

100–32.0

January 1924–April 1924

1.0 times

1.8 times

32.0–58.2

January 1921–December 1923

87.6 bn. times

7.5 bn. times

100–8.5

December 1923 to June 1924

0.9 times

2.2 times

8.5–20.5

Austria

Hungary February 1924

Poland January 1924

Germany October 1923

Notes 1. See Sargent (1982) for the data sources 2. For Poland, January 1922 instead of January 1921 serves as the reference point because during the period between January 1921 and January 1922, the exchange rate of the Polish mark against the U.S. dollar depreciated by a factor of 4.4, while the price level increased by a factor of only 2.4. This supplies evidence for the underestimation of the price index recorded in 1922

But, immediately after fiscal and monetary reform was announced in October 1923, the astronomical price surges stopped within just two months, while the nominal banknote balance still increased. Consequently, the real banknote balance recovered from 8.5 to 20.5 for the period between December 1923 and June 1924. There are two similarities and three differences between the German interwar hyperinflation and the Japanese immediate postwar price surge. To start, in terms of similarities. First, the real banknote balance shrank similarly: from 100 to 8.5 in Germany, and from 100 to 9.1 in Japan. Second, the high inflation stopped suddenly immediately after fiscal and monetary reforms were announced in late 1923 in

1 How Is Strong Money Demand Characterized?

11

Germany and after intensive tax reforms were implemented during the second half of the 1940s in Japan. Now in terms of differences. First, the real banknote balance declined from normal to very low in Germany, but from very high to normal in Japan. Second, compared with before the price surge, the real banknote balance declined to 20.5% of its earlier level in Germany, but returned to its prewar level in Japan. Third, Germany implemented currency redenomination after price stabilization, but Japan did not. More concretely, Germany redenominated the price level by one-trillionth in July 1924, about six months after the high inflation ceased. By contrast, in Japan, and as discussed in the preface, a postcard stamp was 2 sen (two-hundredths of a yen) in 1937, and 5 yen in late 1951. The exchange rate of yen was then 4 yen 27 sen per dollar in 1940, and 360 yen per dollar in 1949. In this way, Germany dropped 12 zeros from its currency, but Japan kept two zeros as it stood. The interwar inflationary experiences of Austria, Hungary, and Poland display the above three differences in common, with the real banknote balance declining to 92.8% of its earlier level in Austria, 48.9% in Hungary, and 58.2% in Poland. All three countries also implemented currency redenomination: one over 14,400 in Austria, one over 14,500 in Hungary, and one over 1.8 million in Poland.

2 Government Debt, Private Saving, and Money Demand 2.1 Fiscal Conditions When Money Demand Was Stable In this section, I briefly examine the fiscal conditions faced by the Japanese government from a long-run perspective. Figure 6 plots the time series of the ratio of public debt to nominal GNE or GDP (the debt–output ratio) for the period between 1885 and 2019. While the Marshallian k was stable at its long-run level, monetary policy never intervened in fiscal policy. For example, when k was stable at about 10% from 1890 to 1937, the financing of public debt was through either private savings or foreign borrowing. As Japan’s expenditure on the Russo-Japanese War (1904– 1905) was financed from home and abroad, the debt–output ratio increased from 22.9% in 1903 to 68.5% in 1905. The accumulated debt was repaid largely thanks to economic booms during World War I. The debt–output ratio then decreased to 22.6% in 1919. In the 1920s, however, public debt started to accumulate again with policy responses to the Great Tokyo Earthquake in September 1923, and the financial panic in 1927. Accordingly, the debt–output ratio increased to 40.4% in 1929. In the early 1930s, public debt further accumulated with the policy responses to the Showa Depression following the Great Crash in October 1929, and the Manchurian Incident in September 1931. The debt–output ratio reached 57.9% in 1932, even before the Second Sino-Japanese War started in July 1937. After the Marshallian k returned to its postwar long-run trend, or 8% in the early 1950s, the debt–output ratio was stable and quite low, or around 10% in the 1950s and

12

Introduction: Toward a Monetary and Fiscal Theory …

200%

150%

100%

50%

0%

Government debt/Nominal GNE (GDP) Monetary base/Nominal GNE (GDP)

BOJ notes/Nominal GNE (GDP)

Fig. 6 Government debt and money, 1885–2019. Notes (1) In terms of government debt (measured at the end of each fiscal year), see Statistics Department, BOJ (1966) for the period 1885–1965, and EOHPF, MOF (1978) for the period 1966–1975, and Flow of Funds in BOJ (2020) for the period 1976–2019. (2) Government debt is as of fiscal year-end. (3) Wartime government debt includes that issued by the special account for extraordinary military expenses for the period 1937–1945 but excludes that held by the Overseas Funds Bank for 1945. See chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War” for details. (4) The postwar government debt consists of Treasury Bills (Financing Bills), government bonds, Fiscal Investment and Loan Program (FLIP) bonds, and FLIP agency bonds. (5) For monetary base (measured at the end of each calendar year), Money and Deposits → Monetary Base in BOJ (2020). (6) See the notes accompanying Fig. 1 for nominal GNE (GDP) and BOJ notes in circulation

1960s. But in the 1970s, the debt–output ratio increased from 8.8% in 1970 to 31.7% in 1980. At this time, the Japanese government was forced to respond to many policy issues, including the Nixon Shock in August 1971, the shift to a floating exchange rate system in 1973, the first oil shock in 1973, and the second oil shock from 1978 to 1979. In the 1980s, the debt–output ratio continued to increase to 52.5% in 1987 but declined to 40.2% in 1990 thanks to economic booms in the second half of the 1980s. In this way, the debt–output ratio was already high before k started to deviate upward from its long-run trend in late 1995.

2.2 Fiscal Conditions During the Controlled-Economy Period What, then, were the fiscal conditions when strong money demand played an active role in supporting public debt? In the first half of the controlled-economy period, from 1937 to 1945, the debt–output ratio increased rapidly from 58.5% in 1937 to 84.1% in

2 Government Debt, Private Saving, and Money Demand

13

90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

Fig. 7 Nominal private consumption/nominal GNE, 1930–1960. Note (1) For nominal GNE and private consumption, see EPA (1964), where the data from 1930 to 1944 and from 1952 to 1960 are for calendar years, those for 1946 to 1951 are for fiscal years, and the data for 1945 are not available

1940, to 204.0% in 1944, and to 174.2% in 1945.6 Initially during the war the increase in public debt was financed through private saving. Private saving indeed increased remarkably because of a sort of forced saving policy.7 According to Fig. 7, the ratio of nominal private consumption to nominal GNE (the consumption ratio) decreased from 64.3% in 1936 to 35.6% in 1944.8 The reverse side of this marked decrease in the consumption ratio is that private saving expanded significantly. According to Fig. 8, the ratio of net private saving to nominal GNE increased from 16.7% in 1936 to 31.0% in 1944. However, despite the huge growth in private saving, the increase in public debt was almost equal to private saving from 1937 to 1941, and the former even exceeded the latter in 1942–1944 (see Fig. 8). More precisely, the increment in public debt 6 The decrease in the debt–output ratio from 1944 to 1945 was due to an accounting manipulation by

the Overseas Funds Bank (OFB). The OFB, founded in February 1945, took over the government liabilities underwritten by reserve banks in north/central China and southeast Asia, and put them outside the special account for extraordinary military expenses. Thus, these public liabilities were not included in the formal government accounts. See Sect. 1 in chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”. 7 In April 1938, the Ministry of Finance set up the National Savings Promotion Bureau. This bureau encouraged (and even forced) people to make deposits (particularly government postal savings) and to buy public bonds. 8 According to Koike (2019), the estimation of wartime private consumption, including EPA (1964), is heavily overestimated. Thus, the estimation of private saving by EPA (1964) may be seriously underestimated.

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Introduction: Toward a Monetary and Fiscal Theory …

100%

80%

60%

40%

20%

0%

-20%

Change in government debt/nominal GNE

Net private saving/nominal GNE

Fig. 8 Government debt growth and private saving, 1930–1960. Note See the notes accompanying Fig. 1 for nominal GNE and private saving, and Statistics Bureau, BOJ (1966) for government debt, measured at fiscal year-end

exceeded net private saving by 28.3% over 24.9% in 1942, 43.8% over 26.1% in 1943, and 89.7% over 31.0% in 1944. There were two financial sources for public debt growth exceeding private saving. First, as discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, while a considerable share of national income leaked from the formal economy to the underground economy during the war, black marketeers held copious amounts of BOJ notes to mask their illicit income with the uninscribed nature of banknotes. Their vast holdings of BOJ notes, emerging as strong money demand in the formal economy, helped the leaked income to flow back to the Japanese treasury. Note that this additional black market money demand was not included in private savings in the formal economy. Second, as discussed in chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”, the government required not only the BOJ, but also reserve and central banks in the occupied territories to underwrite public debt directly.9 The banknotes issued by the reserve/central banks were absorbed by local currency demand. In this way, public debt expansion beyond private saving was funded through strong money demand from both the underground economy and the occupied territories. 9 More

precisely, as discussed in Sect. 2 in chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”, the government’s deals with the reserve and central banks in the occupied territories were intermediated by the Bank of Chosen and the Yokohama Specie Bank.

2 Government Debt, Private Saving, and Money Demand

15

Table 1 in chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War” describes how the war financing worked. In 1944, for example, total war expenditure, included in the special account for extraordinary military expenses, amounted to 73.5 billion yen. While only 9% of the expenditure was covered by tax revenues, 66.8 billion yen was financed by public debt. Out of 66.8 billion, 23.1 billion yen was covered by bond and money demand included in private saving, 6.4 billion yen was funded through money demand from the underground economy, and 34.2 billion yen was financed by direct deals with the reserve/central banks in the occupied territories. The contribution to money demand by black markets provided 10% of public debt finance in 1944, and this increased to 43% in 1945. As discussed, the rapid wartime growth of public debt in Japan was financed by three sources: (1) forced private saving, (2) money demand from the underground economy, and (3) direct deals with the reserve/central banks in the occupied territories. But these three financial sources disappeared immediately after the war. First, as shown in Fig. 7, the consumption ratio increased, jumping from 36% in 1944 to 70% in 1946 in the absence of forced saving. Accordingly, net private saving declined to almost zero immediately after the war, as shown in Fig. 8. Second, part of national income continued to leak to the underground economy, but the leaked income never returned to the treasury through the holdings of BOJ notes by black marketeers. This was because the black-market dealers were no longer interested in holding BOJ notes for the reasons described in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”. Third, the occupied territories were all gone after Japan’s defeat. Given the above fiscal condition, the huge public debt was repaid largely by sharp inflation immediately after the war. As mentioned in Sect. 1.2, the price level continued to surge up to the late 1940s, until money demand returned to its normal level, and fiscal surpluses turned largely positive through intensive tax reforms. The debt–output ratio declined from 174.2% in 1945 to 18.9% in 1949. When the price level ceased to surge by the late 1940s, the public debt, which had already been devalued heavily by sharp inflation, was then fully backed by fiscal surpluses. In this way, price surges worked to reduce the real balance of public debt, while the appreciable improvement in fiscal surpluses helped to prevent the price surges from descending into genuine hyperinflation. There is one more remark on the immediate postwar fiscal conditions. While the relative size of public debt decreased massively, as shown above, public debt continued to increase in nominal terms during the second half of the 1940s; the nominal balance of public debt was 199.5 billion yen in 1945, and it continued to increase to 637.3 billion yen by 1949. How did the government finance its borrowing? In 1946, private saving was slightly positive, and public saving was largely negative. In all likelihood, the Japanese government financed its borrowings from private deposits, which were frozen temporarily under the EFM in 1946 (see Sect. 2.4.2 in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”). Then, poor private saving was supplemented by black market resources; by barter, households and firms exchanged their

16

Introduction: Toward a Monetary and Fiscal Theory …

own durables and inventories for necessary and essential goods from black markets. Because public saving turned positive from 1947 onward, borrowing in some public sectors could be covered by saving in other public sectors. As discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, the private sector continued to rely on the resources obtained from black markets by barter up until the late 1940s.

2.3 Fiscal Conditions in an Environment with Near-Zero Interest Rates What were the fiscal conditions when money demand was strong after late 1995? As shown in Fig. 6, the debt–output ratio, which increased from 40.2% in 1990 to 53.1% in 1995, moved above 100% in 2002, above 150% in 2010, and reached 187.4% in 2018. Behind this acceleration of the debt–output ratio, the Japanese government was forced to respond to the Great Hanshin–Awaji Earthquake in January 1995, the national financial crisis of 1997–1998, the global financial crisis of 2007–2008, and the Great East Japan Earthquake in March 2011. At the same time, it postponed much needed and comprehensive tax and social security reforms. In the contemporary context, the domestic financial source of growing public debt is only public bond and money demand from the private sector, both of which originate from private saving. There are two remarkable changes in terms of how the rapid growth of public debt has been supported by private saving. First, private saving gradually declined, and was sometimes short of increases in public debt. As shown in Fig. 9, the ratio of net private saving to nominal GDP declined from 17.4% in 1980 to 7.3% in 2019. From the 1980s until the first half of the 1990s, private saving was large enough to cover growing public debt, with the remaining saving directed to private investment. But, from the second half of the 1990s, private saving approached the increase in public debt. From 2011 to 2014, the latter dominated the former. During that period, net exports were negative. Thus, the government financed its debt indirectly from abroad. Given such private saving shortages, private investment in Japan was very much crowded out. Second, the government liabilities were gradually replaced by the BOJ liabilities, including banknotes and reserves. Up to 2000, the ratio of monetary base (BOJ notes and reserves) to nominal GDP was higher than the Marshallian k (BOJ notes only) by just 1%. But, when quantitative easing was adopted from March 2001 to March 2006, the monetary base ratio was higher than k by some 7% at its maximum. After excess reserves were renumerated at 0.1% in October 2008, the monetary base ratio increased rapidly to more than 50% in 2014. The BOJ set the interest rate on excess reserves at zero or –0.1% from January 2016. Nevertheless, the monetary base ratio continued to rise to 92.6% in 2019. Thus, the BOJ liabilities replaced around half of the government liabilities.

2 Government Debt, Private Saving, and Money Demand

17

20%

15%

10%

5%

0%

-5%

Change in government debt/nominal GDP

Net private saving/nominal GDP

Fig. 9 Government debt growth and private saving, 1980–2019. Notes (1) Private saving is for a fiscal year and defined as the sum of saving of nonfinancial incorporated enterprises, financial institutions, households including private enterprises, and private nonprofit institutions serving households. (2) See the notes accompanying Fig. 6 for government debt, and ESRI (2009, 2019) for private saving and nominal GDP, both of which are for a fiscal year

Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” and “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan” explore the second point in depth. These chapters theoretically investigate how public bonds and money are interchangeable at near-zero interest rates and present a case where government liabilities find support not as public bonds, but as money by strong money demand at near-zero interest rates. In addition, the chapters discuss what would happen to the Japanese economy if strong money demand disappeared as nominal interest rates increased from zero. In this respect, the first point is surely important. Tight public bond markets, resulting from poor private saving, may jeopardize the zero-interest rate environment and trigger the disappearance of strong money demand. More concretely, as discussed in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, a large-scale inland earthquake in Tokyo, whose economic damages are expected to reach several years’ worth of private savings, may trigger a sharp rise in interest rates.

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Introduction: Toward a Monetary and Fiscal Theory …

3 Toward a Monetary and Fiscal Theory of the Price Level 3.1 Two Standard Theories of the Price Level: QTM and FTPL As discussed in the previous section, the QTM held approximately in the modern Japanese economy, when money demand was stable at its long-run level, with the price level increasing as much as money quantity given real output. However, if money demand was growing or contracting, the QTM clearly broke down and the price level and money quantity never moved together. However, this does not mean that the fiscal theory of the price level (FTPL), an influential alternative to the QTM, was applicable to the two occasions where money demand was strong in Japan. In the FTPL, the price level is determined to the extent that the real balance of public bonds is backed by future fiscal surpluses. As demonstrated by the wartime and contemporary Japanese experiences discussed in Sect. 2, the real balance of public bonds seems to be backed by several factors other than future fiscal surpluses, including forced saving, money demand from the underground economy, currency demand in occupied territories, strong money demand driven by near-zero interest rates, and even public bond price bubbles. Thus, it is difficult to conclude that money markets alone determine the price level, as in the QTM, or by fiscal policies alone, as in the FTPL. Instead, it seems more appropriate to claim that the price level is determined by the interaction between public bond and money markets. Allow me to propose a monetary and fiscal theory of the price level (MFTPL). To begin, I present simple versions of the QTM and the FTPL. The consolidated government, consisting of the central government and the central bank, issues money (M s (t)) and public debt (B s (t)) to households. Both M s (t) and B s (t) are at the end of the period. The government pays nominal interest i(t) on public bonds held by householdsB d (t − 1). In addition, it imposes lump-sum taxes tax(t) (in real terms) on households and undertakes government consumptiong(t), (also in real terms). With the price levelP(t), the government’s intertemporal budget constraint from time t − 1 to time t is written as follows: B s (t) − B s (t − 1) B d (t − 1) M s (t) − M s (t − 1) + + tax(t) = g(t) + i(t) (1) P(t) P(t) P(t) Suppose that both money and public bond markets are in equilibrium: M s (t) = M (t) = M(t), and B s (t) = B d (t) = B(t). The real rate of interest ρ(t) is defined as 1 + ρ(t) = P(t−1) [1 + i(t)]. Then, Eq. (1) is rewritten as: P(t) d

1 B(t − 1) + M(t − 1) = [tax(t) − g(t)] P(t − 1) 1 + ρ(t) 1 i(t)M(t − 1) 1 B(t) + M(t) + + . 1 + i(t) P(t − 1) 1 + ρ(t) P(t)

(2)

3 Toward a Monetary and Fiscal Theory of the Price Level

19

The first term on the right-hand side of Eq. (2) corresponds to real fiscal surpluses at time t, and the second term to real seigniorage at time t. Note that the one-periodahead fiscal surplus is discounted at the real interest rate, but the one-period-ahead seigniorage is discounted at the nominal interest rate. Here, real seigniorage arises from a fact that the consolidated government issues money at zero nominal interest rates. Real seigniorage increases with the nominal interest rate and the real money balance. B(t) , and the real Here the real balance of public bonds is defined as b(t) = P(t) balance of money as m(t) = M(t) . The present values of the real fiscal surpluses and P(t) seigniorage are expressed as follows:  ∞   tax(t + τ ) − g(t + τ ) τ b (t) = k=1 (1 + ρ(t + k)) τ =1 f

s(t) =

 ∞   i(t + τ )m(t + τ − 1) τ k=1 (1 + i(t + k)) τ =1

(3)

(4)

Then, the government’s lifetime budget constraint is written as:   B(t) + M(t) b(t + τ ) + m(t + τ ) f = b(t) + m(t) = b (t) + s(t) + lim τ . (5) τ →∞ P(t) k=1 (1 + ρ(t + k)) The third term on the right-hand side of Eq. (5) is the terminal condition. In most cases, the terminal condition converges to zero. Thus, the present value of future fiscal surpluses and seigniorage backs the real balance of public bonds and money. In money markets, the real money balance (supply) is equal to real money demand m d (t). M(t) = m d (t) P(t)

(6)

If real money demand is stable at m d in the QTM, then the price level P(t) is proportional to M(t). d d Given constant real  money demand m , Eq. (4) is written as s(t) = m , because ∞  i(t+τ ) τ = 1 as in perpetual floating-rate bonds. If the real money τ =1 k=1 (1+i(t+k)) balance is constant, and the zero terminal condition is satisfied, then Eq. (5) is simplified as: B(t) = b f (t). P(t)

(7)

According to the QTM, the central bank chooses money supply M(t), and the price level P(t) is determined by Eq. (6) under stable money demand. Given the

20

Introduction: Toward a Monetary and Fiscal Theory …

price level determined in this way, the central government chooses the sequence of fiscal surpluses (tax(t) − g(t)) such that Eq. (7) holds. In the FTPL, on the other hand, the central bank chooses not the money supply, but the nominal interest rate i(t). In this case, only the real money balance m d (t) is determined. Thus, Eq. (6) cannot pin down the price level P(t). Instead, the government’s lifetime budget constraint (Eq. (5)) determines the price level with the zero terminal condition satisfied: B(t) = b f (t) + s(t) − m d (t) P(t) More concretely, P(t) is determined by the above equation, given real variables b f (t), s(t), and m d (t), and a nominal variable B(t). In most cases, the FTPL assumes Eq. (7) as the government’s lifetime budget constraint. However, Eq. (7) is not usually justified by assuming stable money demand m d ; the FTPL and the QTM are only equivalent if money demand is constant over time. In the FTPL, Eq. (7) is often justified by the absence of money markets. An alternative justification for Eq. (7) is, as in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, that all seigniorage is reimbursed to households. In either case, given a combination of b f (t) and B(t), P(t) is determined by Eq. (7). In this book, Eq. (7) is sometimes reinterpreted as not the government’s lifetime budget constraint, but the supply–demand balance in public bond markets. That is, it is assumed that public bonds are held by investors to the extent that they are fully backed by future fiscal surpluses. Here, b f (t) corresponds to real public bond demand. A reason for this reinterpretation of Eq. (7) is that it is more natural for the price level to be determined not by someone’s budget constraint, but according to market equilibrium in the competitive equilibrium context.

3.2 Five Cases of a Monetary and Fiscal Theory of the Price Level: An Overview 3.2.1

Big Inflations in Interwar Europe

In cases where the QTM is not applicable, fiscal policy decisions usually precede those on monetary policy. Such cases are called fiscal dominance by Sargent and Wallace (1981), and active fiscal policies by Leeper (1991). In this section, we begin with the case where, as a result of undisciplined fiscal policies, the real public bond balance is not fully backed by future fiscal surpluses: B(t) > b f (t) P(t)

(8)

3 Toward a Monetary and Fiscal Theory of the Price Level

21

Equation (8) may be reinterpreted as excess supply in public bond markets. Under the standard FTPL, the price level is immediately adjusted such that equality may be recovered in Eq. (8). As mentioned, however, the real public bond balance is backed by several factors other than future fiscal surpluses. Thus, we instead present five cases for an MFTPL, in which public bond and money markets simultaneously work to determine the price level. As Sargent (1982) argues, the strong upward pressures on the price level were from two sources in interwar Europe. First, the price level surged as long as real money demand was shrinking. Second, the price level soared to the extent that the real public bond balance was not backed by future fiscal surpluses. Then, the price level ceased to surge after real money demand was stabilized, and the real public bond balance was fully backed by future fiscal surpluses. In this way, monetary and fiscal conditions simultaneously worked to promote and then prevent price surges. More precisely, the four countries in interwar Europe—Austria, Hungary, Poland, and Germany—issued central banknotes at zero interest rates, and replaced public debt by banknotes. They attempted to close the gap between the real public debt B(t) and the present value of future fiscal surpluses b f (t) by supplementing balance P(t) (t)]+M (t) seigniorage s(t) as additional revenues, or to establish [B(t)−MP(t) = b f (t) + d s(t). However, contracting real money demand m (t) during a highly inflationary process never created sufficient seigniorage. Then, b f (t) + s(t) was far short of B(t) B(t) . Unbacked public debt ( P(t) > b f (t) + s(t)) itself created considerable upward P(t) pressures on the price level and accelerated the contraction of real money demand as well as the reduction of seigniorage. Such a vicious cycle between unbacked public debt, shrinking real money demand, and falling seigniorage could only be broken through drastic fiscal and monetary reform. That is, b f (t) improved substantially, real money demand was stabilized at m d , and seigniorage s(t) recovered to m d . f B(t) Then, P(t) − m d = b (t) held. Once public bonds were fully backed by future fiscal surpluses, and real money demand was stabilized, no additional pressures on the price level were created, and the price surges stopped. s

3.2.2

s

A Case of the Controlled Economy in Japan

As discussed briefly in Sect. 2.2, and in detail in chapters “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II” and “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”, the wartime Japanese government suffered from a disastrous tax revenue shortfall and faced Eq. (8) in a severe manner. Thus, the B(t) and b f (t) using the following government attempted to close the gap between P(t) financial mechanisms. (1)

Forcing households to hold public bonds directly or indirectly through banks (B f or ced (t)).

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Introduction: Toward a Monetary and Fiscal Theory …

(2)

(3)

Issuing massive amounts of BOJ notes against real money demand from not only the formal economy (m f or mal (t)), but also the underground economy (m black (t)). Requiring reserve and central banks in the occupied territories to underoccupied write public debt directly by issuing banknotes (Mi (t) for bank i, occupied i = 1, . . . , I ), which were held by local currency demand (m i (t)).

In this version of MFTPL, the supply–demand balance in public bond and money markets held in a complicated manner as follows. • Domestic public bond markets:

B(t) − B f or ced (t) − M s (t) − P(t)

I

occupied (t) i=1 Mi

= b f (t),

where P(t) denotes the domestic price level. – Domestic money markets:

M s (t) = m f or mal (t) + m black (t) P(t) – Money markets in occupied territory i:

occupied

Mi

Pi (t)

(t)

occupied

= mi

(t)

where Pi (t) denotes the price level in territory i. Immediately after the war, however, forced saving, money demand from the underground economy, and the occupied territories themselves all instantly disappeared. Accordingly, as long as public bonds remained unbacked by future fiscal surpluses B(t) > b f (t)), and before real money demand was stabilized at the long-run level ( P(t) (t) ( MP(t) > m L R , where m L R denotes the long-run level of real money demand), the s

B(t) price level continued to surge. Up until the late 1940s, P(t) was backed by b f (t) because of intensive tax reforms, and real money demand returned to its long-run level. By then, the price surge had stopped.

3 Toward a Monetary and Fiscal Theory of the Price Level

3.2.3

23

Two Cases of a Zero-Interest Rate Environment in Japan

As discussed in Sect. 2.3, the Japanese government is currently facing Eq. (8), because of a succession of expansionary fiscal policies together with the postponement of drastic tax and social security reforms. Nevertheless, the government can sustain huge public bonds in the near-zero interest rate environment. This book proposes two cases in which this seemingly impossible phenomenon is indeed feasible. In chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy”, public bonds and money are treated as a whole, because both are close substitutes at near-zero B(t) > b f (t)) interest rates. More concretely, excess supply in public bond markets ( P(t) ), which results from is absorbed by excess demand in money markets (m d (t) − M(t) P(t) strong money demand at zero rates; that is, m d (t) −

M(t) P(t)

=

B(t) P(t)

− b f (t) holds. As

B(t) > b f (t) long as unbacked public bonds are supported by strong money demand, P(t) never creates upward pressure on the price level. There are two remarks on this monetary and fiscal equilibrium. First, excess demand in money markets is extremely fragile with respect to an increase in nominal interest rates. Once the nominal rate of interest takes off from zero, excess demand disappears immediately, and the economy then experiences price surges and interest rate hikes. Unless public bonds are fully backed by future fiscal surpluses, the price surge then degenerates into genuine hyperinflation. Second, if public debt and money markets are in excess demand as a whole, then there emerges excess supply in goods/labor markets. This prediction is suggestive of the observation that aggregate demand often stagnated in goods markets, and unemployment frequently grew in labor markets, seemingly despite the extremely low interest rate policy of the past quarter century in the Japanese economy. In chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, it is assumed that seigniorage is reimbursed to households in a lump-sum manner. Then, the government’s lifetime budget constraint is written  b(t+τ ) f  . In this case, neither money supply nor asb(t) = b (t) + lim τ k=0 (1+ρ(t+k)) τ →∞ demand appears in the government’s budget constraint. But, as rigorously proved in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, as nominal interest rates approach zero, the terminal condition  b(t+τ ) ( lim τ (1+ρ(t+k)) ) converges to not zero, but finite positive. The non-zero k=0 τ →∞ terminal condition is often called a public bond price bubble. In this case, the bubble supports unbacked public bonds. Unfortunately, the bubble is as fragile as the excess demand in money markets. If the bubble bursts at some point in the future, then the price level surges and interest rates jump. In addition, the government is forced to recover fiscal sustainability to prevent price surges from falling into genuine hyperinflation. As explored in detail in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, this model can precisely replicate the stable prices, near-zero interest rates, and flattening yield curves, all of which have been observed over the past quarter century in the Japanese economy.

24

3.2.4

Introduction: Toward a Monetary and Fiscal Theory …

Huge Seigniorage from Negative Interest-Bearing Central Bank Cryptocurrencies

As discussed in chapter “Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?”, the introduction of cryptocurrencies by central banks also contributes to the dissolution of the inequality in Eq. (8). One important character of central bank cryptocurrencies (CBCCs) is that they can be renumerated in either positive or negative interest rates. Here, currency interest rate i c (t) differs from public bond interesti(t), the latter being determined in markets, but the former chosen by the central bank. In this case, it is the differential between the public bond and currency interest rates i(t) − i c (t) not the public bond interest rate i(t) that usually constitutes the source of seigniorage. There are two interesting cases. First, when the public bond interest coincides with the currency interest rate (i(t) = i c (t)), the model is basically the same as that in chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” (the first case in Sect. 3.2.3), in which public debt and money are equivalent. The model in chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” is in fact a special case of that in chapter “Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?” with i(t) = i c (t) = 0. Second, when the public bond interest rate is positive, but the currency interest rate is negative (i(t) > 0 > i c (t)), the consolidated government can receive seigniorage in addition to future fiscal surpluses to support the real public bond balance. Let me explore the second case in more detail. Suppose that real money demand is stable at m d , and that the public bond and currency interest rates are constant value of future seigniorage, or Eq. (4) (i(t) = i, i c (t) = i c ).10 Then, the present  ∞ c

c

i−i c d = m d 1 − ii > m d . If s = m d 1 − ii is rewritten as s = m τ =1 (1+i)τ is substituted into Eq. (5), and the terminal condition converges to zero, Eq. (5) c is rewritten as b(t) − b f (t) = − ii m d > 0. The consolidated government can c then obtain additional revenues − ii m d > 0 to repay its public bonds. In particular, when the public bond interest is close to zero, the negative currency interest rate yields enormous revenues for the government. Here, a more negative currency can be interpreted as higher taxes on currency holders. As the above five cases demonstrate, the price level was not determined by either monetary conditions alone, as in the QTM, or fiscal conditions alone, as in the FTPL, but by a framework of MFTPL, in which both monetary and fiscal conditions simultaneously worked to determine the price level. The details of each case are presented and described in what follows.

real money demand m d is decreasing in i − i c , but here assumed to be inelastic with respect to i − i c unless i − i c is close to zero.

10 Rigorously,

Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II

Abstract Employing the Japanese case of large-scale black markets under extensive price controls during and immediately after World War II, we first explore how much income leaked out of the formal economy into the black markets. Then, we investigate the extent to which the circulation of Bank of Japan (BOJ) notes helped the leaked income to flow back into the formal economy when the notes were held as an instrument to conceal illicit income by the black marketeers. According to our estimates, 6–30% of national income leaked into the black markets in the above period, while more than 40% of the leaked income returned to the treasury as massive seigniorage revenues in the last years of the war. Inflation was not too high during the war because of the black marketeers’ strong money demand. After the war, however, the black marketeers shifted their portfolios from BOJ notes to physical assets and land, thereby reducing their money demand and accelerating inflation. We also demonstrate that the black markets helped to reserve scarce physical resources for the post-control economy starting in the late 1940s.

1 Introduction Central banknotes, particularly large denomination bills, are considered to be an effective instrument for black marketeers to conceal illicit income thanks to their uninscribed nature (Rogoff, 2016). Beyond such a microeconomic consideration, however, there seems to be little rigorous research on any macroeconomic relationship between central banknotes and black market transactions. This chapter examines the Japanese economy in the Second Sino-Japanese War (1937–1945) and the Pacific War (1941–1945) during World War II, and the postwar years of 1945 to 1949, which were part of the occupation period ending in 1952. During the years 1937–1949, the Japanese economy was controlled heavily by rationing and price controls. In this period, large black markets developed because of extensive but ineffective price controls,1 while the Bank of Japan (BOJ) issued massive quantities of banknotes. 1 While

many papers, including Rockoff (1984) for the US and Williams (1945) for non-US countries, point out that extensive price controls triggered the emergence of black markets, little research © Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9_2

25

26

Central Banknotes and Black Markets … 60%

30%

25%

50%

20% 40% 15% 30% 10% 20% 5% 10%

0%

0%

-5%

Statistical disecrepancy/nominal GNE Marshallian k (outstanding BoJ notes/nominal GNE, right scale)

Fig. 1 Relative statistical discrepancy and Marshallian k, 1930–1955. Notes (1) See Statistics Department, BOJ (1966) and EPA (1964) for the data sources. (2) Marshallian k is defined as the outstanding BOJ notes over nominal GNE. (3) The statistical discrepancy is defined as the difference between nominal aggregate expenditure and income. (4) The computation of nominal GNE for 1945 is described in Sect. 4.2

Thus, this period is potentially suitable for a careful study of the macroeconomic interdependence between central banknote issuance and black markets. We consider two macroeconomic phenomena observed during the period 1937– 1949, both of which were seemingly unrelated to each other. As statistical discrepancies in the national accounts demonstrate in Fig. 1, aggregate expenditure consistently exceeded aggregate income in nominal terms by more than 5% of nominal gross national expenditure (GNE) in this period. As shown in Fig. 1, however, Marshallian k, which is defined as the outstanding BOJ notes divided by nominal GNE, started to deviate upward from its long-run average of 10% in 1937, peaked at around 50% in 1945, and reverted quickly to 10% by 1949. Thus, in the years 1937 to 1949, the statistical discrepancies and Marshallian k tended to move together. Both deviated upward from their long-run trends during the war, while they decreased rapidly immediately after the war. This chapter presents a simple macroeconomic framework within which these two seemingly disconnected phenomena—serious inconsistencies in the national accounts and strong aggregate demand for BOJ notes—can be interpreted consistently. We first prove that a statistical discrepancy between nominal aggregate expenditure and income serves as an exact measure of income leakages into the black markets has been done in terms of economy-wide interactions between the formal economy and black markets.

1 Introduction

27

in the simultaneous presence of black market prices and official prices. Given this theoretical interpretation, 6–30% of national income was estimated to leak out of the formal economy into the black markets in the years 1937–1949. As a result of the massive income leakages into the black markets, those in the formal economy, both public and private sectors, were subject to severe financial shortages in the sense that net national savings fell short of net investment plus net exports. Then, we establish a theoretical relationship between such income leakages into the black markets and aggregate demand for central banknotes from the black marketeers. The circulation of BOJ notes helped the leaked income to return to the financially deficient formal economy, when BOJ notes were eventually held as an instrument for concealing illicit income by the black marketeers. According to our results, in the last years of the war (1943–1945), more than 40% of the leaked income returned to the treasury as massive seigniorage revenues thanks to strong money demand from the black markets, which in turn mitigated substantially the price impact of the massive issuance of BOJ notes. In this way, largely positive statistical discrepancies can be interpreted as evidence of income leakages into the black markets, while a quite high Marshallian k can be elucidated as confirmation of strong money demand from the black marketeers, who in turn received the income leaking from the formal economy. This chapter contributes to the literature on the measurement of the informal economy2 by presenting explicit theoretical foundations for such yardsticks. In the existing literature, statistical discrepancies between nominal aggregate expenditure and income have been frequently regarded as a proxy for the size of the underground economy (see O’Higgins, 1989).3 As Thomas (1999), Tanzi (1999), and others argue, however, such statistical discrepancies do not necessarily have theoretical justifications as a measure of the informal economy.4 This chapter alternatively presents a theoretically convincing case where a statistical discrepancy serves as an exact measure of income leakages into black markets in the presence of price controls. This chapter also offers a theoretical framework in which aggregate demand for central banknotes is tightly linked with income leakages into black markets. Without any explicit theoretical justification, several papers argue that monetary measures may serve as proxies for the scale of black market transactions. For example, cash/deposit ratios are proposed by Cagan (1958), Gutmann (1977), and Bhattacharyya (1990), while currency demand measured in terms of Marshallian k is proposed by Feige (1989). The justification for these measures is frequently based on a casual observation that black marketeers hold central banknotes to conceal illicit income. This chapter instead demonstrates an upward deviation of Marshallian k 2 See

Frey and Pommerehne (1982), Feige (1989), Schneider (2005), and Georgiou (2010) for a survey of this field. 3 In the context of the Japanese national accounts, Mizoguchi and Nojima (1993) and Mizoguchi (1996) informally state that the presence of black markets was responsible for largely positive statistical discrepancies in the postwar EPA national accounts (EPA, 1964). 4 In addition, econometric studies, including Gartaganis and Goldberger (1955) and Adams and de Janosi (1966), point out that statistical discrepancies in peacetime periods reflect various kinds of measurement errors.

28

Central Banknotes and Black Markets …

from its long-run average as reflecting strong money demand from black markets, thereby overcoming the theoretical drawbacks involved in the preceding papers. Finally, this chapter presents a case in which high tension between efficiency and inequality is induced by illegal transactions in a heavily regulated economy. Obviously, any resource allocation through illegal transactions involves uneven wealth distribution to illicit dealers. However, a role that was played potentially by transactions using BOJ notes and barter transactions with the black marketeers during the controlled-economy period may be interpreted as a second-best response to heavy economic controls. According to our results, for example, the outstanding assets, which were accumulated mainly in the form of BOJ notes during the war, and household durables and factory inventories after the war by the black marketeers, reached close to the size of the national economy by the late 1940s. Consequently, an extremely unfair distribution of wealth toward the black marketeers emerged, but illegal cash transactions and illicit barter transactions in the black markets helped to reallocate those resources from the controlled economy to the post-control economy, which finally took off after most economic controls were lifted in the late 1940s. Here, we would like to give readers advance notice. According to the above hypothesis, (1) a substantial portion of aggregate income leaked into the black markets when the Japanese economy was heavily controlled, (2) strong money demand from the black marketeers helped the leaked income to flow back to the formal economy during the war, and (3) illegal transactions in the black markets worked to release scarce resources from inefficient uses during the controlledeconomy period. However, it is next to impossible to prove this working hypothesis rigorously because of the poor quality of the contemporary statistical data. Thus, we attempt to convince readers that it is indeed plausible by exploiting the macroeconomic statistics that were reconstructed by the occupation authorities and the Japanese government in the postwar period. This chapter is organized as follows. Section 2.2 offers a brief description of the price controls that were imposed during and immediately after the war. Section 2.3 presents a theoretical justification for the statistical discrepancy as an exact measure of income leakages into black markets. In addition, it offers a theoretical framework in which aggregate demand for central banknotes is tightly linked to income leakages into black markets. Section 2.4 interprets the Japanese national accounts as well as the monetary statistics of the 1930s and 1940s using the framework presented in Sect. 3. Section 5 concludes the chapter.

2 A Brief History of the Controlled Economy in the Years 1937–1949

29

2 A Brief History of the Controlled Economy in the Years 1937–1949 2.1 Price Controls During and Immediately After the War5 A fundamental problem faced by the Japanese economy during and immediately after World War II was its stagnant production. According to the Economic Planning Agency (EPA, 1964), real GNE was sluggish in the 1940s; for example, in 1934– 1936 constant prices, real GNE was 13.4 billion yen in 1930, and 22.1 billion in 1939, but only 20.1 billion in 1944, 10.9 billion in 1946, and 16.2 billion in 1950.6 Among the possible factors responsible for the prolonged stagnant production in the 1940s, a shortage of imported goods was the most crucial. In particular, production by munitions factories, which were heavily dependent on imports of intermediate goods from the Allies, declined substantially because of a series of economic blockades imposed by the Allies starting in the late 1930s. Even after the war, the General Headquarters of the Allied Powers (GHQ) (the occupation army in Japan) imposed strict restrictions on imports with exceptions for humanitarian purposes. It was after these import restrictions were lifted for heavy oil in 1947 and for other commodities in 1948 that Japanese production started to recover from serious economic stagnation. Given such a serious shortage of materials and products, the government was forced to prioritize the distribution of scarce resources, for example to munitions industries during the war, and to heavy industries including coal and steel during the postwar reconstruction. At the same time, the government had to implement extensive price controls so that excess demand resulting from wide-ranging rationing might not lead to rapidly rising prices.7 For this purpose, the wartime government legislated the Temporary Import/Export Grading Measures Law (TIEGML), the Temporary Funds Adjustment Law, and the Material Mobilization Plans (MMP) in 1937, the Total National Mobilization Law (TNML) in 1938, and the Productive Capacity Expansion Plans in 1939. Initially under the TIEGML in 1937 and the TNML in 1938, and later by the Price Control Order (PCO) enacted in 1939, the government set official prices at extremely low levels for most final and intermediate goods. Both wages and housing rents were also heavily regulated by the PCO. Accordingly, especially in intermediate goods markets, producers had a strong incentive to sell their own goods in black markets at higher prices and to retain their illegal earnings off the books. At the same time, because of strict rationing, producers were forced to purchase goods through undercover dealings. Consequently, expensive intermediate goods obtained from black markets increased production costs, but producers had to disclose sales of all intermediate and final goods at the cheap official prices. Then, producers in official 5 The

description in this subsection is based mainly on Nakamura (1974, 1983). column (1) in Table 5. 7 Nakamura (1983) describes in detail the legislation process of economic controls for the years 1937–1945. 6 See

30

Central Banknotes and Black Markets …

markets had to carry considerable losses, for which they were often compensated by government subsidies such as the subsidies to offset price differentials and the loss compensation. In addition, consumers needed to purchase expensive goods from black markets in the final years of the war. The police force launched a crackdown on illegal transactions in late 1938, but from 1941, its control began weakening gradually, partly because of a shortage of police officers and partly because of the frequent involvement of military personnel in undercover transactions. According to Kikuchi (1947) and Miwa (2015), as a consequence of ineffective material allocations under the MMP, some munitions factories were rationed unnecessarily and they disposed of their excess rations of goods into illegal markets. In addition, Kikuchi (1947) documents that after munitions factories were forced to achieve extremely demanding production targets imposed by the Munitions of War Act in late 1943, they started to purchase a large amount of raw materials from illegal dealers. Nishida (1994) also points out that munitions factories purchased consumption goods from illegal dealers on behalf of their managers and employees in the period 1943–1945. In this way, munitions factories emerged as both sellers and buyers in black markets in the final years of the war. While there are few time-series data for black market prices during the wartime period,8 Morita (1963) presents the effective wholesale/retail price indexes that reflect both official and black market transactions. The effective indexes, often called the Morita indexes, were compiled by the BOJ in the final years of the war and were employed in estimating nominal aggregate expenditure initially by the United States Strategic Bombing Survey (USSBS) (1946) and later by the EPA (1964).9 As reported in Table 1, the effective-to-official price ratio increased from 1.08 in 1940 to 1.45 in 1944 for wholesale prices, and from 1.07 in 1940 to 1.93 in 1944 for retail prices.10 The extensive rationing and price controls were maintained even after the war. The PCO was replaced by the Price Control Law in 1946, while the MMP was switched to the Material Supply and Demand Planning Program in 1945, which was reformulated as the Priority Production System in 1946. In the aftermath of the war, the government concentrated its material and financial resources in heavy industries, in particular coal and steel. As in the wartime period, the government offered subsidies to offset price differentials for heavy industry products. 8 Mizoguchi

(1995) reports the black-to-official market price ratios of several consumption goods for the first quarter of 1944; for example, 7.45 for rice/wheat, 3.12 for vegetables, 4.73 for fish, 5.25 for meat, and 5.56 for seasonings. 9 As Morita (1963) explains, the effective wholesale price index was computed as the nominal amount of transactions by drafts divided by the quantity of commodity transactions, while the effective retail price index was computed as the nominal amount of transactions by cash divided by the quantity of commodity transactions. While these effective price indexes (the Morita indexes) were recognized as far from perfect measures among experts including even Yuzo Morita, there was no alternative to the Morita index as a measure of wartime transaction prices. 10 Before most final and intermediate goods were regulated heavily by the PCO in 1939, the BOJ official price indexes included not only regulated prices, but also unregulated ones. Thus, the BOJ’s official price indexes and the effective price indexes (the Morita indexes) were close to each other under price controls in the late 1930s.

121.4

128.1

141.5

158.4

169.7

184.6

197.5

223.8

1937

1938

1939

1940

1941

1942

1943

1944

201.7

180.2

169.8

165.0

163.1

140.4

125.3

109.4

100.0

(2) Retail

325.0

266.5

235.9

184.2

170.7

145.4

125.7

118.9

100.0

Relative to (1)

(3) Effective wholesale price

Morita index

Note See Statistics Department, BOJ (1966) and EPA (1964) for the data sources

100.0

1936

(1) Wholesale

Official price indexes

1.45

1.35

1.28

1.09

1.08

1.03

0.98

0.98

1.00

390.0

312.3

265.6

204.1

175.0

134.8

120.3

108.6

100.0

Relative to (2)

(4) Effective retail price

1.93

1.73

1.56

1.24

1.07

0.96

0.96

0.99

1.00

Table 1 Comparison of the wholesale and retail price indexes with the Morita index, 1936–1944 (standardized as of 1936)

355.8

291.3

251.0

206.7

183.7

144.2

117.3

105.8

100.0

Relative to (1)

(5) GNE deflator

1.59

1.48

1.36

1.22

1.16

1.02

0.92

0.87

1.00

2 A Brief History of the Controlled Economy in the Years 1937–1949 31

32

Central Banknotes and Black Markets …

According to Statistics Department, BOJ (1966), the black-to-official market price ratio was fairly high for production goods: 7.2 in 1946, 5.3 in 1947, 2.9 in 1948, and 1.7 in 1949. The government began to lift price controls as well as resource rationing from early 1949, when the Dodge Line was proposed as a fiscal reconstruction plan by the GHQ. By the late 1940s, the black markets almost disappeared.

2.2 Government Subsidies to Offset Price Differentials As mentioned above, during the wartime period, producers in munitions industries always carried enormous losses as a result of their purchases of expensive intermediate goods in black markets and their sales of cheap final goods in official markets. A substantial fraction of such losses was compensated for by the subsidies and loss compensation from the government. According to Nakamura (1974), for example, the Japan Coal Company was founded as a public institution to control coal markets in 1939. The company purchased coal from all domestic mines at cost prices and sold them to final users through private coal companies at official prices, which were much cheaper than the cost prices. In 1944, the official price was about half of the cost price. The corporate losses resulting from the extensive price controls were even larger for heavy industries after the war. The losses were initially financed from the Reconstruction Finance Bank (RFB), which was backed by the BOJ’s underwriting, and were later subsidized or compensated for by the government. Employing accounting data from the Hokkaido Colliery and Steamship Company, Miwa and Ramseyer (2004) document that the official coal prices were updated extremely slowly despite persistent high inflation and equaled only around 40% of the cost prices in early 1948. In this way, most losses resulting from such large price differentials were eventually covered by the government subsidies and the loss compensation. Accordingly, these losses were transferred from private companies to the government, which in turn financed these subsidies mainly by letting the BOJ underwrite public bonds as described in the next subsection. The subsidies and loss compensation paid to heavy industries accounted for 17.8, 23.8, and 30.2% of general account expenditure in 1947, 1948, and 1949, respectively (Nakamura, 1974). By the order of the GHQ, however, the government could not pay any subsidy or compensation for corporate losses by the early 1950s.

2 A Brief History of the Controlled Economy in the Years 1937–1949

33

2.3 Massive Issues of BOJ Notes During and Immediately After the War Let us briefly describe some institutional details of the large-scale money issuance by the BOJ during the wartime and postwar periods. Finance Minister Takahashi Korekiyo initiated the large-scale money issuance by requesting the BOJ to underwrite new issues of public bonds directly and to issue in turn BOJ notes to the government in November 1932. Even after the assassination of Takahashi in 1936, the government continued the money issuance throughout World War II. The BOJ’s underwriting was initially introduced not as a fiscal instrument for the government but as a macroeconomic stimulus measure. While the BOJ directly underwrote public bonds during the years 1932–1936, it resold to the private banks more than 90% of what it purchased directly from the government. That is, the BOJ withdrew most of the newly issued banknotes from the economy. This implies that the government eventually financed its own deficit by borrowing not from the BOJ but from the private banks (Shima, 1983). As analyzed in detail by Shibamoto and Shizume (2014), the above monetary policy together with suspension of the gold standard worked effectively to stimulate the economy, mainly through a marked depreciation of the yen. However, the BOJ had employed direct underwriting as a powerful fiscal tool since the Second Sino-Japanese War began in 1937. Even after 1937, the BOJ continued to resell most of their direct purchases of public bonds to private banks; however, the private banks did not finance the bond purchases from the BOJ with deposits from private savings, but with credit provided directly by the BOJ. This was equivalent to the government receiving credit from the BOJ via the private banks.11 After February 1942, the upper limit on the issue of BOJ notes was determined solely by the Minister of Finance.12 Even in the aftermath of the war, the BOJ kept underwriting public bonds directly from the government. While the GHQ prohibited the BOJ from underwriting longterm public bonds in November 1945, the BOJ was still allowed to underwrite shortterm public bonds. After the Public Finance Act was legislated in March 1947, the BOJ could not underwrite any public bonds in principle. However, the BOJ underwrote the short-term bonds issued by the RFB, which was founded as a public financial institution in January 1947. The RFB was not classified as a governmental body, and the BOJ was able to underwrite the RFB’s short-term bonds even under the Public Finance Act. By underwriting the RFB bonds, the BOJ issued banknotes to the value of 39.6 billion yen in 1947 and 37.2 billion yen in 1948, which accounted for about 30% of the total issuance in those years. However, the RFB was not allowed 11 The BOJ provided funds to the private banks, which in turn used the public bonds as collateral at the BOJ. Because the lending rate charged by the BOJ was lower than the yield on the long-term public bonds, the private banks were willing to purchase the public bonds by receiving inexpensive credit from the BOJ. 12 Japan suspended the gold standard in December 1931, but the outstanding BOJ notes had been constrained by the amount of specie reserves up to January 1942.

34

Central Banknotes and Black Markets …

to issue any additional bonds from April 1949 under the direction of the GHQ. In this way, the BOJ developed large-scale direct underwriting of public and quasi-public bonds from November 1932 to March 1949.

2.4 A Possible Macroeconomic Interaction Between the Circulation of BOJ Notes and the Black Markets: A Descriptive Explanation 2.4.1

Two Channels by Which the Leaked Income Returned to the Formal Economy

Before presenting a theoretical framework in Sect. 3, this subsection describes the income transfers between the formal economy and the black markets during and after the war. One of the most serious problems of the controlled economy was that the private agents in the formal economy received sales and wages at cheap official prices, but made some payments at expensive black market prices. Accordingly, private firms carried enormous losses, while consumers had an excess of payments over revenues. However, the government could not impose taxes on financially deficient private agents in order to finance large-scale deficits resulting from war expenditures, the reconstruction costs, and the subsidies for covering private corporate losses. The flip side of such severe financial shortages experienced by the formal economy was that the black marketeers received the income leaking from the formal economy as illegal margins resulting from purchases from the formal agents at cheap prices and sales to them at expensive prices. There were potentially two ways to return the hidden income from the black markets to the formal economy. In the first channel, the private agents in the formal economy bartered directly with the illegal dealers by exchanging inventories held by factories and durables held by households for resources from the black marketeers. For large-scale illegal transactions, the private agents in the formal economy employed housing and land as a medium of exchange.13 The undercover dealers in turn held inventories, durables, and immovable properties as stores of value. Note that the durables and inventories, which were produced previously and stored by the formal private agents, were exchanged for the resources that were produced currently and obtained through illegal transactions by the black marketeers. As the second channel, the BOJ’s direct underwriting of public bonds served as an inevitable fiscal instrument for the government because (1) the government could not 13 When the PCO was enacted in 1939, house rents were heavily controlled, but the prices of housing

and land were beyond the scope of the order. In 1939, newly built houses were targeted by the price controls, but secondhand homes were not. Consequently, the owners of secondhand homes had a strong incentive to sell their houses instead of renting them cheaply. According to Ono (2007), old houses were traded actively as a type of speculation in black housing markets during the years 1943 to 1944.

2 A Brief History of the Controlled Economy in the Years 1937–1949

35

obtain any more resources from the private agents suffering from income leakage into the black markets, (2) the government as a legitimate body could not deal directly with the black marketeers, but it could deal with the BOJ as another legitimate body, (3) BOJ notes newly issued to the government ultimately moved into the black markets because the total expenditure made by those in the formal economy exceeded the total income received by them, and (4) the black marketeers in turn held newly issued BOJ notes to conceal illicit income by exploiting their uninscribed nature.14 In this way, strong money demand from the black marketeers, who received a part of the national income leaking from the formal economy, created large seigniorage revenues for the financially deficient government. In the years 1947–1949, however, as the black marketeers reduced demand for BOJ notes for the reasons described in Sect. 4.5, the government relied more and more on taxes imposed on households and firms for fiscal revenues.

2.4.2

The Circulation of BOJ Notes During and After the War

It is quite difficult to obtain precise information regarding how BOJ notes circulated in the black markets under the extensive price controls, but there was one occasion where BOJ notes, which had been handed over from one illegal dealer to another, came to light in the formal economy. This occurred when the BOJ forced the holders of BOJ notes to exchange old bills for new bills under the EFM enforced in February 1946.15 Their policy purpose was to identify the black market income as precisely as possible and to impose capital levies on it of as much as 100%.16 According to Editorial Office of History of Public Finance in Showa Era (EOHPF), MOF (1976), the amount of outstanding BOJ notes decreased dramatically from 61.8 billion yen on 18 February 1946 to 15.2 billion yen on 12 March following the official announcement on 16 February. The BOJ eventually collected 50.3 billion yen in old bills, of which 9.0 billion yen were collected from the rural districts of southern Kanto, Tokai, and Kinki, while 8.1 billion yen were collected from the urban districts of Tokyo and Osaka. These statistics indicate that illegal dealings were most active in the agricultural and commercial sectors. After new bills began to circulate, the amount of outstanding BOJ notes began rising again to 136.3 billion yen as of June 14 Most of the public bonds were issued as uninscribed during and immediately after the war, but their coupons and principals needed to be cashed at financial institutions where identification of bond holders was required. 15 More precisely, the government officially announced the EFM on the evening of Saturday, 16 February. The measure included the following provisions. First, old bills would cease being legal tender after 2 March. Second, the deposits at financial institutions using old bills could be made until 7 March (later revised to 9 March). Third, withdrawals from deposits using new bills were severely restricted; that is, deposits were effectively frozen. 16 In December 1945, the government suggested that the BOJ might collect old bills in exchange for new bills. Surprised by the intention of the government and the BOJ, major illegal dealers rushed to trade any cash on hand for physical materials and food, and they in turn refused to sell their inventories for old bills. Consequently, a substantial portion of the black markets disappeared until the exchange for new bills was completed in March 1946.

36

Central Banknotes and Black Markets …

1947, and 230.5 billion yen as of June 1948. The majority of new bills were held within the commercial sector rather than the agricultural sector. Although EOHPF, MOF (1976) claimed that a substantial proportion of new bills still continued to be held by the illegal dealers, most of the new bills were actually held for transaction purposes by those in the formal economy (see Sect. 4.5).

3 A Theoretical Relationship Between Black Markets and Money Demand Under Price Controls 3.1 A Simple Model of Possible Effects of Price Controls on the National Accounts This subsection demonstrates that if official and black market prices are present simultaneously, then a positive statistical discrepancy between aggregate expenditure and income in the national accounts serves as a measure of income leakages into black markets. We simplify the historical situation described in Sect. 2.2 as follows: (1) In corporate accounting, producers disclose sales of all final and intermediate goods at official prices, but record purchases of intermediate goods from underground dealings at black market prices. (2) The margins earned by selling to underground dealers are off the books. (3) Consumers purchase some consumption goods from black markets. Let us explore below the possible effects of price controls on the national accounts. om bm bm , P om Here, Pinter f inal , Pinter , and P f inal denote official and black market prices for om bm intermediate and final goods, respectively. For intermediate goods, Vinter and Vinter om denote the transaction volume in official and black markets. For final goods, V f inal and V fbm inal denote the transaction volume in each market. The transaction value of om om om V inter (P om intermediate goods (final goods) is Pinter f inal V f inal ) at official markets and bm

bm

bm Pinter V inter (P bm f inal V f inal ) at black markets. It is assumed that the purchases of goods are valued at transaction prices and the sales of goods are valued at official prices. The black market margins are not reported at all. According to the above valuation practice, the nominal expenditure on all final goods YnE is computed at transaction prices as follows. Note that a variable with the subscript n denotes a nominal variable.

    bm om bm om om bm bm om bm YnE = P om f inal V f inal + P f inal V f inal = P f inal V f inal + V f inal + P f inal − P f inal V f inal

(1) Nominal aggregate income, measured as value added YnV A , is calculated at official prices for sales and transaction prices for purchases:  om   om  om bm bm Vinter + Vinter + P om YnV A = Pinter f inal V f inal + V f inal

3 A Theoretical Relationship Between Black …

37

  om om bm bm − Pinter Vinter + Pinter Vinter  om   bm  bm bm om = P om f inal V f inal + V f inal − Pinter − Pinter Vinter .

(2)

Finally, the unreported margin in black markets Ynbm corresponds to:  bm  bm   bm om om Ynbm = P bm f inal − P f inal V f inal + Pinter − Pinter Vinter . As Eqs. (1) and (2) imply, aggregate expenditure increases by the additional cost of final goods purchased from black markets, while aggregate income decreases by the additional cost of intermediate goods procured from illegal transactions. Consequently, the statistical discrepancy between aggregate expenditure and aggregate income S D n is exactly equal to the unreported illegal margin:  bm  bm   bm om om bm S D n = YnE − YnV A = P bm f inal − P f inal V f inal + Pinter − Pinter Vinter = Yn . (3) In this way, the statistical discrepancy S D n corresponds to the unreported margins earned by illegal dealers Ynbm , and can be interpreted as income leakages from formal markets into black markets. Given nominal aggregate expenditure and nominal aggregate income by Eqs. (1) and (2), the GNE and GNI (gross national income) deflators are defined as follows:

PGN E =

    om bm bm om bm P om f inal V f inal + V f inal + P f inal − P f inal V f inal bm V fom inal + V f inal

  bm om = P om f inal + P f inal − P f inal

PGN I =

 om P om f inal V f inal

V fbm inal

bm V fom inal + V f inal    bm bm om + V fbm inal − Pinter − Pinter Vinter

(4)

bm V fom inal + V f inal

  bm om = P om f inal − Pinter − Pinter

bm Vinter bm V fom inal + V f inal

(5)

om GN I om holds. If P om and P bm That is, P G N E > P om f inal > P f inal = Pinter = P f inal = bm bm Pinter = P , then the real share of black markets can be computed from these prices. bm f inal V fbm inal

bm +V Vinter

V fom inal +

=

P G N E −P G N I P om P bm −1 P om

(6)

38

Central Banknotes and Black Markets …

3.2 Income Leakages into Black Markets and Aggregate Demand for Central Banknotes In this subsection, the argument presented in Sect. 3.1 is translated into a more realistic setup of the national accounts. The following assumptions are made for this purpose: (1) The economy is closed. (2) Any expenditure is evaluated in terms of transaction prices, which reflect both black market and official prices. (3) Transaction prices of final goods increase by indirect taxes and decrease by subsidies. (4) Even if durables held at home and inventories concealed at factories are bartered illegally for resources from black marketeers, any decline in inventories held by households and corporate sectors in the formal economy are not recorded in the national accounts. (5) Nominal rents on public capital are zero. Given a positive statistical discrepancy between aggregate expenditure and income (S D n,t > 0), the saving–investment equality no longer holds in the national accounts. Let us start from:   E P G P P = Cn,t + Cn,t + PtI K tP − K t−1 + δ K t−1 Yn,t   G G VA VA = Yn,t + δ K t−1 + S Dn,t > Yn,t , + PtI K tG − K t−1

(7)

P G where Cn,t and Cn,t denote nominal private and government consumption in terms of transaction prices, K tP and K tG designate real capital of both the private and public sectors, and PtI and δ signify transaction prices of investment goods and depreciation rates. Aggregate value added including only officially reported income VA E ) decreases relative to aggregate expenditure at transaction prices (Yn,t ) by a (Yn,t statistical discrepancy (S D n,t ). Then, net national savings (the right side of the inequality below) are short of net investment (the left side):

      P   P P G VA G G + PtI K tG − K t−1 > Yn,t − δ K t−1 − Cn,t + Cn,t + K t−1 PtI K tP − K t−1 That is, those in the formal economy, both private and public sectors, suffer from financial shortages. As discussed in Sect. 4.1, private agents can cover such financial shortages by bartering household durables and factory inventories for resources from black marketeers, while a government can finance fiscal deficits by seigniorage revenues by issuing central banknotes indirectly to illegal dealers. Let us derive the budget constraints of private agents and a consolidated government (consisting of a general government and a central bank) in the formal economy. First, private agents in the formal economy are subject to the following budget constraint:    F    P P P F + Mn,t − Mn,t−1 + Bn,t − Bn,t−1 + PtI K tP − K t−1 + δ K t−1 Cn,t P P dir = Rn,t PtI K t−1 + Wn,t L t + i t Bn,t−1 − Tn,t + BT n,t

(8)

3 A Theoretical Relationship Between Black …

39

F dir where Mn,t , Tn,t , and BT n,t denote demand for central banknotes from the formal economy, direct taxes, and resources obtained from black markets by barter transacind ) and subsidies (Sn,t ) tions, respectively. By assumption (3), both indirect taxes (Tn,t P , Wn,t , i t , and L t signify are reflected in the transaction prices of final goods. Rn,t nominal rents on private capital, nominal wages, nominal rates of interest, and labor supply. Bn,t represents outstanding public bonds held by private agents, excluding public bonds held by a central bank. By assumption (4), any decline in household and corporate inventories induced by barter transactions with illegal dealers is not recorded in the national accounts. Second, a consolidated government’s budget constraint is formulated as:

  G G G + Sn,t + i t Bn,t−1 + PtI K tG − K t−1 + δ K t−1 Cn,t   S     dir ind S = Tn,t + Tn,t + Mn,t − Mn,t−1 + Bn,t − Bn,t−1 ,

(9)

S S S where Mn,t designates aggregate money supply and Mn,t − Mn,t−1 corresponds to seigniorage revenues. Only private agents in the formal economy hold public bonds. By assumption (5), nominal rents on public capital are zero. VA By assumption (3), aggregate income at factor prices (Y n,t ) is equal to aggregate value added at transaction prices minus net indirect taxes (indirect taxes net of ind − Sn,t ). Then, aggregate (gross) income at factor prices is determined subsidies, Tn,t P P PtI K t−1 ) and labor income (Wn,t L t ): according to capital (Rn,t VA  ind  VA P P Y n,t = Y n,t − Tn,t − Sn,t = Rn,t PtI K t−1 + Wn,t L t

(10)

Either capital or labor income increases with the help of subsidies from the government and decreases with the payment of indirect taxes to the government. Note that the amount of aggregate income at factor prices is unchanged despite direct taxes, which serves only as income ex post transfers between a government and private agents within the formal economy. However, black marketeers allocate income leakages from the formal economy between adding central banknotes to their portfolios (cash transactions) and providing resources through barter transactions with private agents in the formal economy:   B B + BT n,t, − Mn,t−1 S D n,t = Mn,t

(11)

B where Mn,t stands for demand for central banknotes from black markets. Substituting Eqs. (8), (9), (10), and (11) into Eq. (7) leads to:



  F  S S F B B − Mn,t − Mn,t−1 = Mn,t − Mn,t−1 − Mn,t−1 = S D n,t − BT n,t Mn,t

(12)

That is, aggregate money supply in excess of money demand from the formal economy [the left side of Eq. (12)] is now absorbed by money demand from black

40

Central Banknotes and Black Markets …

B B markets (Mn,t − Mn,t−1 ), which in turn comes from part of the income leakages into black markets (S D n,t − BT n,t ). As in Cagan (1956), normal money demand from the formal economy is specified E ) under unit income elasticity as proportional to nominal aggregate expenditure (Yn,t and decreasing in the nominal rate of interest i t . That is, relative money demand F MF Mn,t from the formal economy ( Y n,t = E ) is decreasing in the nominal rate of interest: YE n,t



n,t

m(i t ), where m (i t ) < 0. Unless money demand is extremely interest sensitive in the MF neighborhood of zero nominal interest rates, then Y n,t = m(i t ) can be approximated E n,t as a fixed rate m. As reported in the last column of Table 2, the nominal rate of Table 2 Deflators, price indexes, and the official discount rates, 1930–1951 (1934–1936 as base years) GNE deflator

GNI deflator

Wholesale price index (relative to GNE deflator in parentheses)

Retail price index (relative to GNE deflator in a parentheses)

Official discount rate (%)

1930

1.03

1.02

0.89

(86%)

1.01

(98%)

5.4

1931

0.90

0.89

0.75

(83%)

0.89

(98%)

5.4

1932

0.93

0.95

0.83

(89%)

0.89

(96%)

5.3

1933

0.98

1.01

0.95

(97%)

0.95

(97%)

4.0

1934

0.97

0.96

0.97

(100%)

0.97

(100%)

3.7

1935

1.01

1.03

0.99

(98%)

0.99

(98%)

3.7

1936

1.04

1.07

1.04

(100%)

1.04

(100%)

3.4

1937

1.10

1.03

1.26

(114%)

1.14

(103%)

3.3

1938

1.22

1.08

1.33

(109%)

1.30

(107%)

3.3

1939

1.50

1.35

1.47

(98%)

1.46

(97%)

3.3

1940

1.91

1.77

1.64

(86%)

1.70

(89%)

3.3

1941

2.15

2.01

1.76

(82%)

1.72

(80%)

3.3

1942

2.61

2.38

1.91

(73%)

1.77

(68%)

3.3

1943

3.03

2.76

2.05

(68%)

1.87

(62%)

3.3

1944

3.70

3.30

2.32

(63%)

2.10

(57%)

3.3

1945

7.50

3.50

(47%)

3.08

(41%)

3.3

1946

43.70

16.27

(37%)

18.93

(43%)

3.4

1947

109.40

93.44

48.15

(44%)

50.99

(47%)

3.7

1948

191.40

165.98

127.90

(67%)

149.60

(78%)

4.5

1949

233.30

219.48

208.80

(89%)

243.40

(104%)

5.1

1950

243.00

241.83

246.80

(102%)

238.10

(98%)

5.1

1951

295.30

286.83

342.50

(116%)

309.50

(105%)

5.3

35.24

Notes 1. See Statistics Department, BOJ (1966) and EPA (1964) for the data sources 2. The computation of the 1945 GNE deflator is described in Sect. 4.2.

3 A Theoretical Relationship Between Black …

41

interest was indeed far above zero in the years 1937 to 1949: it was slightly higher than 3%. Using this fact, Eq. (12) reduces to: 

  E   B  S S E B − m Yn,t = Mn,t − Mn,t−1 − Mn,t−1 − Yn,t−1 Mn,t

(13)

and it is further rearranged as: 

S Mn,t E Yn,t

 −m −



S Mn,t−1 E Yn,t−1

 −m

=

B B − Mn,t−1 Mn,t E Yn,t

−

E E − Yn,t−1 Yn,t E Yn,t



S Mn,t−1 E Yn,t−1

 −m . (14)

MS

According to Eq. (14), Marshallian k of the formal economy ( Y n,t E ) deviates n,t upward from its normal rate m to the extent that money demand is strong from black B B Mn,t −Mn,t−1 > 0), and deviates downward from m when nominal economic E Yn,t E E Yn,t −Yn,t−1 ( Y E ) is fast and/or when Marshallian k was previously high relative to n,t

markets ( growth MS

m ( Y n,t−1 − m > 0). E n,t−1 Note that the flow of funds differs considerably between the cases with and without black markets. In a standard model without black markets, the statistical discrepancy is always zero. As shown in Fig. 2a, b government finances fiscal deficits by issuing both central banknotes and public bonds to households. In this case, the new issue of central banknotes is absorbed completely by household savings. However, once a part of aggregate income leaks from the formal economy into black markets, not only households, but also black marketeers hold central banknotes, which are newly injected into the economy by a central bank’s direct underwriting. As shown in Fig. 2b, new central banknotes are held by both those in the formal economy who are interested in cash transactions, and those in black markets who are interested in concealing illicit income.

4 Interpretations of Statistical Discrepancies and Marshallian k in the Years 1937 to 1949 4.1 On Constructions of the National Accounts We interpret the wartime and postwar EPA national accounts and monetary statistics using the theoretical frameworks presented in Sect. 3. The EPA (1964)17 compiled the annual national accounts from 1930 to 1951 with 1934–1936 as the base years,

17 The

EPA (1964) reports the accounts of 1946–1951 in terms of a fiscal year.

42

Central Banknotes and Black Markets …

a

Central Bank Private Sectors

Money

Government

Public Bonds

b

Formal

Underground Money

Central Bank Government

Money

Private Sectors

Black Barter

Markets

Public Bonds

Income Leakage

Fig. 2 a Money issuance in a standard model. b Money issuance in the presence of black markets

but no data for 1945 were available.18 However, data on the value of outstanding BOJ notes and the wholesale/retail price indexes (official price indexes) are available from Statistics Department, BOJ (1966) without any missing observations. There are three issues to be addressed regarding the EPA national accounts. First, the expenditure account was constructed using transaction prices recorded by the Morita index rather than official prices (Mizoguchi & Nojima, 1993). For example, the consumption expenditure series from several production-side statistics were first valued item by item at the official prices. Then, these series were adjusted by the effective retail price index (Morita index) explained in Sect. 2.1, which reflects both official and black market prices. As shown in Table 1, the Morita indexes (the effective prices) and the GNE deflator indeed behave similarly in relation to the official prices (the wholesale/retail prices). In this way, the underestimation of expenses driven by cheaper official prices was corrected to some extent using the effective price indexes (Morita indexes) to measure transaction prices in the expenditure account. For the postwar data, black market prices were surveyed directly by the BOJ and were considered explicitly in constructing the expenditure account. 18 Ohkawa et al. (1974) construct the Japanese national accounts for the years 1885–1940. Fukao et al. (2015) present a more comprehensive version of the Japanese national accounts for the period 1874–2008. Jean-Pascal et al. (2016) present a brief history of the Japanese national accounts.

4 Interpretations of Statistical Discrepancies …

43

Second, the EPA national accounts computed aggregate income independent of the expenditure account. On the one hand, employee compensation was aggregated from several surveys of the wages and the labor force. On the other hand, corporate income was aggregated from corporate tax return data with due consideration to differences between business and taxation accounting. In the taxation data, black market margins were unlikely to be included. Here, we should note that the computation of corporate income differs entirely between the EPA national accounts and the recent versions of the Japanese national accounts. In the latter accounts, corporate income is never aggregated directly from corporate tax returns but instead is computed as a residual by subtracting the estimated employee compensation from the aggregate value added at the production side.19 Third, while the Japanese government and private corporations conducted military and economic activities in overseas territories during the wartime period, the domestic (interior) economy was almost completely separated from the economies of the overseas territories in terms of income transfers. As documented in detail by Hara (1976), under the strict capital controls coupled with the fixed exchange rate system, the income transfers to/from the overseas territories were constrained tightly. The relative size of the net income transfers was much less than 1% of nominal GNE during the wartime period. As demonstrated in detail in chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”, most overseas military and industrial activities were financed within each territory through the banknotes that were issued by the reserve/central banks in the occupied territories.20 Accordingly, the level of aggregate income in the domestic economy was influenced only slightly by the scale and scope of the economic activity in the overseas territories.

4.2 Approximation of Nominal GNE and Minimum Statistical Discrepancy in 1945 As mentioned above, the EPA (1964) failed to report any statistics for 1945. Here, both nominal GNE and a minimum value of the statistical discrepancy are approximated for 1945 in a rather heroic manner. First, the nominal GNE of 1945 is approximated 19 According to Yamamoto (2011), France, England, Finland, Germany, Norway, and Spain follow the same method used currently by the Japanese government. In Canada, the United States, and Australia, however, corporate income is aggregated from corporate accounting data together with corporate tax return data. Fujiwara and Ogawa (2016) compute recent aggregate corporate income from tax return data for the Japanese economy. 20 Hattori and Oguro (2016) estimate the amount of seigniorage revenues generated from direct underwriting of Japanese public debts by both the central banks in the colonial territories and the reserve banks in the occupied territories. Chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War” analyzes in detail how the war expenditures in the Japanese occupied territories were financed through the colonial central banks and the local reserve banks during the Pacific War.

44

Central Banknotes and Black Markets …

as follows.21 The ratio between the 1944 and 1945 values of real GDP is obtained from Mizoguchi and Nojima (1993): that is, 7.4 trillion yen in 1944 versus 5.6 trillion yen in 1945 (1955 constant prices). Then, the 1945 value of real GNE is computed as 15.3 billion yen given that the EPA (1964) reports its 1944 value as 20.1 billion yen 5.6 ≈ 15.3). The GNE deflator is chosen as in 1934–1936 constant prices (20.1 × 7.4  GN E  GN E GN E P1945 P1946 1 P1944 7.5 such that P W P I = 2 P W P I + P W P I can hold under the assumption that the GNE 1945

1944

1946

deflator (PtG N E ) and the wholesale price index (PtW P I ) comoved smoothly between the years 1944 and 1946. Thus, the 1945 value of nominal GNE is approximated as 114.5 billion yen by the product of the above computed real GNE and GNE deflator (15.3 × 7.5 ≈ 114.5). Second, the minimum value of the statistical discrepancy is obtained for 1945 from Eqs. (12) and (13):  S   E  S E B B − Mn,1944 − Yn,1944 − Mn,1944 − m Yn,1945 = Mn,1945 S D n,1945 ≥ Mn,1945 That is, the minimum value of the statistical discrepancy is determined using the value of additional money demand from the black markets. From 1944 to 1945, the aggregate money supply expanded by 37.7 billion yen from 17.7 billion yen to 55.4 billion yen, while, as estimated above, nominal GNE increased by 40.0 billion yen from 74.5 billion yen to 114.5 billion yen. Given that m is set at 10% or the MS prewar average of Y n,t E , the statistical discrepancy S D n,1945 is computed as at least n,t 33.7 billion yen or 29.4% of nominal GNE as follows: 37.7 − 0.1 × 40.0.

4.3 Largely Positive Statistical Discrepancies Let us first examine the relative magnitude of the statistical discrepancies of the EPA national accounts. All nominal macroeconomic variables are expressed below in terms of their ratio to nominal GNE. Without any simultaneous presence of official and black market prices, the sum of net investment and net exports should be equal to net national savings with zero statistical discrepancy. As shown in Fig. 3, however, the sum of net investment and net exports, computed from the expenditure account, exceeded net national savings, calculated from the income account in the years 1937– 1949. Consequently, there emerged largely positive statistical discrepancies of more than 5% of nominal GNE in these years, during which the economy was subject to strict price controls. Before 1937 and after 1949, net investment plus net exports was close to net savings, and the statistical discrepancy ranged between zero and 5%. Using the model presented in Sect. 3, we can infer from these significant discrepancies that large amounts of income leaked into the black markets in the price control period.

21 In an informal memo, Yasushi Iwamoto proposed the method by which the 1945 value of nominal

GNE is computed.

4 Interpretations of Statistical Discrepancies …

45

35%

30%

25%

20%

15%

10%

5%

0%

-5% (net investment + net export)/nominal GNE

Net national saving/nominal GNE

Statistical disecrepancy/nominal GNE

Minimum statistical discrepancy/nominal GNE

Fig. 3 Net investment, net national saving, and statistical discrepancy, 1930–1955. Notes (1) See Statistics Department, BOJ (1966) and EPA (1964) for the data sources. (2) The computation of nominal GNE and the minimum statistical discrepancy for 1945 is described in Sect. 4.2. (3) Net investment is defined as the sum of net investment and current account balances, while net savings are defined as gross savings net of depreciation

During the wartime period, the discrepancy ratio peaked temporarily at 11.8% in 1938, and it declined gradually to 6.4% in 1941. Then, the ratio increased again gradually to 10.9% in 1944. Given the minimum value of the statistical discrepancy estimated in Sect. 4.2, the ratio reached at least 29.4% in 1945. That is, at least one third of the national income leaked into black markets just before and after the war’s end in August 1945. Such wartime movements in the discrepancy ratio can be interpreted broadly as reflecting several institutional aspects of black market activities. The ratio was high immediately after the government controls were implemented in 1937. One possible reason for this immediate increase was that ineffective rationing helped to create black markets from the very beginning of rationings and price controls.22 From late 1938, stronger surveillance of illegal transactions by the police contributed to a decline in the ratio. However, the ratio began to increase again from 1941, partly because of a reduction in the size of the police force, and partly because of heavier involvement of military personnel and munitions factories in undercover dealings. In

22 Miwa

(2015) reports the cases of inefficient rationing, which was induced by the Material Mobilization Plans. According to the USSBS (1947), the Japanese government was never able to establish an efficient overall control of rationing and prices, and to crack down effectively on illegal transactions in comparison with the US Office of Price Administration.

46

Central Banknotes and Black Markets …

this way, a substantial portion of the national income leaked into the black markets in the last years of the war. Viewed differently, the wartime pattern of the relative statistical discrepancies was driven by the fact that the revision of official prices lagged substantially behind changes in black market prices during the war. Equation (3) implies that statistical om discrepancies widen when official prices (P om f inal and Pinter ) are well below black bm market prices (P bm f inal and Pinter ). According to Table 2, the wholesale/retail price indexes as a proxy for the official prices tended to be low relative to the GNE deflators, which partly reflected the black market prices from 1937 to 1945. For example, the retail price index was 103% of the GNE deflator in 1937, but was only 41% in 1945. In the postwar period, however, the statistical discrepancy ratio was quite high (19.4%) in 1946, after which it gradually decreased but still remained high. The ratio was 14.6% in 1947 and 13.3% in 1948. For the years 1946 to 1948, the official prices still failed to catch up with the black market prices. As shown in Table 2, for example, the retail price index was only 43% of the GNE deflator in 1946, 47% in 1947, and 78% in 1948. In 1949, the discrepancy ratio of 5.9% was not negligible, but was not high compared with previous years. By the late 1940s, the government had removed most economic controls and the black markets consequently disappeared. According to Table 2, the wholesale/retail price indexes were quite close to the GNE deflator in 1950. Figure 4 depicts the relative magnitude of the financial surpluses, defined as net savings minus net investment, by the public and private sectors separately. A sharp contrast in financial surpluses between the wartime and the postwar periods is observed in this figure. During the war, on the one hand, the private sector had financial surpluses thanks mainly to forced savings and subsidies from the government, while the public sector had enormous financial deficits because of low tax revenues and large-scale fiscal expenditures including subsidies to the private sector. In the aftermath, on the other hand, the public sector generated financial surpluses except in 1946 thanks mainly to improving tax revenues, while the private sector carried large financial deficits despite subsidies from the government. An improvement in the public financial surpluses helped to back outstanding public bonds. Throughout the two periods, however, the continuation of largely positive statistical discrepancies implies that the financial surplus of one sector could not cover completely that of the other in the formal economy.

4.4 GNE and GNI Deflators and Official Prices Let us next examine the behavior of the GNE and GNI deflators together with the official prices that were recorded in the wholesale/retail price indexes. All deflators and price indexes were standardized using the base years 1934–1936. As Eqs. (4) and (5) imply, the official prices should be between the GNE and GNI deflators. As shown in Table 2 and Fig. 5, however, the official prices were between both deflators

4 Interpretations of Statistical Discrepancies …

47

25% 20% 15% 10% 5% 0% -5% -10% -15% -20% -25%

Private surplus/nominal GNE Statitical discrepancy/nominal GNE

Public surplus/nominal GNE

Fig. 4 Relative financial surplus in private and public sectors, 1930–1955. Notes (1) See Statistics Department, BOJ (1966) and EPA (1964) for the data sources. (2) The private financial surplus is defined as 1 private net savings, minus [2] private net investment including inventories and housing, minus [3] current account balances. (3) The public financial surplus is defined as [4] public net savings, minus [5] public net investment including inventories 7 6 5 4 3 2 1 0 -1

GNE deflator

GNI deflator

Wholesale price index

Fig. 5 A comparison among GNE deflator, GNI deflator, and wholesale price index in logarithm, 1930–1951 (1934–1936 as base years). Notes (1) See Statistics Department, BOJ (1966) and EPA (1964) for the data sources. (2) The GNE and GNI deflators are computed using Eqs. (4) and (5)

48

Central Banknotes and Black Markets …

only in 1939. For both the wholesale and retail prices, the official prices were above the GNE deflators in 1937 and 1938, and below the GNI deflators for the years 1940–1949. There are three possible reasons for the deviation of the two deflators from the theoretical prediction. First, the two deflators and the official price indexes differed substantially in the coverages and weights of the commodity baskets in particular for the wartime data. As mentioned in Sect. 2, the two deflators were based on the Morita indexes, which were constructed in quite an ad hoc manner without taking any simple or weighted average of commodity baskets. However, the official price indexes were computed as a simple average of official prices for a certain commodity basket. Second, the Morita indexes might have failed to capture precise information about black market prices, and those prices were inferred to be too low from the indexes. According to Eqs. (4) and (5), the GNE deflator is underestimated if the black market prices of final goods (P bm f inal ) are too low, while the GNI deflator is overestimated if bm the black market prices of intermediate goods (Pinter ) are too low. Third, the GNI deflator was estimated to be too high for the following reason. The V bm real share of intermediate goods procured from black markets ( V om inter bm ) would f inal +V f inal have been underestimated if firms had been reluctant to report transactions with illegal dealers in filing corporate tax returns. According to Eq. (5), the GNI deflator is too V bm is too low. Given the last two reasons, the statistical discrepancies high if V om inter bm f inal +V f inal reported by the EPA (1964) offer a lower bound for the size of the income leakages into the black markets. In the light of the above inconsistency between the GNE/GNI deflators and the official price indexes (wholesale/retail price indexes), Eq. (6) cannot be employed to V bm +V bm

f inal ). Thus, the share is approximated derive the real share of black markets ( V inter om +V bm f inal f inal GN E GN I

under the assumption that P bm ≈ P +P . The black-to-official market price 2 P bm ratios ( P om ) are available from Statistics Bureau, BOJ (1966) for the postwar period between 1946 and 1951. As reported in Table 3, the real share of black markets ranged between 2.4 and 8.7% in the years 1946 to 1950. Given that the black-to-official market price ratio is close to one, the ratio of 29.1% in 1951 is meaningless. As mentioned above, the EPA national accounts are likely to underestimate the scale of the income leakage into the black markets. Thus, the real share of the black markets reported in Table 3 should be interpreted as its lower bound.

4 Interpretations of Statistical Discrepancies … Table 3 Real share of black markets for the postwar period, 1946–1951

Black-to-official ratio

49 Real black market share (%)

1946

7.2

3.5

1947

5.3

3.7

1948

2.9

7.5

1949

1.7

8.7

1950

1.2

2.4

1951

1.1

29.1

Notes 1. See Statistics Department, BOJ (1966) for the data sources 2. The real share is computed according to Eq. (6) under the assumption described in Sect. 4.4

4.5 Marshallian k and Money Demand from the Black Markets 4.5.1

Marshallian k Deviating from Its Long-Run Average

As pointed out in Sect. 1, Marshallian k, defined as the outstanding BOJ notes over nominal GNE, started to deviate from its long-run average of 10% in 1937, peaking at around 50% in 1945 and reverting quickly to 10% by 1949 (see Fig. 1). More concretely, in the years 1937 to 1945, the outstanding BOJ notes on issue increased by a factor of 24.1 times, while nominal GNE increased by only 4.9 times. Accordingly, Marshallian k rose from 10.1 to 48.4%. In the years 1945–1949, however, nominal GNE increased by 29.5 times, whereas the outstanding BOJ notes on issue increased by only 6.4 times. As a result, Marshallian k decreased from 48.4 to 10.5%. As discussed descriptively in Sect. 2.4 and analytically in Sect. 3.2, there is a possibility that the national income leaking out of the formal economy created strong demand for BOJ notes from the black marketeers who received the leaked income. In other words, the circulation of BOJ notes encouraged the leaked income to flow back to the treasury as large seigniorage revenues. Then, this strong money demand from the black markets caused an upward deviation of Marshallian k from its long-run average. As emphasized above, national income continued to leak out of the formal economy into the black markets throughout the controlled period 1937–1949. However, Marshallian k deviated substantially from its long-run average of 10% during the war but reverted quickly to 10% in its aftermath. It follows that the black marketeers made a considerable investment in BOJ notes in the former period 1937– 1945, but they shifted their portfolios from BOJ notes to physical assets in the latter period 1945–1949. We next examine this possibility quantitatively. Equation (13) allows us to allocate an increment in aggregate money supply S S F − Mn,t−1 ) between additional money demand from the formal economy (Mn,t − (Mn,t F B B Mn,t−1 ) and from the black markets (Mn,t − Mn,t−1 ). The former demand was driven

50

Central Banknotes and Black Markets …

mainly by transactions and it is assumed to be proportional  GNE at a  E to nominal F E F , where m is − Mn,t−1 is replaced by m Yn,t − Yn,t−1 constant rate of m. Then, Mn,t assumed to be 0.1 as the long-run average of Marshallian k. Table 4 reports the magnitude (relative to nominal GNE) of additional money demand from the formal economy (column (a)) and from the black markets (column (b)). Additional money demand from the formal economy hovered at around 1.5% of nominal GNE up to 1944, but it expanded with nominal GNE after the war: that is, it was 7.6% of nominal GNE in 1946, 6.4% in 1947, and 5.1% in 1948. Additional demand from the black markets was also high in the final years of the war: that is, it was 3.4% in 1943, 8.6% in 1944, and 29.4% in 1945. However, it was only in 1947 that the black marketeers expanded their money holding during the postwar period. The negative number reported in 1949 (–2.1%) suggests that the black marketeers Table 4 Marshallian k and money demand from the black markets, 1937–1949 Marshallian k (%)

Change in Marshallian k (%)

Additional money demand/nominal GNE (a) From formal economy (%)

(b) From black markets (%)

(c) Nominal GNE growth index (%)

1937

9.8

−0.6

2.4

−0.5

24.0

1938

10.3

0.4

1.3

0.4

12.5

1939

11.1

0.8

1.9

0.9

19.0

1940

12.1

1.0

1.6

1.2

16.0

1941

13.3

1.2

1.2

1.5

12.2

1942

13.1

−0.2

1.7

0.4

17.4

1943

16.1

2.9

1.5

3.4

14.8

1944

23.8

7.7

1.4

8.6

14.3

1945

48.4

24.6

3.5

29.4

34.9

1946

19.7

−28.8

7.6

0.4

75.9

1947

16.7

−2.9

6.4

3.2

63.7

1948

13.3

−3.4

5.1

0.0

50.9

1949

10.5

−2.8

2.1

−2.1

21.1

Notes 1. See Statistics Department, BOJ (1966) and EPA (1964) for the data sources 2. Marshallian k is defined as the outstanding BOJ notes over nominal GNE 3. Additional money demand from the formal economy (normal transaction demand) is computed   E −YE by 0.1 Yn,t n,t−1 in Eq. (14) B −MB 4. Additional money demand from the black markets (Mn,t n,t−1 ) is calculated by Eq. (13) with

m = 0.1 5. The nominal GNE growth index is defined as

E −Y E Yn,t n,t−1 E Yn,t

in Eq. (14)

4 Interpretations of Statistical Discrepancies …

51

reduced their cash holdings at the very end of the controlled-economy period. While large quantities of BOJ notes were issued even after the war, the new notes were held for transaction purposes by those in the formal economy and no longer as a financial instrument by those in the black markets. According to Eq. (14), strong additional demand for BOJ notes from the black markets contributed to the upward deviation of Marshallian k. During the war, particularly in 1943, 1944, and 1945, stronger money demand from the black markets made Marshallian k increase above its long-run average of 10%. After the war, however, this strong demand disappeared except in 1947. Instead, high nominal economic Y E −Y E

MS

− m > 0) growth (measured in n,t Y E n,t−1 ) and previously high Marshallian k ( Y n,t−1 E n,t n,t−1 contributed jointly to a steep decline in Marshallian k.

4.5.2

Black Marketeers’ Portfolios During and After the War

The above findings imply that immediately after the war the black marketeers allocated more of their portfolios to physical assets, such as household durables, factory inventories, and even old houses obtained through barter transactions, than to BOJ notes received through cash transactions. Equation (12) allows us to separate an investment in such physical assets (BT n,t ) from an investment in BOJ notes B B − Mn,t−1 ). Then, it is possible to examine the extent to which the leaked income, (Mn,t measured as the statistical discrepancy (S D n,t ), returned to the formal economy M B −M B

through cash transactions in the black markets by n,tS Dn,tn,t−1 . As shown in Fig. 6, less than one fourth of the leaked income returned to the formal economy (more precisely to the treasury) in the years 1937 to 1942. By issuing BOJ notes indirectly to the black markets, however, the government refinanced 37.6% of the leaked income in 1943 and 78.8% in 1944. Given that additional money demand from the black markets amounted to 29.4% of nominal GNE in 1945,23 quite a large portion of the leaked income was expected to return to the formal economy through illicit cash transactions. After the war, however, the black marketeers did not add BOJ notes to their portfolios, except in 1947. In 1949, they even disposed of cash on hand equivalent to 35.5% of the leaked income, thereby switching their portfolios completely to physical assets. A major reason for this shift from BOJ notes to physical assets after the war is that the black marketeers were extremely reluctant to hold BOJ notes in response to the high inflation postwar. In terms of the GNE deflator, the annual inflation rate ranged between 10 and 20% during the war, but it jumped to 103% in 1945, 483% in 1946, 150% in 1947, and 75% in 1948. In turn, the reluctance of the black marketeers to hold BOJ notes reduced aggregate money demand, thereby further increasing the high inflation rates. In addition, the black marketeer’s shift from BOJ notes to

23 As

described in Sect. 4.2, additional money demand from the black markets is equivalent to the minimum value of the statistical discrepancy by construction.

1450

2589

2209

1538

1340

1869

1909

2200

4493

2105

1746

1850

1938 21,959

1939 22,053

1940 20,628

1941 20,884

1942 20,835

1943 21,063

1944 20,135

1945 15,262

1946 10,870

1947 11,965

1948 13,924

538

42,344

1,904

33,698

6412

2173

222

651

466

295

114

−124

(2) Statistical (3) Additional discrepancy money (real) demand from black markets (nominal)

1937 21,300

(1) Real GNE

463

806

1,048

5,855

2,760

1,254

623

653

394

1847

1359

2062

467

1192

1784

1037

1294

2012

2496

−8 190

1562

−112

(4) Real money (5) Increment balances in in physical black assets in markets black markets (real)

17,112

15,265

13,906

11,844

11,844

11,377

10,185

8,402

7,364

6,070

4,058

1562

(6) Real physical assets in black markets

Table 5 Black marketeers’ portfolios, 1937–1949 (unit: million yen, 1934–1936 constant prices)

17,575

16,071

14,954

17,699

14,604

12,631

10,808

9,054

7,758

6,261

4,050

1450

126.2%

134.3%

137.6%

116.0%

72.5%

60.0%

51.9%

43.4%

37.6%

28.4%

2.6

5.0

7.0

33.1

18.9

9.9

5.8

7.2

5.1

3.0

18.4% −0.2

(continued)

(8) Share of money relative to black market wealth (real, (4)/(7)) (%) 6.8% −7.8

(7) Outstanding black market wealth (real, (4) + (6)), and the ratio relative to real GNE ((7)/(1))

52 Central Banknotes and Black Markets …

857

−71,068

(2) Statistical (3) Additional discrepancy money (real) demand from black markets (nominal)

76

1162

(4) Real money (5) Increment balances in in physical black assets in markets black markets (real)

18,274

(6) Real physical assets in black markets

18,349

126.8%

(7) Outstanding black market wealth (real, (4) + (6)), and the ratio relative to real GNE ((7)/(1))

0.4

(8) Share of money relative to black market wealth (real, (4)/(7)) (%)

 

E −Y E −0.1 Yn,t n,t−1

PtG N E

S −M S Mn,t n,t−1



BT n,τ τ =1937 PτG N E

t

4.6 Column (7) is the sum of columns (4) and (6). Column (8) is the ratio of (4) to (7)

4.5 Column (6): The accumulation of real barter transactions is computed by

S D n,t −



4.4 Column (5): Real barter transactions between formal and black markets are computed using Eqs. (12) and (13), or

Pt

BT n,t PtG N E

=

    S E B − MB S E 4.2 Column (3): Additional money demand from the black markets is computed using Eq. (13), or Mn,t n,t−1 = Mn,t − Mn,t−1 − 0.1 Yn,t − Yn,t−1    B − MB 4.3 Column (4): Real money balances are computed by G1N E tτ =1937 Mn,t n,t−1

Notes 1. See Statistics Department, BOJ (1966) and EPA (1964) for the data sources 2. The computation of real GNE and the minimum statistical discrepancy for 1945 is described in Sect. 4.2 3. It is assumed that the black marketeers did not add any physical assets to their portfolios in 1945 4. Each column is described as follows: 4.1 Column (2) is the nominal statistical discrepancy over the GNE deflator

1949 14,471

(1) Real GNE

Table 5 (continued)

4 Interpretations of Statistical Discrepancies … 53

54

Central Banknotes and Black Markets …

100%

80%

60%

40%

20%

0%

-20%

-40%

-60%

Fig. 6 Financial shortages financed by demand for BOJ notes from black markets, 1937–1949. Notes (1) See Statistics Department, BOJ (1966) and EPA (1964) for the data sources. (2) The coverage of income leakages by issuing BOJ notes to the black markets is computed using Eqs. (12)   and (13), or

B −M B Mn,t n,t−1 S D n,t

=

S −M S E E Mn,t n,t−1 −0.1 Yn,t −Yn,t−1

S D n,t

physical assets might have been driven by BOJ’s intention to switch from old bills to new bills, which was hinted at by the government in late 1945 (see Sect. 4.2). Table 5 reports the portfolios held by the marketeers in real terms. It  black  B  1 t B computes real money balances in column (4) P G N E τ =1937 Mn,t − Mn,t−1 ), real t  n,τ physical assets in column (6) ( tτ =1937 BT ), total wealth in column (7), and the PτG N E ratio of real money balances to total wealth in column (8). Here, the nominal value is converted to the real value by the GNE deflator (PτG N E ) with 1934–1936 as the base years. Because of the absence of data, the black marketeers were assumed to add no physical assets to their portfolio in 1945. In addition, real physical assets held by the black marketeers were assumed not to be depreciated over time. What is surprising is that real money balances increased to 5.9 billion yen in 1945, but declined almost to zero in 1949. However, real physical assets grew continuously from 13.9 billion yen in 1946 to 18.3 billion yen in 1949 even after the war. Accordingly, the ratio of BOJ notes to total wealth peaked at 33.1% in 1945 and declined to zero in 1949. The black marketeers accumulated wealth rapidly including BOJ notes during the war; however, they dramatically shifted their holdings away from BOJ notes to physical assets immediately after the war. The total wealth held by the black marketeers, reported in column (7) in Table 5, almost equaled the real size of the national economy (real GNE) by the end

4 Interpretations of Statistical Discrepancies …

55

of the war and continued to grow until the controlled economy ended in the late 1940s. For example, the total wealth of the black marketeers was equal to 72.5% of real GNE in 1944, and 126.8% in 1949. These findings suggest that the black market transactions helped to transfer physical resources such as household durables, factory inventories, housing assets, and land from the wartime activities and even from postwar reconstructions to the post-control economy, which finally began to grow after the economic controls imposed by the government and the import restrictions by the GHQ were all lifted by the late 1940s.24,25

5 Conclusion This chapter provides three important lessons. First, the circulation of central banknotes is closely related to the emergence of black market transactions, but there is by no means a one-to-one correspondence between the two. In the heavily controlled Japanese economy from 1937 to 1949, a substantial portion of the national income leaked out of the formal economy and into the black markets. Thus, the black marketeers accumulated enormous amounts of wealth throughout the period. However, BOJ notes were a major financial instrument among the black marketeers only in the final years of the war. While large quantities of BOJ notes were issued even after the war, the new notes were held for transaction purposes by those in the formal economy, but not as a financial instrument by those in the black markets, who made a dramatic shift from BOJ notes to physical assets in their portfolios. In the postwar period, declining money demand from the black markets contributed to the acceleration of inflation. Second, as discussed in chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, how public debt was backed differed between during the war and immediately after the war. During the war, a huge amount of public debt was supported partly by strong money demand, originating from the underground economy. Immediately after the war, however, the value of public bonds, which had already been devalued heavily by the postwar sharp inflation, was then backed basically by an improvement in fiscal surpluses, resulting from intensive tax reforms. The latter fiscal backing prevented the postwar price surge from falling into genuine hyperinflation. Third, high tension between efficiency and inequality is caused by illegal transactions in an inefficient economy, which was first pointed out by Leff (1964).26 Given 24 As reported in Mizoguchi and Nojima (1993), real GDP peaked at 7.7 trillion yen (1955 constant prices) in 1942 during the war, while it exceeded 7 trillion yen in 1952 and reached 8.3 trillion yen in 1955. 25 Kosai (1986) suggests that scarce physical resources, which had been retained in the formal and informal sectors during the war, and unexploited for the postwar reconstructions, contributed to economic growth starting in the late 1940s. 26 Leff (1964) presents a case in which bureaucratic corruption, often involving illegal transactions, may make a military-oriented government more friendly to business, but create vested interests

56

Central Banknotes and Black Markets …

a heavily controlled economy, such as the wartime and postwar Japanese economies, illegal transactions may be interpreted as a second-best response to heavy economic controls. In the final years of the war, for example, illegal cash transactions helped to return the leaked income to the financially deficient treasury in the form of large seigniorage revenues. After the war, however, illegal barter transactions helped physical resources such as household durables and factory inventories to escape from inefficient uses in the controlled economy into efficient uses in the post-control market economy, which finally began to grow after most economic controls were lifted in the late 1940s. What is obvious here is that any resource allocation through illegal transactions, either cash or barter, cannot be considered unconditionally as a fair allocation device. Only after a government confiscates financial and physical resources accumulated in black markets, and redistributes them equally among those in the formal economy, can illegal transactions in a controlled economy be justified in the long run. In this light, the EFM announced by the Japanese government in February 1946, which included forcing the deposit of old BOJ bills and imposing extremely high capital levies on frozen deposits as explained in Sect. 4.2, may be interpreted as one example of such an efficient—as well as fair—policy scheme. Following the introduction of this measure, concealed cash assets were confiscated by the government, but illicit physical assets were still held among the black marketeers. In addition, those who had nothing to do with illegal dealings, but held nominal assets such as cash and public bonds as a main saving instrument were hurt heavily by capital levies on frozen deposits, Thus, the above measure remained imperfect given that the black marketeers shifted their portfolio holdings from BOJ notes to physical assets after the war.

among those in a ruling class, whose elimination requires a new center of power outside the bureaucracy. Interpreting the Japanese experience along the lines of Leff (1964), the wartime and postwar black market transactions helped to reallocate at least partially scarce resources from military purposes to civilian purposes, whereas their adverse effects were eliminated, though not entirely, by the postwar democratization promoted by the new government and the occupation forces.

On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War

Abstract This chapter demonstrates how wartime seigniorage benefits for the occupation forces and postwar withdrawal costs for the defeated government were balanced in large-scale monetary operations in the Japanese occupied territories during the Pacific War (from December 1941 to August 1945). The Japanese government financed war expenses locally by two methods. First, the government forced extemporaneously installed reserve banks in north/central China and the southern regions (Southeast Asia) to issue enormous quantities of banknotes. Second, it requested existing central banks in Manchuria, Indochina, and Thailand to underwrite Japanese government debts by issuing legal tender. In the former territories with high inflation rates, poor circulation of reserve banknotes limited the purchasing power of the occupation forces, but the cost to the postwar government of withdrawing banknotes was minimal. In the latter territories with relatively mild inflation rates, however, good circulation of legal tender generated substantial seigniorage for the occupation forces, but there were substantial costs to the defeated government of repaying its liabilities to the central banks of the previous territories.

1 Introduction This chapter explores how the Japanese government financed local war expenditures in the occupied territories by large-scale monetary operations during the Pacific War, starting in December 1941 and ending in August 1945. In particular, it carefully examines how wartime seigniorage benefits for the occupation forces were balanced by postwar withdrawal costs for the defeated government. In north/central China, the Japanese government installed extemporaneously two reserve banks (the Federal Reserve Bank of China (FRBC) in Peking in 1938, and the Central Reserve Bank of China (CRBC) in Nanjing in 1941) with the collaboration of puppet governments and forced these banks to underwrite Japanese government debts by issuing their banknotes. In the southern regions (southeast Asia), the Southern Development Bank (SDB), founded as a public financial institution in 1942, was in charge of managing existing military scrip and issuing new notes there. In Manchuria, Indochina, and © Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9_3

57

58

On Large-Scale Monetary Operations in the Japanese …

Table 1 Financing military expenses in/outside Japan by Bank of Japan, reserve/central banks in the occupied territories, and private savings, 1937–1945 (unit: million yen) Special account for extraordinary military expenses Total

Changes in Financial sources outstanding public Expense Expense debts Total Additional at home in demand occupied for BOJ territories notes from the black markets

Financed by Net reserve/central private banknotes in saving occupied territories

1937

2034

1655

379

2053

3453

−124

3577

1938

4795

3121

1674

4566

4438

114

4324

1939

4844

3598

1246

5644

6931

295

6636

1940

5723

4441

1282

7437

9176

466

8710

1941

9487

6562

2925

10,784

12,501

651

11,850

1942

18,753

14,074

4679

15,366

13,772

222

1943

29,818

20,031

9787

27,963

24,113

2173

5297

16,643

1944

73,493

30,028 43,465

66,837

63,736

6412

34,218

23,106

1945

46,254

33,763 12,491

47,503

23,723 20,557

3166

Total of 149,565 1943-45

83,822 65,743

142,302

111,573 29,143

42,681

39,749

Total of 195,201 117,273 77,928 1937-45

188,152

161,845 30,768

42,681

88,396

13,550

n.a.

Notes 1. Emi and Shionoya (1966), p. 188, and Editorial Office of History of Public Finance in Showa Era (EOHPF), MOF (1955), p. 199, for the special account for extraordinary military expenses, Statistics Department, BOJ (1966), pp. 159 and 193, for outstanding public debts and BOJ notes, EOHPF, MOF (1955), p. 179, for the issue of banknotes by the reserve/central banks in the occupied territories, and Ohkawa et al. (1974), p. 191, for net private savings. Financing by BOJ notes in 1945 is computed up to August 1945   2. Additional demand for BOJ notes from the black markets is computed by Mt − Mt−1 − 0.1 ×   Yt − Yt−1 , where Mt and Yt denote the balance of BOJ notes in circulation and nominal GNE, respectively

Thailand, however, existing central banks (the Central Bank of Manchuria (CBM), the Bank of Indochina (BOI), and the Bank of Thailand (BOTh)) were requested to issue legal tender to underwrite Japanese government debt. According to statistics compiled by the Japanese government after the war, the reserve banks in the occupied territories seemed to contribute substantially to war finance during the Pacific War. According to Table 1, 149.6 billion yen were spent from the special account for extraordinary military expenses (EME special account) during the years 1943–1945. While only 5% was covered by taxes,1 the remaining 1 It

is assumed that tax revenues were first allocated to the general account with the remainder appropriated to the EME special account. In the years 1943–1945, 142.3 billion yen out of 149.6 billion yen was covered by government debts.

1 Introduction

59

95% was financed by (1) forcing households in the interior to purchase public bonds (inside the formal economy), and (2) demand for BOJ notes from the black markets as discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II” (outside the formal economy, not included in private saving in the formal sector).2 Besides the above two, a considerable portion of local military expenses in the occupied territories (65.7 billion yen) was covered by (3) borrowing from the reserve banks and the central banks there. In addition, the Overseas Funds Bank (OFB), founded in February 1945 by the Japanese government, intermediated between the occupation forces and the reserve banks in north/central China and the southern regions, and extended lending up to 522.8 billion yen completely outside the EME special account. In sum, the reserve banks in the occupied territories contributed 36.9 billion yen inside the EME special account, and 522.8 billion yen outside of it in the last three years of the war. Given that nominal GNE in Japan amounted to about 100 billion yen in 1945, the scale of war finance by the reserve banks was extremely large, and much greater than that by the BOJ or by the central banks in the occupied territories. However, the above statistics would be somewhat misleading without any explicit consideration of the following facts. First, the Japanese government maintained fixed exchange rates between the Japanese yen and local currencies in the occupied territories until the end of the war. Second, the regions in which the reserve banks operated suffered from high inflation rates, while inflation rates were relatively low in the regions where the central banks funded the occupation forces. These two facts jointly reduced the purchasing power of the occupation forces substantially from the face value in the former regions. According to the estimation results, the transfers to the occupation forces through the reserve banks in north/central China and the southern regions amounted to 559.7 billion yen at face value, but only 7.2 billion at purchasing power parity (PPP) with December 1941 as a base month/year. This was equivalent to at most a few percent of the nominal economic scale of mainland China and the southern regions. In comparison, the transfers to the occupation forces through the central banks in Manchuria, Indochina, and Thailand reached only 5.8 billion yen at face value, but still 3.6 billion yen at PPP. This accounted for 5–20% of the vanquished countries’ nominal GDP. This finding is consistent with Huff and Majima (2013) on the wartime transfers to the occupation forces in Indochina and Thailand. However, the transfers to the Japanese government through the issue of BOJ notes amounted to more than 20% of its nominal GNE in 1945. In this way, the Japanese government developed large-scale monetary operations by forcing the reserve banks in north/central China and the southern regions to issue enormous amounts of banknotes, but the occupation forces failed to acquire much purchasing power from such extensive monetary finance. In contrast, the monetary 2 As implied by chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy

During and Immediately After World War II”, it is assumed that demand for BOJ notes from the formal economy was 10% of nominal GNE.

60

On Large-Scale Monetary Operations in the Japanese …

operations that were developed by the BOJ in Japan (as discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”), and by the central banks in Manchuria, Indochina, and Thailand, were relatively successful. A major reason for this sharp contrast is that strong demand for banknotes (legal tender) as a store of value came from black market dealers in Japan as documented in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, and from farmers in rural districts in Indochina and Thailand as discussed in Huff and Majima (2013). However, immediately after the end of the war, this successful wartime financing in Manchuria, Indochina, Thailand, and Japan turned out to be an immense burden on the defeated government. The government had to repay its considerable liabilities to the central banks in Indonesia and Thailand using gold bullion, was deprived of access to the still valuable Central Bank of Manchuria by the Red Army of the Soviet Union, and was forced to devalue its enormous public debt underwritten by the BOJ through high inflation and heavy taxes, as discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”. However, just before the war ended, the Japanese government could easily retire the already heavily devalued banknotes that were issued by the reserve banks in north/central China and the southern regions. There has been little research on wartime financial exploitation in occupied economies. Huff and Majima (2013) examine the financial exploitation of southeast Asia during Japan’s World War II occupation, while Occhino et al. (2008) estimate the forced transfers from France to Nazi Germany. Scherner (2015), and White (2016) also explore Germany’s system of financing occupation. A particular feature of war financing in the Japanese occupied territories is that the Japanese government borrowed from reserve/central banks in the occupied territories. As Scherner and White (2016), Scherner (2015), and others analyze in detail, Nazi Germany forced the occupied governments to make occupation payments, while in most cases the occupied countries had to finance such payments by issuing their own public bonds and printing their own legal tender. Accordingly, after the war, the previously occupied countries had to redeem their public bonds, withdraw legal tender, or reduce the real value of public bonds and banknotes by high inflation. In contrast, the Japanese occupation forces could enjoy seigniorage revenues in Manchuria, Indochina, and Thailand during the war, but after the end of the war, the Japanese government had to repay its liabilities to the occupied countries in order to withdraw its legal tender. This chapter is organized as follows. Section 2 describes how the reserve banks and the central banks in the occupied territories funded the Japanese occupation forces. Section 3 compares the transfers to the occupation forces by the reserve banks and the central banks at face value and at regional PPP exchange rates, and it evaluates the relative size of the transfers in terms of ratios to the nominal macroeconomic scale of the occupied countries. In addition, it explores how the wartime obligations to the occupied countries were repaid by the Japanese government after the war. Section 4

1 Introduction

61

discusses how the reserve banknotes issued in north/central China and the southern regions failed to create strong money demand among people in these regions.

2 Monetary Operations by the Reserve Banks and the Central Banks in the Occupied Territories 2.1 Military Scrip and the Reserve Banks on the Continent Before the invasion of north China by Japanese military forces in 1937 (the Marco Polo Bridge Incident), the Japanese government had founded the Bank of Taiwan (BOTw) in 1899, the Bank of Chosen (BOChs) in Korea in 1911, and the Central Bank of Manchuria (CBM) in Manchuria in 1932 as the central banks in each colonial territory on the continent. The government adopted a currency policy by which each central bank issued not BOJ notes, but its own legal tender in order to protect the interior economy from possible influences of the colonial economies. The colonial yen was set at par with the Japanese yen, and this fixed rate was maintained until the end of the war. In north China, three Chinese government-managed banks (the Central Bank of China, the Bank of China, and the Bank of Communications) started to issue legal tender as nonconvertible banknotes in 1935. Immediately afterwards, the Japanese government attempted to establish a reserve bank in order to challenge the circulation of legal tender, but it failed to do so. When the Marco Polo Bridge Incident expanded into the Second Sino-Japanese War in 1937, the Japanese government established the special account for EME. The occupation force paid local expenses in occupied territories in either military scrip, or banknotes issued by the above colonial central banks or the newly installed reserve banks. How such local expenses were recorded in the EME special account depended on whether the occupation forces paid them by banknotes or military scrip. When payment was made by banknotes, the government financed expenditure from the special account by issuing public bonds in Japan, and remitted funds to local central/reserve banks that issued banknotes for the occupation forces. Payment by military scrip, however, had a rather problematic consequence. Military scrip consisted of government-issued notes in the sense that they were eventually backed by claims against the EME special account on the BOJ balance sheet (see Fig. 1), but they differed from standard public bonds in the sense that any expense from the special account was never executed before the scrip was finally redeemed. In the latter respect, military scrip served as public compensation (delivery) bonds and was not included as outstanding public debts as long as it circulated in markets. Because of the convenience of unexecuted payments and unrecorded public debts, the government basically preferred payment by military scrip to that by banknotes. Initially, the occupation forces carried BOChs notes in north China, mainly because BOChs notes had already circulated there. However, BOChs notes failed

62 Fig. 1 Issuance of military scrip by the Japanese government

On Large-Scale Monetary Operations in the Japanese …

Bank of 䠦 apan Assets (ii) Claims against the EME special account

Liabilities (i) Military scrip deposited by the Japanese government

to circulate as a medium of exchange, but they served as a speculative instrument. Once BOChs notes were employed for local payment by the occupation forces, they started to depreciate against Chinese legal tender in Peking, but they still appreciated against it in Shanghai. Given such opportunities of arbitrage, BOChs notes were transferred from Peking to Shanghai, converted to legal tender there, brought back to Peking, and then converted again to BOChs notes. Such transfers between Peking and Shanghai were ongoing. Accordingly, BOChs notes were retired from circulation as a means of exchange in north China. In central China, however, the occupation forces carried yen-denominated military scrip as well as BOJ notes. After BOJ notes were soon retired from circulation, except in Shanghai, military scrip served as a payment instrument. The government made every possible effort to circulate scrip as a medium of exchange. For example, clearing houses were installed for military-scrip-based transactions, while local banks were forced to receive deposits by military scrip. Nevertheless, their efforts were not necessarily successful. Given that BOChs notes and military scrip were not well received as payment instruments in north/central China,3 the government supported a puppet government’s attempt to found reserve banks in north/central China. The FRBC was opened in Peking in March 1938, and the CRBC was opened in Nanjing in January 1941. However, neither the FRBC yen notes nor the CRBC yuan notes were circulated widely in the territories, because they still had to compete with Chinese legal tender, which was supported indirectly by financial assistance from the United States and the UK, and with native bank checks, which were exchanged in a private draft clearing house in Shanghai (called the Wei Wah system).4 Given such limited circulation, the Japanese government faced difficulties in using FRBC notes or CRBC notes as a monetary instrument of seigniorage.

3 In South China, including Hong Kong, military scrip was employed as a payment instrument until

the end of the war (August 1945). Outstanding scrip amounted to 42.7 thousand yen and was small relative to the circulation of scrip and reserve banknotes in north/central China. 4 See Kojima (1941) and Takaishi (1970a).

2 Monetary Operations by the Reserve Banks and the Central …

63

2.2 Bilateral Depositing as Fiscal Instruments 2.2.1

With the Federal Reserve Bank of China and the Central Reserve Bank of China

When the military forces started to invade the southern regions in 1941, the Japanese government ordered the BOChs, BOTw, CBM, and the Yokohama Specie Bank (YSB) to seize foreign banks such as the Hong Kong and Shanghai Banking Corporation (HSBC) and the National City Bank. The three Chinese government-managed banks in north/central China were forbidden to issue any legal tender. In 1942, the Wei Wah system in Shanghai was taken over by a new clearing system that was operated under the direction of the CRBC.5 Consequently, the FRBC and the CRBC could finally acquire a currency monopoly there. The government adopted a fixed exchange rate for both FRBC yen and CRBC yuan until the end of the war in August 1945, thereby attempting to support the value of these currencies. FRBC yen was set at par with BOJ yen in March 1938, while 100 CRBC yuan was set at 18 BOJ yen in May 1942. Note that any payment associated with FRBC notes and CRBC notes was recorded in terms of these fixed rates in the EME special account. Given the above currency monopoly and fixed exchange rates, the government finally decided to use FRBC notes and CRBC notes to cover most war expenses in north China in September 1938 and in central China in August 1942. A bilateral depositing contract, called Azuke-ai, in Japanese, served as a major fiscal instrument.6 In north China, the BOChs made a contract with the FRBC. As Fig. 2 shows that bilateral depositing worked as follows: (1) (2) (3) (4) (5)

The BOChs Tokyo branch received a military payment that was made from the EME special account by the Japanese government. At the Peking branch, the BOChs issued a notional deposit to the FRBC. At the Peking main office, the FRBC instead issued a deposit to the BOChs. At the same time, the BOChs Tokyo branch provided uncollateralized credits to the Japanese government. The BOChs Peking branch withdrew cash in the form of FRBC notes from its deposit at the FRBC and delivered FRBC notes to the occupation forces in Peking as an agency of the BOJ.

Under the above contract, the notional deposits by the FRBC at the BOChs were supposed to be cashed only after the uncollateralized loans were repaid to the BOChs by the government. The rates of interest on the uncollateralized loan and the notional 5 According to Kojima (1943), properties such as land were offered as collateral by commercial and

native banks that were participating in the Wei Wah system. In a new clearing system, however, such collateral requirements were abolished. Consequently, CRBC notes and checks were convertible with each other, but both were no longer backed by real assets in the system operated by the CRBC. 6 Tatai (2002) describes in detail how bilateral depositing worked among the FRBC, BOChs, and the Japanese government.

64

On Large-Scale Monetary Operations in the Japanese …

Bank of Chosen Assets (i) Payments from the EME special account

Liabilities

(ii) Notional (iv) Uncollaterized deposit to FRBC credits to the Japanese government

Federal Reserve Bank of China Assets

Liabilities (iii) Deposit to BOCs

(ii) Notional depoist from BOCs (v) Withdrawn in FRBC notes by BOCs

Fig. 2 Financing military expenses by bilateral depositing arrangements between the Bank of Chosen and the Federal Reserve Bank of China

deposit were set at rather low levels. In addition, when the loan to the government was due, or the currency in which the deposit should be cashed, was not specified at all in the contract. In fact, no portion of the principal was repaid to the FRBC through the BOChs at all during the war. In this way, the BOChs intermediated between the Japanese government and the FRBC, and the government financed military expenses in north China by the issue of FRBC notes. As mentioned above, under the above monetary scheme, the FRBC was not allowed to withdraw the notional deposit at the BOChs Peking branch unless the uncollateralized loans were repaid by the government. Thus, the BOChs Tokyo office did not have to transfer any BOJ notes or gold bars to its Peking office as reserves or financial species. That is, without transporting any specie to the BOChs Peking branch, the government could finance military expenses in north China by the issue of FRBC notes. The YSB made the same bilateral depositing contract with the CRBC and helped the government to finance military expenses in central China by the issue of CRBC notes.

2.2.2

With the Southern Development Bank and the Overseas Funds Bank

When the occupation forces invaded the southern regions, including Indonesia, Burma, Malaya, and the Philippines as of December 1941, they used local-currencydenominated military scrip for most payments. In April 1942, the government decided to found the SDB as a sort of central bank to manage various kinds of local-currencydenominated scrip. The SDB opened a main office in Tokyo and six regional headquarters in Manila (the Philippines), Batavia (Java), Palembang (Sumatra), Rangoon (Burma), Singapore (Malaya), and Kuchin (Borneo).

2 Monetary Operations by the Reserve Banks and the Central …

65

By issuing SDB notes in the form of dollars (Malaya and Borneo), guilders (Java and Sumatra), rupees (Burma), and pesos (the Philippines), the SDB replaced localcurrency-denominated military scrip with SDB notes, although the same scrip bills were used as its notes. For this reason, military scrip replaced by the SDB and its notes are referred to interchangeably throughout this paper. Then, the SDB started to make uncollateralized credits directly to the Japanese government in April 1943. Each local currency was fixed at par with notional yen, which was a hypothetical currency and served only for accounting purposes. Any military payment associated with SDB notes was recorded in terms of notional yen in the EME special account. In March 1945, all the above monetary schemes through the reserve banks (FRBC, CRBC, and SDB) were taken over by the OFB, which was founded secretly as a public financial institution in Tokyo. Then, the OFB intermediated between the reserve banks (FRBC, CRBC, and SDB) and the Japanese government, rather than the BOChs or YSB. One important difference from the previous schemes was that any military payment through the OFB was no longer recorded in the EME special account, but instead in a secret fiscal account. A major reason for this was that inflation rates were extremely high in north/central China and the southern regions. The EME special account would have amounted to astronomical figures if military payments had been recorded there in terms of fixed exchange rates. By founding the OFB, the government thus hid from the public the skyrocketing military expenses at face value for the occupied territories.

2.2.3

With the Central Bank of Manchuria, the Bank of Indochina, and the Bank of Thailand

In Manchuria, Indochina, and Thailand, the government implemented another kind of monetary operation by employing not newly created banknotes such as FRBC notes, CRBC notes, or SDB notes, but existing legal tender issued by central banks on the continent.7 In the three countries, the occupation forces used not military scrip but local legal tender for most payments from the beginning of the war. In April 1944, the YSB started bilateral depositing with the CBM. That is, the YSB helped the government to receive uncollateralized credits from the CBM by the issue of CBM yen notes, whose currency unit was at par with BOJ yen. Similarly, in April 1944, the YSB initiated bilateral depositing with the BOI through the issue of BOI piastre notes, and the BOJ conducted the same operation with the BOTh through the issue of BOTh baht notes. Both piastre and baht were at par with BOJ yen. The above bilateral depositing arrangements between the Japanese government and the three central banks served as not only a fiscal instrument for the government, but also as provisions of yen currency for cross-border settlements for these banks. Immediately after Manchuria, Indochina, and Thailand allied themselves with Japan, they were isolated from the dollar/pound blocks, and suffered from a shortage of 7 Huff

and Majima (2013) describe in detail the financial arrangements between the YSB and the BOI and between the BOJ and the BOTh.

66

On Large-Scale Monetary Operations in the Japanese …

currency for cross-border settlements. The bilateral depositing scheme thus allowed these central banks to purchase yen using their own legal tender for settlements in the yen block. For this purpose, these central banks could withdraw yen currency from deposit accounts (called ‘special yen’ accounts), which were held at the YSB under the bilateral depositing contract. For the contracts with the BOI and BOTh, the uncollateralized loans to the government were expected to be redeemed by delivery of gold bars.

3 Transfers to the Occupation Forces from the Viewpoint of the Occupier and the Occupied 3.1 Scale of the Transfers to the Occupation Forces at Face Value and at PPP Let us first examine in detail the scale of the transfers to the occupation forces at both face value and PPP. As shown in Table 2, the occupation forces received large-scale transfers from the FRBC in north China, the CRBC in central China, and the SDB in the southern regions in the years 1943–1945. The transfers from those reserve banks amounted to 5.3 billion yen in 1943 and 31.6 billion yen in 1944. When the OFB intermediated bilateral depositing with the reserve banks in 1945, the amount reached 522.8 billion yen. In contrast, the transfers from the central banks in Manchuria, Indochina, and Thailand were relatively modest at 2.6 billion yen in 1944, and 3.2 billion yen in 1945. According to these figures, the transfers to the occupation forces from the reserve banks in north/central China and the southern regions were overwhelmingly dominant. However, the above statistics would be misleading without careful consideration of the price differences among the regions. According to Table 3, during the period from December 1941 to December (or September) 1944, wholesale prices increased by only 8.6% per year in Tokyo, but the regions where the transfers were made through the reserve banks experienced high inflation. During the same period, wholesale prices skyrocketed annually by 84.7% in Peking/Tianjin (north China), by 198.8% in Shanghai (central China), and by 355.5% in Singapore (southern regions). However, the regions where the transfer was made through the central banks experienced relatively mild inflation. During the same period, wholesale prices increased annually by 14.7% in Xinjing (Manchuria), by 37.5% in Saigon (Indochina), and by 53.3% in Thailand. Such a difference between the two regions is magnified greatly once 1945, the last year of the war, is included. For example, the annual inflation rate accelerated from 198.8 to 731.8% in Shanghai, but it increased moderately from 37.5 to 42.3% in Saigon. As mentioned before, the government fixed exchange rates against local currencies up to the end of the war, and any transfer to the occupation forces was recorded in terms of fixed exchange rates in the EME special account in 1943 and 1944 and

3 Transfers to the Occupation Forces from the Viewpoint …

67

Table 2 Financing local military expenses by reserve/central banks in the occupied territories, 1943–1945 (unit: million yen) Starting date

Intermediation between the Japanese government and a local reserve/central bank

Local reserve/central bank

Credits to the Japanese Government (million yen) 1943

1944

1945

Total

North China

April 1943

Bank of Chosen (taken over by Overseas Funds Bank in 1945)

Federal Reserve Bank of China

920

4210

52,300

57,430

Central China

August 1942

Yokohama Specie Bank (taken over by Overseas Funds Bank in 1945)

Central Reserve Bank of China

2727

17,912

462,503

483,142

Southern regions

April 1943

Southern Regions Development Bank (taken over by Overseas Funds Bank in 1945)

1650

9450

8000

19,100

subtotal

5297

31,572

522,803

559,672

1400

2000

3400

Manchuria (east-north China)

April 1944

Yokohama Specie Bank

Central Bank of Manchou

Indochina

April 1944

Yokohama Specie Bank

Bank of Indochina

755

496

1251

Thailand

April 1944

Yokohama Specie Bank

Bank of Thailand

491

670

1161

Subtotal Total

5297

2646

3166

5812

34,218

525,969

565,484

Note EOHPF, MOF (1955), pp. 179 and 382

in the secret account of the OFB in 1945. Thus, high inflation contributed directly to fiscal expansion in the transfers in north/central China and the southern regions. To correct for such impacts of high inflation, the face value of the transfer is now T okyo T okyo and Pti denote time-t wholesale prices in adjusted by PPP or Pt P i , where Pt t

100

101

107

131

131

145

148

149

150

150

153

158

160

163

168

175

Jun-37

Dec-37

Dec-38

Dec-39

Dec-40

Dec-41

Mar-42

Jun-42

Sep-42

Dec-42

Mar-43

Jun-43

Sep-43

Dec-43

Mar-44

Jun-44

1936 average

Tokyo

179

170

168

159

159

152

150

149

150

148

146

140

126

112

100

Taipei

207

200

193

187

186

179

173

169

167

165

164

157

151

123

104

100

Soeul

100

281

262

254

242

238

235

232

216

212

210

208

198

159

125

100

2156

1504

1382

1227

1184

1220

817

618

645

565

518

409

261

100

22,923

16,320

11,066

8669

6556

4733

3399

2935

2575

1782

1650

567

342

155

130

116

100

Xinjing Peking/Tianjin Shanghai

203

135

100

169

129

100

5154

1976

1196

437

247

245

200

186

100

388

153

141

128

114

100

492

304

227

199

166

150

134

139

140

102

100

Thailand Saigon Manila Kuchin Batavia (Indochina) (Philippines) (Borneo) (Java)

Table 3 Wholesale price indexes in the interior, colonies, and occupied territories, June 1937–August 1945

886

707

432

384

308

100

4469

2922

1201

807

405

352

100

Palembang Singapore (Sumatra) (Malaya)

(continued)

3635

2629

1718

1253

900

705

100

Rangoon (Burma)

68 On Large-Scale Monetary Operations in the Japanese …

12.9%

Annual rate from Dec. 41 to Aug. 45

8.1%

10.0%

22.5%

14.7%

301.7%

84.7%

13,643

33,491

731.8%

198.8%

3,898,815

1,457,588

262,150

113,251

69.5%

53.3%

692

360

42.3%

37.5%

364

260

504.4%

14,285

14,285

14,084

173.5%

102.2%

4000

827

157.3%

152.6%

3197

2421

1752

1279

Thailand Saigon Manila Kuchin Batavia (Indochina) (Philippines) (Borneo) (Java)

159.5%

157.0%

3300

3252

2253

1698

1,279

394.1%

355.5%

35,000

10,766

6471

Palembang Singapore (Sumatra) (Malaya)

678.9%

336.8%

185,648

30,629

12,700

8707

5765

Rangoon (Burma)

Note Huff and Majima (2013), pp. 955–956, for Thailand and Indochina, and Statistics Department, BOJ (1966), p. 381, for the other regions. For Xinjing (Manchuria), Peking/Tianjin, and Shanghai, the period between December 1944 and August 1945 is complemented by Minami and Makino (2014), pp. 509 and 416

8.6%

84,840

Annual rate from Dec. 41 to Sep. (Dec.) 44

25,480

438

219

Aug-45 226

2799

7055

Jun-45

303

192

213

217

Mar-45

181

185

Xinjing Peking/Tianjin Shanghai

182

Soeul

Dec-44

Taipei

Sep-44

Tokyo

Table 3 (continued)

3 Transfers to the Occupation Forces from the Viewpoint … 69

70

On Large-Scale Monetary Operations in the Japanese …

Tokyo and region i, respectively. Under this adjustment, overvaluation of the transfers in a region with high inflation is corrected properly. Table 4 reports the scale of the transfers to the occupation forces in each region at both face value and PPP, with December 1941 as a base month/year. In north/central China and the southern regions, the transfers amounted to 5.3 billion yen at face value and 1.4 billion yen at PPP in 1943, 31.6 billion yen at face value and 2.6 billion yen at PPP in 1944, and 522.8 billion yen at face value and 3.3 billion yen at PPP in 1945. In the years 1943–1945, the total transfers in those regions amounted to 559.7 billion yen at face value, but only 7.2 billion yen at PPP. In Manchuria, Indochina, and Thailand, however, the transfers to the occupation forces amounted to 2.6 billion yen at face value and 1.8 billion yen at PPP in 1944, and 3.2 billion yen at face value and 1.8 billion yen at PPP in 1945. In total, the transfers in those regions were only 5.8 billion yen at face value, but still 3.6 billion yen at PPP. In comparing the two regions, the transfers in the latter regions account for only 1% (5.8 billion yen relative to 559.7 billion yen) of the transfers in the former regions at face value, but still 50% (3.6 billion yen relative to 7.2 billion yen) of them at PPP. Viewed differently, the occupation forces in north/central China and the southern regions acquired little purchasing power despite extremely large-scale transfers at face value. However, the forces in Manchuria, Indochina, and Thailand obtained substantial purchasing power even from modest transfers at face value. Let us finally compare the domestic transfers to the government financed by the BOJ with the transfers to the occupation forces through the reserve/central banks. Here, monetary operations by the BOJ are measured by the annual increment in outstanding BOJ notes.8 According to Table 5, the transfers by the reserve banks exceeded the monetary operations by the BOJ at face value, but the latter exceeded the former at PPP. In 1945, for example, monetary operations by the BOJ amounted to 24.6 billion, and monetary operations by the reserve banks reached 522.8 billion yen at face value. At PPP, however, the latter was only 3.3 billion or 13% of the former. As long as relative prices between Japan and the occupied territories are taken into consideration properly, monetary operations by the BOJ were still dominant in the war financing of the Japanese government.

3.2 Transfers to the Occupation Forces from the Viewpoint of the Occupied Countries 3.2.1

Real Money Balances and Real Seigniorage

How effectively the transfers to the occupation forces were financed by the issue of banknotes depended on how strongly those in the occupied territories demanded such 8 Hattori

and Oguro (2016) estimate the scale of monetary operations by the BOJ during and immediately after the war by various measures.

25.5

16.3

Central China

Southern regions

1381

34,218

2646

491

755

1400

31,572

9450

17,912

4210

Face value

4365

1792

174

370

1248

2573

232

1274

1068

At PPP

1945

22.5

42.8

74.1

0.5

0.4

3.0

PPP (%)

525,969

3166

670

496

2000

522,803

8000

462,503

52,300

Face value

5126

1845

151

212

1482

3280

36

1665

1579

At PPP

Total

565,484

5812

1161

1251

3400

559,672

19,100

483,142

57,430

Face value

10,872

3637

325

582

2730

7235

537

3634

3064

At PPP

Note EOHPF, MOF (1955), pp. 179 and 382, for monetary operations by the reserve/central banks in the occupied territories. Purchasing power parity exchange rates with December 1941 as base month are computed from the wholesale price indexes reported in Table 3. For the southern regions, wholesale prices from Singapore are used

Total

5297

35.4

Thailand

Subtotal

49.0

2.5

7.1

25.4

Indochina

1381

269

695

417

89.2

5297

1650

2727

920

Manchuria

Subtotal

45.3

North China

1944 PPP (%)

At PPP

PPP (%)

Face value

1943

Table 4 Size of monetary operations by reserve banks and central banks in the occupied territories in terms of face value and PPP, 1943–1945 (unit: million yen)

3 Transfers to the Occupation Forces from the Viewpoint … 71

72

On Large-Scale Monetary Operations in the Japanese …

Table 5 A comparison of scale of monetary operations between Bank of Japan and reserve/central banks in the occupied territories, 1943–1945 (unit: million yen and % of Japan’s nominal GNE) By Bank By reserve banks in of Japan north and central China, and southern regions Face value

By central banks in Manchuria, Thailand, and Indochina

Total

Japan’s nominal GNE

Face value At PPP Face value At PPP Face value At PPP

1943 3117 (4.9%)

5297 (8.3%)

1381 (2.2%)

8414 (13.2%)

4498 (7.0%)

63,820

1944 7480 (10.0%)

31,572 (42.4%)

2573 (3.5%)

2646 (3.6%)

1792 (2.4%)

41,698 (56.0%)

11,845 (15.9%)

74,500

1945 24,554 (21.5%)

522,803 (456.7%)

3280 (2.9%)

3166 (2.8%)

1845 (1.6%)

550,523 (480.9%)

29,680 114,467 (25.9%)

Total 35,151

559,672

7235

5812

3637

600,635

46,023

Note Statistics Department, BOJ (1966), p. 193, for outstanding BOJ notes, 1945, Ohkawa et al. (1974), p. 179, for 1943 and 1944 nominal GNE of Japan, and chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II” for 1945 nominal GNE of Japan. For the other data, the same as in Table 4. Monetary operations by the BOJ are computed as the annual increment in outstanding BOJ notes, where the 1945 figures are from January to August 1945. The numbers in parentheses are the ratio relative to nominal GNE

banknotes. The real value of seigniorage (St ) is usually measured by the annual increment in outstanding banknotes (Mt+1 ) divided by prices (Pt ), where the money stock is defined at the beginning of each period. Thus, real seigniorage can be decomposed into real money balances and monetary expansion as follows. St =

Mt+1 Mt Mt+1 = Pt Pt Mt

When money demand ( MPtt ) is strong, monetary expansion dominates price increases, thereby enhancing real money balances. Consequently, real seigniorage ( MPtt+1 ) increases with real money balances. Conversely, weak money demand results in declines in both real money balances and real seigniorage. Table 6 computes real money balances as well as real seigniorage for the monetary operations of the central banks (BOJ, CBM, BOI, and BOTh) and the reserve banks (FRBC, CRBC, and SDB) in the years 1942 to 1945. As discussed in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, with the help of strong demand for BOJ notes, the BOJ expanded the issue of banknotes under relatively stable price conditions and increased both real money balances and real seigniorage substantially. The central banks in the occupied territories, such as the CBM, BOI, and BOTh, successfully increased real money balances and real seigniorage, although not by as much as the

109

123

151

Dec-42

Dec-43

Dec-44

Aug-45

169

864

10,384

Dec-42

Dec-43

Dec-44

Aug-45

237,316

68

121

169

100

69

112

149

100

131

202

282

Dec-43

Dec-44

Aug-45

126

99

113

100

154

109

100

100

513

267

150

9,943

3,059

341

100

Price

Real balance

105

112

111

100

379

538

300

100

42

75

124

100

Real balance

20

65

100

173

155

100

Real seigniorage

19,468,219

10,622,956

1,954,807

463,261

Outstanding banknotes

Real seigniorage

Real seigniorage

Southern Development Bank

279

270

165

100

Real balance

Note Huff and Majima (2013), pp. 955–956, for Thailand and Indochina, and EOHPF, MOF (1955), p. 337, for the other regions. Prices are adopted from Table 3. For southern regions, wholesale prices from Singapore are used

100

Dec-42

Real balance

Bank of Thailand

2,697,231,000

139,698,667

19,150,328

3,477,345

Real seigniorage

114,705

3,332

326

100

Real seigniorage

Price

182

227

209

100

Real balance

8,800,000

5,876,854

3,011,187

Price

81

116

141

100

Outstanding banknotes

1,261,531 1,669,631

Bank of Indochina

132,603,000

15,840,886

3,761,583

963,962

1,581,008

100

Dec-41

Real balance

Price

189

131

109

100

Central Reserve Bank of China

Outstanding banknotes

Real seigniorage

1393

518

245

100

Price

393

201

132

100

Federal Reserve Bank of China

42,300,101

17,745,992

10,266,161

5,978,816

7,148,685

100

Dec-41

Outstanding banknotes

Central Bank of Manchou Real seigniorage

Price

Real balance

Price

Outstanding banknotes

Bank of Japan

Table 6 Real balances of legal tender and banknotes in central banks and reserve banks, December 1941–August 1945 (unit: thousand yen for outstanding banknotes, and prices, real balances, and real seigniorage standardized at 100 as of Dec. 1942 or Dec. 1943)

3 Transfers to the Occupation Forces from the Viewpoint … 73

74

On Large-Scale Monetary Operations in the Japanese …

BOJ. This indicates that there was strong demand for legal tender in those occupied territories. However, the reserve banks, such as the FRBC, CRBC, and SDB, were unable to produce much real seigniorage by issuing banknotes. Both real money balances and real seigniorage peaked in December 1943 in most cases and declined quickly by August 1945. In the case of the CRBC, for example, real money balances increased from 100 (standardized as of December 1942) to 169 in 1943 but declined to 68 in 1945. In the case of the SDB, real seigniorage dropped sharply from 100 in 1943 to 20 in 1945. Some possible reasons for such a sharp contrast between the regions with the central banks and the regions with the reserve banks will be discussed in the concluding section.

3.2.2

Scale of the Transfers to the Occupation Forces Relative to the Occupied Countries’ Economic Scale

Let us next explore the relative scale of the transfers to the occupation forces from the viewpoint of the occupied countries. The transfers are examined in terms of the ratio to the occupied country’s nominal GDP. According to Table 7, the transfers through the CBM accounted for around 10% of the nominal GDP of Manchuria in Table 7 Impacts of transfers to the occupation forces through central banks relative to the macroeconomies of Manchuria, Indochina, and Thailand, 1943–1945 (unit: million yen, million piastres, and million baht)

Japan (yen)

Transfer to Japanese government/occupation forces

Relative to Local local nominal nominal GNE/GDP (%) GNE/GDP

Bank of Japan 1943

3117

4.9

63,820

1944

7480

10.0

74,500

1945

24,554

21.5

114,467

1944

1400

11.6

Manchuria (yen)

Central Bank of Manchou

1943

12,059

1945

2000

Indochina (piastres)

Bank of Indochina

1944

755

22.1

3424

1945

496

13.4

3711

Thailand (baht)

Bank of Thailand

1944

491

6.9

7119

1945

670

5.4

12,505

Note Huff and Majima (2013), p. 942, for nominal GDP of Indochina and Thailand, Yamamoto (1997), Table 1, for nominal national income of Manchuria, and Ohkawa et al. (1974), p. 179, for 1943 and 1944 nominal GNE of Japan, and chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II” for 1945 nominal GNE of Japan. The 1943 relative ratio of Manchuria is computed from 1943 nominal national income. One unit of piastre, baht, or Manchurian yen was fixed at one unit of Japanese yen

3 Transfers to the Occupation Forces from the Viewpoint …

75

Table 8 Impacts of transfers to the occupation forces through the reserve banks in North/Central China on the Chinese macro economy, 1943–1945 Transfer in north/central China (million yen)

Transfer in north/central China (million yuan)

Relative to hypothetical nominal GDP Tianjin price (%)

Shanghai price (%)

1943

3647

20,261

0.88

0.88

1944

22,122

122,900

1.12

0.70

1945

514,803

2,860,017

2.23

0.87

Note Minami and Makino (2014), pp. 414–416, for urban wholesale price indexes, and Minami and Makino (2014), p. 452 for nominal GDP. Nominal GDP of 1943, 1944, and 1945 are hypothetically constructed under the assumption that real GDP was constant in the years 1940–1945, and deflators increased as urban wholesale prices increased. Regarding urban wholesale price indexes, national averages are available up to 1943, and city averages are available for Tianjin and Shanghai in 1944 and 1945. The exchange rate between the yuan and yen was fixed at 18 yen per 100 yuan

1944. The transfers through the BOI reached 22.1% of nominal GDP in 1944, and 13.4% in 1945, while the transfers through the BOTh amounted to 6.9% of nominal GDP in 1944, and 5.4% in 1945. In sum, nonnegligible portions of nominal GDP of the occupied countries were transferred to the occupation forces through the issue of legal tender by the central banks in the occupied territories. It is difficult to obtain nominal GDP data for mainland China for the years 1943– 1945. Hence, hypothetical nominal GDP is computed under the following heroic assumptions. First, real GDP was constant in the years 1940–1945. Second, deflators increased as urban wholesale prices increased. As for urban wholesale price indexes, national averages are available up to 1943, and city averages are available for Tianjin and Shanghai in 1944 and 1945. Thus, the hypothetical nominal GDPs of 1944 and 1945 are computed by the city averages. According to Table 8, the relative transfers through both the FRBC and CRBC accounted for 0.88% in 1943, between 0.70% and 1.12% in 1944, and between 0.87% and 2.23% in 1945. In the case of Indonesia, the SDB issued its banknotes in Java and Sumatra to finance the transfers to the occupation forces. Table 9 computes Marshallian k and relative seigniorage from outstanding SDB notes in Indonesia. Marshallian k as a measure of the strength of money demand is defined as outstanding SDB notes divided by nominal GDP, while relative seigniorage is defined as the annual increment in outstanding SDB notes divided by nominal GDP.9 As Marshallian k implies, money demand increased up to 1944, and then it declined suddenly in 1945. However, seigniorage accounted for 3.23% of nominal GDP in 1943, 4.66% in 1944, and 0.91% in 1945. In sum, the relative scale of the transfers to the occupation forces in north/central China and Indonesia was not as large as in Manchuria, Indochina, and Thailand. t not MPtt+1 = M Pt Yt denotes real GDP.

9 Here,

Mt+1 Mt ,

but

Mt+1 Pt Yt

=

Mt Mt+1 Pt Yt Mt

is adopted as relative seigniorage, where

76

On Large-Scale Monetary Operations in the Japanese …

Table 9 Marshallian k and relative seigniorage for Southern Development Banknotes in Indonesia, December 1942–August 1945 (unit: thousand guilders) Jawa

Sumatra

Total

Nominal GDP

Marshallian k (%)

Relative seigniorage (%)

December 1942

56,678

25,828

82,506

4,330,250

1.91

December 1943

133,770

234,690

368,460

8,849,400

4.16

3.23

December 1944

665,678

797,726

1,463,404

23,517,900

6.22

4.66

1,443,866

1,349,332

2,793,198

145,778,780

1.92

0.91

August 1945

Note Huff and Majima (2013), p. 942, for Indonesian nominal GDP, and EOHPF, MOF (1955), p. 338, for outstanding Southern Development Banknotes. Marshallian k is defined as outstanding SDB notes divided by nominal GDP, while relative seigniorage is defined as the annual increment in outstanding SDB notes by nominal GDP

3.3 Redemption of Wartime Obligations at the End of the War When the reserve banks (FRBC, CRBC, and SDB) were liquidated at the end of the war in August 1945, the uncollateralized loans to the government were redeemed mainly by funding from sales of gold bars in China.10 Through the YSB Chinese branches, the OFB sold 35 tons of gold bars just before the end of the war, and raised 502.6 billion yen in China,11 which was used to redeem most of the 522.8 billion yen of obligations to the holders of banknotes in north/central China and the southern regions. Given the extremely depreciated local currencies as a result of high inflation, only 35 tons of gold bars were required to write off seemingly astronomical amounts of the obligations by the OFB.12 The uncollateralized loans owed by the government to the BOI (1.3 billion yen) and the BOTh (1.2 billion yen) were also redeemed by the delivery of gold bars. In addition, the BOJ kept earmarked gold as a liability to Indochina and Thailand. While some earmarks were cancelled, 33.1 tons and 38.9 tons of gold were eventually delivered to the two countries respectively after the end of the war. It follows that more gold bars were required in redeeming the obligations to both Indochina and Thailand than those to north/central China and the southern regions. 10 See Editorial Office of History of Public Finance in Showa Era (EOHPF), MOF (1955), and Takaishi (1970b, 1970c) for the descriptions of this subsection. 11 The local sales of gold bars in China were converted into yen at the wartime fixed exchange rates. 12 The fact that the monetary transfers to the occupation forces were not large in north/central China and the southern regions does not mean that Japan’s labor exploitations and physical confiscations were also small there. See Boldorf and Okazaki (2015) for a wide range of severe exploitations by the Japanese government and the occupation forces in China, the southern regions, and Manchuria.

3 Transfers to the Occupation Forces from the Viewpoint …

77

The CBM experienced a completely different history in the postwar period. The Red Army of the Soviet Union requisitioned most physical and financial assets in Manchuria just before and immediately after the war. The CBM was also seized by the Red Army. Until the spring of 1947, however, CBM yen banknotes were still circulated widely with the scrip carried by the Red Army and legal tender issued by the central bank of the Nationalist government of China. The Japanese government liquidated only the CBM Tokyo branch in 1947. In conclusion, during the Pacific War the occupation forces could obtain substantial purchasing power from the CBM, BOI, and BOTh, but at the end of the war large amounts of gold bars were required to redeem the obligations to Indochina and Thailand. In addition, the entire body of the CBM was confiscated by the Red Army. Meanwhile, a large amount of war finance in the Japanese interior was repaid using high inflation and heavy levies during the postwar period as discussed in detail in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”. However, the occupation forces failed to acquire much purchasing power from the reserve banks in north/central China and the southern regions as a consequence of rather weak demand for these banknotes. At the end of the war, however, relatively small amounts of gold bars were required to write off all obligations in north/central China and the southern regions. In this way, the wartime benefits were balanced by the postwar costs.

4 Discussion It was for the following reasons that the reserve banks in north/central China and the southern regions could not work effectively to finance the transfers to the occupation forces. First, these reserve banks failed to serve as a standard central bank. A central bank provides international currencies for cross-border settlements, facilitates domestic exchange in cooperation with private banks, and stabilizes currency values by maintaining reserves and species. The reserve banks were not successful in either respect. Accordingly, the reserve banknotes did not function as a medium of exchange.13 Second, the reserve banknotes were inconvenient not only as a medium of exchange, but also as a store of value. As discussed by Huff and Majima (2013), farmers in rural districts held legal tender as a store of value in Indochina and Thailand, while as suggested in chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, black market dealers held BOJ notes as a store of value in Japan. During the Pacific War, however, households and firms in north/central China were reluctant to hold the

13 According to Takaishi (1970a), barter transactions in black markets were dominant in north/central

China in the final years of the war.

78

On Large-Scale Monetary Operations in the Japanese …

reserve banknotes, and still deposited their savings at native banks, which could provide domestic exchange between cities and hinterlands.14 Third, the reserve bank currencies were fixed at arbitrary rates against the BOJ yen. Then, conversion at these fixed rates turned out to be misleading in recording the transfers to the occupation forces in the EME special account and the OFB account. In this regard, the reserve bank currencies were not instrumental even as a unit of account either. Ironically enough, the above fixed rates created profitable arbitrage opportunities between FRBC yen and CRBC yuan or between FRBC yen and legal tender yuan in black markets, which in turn allowed native banks to earn huge profits by active speculation, and to compete successfully with the FRBC and the CRBC.15 In sum, the reserve banknotes could not fulfill satisfactorily any characteristic of money: medium of exchange, store of value, or unit of account. For these reasons, the reserve banknotes failed to be circulated widely as a fiscal instrument for the Japanese government. Stated differently, only the well-established central bank’s currencies could allow the government to finance large-scale war expenses. However, if it was relatively successful during the war, such financial exploitations by the Japanese military force had to be repaid in the postwar period by the defeated government, in the form of expensive repayments by gold, high taxes, and high inflation.

14 See 15 See

Iwatake (1990) and Zhaojin (2003). Iwatake (1990) and Zhaojin (2003).

Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy

Abstract In the past quarter century, Japan’s economy has seen rates of interest, including those on long-term public bonds, remain quite low despite colossal accumulation of public debt, while the price level has been mildly deflationary or almost constant despite rapid monetary expansion. In this chapter, these puzzling phenomena are interpreted using a simple disequilibrium analysis framework. The major reasons for adopting disequilibrium analysis are that (1) Japan’s economy often fell into excess supply in both goods and labor markets after short-term rates of interest were controlled below 0.5% in mid-1995, and (2) public bond markets were clearly in serious excess supply given the expectation that the primary fiscal balance was not going to turn into surpluses in the future relevant to those bonds being issued. In the proposed disequilibrium model, excess supply in goods, labor, and public bond markets is absorbed by excess demand in money markets, induced by strong money demand at near-zero interest rates. In particular, strong money demand absorbs public bonds not as investment instruments, but as money substitutes. This chapter also demonstrates that excess demand in money markets in disequilibrium analysis can be interpreted as public bond price bubbles in equilibrium analysis. Given the analogy between the two approaches, as far as the bubble is sustained, mild deflation and near-zero interest rates continue in spite of massive issues of public bonds and rapid expansion of money stocks. On the other hand, once the bubble bursts, money demand shrinks drastically, a wide range of interest rates rise suddenly, and the price level jumps abruptly. With the government’s credible commitment to future fiscal reforms, a one-off price surge would stop immediately at a level two or three times higher than before, but without the reforms, the price process would be hyperinflationary.

1 Introduction Two puzzling phenomena were observed in Japan’s economy in the past quarter century; mild deflation despite rapid monetary expansion, and rapidly declining long-term yields despite colossal accumulation of public debt. These phenomena have frequently been presented as evidence of unconventional policy recommendations, which state that a government should borrow more and repay less for © Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9_4

79

80

Public Bonds as Money Substitutes at Near-Zero …

6

4

2

0

-2

-4

-6

Output gap

Unemployment rate

Fig. 1 Output gap and unemployment rate, 1983, 1Q–2019, 2Q (unit: %). Notes (1) Estimates for the output gap are from Kawamoto et al. (2017), and their updates, compiled by the Research and Statistics Department, BOJ, and are available at www.boj.or.jp/en/research/research_data/gap/ put−actualout put index.htm/. (2) The output gap is defined as potentialout . (3) The unemployment rate potentialout put is compiled by Statistics Bureau of Japan (2020b)

economic stimulus. Emphasizing ‘repay less’, for example, Blanchard (2019) and Blanchard and Tashiro (2019) claim that large-scale fiscal deficits will be sustainable as far as interest rates continue to be lower than economic growth. Those who advocate modern monetary theory (MMT) take this a step further and propose the redemption of maturing public bonds by issuing any amount of central bank money instead of levying heavy taxes.1 What is more complicating, some MMT proponents, including Wray (2019), do not necessarily support the recent macroeconomic policies developed by the Japanese government and Bank of Japan (BOJ). They insist that the Japanese policies did not help at all to achieve a sustainable society with full employment. In this chapter, we investigate whether unconventional policy recommendations such as ‘borrow-more-repay-less’ and ‘repay-by-central-bank-money’ are theoretically justifiable in the context of Japan’s economy. To achieve this, we employ a simple disequilibrium analysis framework for two reasons. First, Japan’s economy often fell into excess supply in both goods and labor markets after mid-1995, when the short-term interest rate was held below 0.5%. As shown in Fig. 1, high unemployment rates and large output gaps (defined as potential minus actual output in this chapter) were frequently recorded in the past quarter century of the Japanese 1 See

Wray (2015) and others for detailed descriptions of MMT and its policy recommendations.

1 Introduction

81

economy, in particular in the first half of the 2000s and in the late 2000s. Second, public bond markets were clearly in serious excess supply given the expectation that the primary fiscal balance was not going to turn into surpluses in the near future.2 The Japanese government began to accumulate public bonds for economic stimulus from the early 1990s. The total of public bonds on issue, including Treasury bills (T-bills), Japanese government bonds (JGBs), and Fiscal Investment and Loan Program (FILP) bonds, was 173 trillion yen (40.5% of nominal GDP) at the end of fiscal year 1989, but this had increased to 411 trillion yen (86.4%) by the end of FY1999, and 1,025 trillion yen (186.9%) by the end of FY2018. The BOJ, on the other hand, began to purchase long-term public bonds (JGBs and FILP bonds) aggressively after a zero interest rate policy (ZIRP) was implemented in February 1999. This continued even more intensively when quantitative and qualitative easing (QQE) was adopted in April 2013. The balance of the BOJ’s own long-term bonds expanded from 40.1 trillion yen at the end of FY1998 to 475.6 trillion yen by the end of FY2018. This last sum represented 51.3% of the total issues of long-term public bonds. In the years from FY1999 to FY2018, the BOJ also expanded the BOJ note issue from 55.3 to 112.4 trillion yen, and the BOJ current reserves from 6.2 to 393.9 trillion yen. The consolidated government, consisting of the general government and the BOJ, financed large-scale fiscal stimulus by issuing to mainly private banks, public bonds, BOJ notes, and BOJ current reserves. According to Fig. 2, the consolidated government’s obligations to the public, excluding the BOJ’s own public bonds, never exceeded 50% of nominal GDP before FY1994, but then began to rise rapidly. They exceeded 100% of nominal GDP in FY2002, and 150% in FY2009, and amounted to 180% in FY2013. Then, they increased more slowly, reaching 190% in FY2018. On the other hand, as shown in Fig. 3, the primary fiscal balance of the general government consistently showed a heavy deficit. It recorded – 9.4% of nominal GDP in FY1998, and – 9.3% in FY2009. As suggested by these figures, the Japanese government behaved as if they had followed ‘borrow-more-repay-less’ policy recommendations faithfully. The above unconventional policies were carried out without any side effects on the price level or interest rate. According to Fig. 4, overnight call rates, which are representative short-term interest rates, stayed below 0.5% from October 1995, and remained negative from March 2016. Long-term yields, which are measured by tenyear JGB yields, declined from 3.6% in April 1995 to below 3% in September 1996, and below 2% in October 1997. After they rose abruptly from 2003 to 2004 summer, they declined again, reaching − 0.06% in March 2016. The consumer price index was almost constant with small variations. The price level was unresponsive to a decrease in the unemployment rate from July 2009 (5.5% in Fig. 1) to February 2017

2 Armstrong and Okimoto (2016) survey the literature on fiscal sustainability in Japan. Imrohoroglu

et al. (2019) update Imrohoroglu et al. (2016), and present detailed simulations of the sustainability of Japan’s fiscal conditions. The Fiscal System Council, MOF (2018) reports the long-term prospects for Japan’s fiscal policies.

82

Public Bonds as Money Substitutes at Near-Zero …

220% 200% 180% 160% 140% 120% 100% 80% 60% 40% 20% 0%

Consolidated government's debt issued to the private sector/nominal GDP BOJ current account balances/nominal GDP BOJ notes issued/nominal GDP

Fig. 2 Consolidated government’s debt issued to the private sector, 1980–2018 (relative to nominal GDP, unit: %). Notes (1) The flow of funds accounts statistics for the general government and BOJ are compiled by Flow of Funds in BOJ (2020). (2) Nominal GDP is based on the annual report of the national accounts, which is compiled by ESRI (2009, 2019)

(below 3%), and it failed to increase considerably except for consumption tax hikes in April 1997, April 2014, and October 2019. However, any conventional economic reasoning behind the above puzzling phenomena is lacking and, thus, it is difficult to justify the unconventional policy recommendations on standard theoretical grounds. According to conventional theory, the current price level increases with current money stocks as in the quantity theory of money (QTM), and decreases with future fiscal surpluses as in the fiscal theory of the price level (FTPL). As explored above, however, the current price level does not have a close relationship with either of them. However, it is indeed possible to explain partially these puzzling phenomena and to justify the unconventional policies loosely by a simple disequilibrium analysis framework, which is a bold departure from conventional equilibrium analysis. In this framework, strong money demand, induced by near-zero interest rates, plays an essential role in making unconventional predictions. For one example, additional issues of money are easily accommodated by excess (strong) money demand, thereby providing no stimulus to the price level. For another example, money and public bonds are close substitutes at near-zero rates in terms of returns, liquidity, and convenience. Accordingly, excess money demand can absorb public bonds as money substitutes, even if public bond supply far exceeds the present value of future fiscal surpluses. The two predictions from the disequilibrium approach offer compelling reasoning against the QTM and FTPL.

1 Introduction

83

6% 4% 2% 0% -2% -4% -6% -8% -10% -12%

Fig. 3 General government’s primary fiscal balance, 1980–2018 (relative to nominal GDP, unit: %). Note (1) The primary fiscal balance of the general government’s account is estimated by ESRI (2009, 2019). Figure 3 differs from Fig. 2 in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan” in that the former covers the entire accounts of the general government, but the latter covers only the general account of the central government

Practical policy implications are also available in the presence of excess (strong) money demand. Massive issues of public bonds by a government are first absorbed as money substitutes by strong money demand from private banks, and can then be purchased from private banks by a central bank. Consequently, a central bank can de facto underwrite newly issued public bonds and refinance maturing ones without any direct transaction with a government, which is strictly prohibited by the Public Finance Act in Japan. Thus, ‘repay-by-central-bank-money’ is legitimately feasible in the presence of excess money demand. Another important implication from the current disequilibrium approach concerns the accommodation of excess supply in goods and labor markets by excess demand in money/public bond markets. In this context, the latter excess demand, driven by strong money demand at near-zero interest rates, creates a macroeconomic environment where the economy is likely to fall into a state of weak aggregate demand. Here, the above recommendations such as ‘borrow-more-repay-less’ and ‘repayby-central-bank-money’ may be justifiable as policy operations for simultaneously mitigating both the excess supply and demand. However, translating the disequilibrium approach into the equilibrium approach may carry alarming suggestions. The appearance of excess money demand as interpreted by the former is likely to be interpreted as the presence of a public bond price bubble by the latter. Consequently, the disappearance of strong money demand at

84

Public Bonds as Money Substitutes at Near-Zero …

14

120

12

110

10

100

8

90

6

80

4

70

2

60

0

50

-2

40 Call rate (collateralized overnight) Call rate (uncollateralized overnight) 10-year JGB yield Consumer price index (all items excluding imputed rents and fresh food, base year: 2015, right scale)

Fig. 4 Short-term and long-term yields and consumer prices, January 1980–November 2019 (unit: %). Notes (1) The overnight call rates, collateralized and uncollateralized, are compiled by financial markets → short-term money market rates in BOJ (2020). (2) Hamacho SCI (a private investment general partnership) computes the monthly averages of the JGB yields from their daily data, which are reported by the MOF. (www.hamacho.net/jp/ in Japanese). (3) The consumer price index is compiled by the Statistics Bureau of Japan (2020a)

above-zero interest rates is interpreted as the bursting of the bubble. With the bubble bursting at some point in the future, the price level and rate of interest will jump to the conventional level. With this eventually expected, the government needs to commit credibly to future fiscal reforms to forestall a price surge that would not stop at a level two or three times as high as before but, rather, lead to hyperinflation. In other words, ‘borrow-more-repay-less’ and ‘repay-by-central-bank-money’ are no longer relevant after strong money demand disappears at above-zero rates. Here, a serious policy dilemma is posed. That is, a policy combination of ‘borrowmore-repay-less’ and ‘repay-by-central-bank-money’ is implemented to escape from a deflationary economy with near-zero interest rates, but such a particular economic environment is required as a precondition for these policies. Once the prerequisite of near-zero interest rates is lost, that is, once interest rates rise significantly above zero, the economy returns to a conventional situation in which the unconventional policy recommendations no longer work. This chapter is organized as follows. In Sect. 2, a simple disequilibrium analysis framework is presented with an emphasis on strong money demand at near-zero interest rates. This is then compared with equilibrium analysis when the rate of interest is both near and above zero. In Sect. 3, the puzzling Japanese experience is interpreted using the disequilibrium approach, and the relevance of unconventional

1 Introduction

85

policy recommendations is examined with extreme care. Section 4 offers conclusions. In the appendix to this chapter, we examine how the BOJ de facto refinanced its own JGBs at maturity without violating strict legal restrictions.

2 A Simple Disequilibrium Analysis Framework From the 1990s up to the present, as discussed in Sect. 1, Japan’s economy often fell into excess supply in goods and labor markets, and public bond markets were judged to be in serious excess supply. Given these observations, we present a simple disequilibrium analysis framework where goods, labor, and public bond markets are in excess supply, and money markets are in excess demand.3,4 More concretely, the markets in excess supply, especially public bond markets, are absorbed by the monetary markets in excess demand. In addition, we demonstrate that in this context disequilibrium analysis is closely related to equilibrium analysis. More concretely, monetary excess demand in disequilibrium analysis corresponds to public bond price bubbles in equilibrium analysis.

2.1 Strong Money Demand Induced by Near-Zero Interest Rates First, let us confirm that in orthodox monetary macroeconomic models, money demand is strong at near-zero interest rates, and is infinitely elastic at the limit ofzero  interest rates. A unit period household utility is typically specified as u(c) + v MP , where utility from both consumption and real money balances is concave, and their marginal utility is convex. That is, u  (c) > 0, u  (c) < 0, u  (c) > 0 for finite c, and

3 The

theoretical framework presented in this section is out of the context of mainstream modern macroeconomics, where all markets are assumed to be in equilibrium simultaneously. Even within modern economics, however, some schools of thought have taken disequilibrium phenomena in money markets seriously. Yeager (1986) surveyed orthodox monetarists, showing that they always considered monetary disequilibrium to be responsible for a systematic relationship between the general price level and monetary aggregates. On the other hand, Zahringer (2012) showed that in Austrian economics, disequilibrium in plural money markets was thought to cause business cycles in a complicated manner. Of course, the orthodox monetarists and the Austrians had sharp disagreements on disequilibrium approaches. In contrast to the orthodox monetarists, Austrian economics took relative prices, not the general price, seriously, and were extremely reluctant to aggregate individual variables to construct macroeconomic variables. 4 Another drastic departure from equilibrium analysis is disequilibrium dynamics, proposed by Iwai (1981). In the so-called Wicksellian case with flexible prices, the price level continues to fall heavily once aggregate demand runs short of aggregate supply. However, this model may not be applied to the current Japanese economy, in which the present price process is not in a deflationary spiral, but only mildly deflationary.

86

Public Bonds as Money Substitutes at Near-Zero …

      v  MP > 0, v  MP < 0, v  MP > 0 for finite MP . In addition, it is assumed that     lim MP →∞ v  MP = 0 and lim MP →∞ v  MP = 0.5 The assumption  that  money demand never saturates at any finite level of real money stocks (v  MP > 0 for finite MP ) is crucial in the following discussion. If   money demand saturates at the upper limit of MP , and v  MP reaches zero there, then strong money demand never emerges. The first-order condition with respect to real money balances dictates that marginal utility from real money balances is equal to the level of nominal interest rates (i), which is evaluated in terms of the marginal utility of consumption. v



Md P



= iu  (c).

(2.1)

d

A derivative of Eq. (2.1) with respect to MP and i with c constant is obtained as follows:  d d MP u  (c) =  d < 0 (2.2) di v  M P

    Given Eqs. (2.1) and (2.2), u  (c) ≥ 0, v  MP ≤ 0, and lim MP →∞ v  MP = 0, real money demand is stronger as nominal interest rates are lower, and it is the more elastic with respect to the lower interest rates. At the limit of zero interest rates, money demand is infinitely interest-elastic. Conversely, if interest rates deviate far from zero, then money demand is much less interest-elastic.

2.2 Excess Supply in Goods, Labor, and Public Bond Markets and Excess Demand in Money Markets A simple disequilibrium analysis framework is presented below. What is implied by ‘disequilibrium’ in this context is that markets are not in equilibrium ex ante or at

5 Ono

(2001), Ono et al. (2004), and others adopt a rather different assumption from real  on  utility /u  (c) > 0. Such money balances to derive a strong liquidity preference. That is, lim M →∞ v  M P P strong demand for money and assets, induced by this unconventional assumption, yields the same predictions as those in this chapter, such as stagnant aggregate demand, high unemployment, and downward pressures on the price level. A major difference between their model and the model presented in this chapter is that in the former any wealth including public bonds are always close substitutes for money in generating liquidity conveniences, but in the latter public bonds and money are close substitutes only at near-zero interest rates. Consequently, the two models make very different predictions once interest rates take off from the zero level; that is, the former is still Keynesian, but the latter returns to a neoclassical model.

2 A Simple Disequilibrium Analysis Framework

87

the beginning of the period, but are cleared on short sides ex post, that is at the end of the period. The consolidated government, which consists of a general government and a central bank, issues money (M s (t)) and public bonds (B s (t)) to households. Each household receives nominal interest rates i(t) on its own public bonds Bid (t − 1), but pays lump-sum taxes taxi (t) in a real term. The government makes real government consumption expenditures g(t), and hires workers from households l gd (t) at real wages w(t). Here, government consumption does not include expenditures on government employment. Given the price level at time t, an intertemporal budget constraint from time t − 1 to time t for the consolidated government is defined as follows. Here, the balance of money and public bonds is defined at the end of the period. B s (t) − B s (t − 1) M s (t) − M s (t − 1) + P(t) P(t) d B (t − 1) + w(t)l gd (t), + tax(t) = g(t) + i(t) P(t)

(2.3)

N N taxi (t), B d (t − 1) = i=1 Bid (t − 1), and N denotes the where tax(t) = i=1 number of households. Private agents are represented by households and firms, with private banks and other financial institutions implicit. Each household supplies labor lis (t) at real wages w(t), makes real consumption expenditures ci (t), and rents physical capital ki (t) at rental fees r (t). Physical capital is depreciated at the rate of δ. In addition, each household pays lump-sum taxes taxi (t) to the government, and holds money Mid (t) and public bonds Bid (t), both of which are issued by the government. Thus, an intertemporal budget constraint from time t − 1 to time t for household i is defined as follows: w(t)lis (t) + [r (t) − δ]ki (t − 1) B d (t − 1) Mid (t − 1) + [1 + i(t)] i P(t) P(t) = ci (t) + [ki (t) − ki (t − 1)] +

+

Mid (t) + Bid (t) + taxi (t) P(t)

Aggregating the above budget constraint over all households leads to: w(t)l s (t) + [r (t) − δ]k(t − 1) +

M d (t − 1) B d (t − 1) + [1 + i(t)] P(t) P(t)

88

Public Bonds as Money Substitutes at Near-Zero …

= c(t) + [k(t) − k(t − 1)] +

M d (t) + B d (t) + tax(t). P(t)

(2.4)

On the other hand, each firm produces all-purpose goods y j (t), costlessly convertible to private and government consumption goods, and physical capital. Firm j pays rent on physical capital k dj at the real rental fee of r (t), and hires workers from households l dj at the real wage of w(t). Accordingly, the valued added by each firm is allocated between capital income and labor income as follows: y j (t) = r (t)k dj (t − 1) + w(t)l dj (t)

(2.5)

Here, excess profits are assumed away for simplicity.  M s  li (t) Given the real wage w(t), labor supply from households l s (t) = i=1    d meets labor demand from firms l d (t) = M j=1 l j (t) as well as from the consolidated government (l gd ). M denotes the number of firms. As mentioned before, money and public bond markets as a whole are cleared That is,  N by dshort sides s at the end s of the Nperiod. N d d i=1 Bi (t − 1)+ i=1 Mi (t − 1) = B (t − 1) + M (t − 1) i=1 Bi (t − 1)+ capital rental markets, on the other hand, holds.6 In physical  N M d j=1 k j (t − 1) = i=1 ki (t − 1) always holds. Substituting these ex post market clearings into Eqs. (2.3), (2.4), and (2.5) leads to the following relationship:

N ⎫ N ⎬ y j (t) − ci (t) + g(t) (ki (t) − ki (t − 1) + δki (t − 1)) + ⎭ ⎩ j=1 i=1 i=1 ⎡ ⎤ N M s d d + w(t)⎣ li (t) − l j (t) − l g (t)⎦ ⎧ M ⎨

i=1

=

j=1

B d (t) − B s (t) M d (t) − M s (t) + P(t) P(t)

Using macroeconomic variables, the above equation is rewritten as7 : N d implied by Eq. (2.6), under the assumption that i=1 Bi (t − 1) + d s s = B (t − 1) + M (t − 1), goods and labor markets are i=1 Mi (t − 1) ex post cleared; that is, {y(t − 1) − [inv(t − 1) + c(t − 1) + g(t − 1)]} +  w(t − 1) l s (t − 1) − l d (t − 1) − l gd (t − 1) {y(t) − [inv(t) + c(t) + g(t)]} = 0. 6 As

N

7 Equation

(2.6) is interpreted to share characteristics of both beginning- and end-of-period formulations in assets markets equilibrium, both of which are proposed by Foley (1975) and others. In end-of-period models, the market-clearing conditions of not only goods markets, but also money and bond markets are defined in terms of flow variables. Here, Walras’s law holds for all of goods, money, and bond markets. In beginning-of-period models, on the other hand, the market-clearing

2 A Simple Disequilibrium Analysis Framework

89

{y(t) − [inv(t) + c(t) + g(t)]}   + w(t) l s (t) − l d (t) − l gd (t)   d   d M s (t) B (t) B s (t) M (t) − + − = P(t) P(t) P(t) P(t)

(2.6)

M where the aggregate value added y(t) is defined by y(t) = i=1 yi (t), while gross investment inv(t) is defined by k(t) − k(t − 1) + δk(t). Excess supply in goods and s labor markets, implied by the left-hand side of Eq. (2.6) is denoted by E x gl (t), or   s E x gl (t) = {y(t) − [inv(t) + c(t) + g(t)]} + w(t) l s (t) − l d (t) − l gd (t) .

(2.7)

As Eq. (2.6) implies, this disequilibrium analysis framework allows us to interpret the current macroeconomic conditions as a situation where excess supply in goods and labor markets is absorbed by excess demand in money and public bond markets. That is, y(t) > inv(t) + c(t) + g(t) and l s (t) > l d (t) + l gd (t) accompanies 

  d  M s (t) B (t) B s (t) M d (t) − + − > 0. P(t) P(t) P(t) P(t)

(2.8)

2.3 Excess Demand in Money Markets at Near-Zero Interest Rates Let us apply, step by step, the disequilibrium analysis discussed in Sect. 2.2 to interpret the macroeconomic phenomena, which are explored in Sect. 1. First, money markets are assumed to be in excess demand as a result of strong money demand at near-zero rates. That is: M s (t) M d (t) > . P(t) P(t)

(2.9a)

In this case, the QTM does not hold, because additional money supply can be absorbed by excess demand without any effect on the price level. Next, public bonds are be supplied of    excess of the present value  P(t+τin  assumed to  ) tax(t+τ )−g(t+τ )−w(t+τ )l gd (t+τ ) ∞ 1 f  . future fiscal surpluses b (t) = P(t) τ =1 τ (1+i(t+k)) k=1

conditions of assets markets are defined in terms of stock variables. In the latter formulation, Walras’s law does not hold. Accordingly, the market clearing conditions of goods markets can be separated from those of assets markets as in the IS–LM model. According to Eq. (2.6), the current setup shares the nature of end-of-period formulations in the sense that Walras’s law holds for all of goods, labor, money, and public bond markets, but it has the property of beginning-of-period formulations in that stock variables appear in the market clearing conditions of assets markets.

90

Public Bonds as Money Substitutes at Near-Zero …

That is: B s (t) > b f (t) P(t)

(2.9b)

In this case, the standard FTPL does not hold, because deteriorations in future primary fiscal balances may not result in an increase in the price level. To satisfy three inequalities, (2.8), (2.9a), and (2.9b), the following inequalities need to be satisfied. M s (t) B s (t) M d (t) − > − b f (t) > 0 P(t) P(t) P(t)

(2.10)

Here, demand for public bonds as purely financial instruments is supposed to be d (t) up to the present value of future fiscal surpluses; BP(t) = b f (t).   s (t) − b f (t) As inequalities (2.10) imply, excess supply in public bond markets BP(t)   d s (t) (t) . Then, how − MP(t) is absorbed in part by excess demand in money markets MP(t) are inequalities (2.10) really possible? How should excess supply in public bond markets be interpreted? One possible interpretation is that public bonds may serve not as financial instruments, but rather as money substitutes at near-zero interest rates. That is, money and public bonds are close to each other in terms of financial returns, liquidity, and convenience.8 While yields on long-term JGBs were still above zero before the beginning of 2016, the expectation that long-term yields would decline toward zero was prevailing among market participants in the JGB markets. Thus, anticipating near-zero yields in the near future, public bond investors held long-term JGBs. In this way, strong money demand, induced by near-zero interest rates, had absorbed not only traditional money, but also public bonds as money substitutes. As Eq. (2.6) implies, excess demand in money markets now absorbs excess supply in public bonds, goods and labor markets. Considering public bonds as money substitutes or quasi goods at near-zero rates as opposed to financial instruments, Eq. (2.6) may be interpreted slightly differently. As goods demand shifts from genuine to quasi goods (public bonds), aggregate demand becomes stagnant in primary goods markets. In this way, goods markets are likely to be in excess supply when public bonds are demanded as quasi goods at near-zero interest rates. We have two comments on the above discussion. First, the proposition that excess demand in money markets absorbs excess supply in other markets depends crucially on the presence of strong money demand at near-zero interest rates. In such a situation, neither the QTM nor the FTPL ever holds; the current price level has no close relationship with current money stocks or future fiscal surpluses. In other words, as soon as short-term interest rates rise above the zero rate of interest, excess demand in 8 As emphasized in chapter “Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?”, when bond interest coincides with currency interest (equal to zero in this case), public bonds are also equivalent to money in that neither generates any additional currency convenience.

2 A Simple Disequilibrium Analysis Framework

91

money markets disappears. Accordingly, both the price level and the rate of interest need to adjust radically as the QTM, and fiscal discipline is forced to recover itself instantaneously. Second, when public bonds are held as money substitutes by private agents, in particular by private banks, a central bank can bypass the strict legal restriction by which it would otherwise be prohibited from directly underwriting newly-issued public bonds from a general government. That is, newly issued public bonds are first purchased as money substitutes by private banks. Then, because private banks are indifferent between holding public bonds and money, a central bank purchases public bonds held by private banks by issuing the central bank’s current accounts (a part of the monetary base). Consequently, the new issue of public bonds to private banks by a general government is replaced by the additional issue of money by a central bank. As discussed in the appendix to this chapter, through the same route, a central bank can escape another legal restriction by which a central bank is not allowed to refund its own long-term public bonds directly.

2.4 A Comparison of Disequilibrium and Equilibrium Analyses Let us compare the disequilibrium approach, presented in Sect. 2.3, with a standard equilibrium analysis framework. For this purpose, the real rate of interest ρ(t) is defined as 1 + ρ(t) = P(t−1) [1 + i(t)], where the nominal rate of interest is deterP(t) mined at the beginning of the period. The present value of future fiscal surpluses can be expressed in terms of the real rate of interest instead of the nominal rate as follows: 1 P(t)    ∞ P(t + τ ) tax(t + τ ) − g(t + τ ) − w(t + τ )l gd (t + τ ) τ k=1 (1 + i(t + k)) τ =1

 ∞ tax(t + τ ) − g(t + τ ) − w(t + τ )l gd (t + τ ) τ = k=1 (1 + ρ(t + k)) τ =1

b f (t) =

A standard equilibrium analysis framework is presented as follows. Assuming that both public bonds and money markets are inequilibrium not only ex post, N d s but also ex ante, or B(t) = B s (t) = B d (t) = i=1 Bi (t), M(t) = M (t) =  N M d (t) = i=1 Mid (t), the iteration of substitution of the consolidated government’s intertemporal budget constraint (Eq. (2.3)) from the present to the future leads to: B s (t) + M s (t) = b f (t) P(t)

92

Public Bonds as Money Substitutes at Near-Zero …

 1 i(t + τ )M(t + τ − 1) τ + P(t + τ − 1) k=1 (1 + i(t + k)) τ =1   s 1 B (t + τ ) + M s (t + τ ) + lim τ τ →∞ P(t + τ ) k=0 (1 + ρ(t + k)) ∞ 

(2.11)

that in Eq. (2.11),  the real fiscal surplus  Note tax(t + τ ) − g(t + τ ) − w(t + τ )l gd (t + τ ) is discounted by the real rate of   −1) is discounted by the interest ρ(t), while the real seigniorage i(t + τ ) M(t+τ P(t+τ −1)   s s B (t+τ )+M (t+τ ) 1 is positive, it is called a nominal rate i(t).9 If limτ →∞ τ (1+ρ(t+k)) P(t+τ ) k=0 public bond price bubble. Conversely, if the terminal condition (transversality condi   s B s (t+τ τ)+M (t+τ ) = 0 , tion) is satisfied, and the bubble term is zero limτ →∞ P(t+τ ) k=0 (1+ρ(t+k)) then the real balance of public bonds and money stocks is equal to the sum of the present value of future fiscal surpluses and seigniorage. Equation (2.11) can be further simplified by the following three assumptions.   s B s (t+τ τ)+M (t+τ ) (1) The transversality condition holds, and limτ →∞ P(t+τ = 0. (1+ρ(t+k)) ) k=0

(2)

(3)

Real normal money demand is assumed to be constant at m QT M , and money d s (t) (t) = MP(t) = m QT M . Consequently, the price markets are in equilibrium, MP(t) level P(t) is proportional to money stocks M s (t), and theQTM holds.   τ i(t+k) =1 As in the valuation of perpetual floating rate bonds, ∞ τ =1 k=1 (1+i(t+k)) holds. Under the above three assumptions, Eq. (2.11) is rewritten as follows: B s (t) M s (t) + = b f (t) + m QT M P(t) P(t)

9 Equation

(2.12)

(2.3) is rewritten as follows:   P(t) tax(t) − g(t) − w(t)l gd (t) B(t − 1) + M(t − 1) = P(t − 1) P(t) P(t−1) P(t) [1 + i(t)] i(t)M(t − 1) B(t) + M(t) + P(t − 1)[1 + i(t)] P(t) P(t−1) P(t) [1 + i(t)]   1 = tax(t) − g(t) − w(t)l gd (t) 1 + ρ(t) i(t)M(t − 1) B(t) + M(t) 1 1 + + 1 + i(t) P(t − 1) 1 + ρ(t) P(t) +

equation implies, the real seigniorage arises on the previous real money balance   As the above i(t)M(t−1) , and is accordingly discounted by the nominal rate of interest. On the other hand, the P(t−1)   real fiscal surplus is defined at the current period tax(t) − g(t) − w(t)l gd (t) , and is consequently discounted by the real rate of interest.

2 A Simple Disequilibrium Analysis Framework

93

(t) By Eq. (2.12), fiscal discipline, BP(t) = b f (t), needs to be established at the price   s (t) = m QT M . level determined by the QTM MP(t) Let us return to the disequilibrium approach. Here, marketsare assumed to be  s cleared in goods and labor markets for simplicity E x gl (t) = 0 . Thus, money and public  d bonds marketss are cleared as awhole, but each market is still in disequilibrium M (t) (t) (t) − MP(t) = BP(t) − b f (t) > 0 . Then, the clearing condition in money and P(t) public bond markets is rewritten as: s

 d  M (t) M s (t) B s (t) f QT M QT M + = b (t) + m −m + . P(t) P(t) P(t)

(2.13)

Let us compare the disequilibrium analysis Eq. (2.13) with the equilibrium analysis Eq. (2.11). Here, seigniorage is assumed to arise largely from normal money demand, or QTM demand m QT M. Then, the present value ∞ M(t+τ −1) τ i(t+τ ) can be approximated by of future seigniorage τ =1 k=1 (1+i(t+k)) P(t+τ −1)    ∞ i(t+τ ) m QT M τ =1 τ (1+i(t+k)) , or m QT M . Thus, Eq. (2.11) is replaced by m QT M itself. k=1

In other words, money supply beyond normal demand (m QT M ) is not backed by any future seigniorage. Then, Eq. (2.11) is rewritten as: M s (t) B s (t) + ≈ b f (t) + m QT M P(t) P(t)   1 B s (t + τ ) + M s (t + τ )  (2.14) + lim τ τ →∞ P(t + τ ) k=0 (1 + ρ(t + k)) Accordingly, strong money demand beyond m QT M in disequilibrium analysis (t) [ MP(t) − m QT M in Eq. (2.13)] corresponds to the asset price bubble in equilibrium   B s (t+τ )+M s (t+τ ) 1 in Eq. (2.14)]10 : analysis [limτ →∞ τ (1+ρ(t+k)) P(t+τ ) d

k=0

  1 M d (t) B s (t + τ ) + M s (t + τ ) QT M −m >0 = lim τ τ →∞ P(t) P(t + τ ) k=0 (1 + ρ(t + k))

10 According to chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary

Japan”, if the transversality condition fails to hold in the equilibrium analysis of Eq. (2.11), then the bubble term, which is finitely positive at asymptotically zero rates of interest, contributes to s (t) appreciation of the real balance of public bonds BP(t) and yields deflationary pressure on the current price level. Kobayashi (2019), Sakuragawa (2019), Murase (2020), and Brunnermeier et al. (2020) also demonstrate that deflationary pressure is generated by the unsatisfied transversality condition in the consolidated government’s budget constraint. Hagedorn (2018) regards government bonds as net wealth in the sense that the bond valuation exceeds the present value of future fiscal surpluses, and presents a similar monetary model.

94

Public Bonds as Money Substitutes at Near-Zero …

In this way, strong money demand (beyond normal demand) in disequilibrium approach may be interpreted as the asset price bubble in equilibrium approach. Here is another comparison. If the consolidated government reimburses seigniorage to households as in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, then its budget constraint (Eq. (2.3)) is rewritten as: B s (t) − B s (t − 1) M s (t) − M s (t − 1) + P(t) P(t)   M s (t) − M s (t − 1) + tax(t) − P(t) d B (t − 1) + w(t)l gd (t). = g(t) + i(t) P(t) Accordingly, when money and public bond markets are all in equilibrium, the government’s life-time budget constraint (Eq. (2.11)) is rewritten as follows:   1 B s (t + τ ) B s (t) = b f (t) + lim τ τ →∞ P(t) k=0 (1 + ρ(t + k)) P(t + τ )

(2.15)

If excess supply in public bond markets by excess demand   isd exactlys cleared s (t) (t) (t) holds in disequilibrium = b f (t) + MP(t) − MP(t) in money markets, then BP(t) analysis. In this case, a comparison between equilibrium and disequilibrium analyses indicates that the excess demand in money markets corresponds to the public bond price bubble in Eq. (2.15):   1 M s (t) B s (t + τ ) M d (t) − = lim τ >0 τ →∞ P(t) P(t) k=0 (1 + ρ(t + k)) P(t + τ ) As explored in detail in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan”, the public bond price bubble   B s (t+τ ) 1 in Eq. (2.15) is finitely positive in a deflationary limτ →∞ τ (1+ρ(t+k)) P(t+τ ) k=0 economy with asymptotically zero rates of interest. A major reason for this finite positivity is intuitively clear. At the limit of deflationary equilibria with zero interest rates, the nominal balance of public bonds converges to a constant.11 Accordingly, the real balance of public bonds appreciates at the rate of deflation, equivalent to the real rate of interest at the zero nominal rate. Thus, its present value, discounted by the real rate ofs interest, converges to a constant, because both the numerator and B (t+τ )/P(t+τ ) grow at the same rate. As a realistic interpretation, the denominator in  τ k=0 (1+ρ(t+k)) consolidated government can roll over public bonds forever at zero interest rates with mild deflation. 11 If both the nominal rate of interest and the price level converge to zero in the limit, B(t)− B(t − 1) also converges to zero in Eq. (2.3).

2 A Simple Disequilibrium Analysis Framework

95

For the same reason, as long as the nominal balance of money stocks s s converges  to a constant in the limit (limτ →∞ M (t + τ ) = M ), another bubble term s 1 M is finitely positive as well. That is, as long as nominal limτ →∞ τ (1+ρ(t+k)) P(t+τ ) k=0 s seigniorage is zero in both i(t + τ )M s (t+ τ − 1)and M s (t + τ ) − M (t + τ − 1), s s B (t+τ )+M (t+τ ) is finitely the entire bubble term in Eq. (2.11) limτ →∞ P(t+τ ) τ (1+ρ(t+k)) k=0 positive. In other words, if the nominal money supply continues to grow, and M s (t + τ ) − M s (t + τ − 1) is always positive, then the bubble term explodes, and no equilibrium path can be found. In this way, the disequilibrium case where excess supply in public bond markets is absorbed by excess demand in money markets at near-zero interest rates can be interpreted as the equilibrium case where the price bubble term emerges in the government’s budgetconstraint with the transversality (terminal) condition unsat   B s (t+τ )+M s (t+τ ) 1 < ∞ . Here, both the QTM isfied 0 < limτ →∞ τ (1+ρ(t+k)) P(t+τ ) k=0  s    (t) f racM s (t)P(t) = m QT M and the FTPL BP(t) = b f (t) fail to hold, and the current price level has no close relationship with current money stocks or future fiscal surpluses. Conversely, with an increase in short-term interest rates, probably above 0.5%, strong money demand will disappear, leading to the bursting of the price bubble. This means that money demand instantaneously shrinks to normal QTM demand s (t) = b f (t) needs to be reimposed at the price level (m QT M ), and fiscal discipline BP(t) determined by the QTM. Now, let us interpret the current condition of the Japanese money markets using the insights developed above. The money (notes and reserves) issued at near-zero rates by the BOJ can be classified into two categories. The first category or interestfree money, denoted by M0s (t), includes the BOJ notes and legal reserves, both of which carry zero interest rates even if market rates of interest rise above zero. The second category or interest-bearing money, denoted by M+s (t), includes the reserves issued beyond the legal reserves, which bear the nominal rate of interest i t (t) in a situation with non-zero market rates. Thus, the second category of money is included in public bonds, more precisely floating-rate public bonds, from the viewpoint of the consolidated government. Given the above disequilibrium interpretation, excess supply in public bonds  s B (t)+M+s (t) − b f (t) is absorbed fully including potentially interest-bearing money  d P(t) s  M0 (t) (t) . Thus, the following − P(t) by excess demand in interest-free money MP(t) inequality holds: B s (t) + M+s (t) M s (t) M d (t) − 0 > − b f (t) P(t) P(t) P(t) Accordingly, once the short-term rate of interest is above zero, money and public bond markets need to clear as follows:

96

Public Bonds as Money Substitutes at Near-Zero …

M0s (t) = m QT M P(t)

(2.16)

B s (t) + M+s (t) = b f (t) P(t)

(2.17)

Equation (2.16) implies that as money demand abruptly shrinks upon an increase from zero in interest rates, the price level immediately jumps to the level determined by the QTM. Equation (2.17), on the other hand, shows that fiscal discipline needs to be established by fiscal reforms at the QTM price level. As discussed in detail in Sect. 3.3, if the consolidated government fails to commit to strict fiscal reforms, then the price surge will not be one-off, but the price process may end in hyperinflation. The above discussion suggests that inconsistency between the QTM and the FTPL emerges when excess money demand disappears. As emphasized by Buiter (2002) and Bassetto (2018), the price level is defined in terms of an inverse of real money demand in the former, but of future fiscal surpluses in the latter. If the latter does not coincide with the former, the price level needs to be consistent with the QTM price, and fiscal sustainability needs to be restored at the QTM price.

3 The Past and Future of Japan’s Economy from the Viewpoint of Disequilibrium Analysis In Sect. 3.1, Japan’s economy in the past quarter century is interpreted using the disequilibrium approach, which is presented in Sect. 2. Section 3.2 explores how strong money demand emerged in the near-zero interest rate environment; it first appeared as ‘demand for public bonds as money substitutes,’ and it then revealed itself as ‘demand for the central bank’s excess reserves.’ Consequently, the consolidated government’s liabilities to the public switched from JGBs to BOJ excess reserves. In Sect. 3.3, Japan’s future possibilities are investigated as an abrupt transition from the unconventional disequilibrium situation to the conventional equilibrium situation.

3.1 Excess Supply in Goods and Labor Markets and Massive Issues of Money and Public Bonds In this subsection, we carefully examine (1) how the consolidated government reduced bond markets by aggressively issuing money  s   s  excess demand in money/public M (t) B (t) and public bonds P(t) in the right-hand side of Eq. (2.6), (2) how it P(t) s dissolved excess supply in goods and labor markets (E x gl (t)) in the left-hand side of Eq. (2.6) by expanding government consumption (G(t)) and employment (L dg (t)),

3 The Past and Future of Japan’s Economy … 25

97 8%

20

6%

trillion yen (constant 2011 price)

15 4% 10 2%

5 0

0%

-5

-2%

-10 -4% -15 -6%

-20

-8%

-25

Real excess supply in goods markets (trillion yen, constant 2011price) Real excess supply in labor markets (trillion yen, constant 2011 price) Real excess supply in goods/labor markets (relative to real GDP, %, right scale)

Fig. 5 Excess supply in goods and labor markets, 1983–2018. Notes (1) Real excess supply in G D Pgap goods markets is computed by real GDP multiplied by 1−G D Pgap , where the GDP gap is defined D P−actualG D P by potentialG , and estimated by Kawamoto et al. (2017) and their updates. See Note potentialG D P 1 in Fig. 1. (2) Real excess supply in labor markets is computed by real labor income multiplied ad justedunemploymentrate by r eallaborincome × 1−ad justedunemploymenrrate , where the adjusted unemployment rate is set at the actual unemployment rate minus 2%, and the compensation of employees, compiled by ESRI (2018, 2020), is employed for real labor income

and (3) how it simultaneously coordinated the former fiscal and monetary policy with the latter economic stimulus. Let us first estimate the scale of excess supply in goods and labor markets. Given potentialout put−actualout put as the definition of output gap rate, the scale of excess potentialout put out putgap 12 supply in goods markets can be computed by r ealG D P × 1−out . Similarly, putgap the scale of excess supply in labor markets can be calculated by r eallaborincome × unemploymentrate . Here, the natural rate of unemployment is heroically assumed to be 1−unemploymentrate 2%, and the actual unemployment rate is adjusted by 2%, while real labor income is approximated by the nominal compensation of employees, deflated by the household final consumption deflator excluding imputed rents. Figure 5 plots excess supply in goods and labor markets respectively and adds the total excess supply in goods and labor markets relative to real GDP. After goods markets were clearly in excess demand in years FY1988 to FY1992, they frequently experienced a serious excess supply situation. In particular, the relative scale of excess supply rose in years FY1993 to FY1994, FY1998 to FY1999, FY2001 to

12 Estimates

for the output gap are from Kawamoto et al. (2017), and their updates.

trillion yen

98

Public Bonds as Money Substitutes at Near-Zero … 800

15%

700

12%

600

9%

500

6%

400

3%

300

0%

200

-3%

100

-6%

0

-9%

Balance of JGBs issued to the private sector by the government (trillion yen) Balance of the monetary base (trillion yen) Increment in the consolidated government's debt issued to the private sector (relative to nominal GDP, %, right scale) Real excess supply in goods/labor markets (relative to real GDP, %, right scale)

Fig. 6 Excess supply in goods and labor markets and the issue of money and JGBs, 1983–2018. See Note 1 in Fig. 1 and Notes 1 and 2 in Fig. 5 for the data sources

FY2002, and FY2008 to FY2009. On the other hand, it declined considerably from FY2010. Given that both money markets and public bond markets in disequilibrium at   are M d (t) near-zero rates, it is difficult to identify money demand P(t) and public bonds  d  (t) demand BP(t) = b f (t) separately. Thus, an increment in the issues of money and public bonds ([M s (t) + B s (t)] − [M s (t − 1) + B s (t − 1)]) is regarded as a proxy for a reduction in excess demand in money/public bond markets. Figure 6 plots the series of the nominal balance of public bonds, excluding the BOJ’s own JGBs, and the monetary base, consisting of BOJ notes and reserves, and adds the increment to the issues of money and public bonds, relative to nominal GDP, as well as that of excess supply in goods and labor markets, relative to real GDP. According to this figure, the consolidated government aggressively issued public bonds to the private sectors up to FY2012, and increased the monetary base from FY2013, thereby attempting to reduce excess demand in money/public bond markets. Figure 7 depicts the scale of government consumption and employment, relative to real GDP, both of which are included in the government final consumption. According to this figure, the government constantly expanded government consumption and employment from the mid-1990s. Let us examine Figs. 6 and 7 year-by-year in more detail. In response to a rise in excess supply in goods and labor markets in FY1993 to FY1994, and FY1998 to FY2002, the government issued large amounts of public bonds in the following

3 The Past and Future of Japan’s Economy …

99

22%

20%

18%

16%

14%

12%

Fig. 7 Real government final consumption expenditure, 1980–2018 (relative to real GDP, unit: %). Notes (1) Government final consumption expenditure is estimated by ESRI (2009, 2019). (2) Grey blocks imply the period in which there emerged excess supply in goods and labor markets

years while concurrently expanding government consumption, thereby attempting to dissolve both excess demand and excess supply simultaneously. On the other hand, in response to an excess supply surge from FY2008 to FY2009, the consolidated government first issued public bonds up to FY2012, and then replaced them with BOJ reserves after FY2013. The above aggressive policy response to expansion in the excess supply in goods and labor markets forms a sharp contrast with the passive response to the excess demand surge from FY1988 to FY1992. In the latter period, the consolidated government did not reduce its issues of money and public bonds and was reluctant to scale down aggregate demand. Accordingly, that excess demand situation continued in goods and labor markets for as long as five years. There is one more remark on the above analysis. According to Eq. (2.6), excess supply in goods and labor markets corresponds one-to-one to excess demand in money/public bond markets; however, this neat equality was not observed in practice during the period of our study. Inside and outside lags may be responsible for this inconsistency; that is, it takes some time for a government to form a particular policy, and for such a policy to yield noticeable effects on the macroeconomy.

100

Public Bonds as Money Substitutes at Near-Zero …

3.2 The BOJ’s Issues of Money and Its Purchases of Public Bonds in the Near-Zero Interest Rate Environment As discussed in Sect. 2, strong money demand from the public, induced by near-zero rates of interest, absorbs not only conventional money such as central banknotes and reserves, but also public bonds as money substitutes. In this subsection, we examine how such strong money demand is revealed as ‘demand for JGBs as money substitutes,’ and ‘demand for BOJ notes and reserves.’ Because the public (mainly the private banks) are almost indifferent between holding money and investing public bonds at near-zero rates, no particular equilibrium path can be picked up theoretically. From the viewpoint of the public, strong money demand was revealed as follows: (1)

(2)

After short-term interest rates fell below 0.5% in mid-1995, demand for BOJ notes gradually expanded. In addition, the private banks began to make large purchases of long- and ultra-long-term JGBs. They anticipated that long-term yields would decline toward near-zero quickly. In this period, strong money demand appeared partly as demand for BOJ notes, and largely as demand for JGBs as money substitutes. (Sects. 3.2.1, 3.2.2, and 3.2.3) Under QQE, starting in April 2013, private banks aggressively exchanged their own JGBs for deposits at the BOJ excess reserves. In this period, strong money demand appeared as demand for BOJ excess reserves. (Sect. 3.2.3).

From the viewpoint of the BOJ, however, the following monetary operations accommodated strong money demand from the public. (3)

(4)

Aggressive BOJ’s purchases of JGBs initially helped to refinance its own JGBs at maturity, but they later contributed to an expansion of the BOJ’s holdings of JGBs. (Sect. 3.2.3 and appendix to this chapter) While the balance of BOJ notes expanded gradually from mid-1995, the balance of BOJ reserves swelled from early 2009, and accelerated after the BOJ implemented QQE in April 2013. (Sect. 3.2.2).

In this way, strong money demand from private banks was initially revealed largely as ‘demand for JGBs as money substitutes’ with the expectation by the private banks of quick declines in long-term yields. Then, ‘demand for JGBs’ was later replaced by ‘demand for BOJ excess reserves’ among private banks. It is often fallaciously believed that the BOJ directly underwrote new issues of JGBs from the beginning. However, it was ‘demand for JGBs as money substitutes’ from the private banks that initially helped large-scale public finance, whereas it was the private banks’ ‘demand for BOJ excess reserves’ that later replaced their earlier ‘demand for JGBs.’ From FY1999, the BOJ was indeed forced to accept a challenging target for purchases of long-term JGBs by the government. The target for purchases of JGBs with shorter than three-year maturity was initially set at 0.4 trillion yen per month, but was raised to 0.6 trillion yen in August 2001, 0.8 trillion yen in December 2001, 1.0 trillion yen in February 2002, 1.2 trillion yen in December 2008, and 1.8 trillion

3 The Past and Future of Japan’s Economy …

101

yen in March 2009. In October 2010, another 1.5 trillion yen per month was added to the above target. Under QQE starting in April 2013, the maturity of JGBs was extended from three years to seven years, while the monthly target was raised to 7 trillion yen. In October 2014, maturity was further extended to ten years, while the monthly target was raised to between 8 and 12 trillion yen. As discussed in detail in the appendix to this chapter, the above large BOJ purchases of JGBs contributed mostly to the redemption of the BOJ’s own JGBs at maturity before QQE began in April 2013. After that, they contributed largely to increments in the BOJ’s own JGBs by replacing ‘demand for JGBs as money substitutes’ from the private banks.

3.2.1

Creation of the Near-Zero Interest Rate Environment

Now, let us look back in more detail at the dramatic changes in the rate of interest starting in the 1990s. As demonstrated in Fig. 4, the short-term rate of interest declined quickly in the first half of the 1990s. The uncollateralized overnight call rates, which are inter-bank rates and the most representative short-term rates, peaked at 8.28% in March 1991, and dropped to 0.47% in October 1995. When the BOJ adopted a ZIRP in February 1999, the call rate was between 0.02 and 0.03%. When the BOJ terminated the ZIRP in August 2000, the call rate increased to above 0.2%. 0.6

0.5

0.4

0.3

0.2

0.1

0.0

-0.1

Fig. 8 Call rate (uncollateralized overnight rate), January 2000–November 2019 (unit: %). See Note 1 in Fig. 4 for the data sources

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Public Bonds as Money Substitutes at Near-Zero …

3.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

3-year versus 1-year 15-year versus 1-year

5-year versus 1-year 20-year versus 1-year

10-year versus 1-year

Fig. 9 Yield spread in JGBs, January 1999–November 2019 (versus one-year yield, unit: %). See Note 2 in Fig. 4 for the data sources

As shown in Fig. 8, when the BOJ began quantitative easing (QE) in March 2001, the call rate was set at almost zero, or between 0.000 and 0.002%. When the BOJ terminated QE in March 2006, the call rate rose to around 0.5%. Upon the collapse of Lehman Brothers in September 2008, however, the call rate was lowered to 0.3% in October 2008, and to 0.1% in December 2008. It had been below 0.1% since March 2009. As the BOJ adopted a negative interest rate policy (NIRP), the call rate had been between − 0.04% and − 0.07% since February 2016. Near-zero rates extended to not only short-term interest rates, but also to medium, long-, and even ultra-long-term yields. According to Fig. 9, the yield spreads, measured in terms of n-year yields versus one-year yields, tended to shrink except for the period between 2003 and 2004 summer.13 For example, ten-year versus oneyear yield spreads peaked at above 1.5% in July 2004, but shrank consistently after that. They stayed at around 1% from 2008 to 2011 and dropped to below 0.5% in mid-2014. Since the BOJ implemented NIRP in February 2016, the yield spread has been below 0.3%. As discussed in Sect. 3.3, long-term interest rates declined more slowly than short-term ones, maybe because longer-term yields reflected possible price surges upon the disappearance of strong money demand in the (far) future, as discussed in chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary 13 According to Nakayama et al. (2004), rapid rises in long- and ultra-long-term yield spreads in mid2004 were triggered by an increase in US long-term yields, and the market participants’ expectation that QE would be terminated quite soon (though it actually ended in March 2006).

3 The Past and Future of Japan’s Economy …

103

450

80

400 60 350 300

40

250 20 200 150

0

100 -20 50 -40

0

BOJ notes issued

BOJ current accounts

Increment in BOJ notes (right scale)

Increment in BOJ current accounts (right scale)

Fig. 10 Balance and increment in BOJ notes and current accounts, 1979–2018 (unit: trillion yen). See Note 1 in Fig. 2 for the data sources

Japan”.14 In any way, not only T-bills, but also medium-, and (ultra) long-term JGBs became eventually closer substitutes for interest-free money.

3.2.2

Aggressive Issues of the BOJ Notes and Reserves

As mentioned above, strong money demand from the public, induced by near-zero rates, was revealed gradually and partly as ‘demand for the BOJ notes.’ As shown in Fig. 10, while the call rate stayed below 5% from FY1986 to FY1989, the balance of the BOJ notes expanded by 3 trillion yen per year. It expanded much faster when the call rate was near-zero from FY1995 to FY2005. After the call rate increased with the termination of QE in FY2006, the BOJ notes increased slowly, but it expanded again after the BOJ set the call rate at below 0.1% in FY2009. On the other hand, the private banks, which are much more sensitive to interest rates than are households, want to keep their BOJ reserves at the legally required level as long as the call rate is quite low, but still above zero. As shown in Figs. 8 and 10, the private banks never held excess reserves at the BOJ in the second half of the 1990s, when the call rate was still above zero. When the call rate was quite close to zero under the ZIRP (from February 1999 to August 2000) and QE (from March 14 Chapter “Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan” explores in a theoretically rigorous manner how longer-term yields decline toward zero slowly given the expectation that the public bond price bubbles will burst in the (far) future.

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Public Bonds as Money Substitutes at Near-Zero …

2001 to March 2006), the balance of BOJ reserves expanded temporarily, but shrank again to the legal reserve limit upon their termination. In October 2008, the BOJ introduced the Complementary Deposit Facility (CDF), in which 0.1% interest was added on the excess reserves (the BOJ reserves in excess of the legal reserves). Thus, the private banks had an incentive to deposit beyond the legal reserves, as long as the market rate was below 0.1%. As shown in Fig. 8, the call rate was still above 0.1%, when the CDF was introduced in October 2008. Accordingly, the BOJ reserves never exceeded the legal reserve limit. After March 2009, however, the call rate was below 0.1%, and excess reserves emerged at the BOJ. The balance of BOJ reserves was 17.3 trillion yen in FY2010, and 23.7 trillion yen in FY2012. In particular, the balance of BOJ reserves expanded annually by around 70 trillion yen after the QQE was introduced in April 2013 (see Fig. 10). However, when the BOJ introduced a NIRP in February 2016, 0.1% interest was no longer added to the excess reserves newly deposited by the private banks, and even –0.1% interest was added on a part of the excess reserves. From FY2016, the balance of BOJ reserves expanded much more slowly; they increased by 67.3 trillion yen in FY2016, 35.5 trillion yen in FY2017, and 15.6 trillion yen in FY2018.

3.2.3

Aggressive Purchases of Long-Term JGBs by the BOJ

Then, let us examine how the BOJ accommodated such strong money demand from the public. As discussed above, strong money demand from private banks was initially revealed mainly as ‘demand for public bonds as money substitutes,’ rather than as ‘demand for BOJ reserves.’ According to Fig. 11, an increment in the BOJ’s own JGBs (black solid line) occupied only a part of the annual issues of JGBs (grey bar) before FY2012, except for FY2001. In FY2001, the BOJ could finance large-scale purchases of JGBs by additional excess reserves from initiating QE. As shown in Fig. 12, the balance of non-BOJ’s own JGBs (thick grey bar) grew much faster than the balance of the BOJ’s own JGBs (thin grey bar). When the BOJ adopted QQE in April 2013, the above trend was reversed. As strong money demand from private banks switched from ‘for public bonds as money substitutes’ to ‘for BOJ excess reserves,’ the BOJ made aggressive purchases of long-term JGBs from private banks. While the government raised the issues of JGBs by 34.6 trillion yen in FY2013, 44.5 trillion yen in FY2013, and 34.3 trillion yen in FY2015, the BOJ expanded its purchase of JGBs by 73.2 trillion yen, 73.5 trillion yen, and 89.8 trillion yen, respectively (see Fig. 11). The BOJ matched this rapid increase in its JGB purchase by an increment in excess reserves. Consequently, the balance of the BOJ’s own JGBs increased from 127.9 trillion yen at the end of FY2012 to 486.0 trillion yen at the end of FY2018, but the balance of non-BOJ’s own JGBs shrank from 731.2 to 538.9 trillion yen in the same period (see Fig. 12). As shown in Fig. 13, under QQE starting from FY2013, the BOJ purchased longterm JGBs from private banks, but sold them T-bills (short-term bonds). Accordingly, the holdings of long-term JGBs concentrated more and more on the BOJ. In FY2018,

3 The Past and Future of Japan’s Economy …

105

100

80

60

40

20

0

-20

-40

Increase in JGBs issued by the government Increase in JGBs held by the BOJ Increase in the monetary base

Fig. 11 Increase in JGBs issued by the government, those held by the BOJ, and the monetary base, 1980–2018 (unit: trillion yen). See Note 1 in Fig. 2 for the data sources 1,200

1,000

800

600

400

200

0

Outstanding JGBs held by non-BOJ

Outstanding JGBs held by the BOJ

Fig. 12 Outstanding JGBs held by the BOJ and non-BOJ, 1980–2018 (unit: trillion yen). See Note 1 in Fig. 2 for the data sources

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Public Bonds as Money Substitutes at Near-Zero …

700 600 500 400 300 200 100 0

Outstanding short-term JGBs held by non-BOJ

Outstanding short-term JGBs held by the BOJ

Outstanding long-term JGBs held by non-BOJ

Outstanding long-term JGBs held by the BOJ

Fig. 13 Outstanding short-term and long-term JGBs held by the BOJ and non-BOJ, 1980–2018 (unit: trillion yen). See Note 1 in Fig. 2 for the data sources

the balance of the BOJ’s own long-term JGBs (475.6 trillion yen) dominated the balance of non-BOJ’s own long-term JGBs (451.8 trillion yen). In this way, the consolidated government’s liabilities to the public by JGBs were replaced largely by those by BOJ notes and reserves.

3.3 The Outlook for Demand for Money and Public Bonds In this subsection, we explore how the price level would behave if strong money demand disappeared abruptly at above-zero interest rates. In the disequilibrium framework, which is presented in Sect. 2.3, excess supply in goods and labor markets is accommodated by excessdemand in money/public d (t) corresponds to not only bond markets. Accordingly, real money demand MP(t)  s  (t) real money supply in a narrow sense MP(t) , but also real public bonds as money  s  (t) substitutes BP(t) − b f (t) , where the BOJ’s own JGBs are excluded in B s (t), and   s excess supply in goods and labor markets E x gl (t) . More concretely, the following real money demand function is obtained from Eqs. (2.6) and (2.7):

3 The Past and Future of Japan’s Economy …

  s M s (t) B (t) M d (t) f s = + − b (t) + E x gl (t) P(t) P(t) P(t)

107

(3.1)

Equation (3.1) may be standardized by real output (y(t)) as:   s E x gl (t) M d (t) M s (t) B s (t) b f (t) = + − + , P(t)y(t) P(t)y(t) P(t)y(t) y(t) y(t)

(3.2)

where real GDP and the household final consumption deflator are used for y(t) and P(t). How is the above real money demand function drawn? Among the variables on the right-hand side of Eq. (3.2), both M s (t) and B s (t) are directly observable, and s excess supply in goods and labor markets (E x gl (t)) can be computed as discussed in Sect. 3.1. Here, the present value of future fiscal surpluses (b f (t)), equivalent to demand for JGBs as investment instruments, is estimated by the following heroic approximation. First, real demand for JGBs as money substitutes is assumed to be s (t) −b f (t) = 0 zero up to FY1994, when interest rates were well above zero. That is, BP(t) before FY1994. demand for JGBs as investment instruments, standardized   Second, f (t) = bˆ f (t) , is assumed to be constant from FY1995 on, and it by real GDP by(t) may be approximated by the FY1983–FY1994 average of the real balance of public bonds. That is, bˆ f (t) ≈ 0.392 after FY1995. The second assumption is justified later more carefully. In Fig. 14a, real money demand specified by Eq. (3.2) is drawn against the call rate (i(t)). According to this figure, real money demand is almost constant at around 9% of real GDP when the call rate is above 0.5%, but is almost infinitely elastic when the call rate is below 0.5%. Given the above shape of real money demand in a broad sense, the following four policy scenarios are available for the consolidated government as demonstrated in Fig. 14b. Scenario 1: The (consolidated) government maintains near-zero interest rates, and then attempts to reduce excess supply by issuing large volumes of money and public bonds. Scenario 2: The government maintains near-zero interest rates, but then gradually retires money and public bonds from markets. Scenario 3: The government fails to maintain near-zero rates. Then, the price level jumps with shrinking money demand, and the government implements fiscal reforms as a result of the disappearance of strong money demand for public bonds as money substitutes. Scenario 4: The government fails to maintain near-zero rates, but also fails to commit to future fiscal reforms. Then, the price process escalates toward hyperinflation. In the past quarter century, the Japanese government and BOJ have developed Scenario 1-like fiscal and monetary policies. A dilemma associated with Scenario

108

Public Bonds as Money Substitutes at Near-Zero … 9

a

8

90

7

91 85 83 84 89

6

Call rate (%)

5 86 92 88

4

87

3

93 94

2 1

95 96

97

0 0%

98

20%

99 00

40%

-1

01

02

03

60%

06 0405

07

80%

08

100%

09

10

11

120%

12 13 15 14 16 1718

140%

160%

Real money demand in a broad sense (relative to real GDP)

b9 8 7

Call rate (%)

6 5 4 3

Scenario 4

2

Scenario 3 1

Scenario 2

0 0% -1

20%

40%

60%

80%

Scenario 1 100%

120%

140%

160%

180%

200%

220%

Real money demand in a broad sense (relative to real GDP)

Fig. 14 a Real money demand in a broad sense, 1983–2018. See Note 1 in Fig. 1, Note 1 in Fig. 2, and Note 1 in Fig. 4 for the data sources. b Four major scenarios. See Note 1 in Fig. 14a

3 The Past and Future of Japan’s Economy …

109

1 is that it had been adopted to escape from a deflationary economy with near-zero interest rates, but required that economic environment as a precondition. In other words, the economy did not escape from a liquidity trap, but it instead got more deeply into the trap under this scenario. Because Scenario 1 was adopted for such a lengthy period, it may be difficult for the government to admit the policy dilemma, hindering a switch from Scenario 1 to Scenario 2 in the near future. What would happen if the government made mistakes in either monetary or fiscal policy? In Scenario 3, the BOJ fails to maintain near-zero interest rates, but the government succeeds in committing to strict fiscal reforms. Below, we investigate how much the price level would adjust, and to what extent fiscal reforms would be required, if Scenario 3 were adopted. For this purpose, as discussed in Sect. 2.4, the BOJ notes and reserves are divided into interest-free money (M0s (t)) and potentially interest-bearing public bonds (M+s (t)). M0s (t) includes BOJ notes and the legal reserves, both of which are interest-free by nature, while M+s (t) includes BOJ excess reserves, the latter of which are floating-rate bonds. Once interest rates take off from zero, not only conventional public bonds, but also excess reserves constitute interest-bearing public bonds for the consolidated government. As in Eq. (3.2), nominal variables are adjusted by both the household final consumption deflator (P(t)) and real GDP (y(t)), while real variables are adjusted by real GDP. Thus, Eq. (3.1) is rewritten as follows: b f (t) M0s (t) M d (t) + = P(t)y(t) y(t) P(t)y(t)   s E x gl (t) M+s (t) B s (t) + + . + P(t)y(t) P(t)y(t) y(t) If the BOJ is unable to control interest rates at near-zero, then strong money demand disappears immediately. Accordingly, there is no room for money demand to accommodate swollen money and public bonds supply. The real balance of interestfree money stocks needs to shrink to normal money demand as follows: m QT M (t) M0s (t) = = mˆ QT M , P(t)y(t) y(t)

(3.3)

where it is assumed that normal real money demand (m QT M (t)) has unit incomeQT M elasticity, and that not m QT M (t), but m y(t)(t) is constant at mˆ QT M . Consequently, the price level is upward adjusted immediately so that Eq. (3.3) can hold, while the nominal rate of interest jumps to the long-run inflation rate plus the real discount rate. In this way, the QTM applies immediately at above-zero interest rates. At the price level determined by Eq. (3.3), on the other hand, the present value of future fiscal surpluses needs to improve until it fully backs the real balance of interest-bearing public bonds as follows:

110

Public Bonds as Money Substitutes at Near-Zero … ∞

B s (t) + M+s b f (t) 1 P(t + τ )[T (t + τ ) − G(t + τ )]  = = P(t)y(t) y(t) P(t) τ =1 y(t + τ ) τk=1 (1 + i(t + k))

(3.4)

Here, only the government’s strong commitment to fiscal reforms enables Eq. (3.4) to hold. To sum up, once the rate of interest takes off from zero, and strong money demand disappears immediately, the QTM, represented by Eq. (3.3), is immediately in force, while Eq. (3.4) has to hold strictly without any public bond price bubble unlike in Eqs. (2.11) and (2.14). f (t) Then, how should mˆ QT M in Eq. (3.3) and by(t) in Eq. (3.4) be computed? Figure 15  s  M0 (t) plots the series of the real balances of interest-free money stocks P(t)y(t) and  s  B (t)+M+s interest-bearing public bonds P(t)y(t) . According to this figure, both real balances remained almost constant in the period between FY1983 and FY1994, during which time interest rates were well above zero. As shown in Fig. 5, excess demand in goods and labor markets and excess supply in money/public bond markets were present in f B s (t)+M s M0s (t) (t) + P(t)y(t)+ > mˆ QT M (t) + by(t) . Thus, the period FY1988 to FY1992; that is, P(t)y(t) the FY1983–FY1994 average of these series may be reasonably interpreted as the 200%

25.0%

180%

22.5%

160%

20.0%

140%

17.5%

120%

15.0%

100%

12.5%

80%

10.0%

60%

7.5%

40%

5.0%

20%

2.5%

0%

0.0%

Real balance of JGBs (excluding those held by the BOJ) and BOJ excess reserves (relative to real GDP, %) Real balance of BOJ notes and legal reserves (relative to real GDP, %, right scale)

Fig. 15 Real balance of BOJ notes and legal reserves, and real balance of JGBs and BOJ excess reserves, 1983–2018 (relative to real GDP, %). Notes (1) See Note 1 in Fig. 1, Note 1 in Fig. 2, and Note 1 in Fig. 4 for the data sources. (2) Nominal balances are deflated by the household final consumption expenditure excluding imputed housing rents. (3) The thick dotted line represents the FY1983–FY1994 average of relative real demand for JGBs, while the thin dotted line represents that of relative real money demand

3 The Past and Future of Japan’s Economy …

upper limit of mˆ QT M and b f (t) y(t)

b f (t) . y(t)

111

It is accordingly assumed that mˆ QT M ≤ 8.9% and

≤ 39.2%.

Let us now take the value of the two real balances at the end of FY2018; B s (t)+M+s P(t)y(t)

M0s (t) P(t)y(t)

=

= 166.2% . If the price level is determined by Eq. (3.3), it needs 22.1% and   ≈ 2.5 . Given to be at least 2.5 times as high as before with real output constant 22.1% 8.9% the price level to satisfy Eqs. (3.3), fails to hold;  interest-bearing public bond  (3.4) B s (t)+M+s b f (t) markets remain in excess supply P(t)y(t) > y(t) . However, if the present value f of future fiscal  22.1%surpluses   (b (t)) is multiplied by 1.7, then Eq. (3.4) strictly holds  166.2% / 8.9% ≈ 1.7 . In this way, with the government’s strong commitment to 39.2% future fiscal reforms, the price level would jump only once before rising gradually according to monetary growth or the QTM. In Scenario 4, the government fails to commit to future fiscal reforms. In the absence of any fiscal reform, Eq. (3.4) can by the price level rising   only be satisfied ≈ 4.2 . In this case, Eq. (3.3) fails rapidly at least 4.2 times its prior level 166.2% 39.2% to hold at the price level determined by Eq. (3.4), and excess demand emerges in M0s (t) < mˆ QT M . Then, the hyperinflationary process interest-free money markets, or P(t)y(t) is initiated to fix excess money demand; inflation accelerates, interest rates continue to rise, and real money demand shrinks toward zero. Another scenario, theoretically narrowly justifiable, but practically highly unlikely, excess ininterest-free/interest-bearing public bond markets   supply    d is that M+s (t) M0s (t) M (t) b f (t) B s (t) − < 0 would be absorbed by + + + P(t)y(t) y(t) P(t)y(t) P(t)y(t) P(t)y(t)  E x s (t)  gl excess demand in goods and labor markets < 0 . One serious problem of y(t) this scenario is that the excess demand needs to be extremely large to accommodate the excess supply. Given the above assumptions, the size of excess supply in goods and labor markets would be 140.2% of real GDP: (8.9% − 22.1%) + (39.2% − 166.2%) = −140.2%. Although this scenario is obviously unrealistic, it has often been discussed among Japanese politicians and bureaucrats in the context of pro-growth economic policy-making.

4 Conclusion Let us return to our original question. Are unconventional policies such as ‘borrowmore-repay-less’ and ‘repay-by-central-bank-money’ theoretically justifiable? Our answer is both yes and no. In some way, those policies are justifiable to the extent that the mildly deflationary environment with near-zero rates continues for a lengthy period. Large-scale economic stimulus financed by massive issues of money and public bonds surely works to reduce excess supply in goods and labor markets and excess demand in money/public bond markets simultaneously. Without any noticeable effect on the price level, strong money demand, induced by near-zero interest rates, can absorb

112

Public Bonds as Money Substitutes at Near-Zero …

not only central banknotes and reserves, but also public bonds as money substitutes. Such policy consequences exhibit a striking contrast to conventional implications from the QTM and FTPL. However, unconventional policies carry inherent contradictions. In the presence of strong money demand, the economy is likely to fall into a state of weak aggregate demand. Unconventional policies can deal with this stagnant state temporarily, but they never remedy it fundamentally. In addition, frequent repetition of these policies contributes to a large shift of financial resources from the private to the public sector. The private deposit-taking banks, including the Japan Post Bank (Yucho Ginko in Japanese), loaned less to the private sector, but more to the government and BOJ in the form of JGBs and BOJ notes and reserves. According to Fig. 16, the loans to the public sector accounted for only 5.7% of the total assets at the end of FY1994, but exceeded 20% at the end of FY2007 and 28% at the end of FY2014. An even more fundamental dilemma is that the unconventional policies are implemented to escape from a deflationary economy with near-zero rates, but require such a particular economic environment as a precondition. As discussed in detail in Sect. 2, once an economy takes off from a deflationary state, strong money demand disappears immediately. In this case, there is no room for money demand to absorb large issues of money stocks or public bonds. While the rate of interest was below 0.5%, large real balances of interest-free money stocks (BOJ notes and legal reserves) and potentially interest-bearing public bonds (JGBs and BOJ excess reserves) could be 80% 70% 60% 50% 40% 30% 20% 10% 0%

Credit to the private sector

Credit to the consolidated government (the general government and the BOJ)

Fig. 16 Share of private deposit-taking banks’ credit to the private sector and the consolidated government, 1980–2018 (relative to the total assets, unit: %). Notes (1) See Note 1 in Fig. 2 for the data sources. (2) The private deposit-taking banks exclude Japan Post, but include the Japan Post Bank

4 Conclusion

113

accumulated. In a normal economy with interest rates above 0.5%, however, it would be impossible to accommodate that level of money stocks and public bonds without price surging or strict fiscal reforms. If the government failed to commit credibly to future fiscal reforms, then the price path would be hyperinflationary. One of the most important policy implications in this chapter is that the public often feel that they were relieved from any future tax obligation thanks to the unconventional policies, but they will eventually have to repay the large amount of public bonds on issue. With a price surge, the public would sacrifice considerable purchasing power whereas, with strict fiscal reforms, they would pay taxes anyway. Without any successful fiscal reform, they might even lose purchasing power irretrievably as a consequence of hyperinflation.

Appendix: How Did the BOJ de facto Refinance Its Own JGBs at Maturity? In this appendix, we show that strong money demand, together with rapidly declining yields on long-term JGBs, helped the BOJ to refund de facto its own JGBs at maturity, without violating any strict restriction imposed by the Public Finance Act. Under the Public Finance Act, the BOJ is prohibited from directly refinancing long-term JGBs for the government.15 The BOJ usually finances a purchase of T-bills, long-term JGBs, and other bonds through either increments to the BOJ’s current accounts (CAs), which are largely reserve deposits, or additional issues of BOJ notes. Accordingly, the BOJ’s net purchases of JGBs almost match increases in the monetary base, which consists of the BOJ notes and CAs. As Fig. 17 shows, however, the BOJ’s net purchases of JGBs and other government liabilities (dotted line) has exceeded changes in the monetary base (solid line) considerably since FY1999. In particular, the former surpassed the latter by more than 100 trillion yen from FY2013. As shown below, these differences have contributed to the BOJ’s de facto refinancing of its own JGBs at maturity. What was happening to the above transactions among the BOJ, government, and private banks is explained as follows: (1) (2)

The government issued new JGBs to private banks to raise funds for redemption of the BOJ’s own JGBs at maturity. The BOJ received funds from the government as a result of redemption of its own JGBs, and appropriated those funds for purchases of newly issued JGBs from private banks.

The above transactions among the BOJ, government, and private banks meant that a net purchase of JGBs by the BOJ was recorded positive in the Market Operations Statistics (MOS), which is compiled by the Financial Markets Department of the 15 However,

the Public Finance Act allows the BOJ to underwrite and refund T-bills for the government directly.

114

Public Bonds as Money Substitutes at Near-Zero …

250

200

150

100

50

0

-50

Change in the monetary base

BOJ's net pruchase of JGBs and other assets

Fig. 17 Changes in the monetary base and the BOJ’s net purchase of JGBs and other assets, 1985– 2018 (unit: trillion yen). Note (1) The MOS, which are compiled by Financial Markets Department, BOJ (2003–2019), report the sources of changes in current accounts at the BOJ

BOJ, but changes neither in the BOJ CAs nor in the balance of the BOJ’s own JGBs appeared in the MOS. Here, withdrawals from the CAs, which are accompanied by new issues of JGBs to private banks by the government, are cancelled out by payments on the CAs, which results from purchases of the same amount of JGBs by the BOJ. In addition, the JGBs maturing at the BOJ were replaced by those purchased from the private banks by the BOJ. Consequently, the BOJ’s net purchases of JGBs were positive in spite of no change in the BOJ CAs under the BOJ’s de facto refinancing of its own JGBs at maturity. Why did the private banks participate in such an irregular refunding of JGBs by the BOJ? Again, strong money demand, driven by near-zero interest rates, helped substantially. The private banks could temporarily absorb newly issued JGBs as money substitutes. In addition, given that long-term yields on JGBs were expected to decline quickly toward zero, the private banks could enjoy capital gains by holding long-term JGBs for an even brief period. Let us describe more precisely how the above de facto refinancing by the BOJ was recorded in the MOS using Fig. 18. The MOS records transactions among the BOJ, government, and private banks in terms of changes in the BOJ CAs. An increase in BOJ notes (ginko-ken yoin in Japanese) is recorded negative because the BOJ notes are withdrawn from the BOJ CAs by the private banks [(8) in Fig. 18]. The BOJ’s net purchases of T-bills, JGBs, and other bonds (kin-yu chosetsu), on the other hand, are recorded positive because the BOJ makes payments on the CAs ((1), (1 ), and (1 )).

Appendix: How Did the BOJ de facto Refinance Its Own JGBs at Maturity?

115

(1’) Net purchase of JGBs from banks

BOJ’s Excess Reserves (1’’) Net purchase of securities from financial markets

Treasury Funds

BOJ’s Legal Reserves

(1) Net purchase of JGBs from banks

(2) Taxes/public insurance premiums and funds raised by issuing JGBs (3) Fiscal expenditure, and redemption of JGBs held by private agents

(4) BOJ’s taxes and payment

BOJ’s own (5) Redemption of JGBs held by BOJ

accounts

(6) Depositing

Government Deposits

Private Non-Financ ial Agents

Private Financial Institutions

(7) Deposits from households and firms fi

BOJ Notes

(8) Net issue of BOJ notes

Fig. 18 Relationship between the Treasury and the private sector, which is intermediated by the BOJ. Note (1) The author constructed this figure based on Policy Research Institute, MOF (1981– 2018), and Financial Markets Department, BOJ (2008)

An increase in the Treasury Funds (TFs), caused by payments of taxes and public insurance premiums by private agents, and funds raised by issuing JGBs to the public including the private banks ((2)), is recorded negative as a result of withdrawals from the CAs by private banks, while a decrease in the TFs, caused by fiscal expenditures, and redemption of JGBs held by private agents ((3)), is recorded positive as a result of payments on the CAs by the government.

116 250 200 150 100 50

Public Bonds as Money Substitutes at Near-Zero … (i) Changes in the BOJ notes (-(8)) (ii) Changes in the Treasury funds ((3)-(4) = -(5)-(6)) (iii) Changes in the BOJ current accounts (iv) BOJ's net purchases of JGBs and other assets ((1)+(1')+(1'')) (iv) - (iii) (i) + (ii)

0 -50 -100 -150

Fig. 19 BOJ’s market operations, 1985–2018 (unit: trillion yen). Note (1) See Financial Markets Department, BOJ (2003–2019) for the MOS

Usually, net changes in the TFs (zaisei tou yoin) are almost zero because an increase in the TFs is approximately cancelled out by its decrease during a given fiscal year.16 However, when the government issues JGBs to redeem the BOJ’s own JGBs at maturity, (1) net changes in the TFs need to be positive, (2) most of the increase in TFs goes to the BOJ’s own accounts to facilitate redemption ((5)), (3) the remainder is put into government deposits at the BOJ ((6)), and (4) the BOJ finally finances its purchase of JGBs from the private banks by the above increases in its own accounts and government deposits. As shown in Fig. 19, the BOJ’s net purchases of JGBs minus increases in the BOJ CAs (black thick line in Fig. 19) are matched exactly by increases in the TFs plus increases in the BOJ note issues, the sum of which is recorded negative in the MOS (grey thick line). Let us now explain the same transactions using the Treasury Funds Statistics (TFS), which are compiled by Policy Research Institute, Ministry of Finance (MOF). The TFS record transactions between the government and BOJ in terms of changes in the TFs. Payments on the BOJ’s accounts for the redemption of the BOJ’s own T-bills and JGBs by the government are recorded negative in the TFS. Regarding T-bills, however, the BOJ is allowed to underwrite T-bills for the government directly, and this is recorded positive as a result of payments on the TFs by the BOJ. As shown in

16 Note that the BOJ’s taxes and payments on the government accounts [(5) in Fig. 18] are excluded

from net changes in the TFs.

Appendix: How Did the BOJ de facto Refinance Its Own JGBs at Maturity?

117

40

(i) Redemption of the BOJ's Treasury bills (-(5))

20

(ii) Redemption of the BOJ's JGBs (-(5))

0

(iii) Redemption of the BOJ's JGBs through the special accounts of the government (-(5)) Changes in government deposits at the BOJ (+(6))

-20

-40

-60

-80

-100

Fig. 20 Transactions between the Treasury and the BOJ’s own accounts, 1985–2018 (unit: trillion yen). Note (1) See Policy Research Institute, MOF (1981–2018) for the TFS

Fig. 20, the redemption of T-bills from the TFs by the government was dominated by the refinancing of T-bills on the TFs by the BOJ up to FY1997. The TFS cover not only the BOJ’s transactions with the general account of the government, but also those with its various special accounts. Redemption of the BOJ’s own JGBs by the special accounts is also recorded negative, whereas sales of JGBs to the BOJ by the special accounts are recorded positive. As shown in Fig. 20, the redemption was sometimes dominated by the sales of the transactions between the BOJ and the special accounts. How had the BOJ expanded holdings of T-bills and JGBs, and refunded them at maturity, given the extremely strong money demand? As demonstrated above, the BOJ usually finances an increase in T-bills and JGBs by an increase in the monetary base, while it de facto refinances its own JGBs at maturity by the redemptionpurchase operations, where purchases by the BOJ immediately follow redemption by the government in de facto refunding JGBs. According to the MOS (Fig. 19), the BOJ had expanded its holdings of JGBs by an increase in the CA (more precisely, excess reserves in the CA), which amounted to about 70 trillion yen from FY2013. On the other hand, the BOJ had refunded its own JGBs by the redemption-purchase operations. The scale of the operations, which can be measured by changes in the TFs, amounted to 30 trillion yen from FY 1999, and exceeded 100 trillion yen from FY2013. On the other hand, according to the TFS (Fig. 20), the BOJ’s own T-bills and JGBs had been aggressively redeemed from FY2001 to FY2005, and even more aggressively since FY2013. Such large-scale redemptions allowed the BOJ to refund

118

Public Bonds as Money Substitutes at Near-Zero …

its own JGBs de facto by the redemption-purchase operations. In addition, the BOJ partly refinanced its own JGBs with government deposits, which increased from FY1999 to FY2000, and from FY2015. Tables 1 and 2 report changes in T-bills and JGBs holdings as well as the scale of their refinance, the latter of which is measured by the BOJ’s net purchases of T-bills and JGBs minus changes in its holdings of T-bills and JGBs. The scale of refinance relative to the balance at the previous year is also reported in both tables. An inverse of this relative scale can be interpreted as the redemption period. For example, if this relative scale is 25%, its inverse implies a four-year rollover period. As shown in Table 1, the BOJ’s own T-bills were aggressively refinanced from FY2002 to FY2005, and from FY2013, while the BOJ reduced its holdings of T-bills. Note that the relative scale of refinance was often larger than 100% because T-bills were usually refinanced in less than one year. As shown in Table 2, however, the BOJ greatly expanded its holdings of long-term JGBs since FY2013. Before FY2012 when the BOJ’s holdings of long-term JGBs Table 1 Scale of changes in Treasury bills held by the BOJ, and its refinance, 2002–2018 Changes in Treasury bills held by the BOJ

Scale of refinance of Treasury bills held by the BOJ

Changes (trillion yen)

Relative to the balance at the previous year (%)

Scale (trillion yen)

Relative to the balance at the previous year (%)

− 7.1

− 19.1

63.8

171

2003

4.3

14.3

34.1

113

2004

− 0.8

− 2.3

44.0

128

2005

− 0.9

− 2.6

25.0

74

2006

− 5.6

− 17.1

24.9

76

2007

− 6.7

− 24.6

24.6

91

2008

1.1

5.3

19.4

95

2009

1.2

5.8

19.6

91

2010

− 4.7

− 20.5

20.4

89

2011

− 1.6

− 8.9

7.1

39

2012

17.4

105.3

14.8

89

2013

10.2

29.9

80.8

238

2014

5.5

12.4

96.4

218

2015

− 2.4

− 4.8

71.8

145

2016

− 6.7

− 14.2

80.1

169

2017

− 18.8

− 46.4

57.1

141

2018

− 11.4

− 52.4

31.7

146

2002 (FY)

Note (1) The scale of refinance of the BOJ’s own T-bills and JGBs is computed by the BOJ’s net purchase of T-bills and JGBs, available from the MOS, minus changes in T-bills and JGBs held by the BOJ, available from the flow of funds accounts statistics (Flow of Funds in BOJ 2020)

Appendix: How Did the BOJ de facto Refinance Its Own JGBs at Maturity?

119

Table 2 Scale of changes in JGBs held by the BOJ, and its refinance, 2002–2018 Changes in JGBs held by the BOJ

Scale of refinance of JGBs held by the BOJ

Changes (trillion yen)

Scale (trillion yen)

Relative to the balance at the previous year (%)

Relative to the balance at the previous year (%)

2002 (FY)

9.1

18.4

4.3

7.4

2003

7.1

12.1

7.7

11.7

2004

− 0.1

− 0.2

14.7

22.4

2005

− 5.0

− 7.6

19.5

32.2

2006

− 11.2

− 18.6

25.6

52.0

2007

− 2.4

− 4.8

16.9

36.0

2008

− 4.2

− 9.0

19.7

46.2

2009

7.6

17.7

14.5

28.8

2010

8.9

17.7

14.0

23.7

2011

11.6

19.6

15.9

22.5

2012

20.7

29.2

24.2

26.5

2013

62.8

68.8

25.2

16.4

2014

66.0

42.8

30.6

13.9

2015

81.8

37.1

33.1

11.0

2016

75.2

24.9

40.6

10.8

2017

49.4

13.1

46.8

11.0

2018

33.0

7.7

54.5

11.9

See Note 1 in Table 1 for the data sources

were less than 100 trillion yen, the relative scale of refinance ranged between 20 and 50%, implying that the BOJ’s own long-term JGBs were refinanced in two to five years. This implied rollover period is consistent with the fact that the BOJ purchased only long-term JGBs with shorter than three-year duration before FY2012. While the BOJ expanded holdings of long-term JGBs from 91.3 trillion yen at the end of FY2012 to 459.6 trillion yen at the end of FY2018, the scale of refinance grew comparatively slowly. Accordingly, the relative scale of refinance declined from 26.5% in FY2012 to 11.9% in FY2018, implying that the BOJ’s own long-term JGBs were refinanced in about nine years. This extended redemption period suggests that the BOJ held JGBs with duration much longer than three years since FY2013.

Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan

Abstract Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy” presented a simple framework of disequilibrium analysis, in which strong money demand, induced by near-zero rates, helps to absorb excess supply in goods, labor, and public bond markets. However, the analysis is at most diagnostic without any theoretical rigor or quantitatively precise simulation. In this chapter presents a formal equilibrium model, in which public bond price bubbles are present temporarily or even persistently, but burst with a tiny probability per year. As discussed in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy”, those bubbles and their bursting in equilibrium analysis are interpretable as excess money demand and its disappearance in disequilibrium analysis. One of the most important implications in this chapter is that the model can yield reasonable predictions concerning the price level and a wide range of public bond yields, not only for the period when the short-term rate was already near zero (from the mid-1990s), but also for the period when it was far above zero (from the mid-1980s to the mid-1990s). For the latter period, the model predicts that the price level switches from mildly inflationary to mildly deflationary, and that the short-term rate declines quickly, but that yield curves remain upward sloping. For the former period, on the other hand, yield curves were gradually flattening at near-zero rates. In terms of future implications, if the bubbles burst, then the price level and rate of interest would jump immediately. As discussed in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy”, strong commitment to future fiscal reforms by a government would help a one-off price surge to stop at a level several times higher than before. Here, it is assumed that a rare but catastrophic event, such as a large-scale inland earthquake in Tokyo, causes the bubbles to burst, leading to sharp declines in real output in the following years. Given a strong aversion to catastrophic endowment shocks, the model is able to yield even more realistic predictions for the price paths and the shape of yield curves, both of which would prevail before the bubbles burst.

© Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9_5

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Long-Run Mild Deflation Under Fiscal Unsustainability …

1 Introduction Bitter debates about Japanese macroeconomic policies have continued over the past quarter century between fiscal reformers and demand-siders. Even after large-scale fiscal interventions against the Covid-19 pandemic were implemented from early 2020, the debates remained active below the surface. On the one hand, citing the compelling evidence of fiscal unsustainability, the fiscal reformers have argued for drastic spending cuts and tax increases to avoid hyperinflation or sovereign default.1 On the other hand, the demand-siders have interpreted mild deflation as an indicator of feeble aggregate demand and proposed that fiscal and monetary expansions be maintained to escape from a liquidity trap.2 Indeed, they have recommended that expansionary policies be continued to prevent interest rates rising even after escape from a liquidity trap. However, both sides have failed to explain why the mild deflation with near-zero interest rates, which began in the mid-1990s, has continued for such a long time in Japan. In contrast to the theories of the fiscal reformers, hyperinflation has not occurred despite the continuation of primary budget deficits, and the theories of the demand-siders have been confounded by the fact that unprecedented expansionary policies have not achieved even mild inflation with low interest rates. Ironically, each side has been able to pursue its own favorable prescription without fear of side effects while mild deflation or price stability has continued together with near-zero interest rates. In such a lukewarm macroeconomic environment, the fiscal reformers could easily hedge against hyperinflation without fear of severe deflation, whereas the demand-siders could simply bet against mild inflation without fear of sharp interest rate hikes. This chapter presents an alternative theory in which fiscal unsustainability resulting from undisciplined fiscal policies is permitted temporarily or even persistently (in contrast to the case in standard monetary models), and in which fiscal sustainability will be restored at some point in the future not by hyperinflation or continuous mild inflation with low interest rates, but largely through a one-off price 1 Many papers, including Braun and Joines (2015) and Imrohoroglu et al. (2016, 2019), convincingly

argue that fiscal sustainability in Japan is never achieved without any drastic tax increases or spending cuts. Armstrong and Okimoto (2016) survey the literature on fiscal sustainability in Japan. 2 On the monetary side, Krugman (1998), Eggertsson and Woodford (2003), and Jung et al. (2005), among others, recommend that a central bank strongly commit to a zero-interest rate policy not only before, but also after, an economy escapes from a liquidity trap. On the fiscal side, Sims (2016) proposes a fiscal stimulus to yield upward pressure on the price level, following the standard implications of the fiscal theory of the price level. Christiano et al. (2011) and Woodford (2011), among others, perceive a liquidity trap as a consequence of weak aggregate demand and demonstrate that the fiscal multiplier is much larger in a liquidity trap than during normal times. In the US context, Bianchi and Melosi (2017) demonstrate that the lack of deflation in the US economy at zero-interest rates can be explained by people believing, with some probability, that aggressive fiscal policies will continue even after an escape from a liquidity trap. As Blanchard (2019) emphasizes, debt rollovers may be feasible even in an economy with much public debt when interest rates continue to be below growth rates. Applying this implication, Blanchard and Tashiro (2019) recommend even more aggressive fiscal policies for the current Japanese economy.

1 Introduction

123

surge accompanied by government’s strict commitments to future fiscal reforms. In other words, in this scenario, a government will repay its own debt largely through a heavy devaluation of nominal public bonds, and partly through a government’s commitment to fiscal reforms. In the model, a price jump is considered a rare event with a probability of occurrence of less than 5% per year, and is accompanied by adverse, indeed possibly catastrophic, impacts on endowments in the years that follow. It is assumed in the model that a government immediately makes a strong commitment to future fiscal reforms when the price level jumps, although fiscal reforms may actually be implemented after the catastrophic shock disappears completely. Within this framework, mild inflation is achieved only after such price surges and is accompanied not by low, but by relatively high, interest rates. This theoretical framework allows us to explain the above seemingly puzzling macroeconomic phenomena in a consistent manner. First, under undisciplined fiscal policies, the government’s intertemporal budget constraint (GIBC)3 is not tightened, but relaxed, when a portion of public debt is unfunded by future fiscal surpluses and supported by price bubbles. Accordingly, it places downward (not upward) pressure on the current price level, which continues until the bubbles that back the unfunded component of the GIBC burst. Once these bubbles burst, the price level immediately surges. Second, at near-zero interest rates, the expected deflation is almost equal to the real rate of interest, but the continuously realized deflation is larger because of the small possibility of price surges in the next period. The probability that the price level will jump to a level proportional to existing money stocks in the next year is very low, but even a remote possibility of sharper price surges driven by faster monetary expansion makes ongoing deflations even more severe. However, to some extent, this tendency is offset by a strong aversion toward the catastrophic risks that follow a price surge, which assists in lowering the real rate of interest and makes the current deflation milder. Third, mild deflation may continue for a long time. Because sharp price surges are considered a rare event, they are hardly likely in the next year and not very likely in the next decade, but most likely in the next half-century. In this model, this probabilistic nature of price surges, with a sharp contrast in likelihood between the near and far future, is reflected in slowly flattening yield curves; (ultra) long-term yields remain relatively high, with the possibility of distant-future price surges, even if short-term yields approach zero. In this way, mild deflation can coexist with fiscal unsustainability and monetary expansion until a one-off price surge occurs. The key feature of the above framework is that it allows for temporary and even persistent fiscal unsustainability, which results from undisciplined fiscal policies, as well as for the restoration of fiscal sustainability largely through price surges and partly through a government’s strict commitment to fiscal reforms. Several issues

3 In this chapter, a government’s intertemporal budget constraint is interchangeable with its life-time

budget constraint.

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Long-Run Mild Deflation Under Fiscal Unsustainability …

related to this feature have been explored intensively in the existing literature on the fiscal theory of the price level (FTPL). First, LeRoy (2004), Bloise (2005), and Bloise and Reichlin (2008) present cases in which the GIBC is relaxed to the extent that the real valuation of public bonds is sustained partially by the unfunded component (the non-zero terminal condition or the bubble component) and a continuum of equilibria emerges. Bassetto and Cui (2018) demonstrate that, given lower real returns, which are induced by either dynamic inefficiency or liquidity premiums on government bonds, the present value of fiscal surpluses is not well defined and the price level is indeterminable only by its lower bound. Kobayashi (2019), Sakuragawa (2019), Murase (2020), and Brunnermeier et al. (2020) present cases where deflationary equilibria emerge as a consequence of the bubble component in the GIBC.4 However, none of these researches explicitly analyzed how fiscal sustainability is restored; that is, in their models, fiscal policies are assumed to be unsustainable forever. Second, many studies, including Davig et al. (2010), Bianchi and Ilut (2017), and Bianchi and Melosi (2017), consider policy environments in which an economy switches between non-Ricardian (active fiscal policies) and Ricardian (passive fiscal policies) regimes.5 The current model differs from these papers because a regime switch is triggered not only by a fiscal policy shift from a non-Ricardian to a Ricardian regime, but also by a one-off price surge, which is a rare and catastrophic event. In our model, a government commits to fiscal reforms immediately after the price level jumps. In the above models, fiscal sustainability is achieved in equilibrium even in the non-Ricardian regime, whereas in our setup, it is not maintained before the occurrence of the one-off price surge. In these respects, the model of Davig et al. (2011) is closest to that in this chapter. Starting from the Ricardian regime (involving an active monetary policy and a stationary transfer process), Davig et al.’s economy hits the fiscal limit as a consequence of a nonstationary transfers process (the nonRicardian policy), and eventually returns to the Ricardian regime as an absorbing state. In their model, fiscal sustainability may be achieved not by drastic cuts in transfer payments, but by unprecedented inflation, which breaks out when growing public debt is stabilized by a passive monetary policy. In terms of the relationship between monetary phenomena and fiscal (un)sustainability, Benhabib et al. (2002) employ the possibility of fiscal unsustainability as an instrument to eliminate ex ante a liquidity trap from possible equilibrium paths. In the neo-Fisherian model of, for example, Schmitt-Grohe and Uribe (2017), deflationary phenomena result from near-zero interest rates, as in the current model, but fiscal sustainability is always achieved for any path of the price level. Given that a one-off price surge is unprecedented by its nature and that it is not apparent in any observations from past decades, it is difficult to establish empirical 4 Hagedorn

(2018) regards public bonds as net wealth in the sense that the public bond valuation exceeds the present value of future fiscal surpluses, and presents a similar monetary model as in this chapter. 5 In the sense of Woodford (1995), a fiscal disturbance is neutralized in the case of Ricardian fiscal policies, but it is not in the case of non-Ricardian policies.

1 Introduction

125

relevance for the current model. To overcome this type of Peso problem, two empirical analyses are conducted. First, instead of regarding a price jump itself as a rare catastrophe, a one-off price surge is assumed to be triggered by a rare and catastrophic event. In Sect. 4, calibration exercises are made under the assumption that a large-scale inland earthquake in Tokyo triggers a one-off price surge. According to the calibration, the model can successfully explain not only the occurrence of mild deflation with near-zero interest rates after the mid-1990s, but also the price stability starting in the mid-1980s, the sharp decline in short-term yields in the first half of the 1990s, and the slowly flattening yield curves in the twenty first century. Second, we search for and examine any episode comparable with a one-off price surge in Japanese monetary history. We examine the sharp price increase following the end of World War II in 1945, which is discussed in detail in Chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, and find that it is empirically convincing to interpret the sharp inflation not as a hyperinflationary phenomenon, but as a one-off price surge event. The remainder of this chapter is organized as follows. Section 2 briefly explains the nominal phenomena observed in Japan’s long-run mild deflation. Section 3 presents a simple exchange economy in which fiscal sustainability is restored by one-off price surges together with a government’s strict commitment to future fiscal reforms. In Sect. 4, the theoretical framework is applied to an examination of the long-run mild deflation experienced in Japan. Section 5 concludes.

2 Three Features of Japan’s Long-Run Mild Deflation This section briefly presents three features associated with Japan’s long-run mild deflation, which commenced in the mid-1990s, together with near-zero interest rates. We emphasize that the price level was stable, despite rapid monetary expansion and heavy fiscal deficits, even before the nominal rate of interest almost reached zero in the mid-1990s, while long-term yields (longer than ten years) and ultra-long-term yields (longer than 20 years) remained relatively high, even after the mid-1990s. Accordingly, the calibration exercises presented in Sect. 4 focus not only on the nominal behavior after interest rates reached the near-zero level in the mid-1990s, but also on the behavior while they were above zero. First, the price level in Japan was quite stable despite rapid monetary expansion. In Fig. 1, the price level per unit of consumption goods (the private consumption deflator,6 adjusted by consumption tax hikes7 ), is compared with the money stocks 6 The

consumption deflator is adopted because it captures a deflationary trend as a result of the nature of the Paasche index. 7 When a 3% consumption tax was introduced in April 1989, most of the existing indirect taxes were abolished. Thus, its introduction had little impact on the average price level. On the other hand, the overall price level increased by around 2% when the tax rate was raised to 5% in April 1997, and again by about 2% when the rate was hiked to 8% in April 2014. The private consumption deflator,

126

Long-Run Mild Deflation Under Fiscal Unsustainability …

3.0

2.5

2.0

1.5

1.0

0.5

0.0

BoJ notes/real GDP in natural logarithm (1955=0) Private final consumption deflator in natural logarithm (1955=0)

Fig. 1 BOJ notes and prices, 1955–2018 (in natural logarithm, 1955=0). Notes (1) The BOJ notes balance is available from the Flow of Funds Accounts Statistics, which are compiled by the Research and Statistics Department, BOJ (Flow of Funds in BOJ (2020)). (2) Real GDP and the private final consumption deflator (excluding imputed rents) are based on the annual report on the national accounts, which is compiled by the Economic and Social Research Institute, Cabinet Office of Japan (ESRI (1998, 2009, 2019)). (3) The private consumption deflator, reported throughout this chapter, is adjusted by the impact of the consumption tax hikes (April 1989, April 1997, and April 2014) on the average price level

per unit of output (the outstanding Bank of Japan [BOJ] notes8 divided by real gross domestic product [GDP]) for the years from 1955 to 2018. Both of the time-series are standardized as of 1955. The price level and the money stocks moved together up to the late 1970s; however, from the mid-1980s, the price level began to stagnate despite continuing monetary expansion. More precisely, the price level inflated only slightly up to the mid-1990s, and then deflated mildly afterwards. Second, Japanese government bonds (JGBs) were valued highly in real terms despite the continuation of the primary budget deficits. As shown in Fig. 2, relative to nominal GDP, the primary fiscal balance of the central government’s general account was close to zero, or even negative, except for 1989–1993. More precisely, the primary balance deteriorated from the early 1970s, reaching −5.0% in 1979. In the 1980s, it recovered gradually, reaching 2.2% in 1991. However, it deteriorated again from the early 1990s, reaching −5.0% in 2012, and then remained negative. On the other hand, as shown in Fig. 3, the outstanding JGBs, adjusted by a real macroeconomic scale or reported throughout this chapter, is adjusted by the impact of these consumption tax hikes on the average price level. 8 Here, the narrowest category of money stocks is chosen.

2 Three Features of Japan’s Long-Run Mild Deflation

127

3% 2% 1% 0% -1% -2% -3% -4% -5% -6%

Fig. 2 Primary fiscal balance of the general account of the central government, 1965–2018 (relative to nominal GDP, %). Note: (1) The primary fiscal balance of the general account in the central government is compiled by the Ministry of Finance (MOF 2020). Fig. 2 differs from Fig. 3, Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy” in that the former covers only the general account of the central government, but the latter covers the entire accounts of the general government

divided by real GDP, grew much faster than the price level (the private consumption deflator) from the early 1970s. Putting the two figures together, the real valuation of the outstanding (growth-adjusted) JGBs improved considerably from the early 1970s, although the primary balance deteriorated substantially for the same period.9 Third, the shape of the yield curves on the JGBs, from one- to 40-year yields, has experienced a dramatic change since the price level started to stagnate in the mid1980s. As shown in Fig. 4, the yield curves were almost flat at relatively high rates in the 1980s. While the short-term (one-year) rate declined quickly in the 1990s, almost reaching zero in 1995, the longer-term rates remained relatively high. Accordingly, the yield curves were upward sloping even when the short-term rate was close to zero. More concretely, the spreads of ten-year (20-year) yields over one-year yields were 2.5% (3.1%) in 1996, 1.3% (2.0%) in 2001, 1.2% (1.6%) in 2006, and 0.9% (1.7%) in 2011. Only in late 2016 did the yield curves flatten substantially, although the emergence of the flat curves for up to ten-year yields (the ten-year term spread

9 According to Ito et al. (2011), Japanese fiscal policy began to lack discipline as early as 1970, and

the debt–GDP ratio was nonstationary from then.

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Long-Run Mild Deflation Under Fiscal Unsustainability …

5

4

3

2

1

0

-1

Nominal public bonds/real GDP in natrual logarithm (1955 = 0) Private final consumption deflator in natural logarithm (1955 = 0)

Fig. 3 Nominal public bonds and prices, 1955–2018 (in natural logarithm, 1955 = 0). See Notes 1, 2, and 3 to Fig. 1 for the data sources 1975

10

1980 1985 1992

8

1995 2001

6

2006 2013 2016

4

2018 1-year yield (2-year yield for 1980)

2

0

-2

Fig. 4 One-year interest rates and yield curves, 1975–2018 (one-year to ten-, 15-, 20-, 25-, 30-, and 40-year yields, %). Note: (1) Hamacho SCI (a private investment general partnership) computes the monthly averages of the JGB yields from their daily data, which are reported by the Ministry of Finance. (www.hamacho.net/jp/ in Japanese)

2 Three Features of Japan’s Long-Run Mild Deflation

129

was only 0.2% in 2016) might have been caused by heavy interventions by the BOJ.10 In 2018, yield curves became slightly steeper.

3 Behavior of the Price Level in the Fiscally Sustainable and Unsustainable Regimes 3.1 Sketching a Model of a Price Surge as a Trigger for a Regime Switch In this section, we describe the following equilibrium behavior step-by-step. Initially, the economy is under a regime in which fiscal unsustainability results from undisciplined fiscal policies (FU regime). During the FU regime, the component that is unfunded by future fiscal surpluses emerges in the GIBC; that is, the terminal condition does not converge to zero, and public bond price bubbles are present temporarily. However, once the bubble bursts, the economy experiences a one-off price surge. As a result, accumulated public bonds are heavily devalued and the government commits to future fiscal reforms. Accordingly, the economy immediately switches from the FU regime to a regime in which fiscal sustainability is restored (FS regime). Here, the price surge, characterized as a rare but catastrophic event, is assumed to serve as a trigger for the above regime switch. That is, the price surge takes place with a small probability in the next year and is accompanied by adverse impacts on endowments in the following years. Upon experiencing this price surge, the economy switches from the FU to the FS regime. The price surge event coincides with bursting bubbles and the government’s strong commitment to future fiscal reforms. One caveat for this setup is that although the government commits to future fiscal reforms upon the price surge, fiscal reforms are likely to be actually implemented after catastrophic shocks disappear completely. One of the most important parts of this section is to demonstrate how discontinuous price movements are modeled as a trigger for the switch from the FU to the FS regime. In the FS regime, the price process is uniquely determined by the quantity theory of money (QTM); both deflationary and hyperinflationary paths are ruled out by several assumptions, as shown in Sect. 3.3. On the other hand, in the FU regime, a continuum of deflationary equilibria emerges once the presence of public bond price bubbles is admitted temporarily or even persistently; that is, we relax the assumption that the terminal condition in the GIBC holds tightly, as shown in Sect. 3.4. Accordingly, a price jump occurs at the regime switch; this discontinues the deflationary trend in the FU regime, and the price level rises up to the QTM price. Because hyperinflationary paths are infeasible in the FU regime under some conditions, a discontinuous price drop from the hyperinflationary trend down to the QTM price never occurs. 10 The

BOJ attempted to flatten the yield curves for up to ten-year yields from September 2016 by carrying out quite generous limit orders for long-term JGBs.

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Long-Run Mild Deflation Under Fiscal Unsustainability …

3.2 A Simple Monetary Model of the Exchange Economy 3.2.1

Basic Setup

As a basic framework, we employ a simple monetary model of the exchange economy proposed by Kocherlakota and Phelan (1999). A representative household has the following preference regarding streams of consumption (ct ) and the real money balance ( MPtt ): ∞ 

 β E0 t

t=0



Mt u(ct ) + v Pt

 ,

(3.1)

  where a discount factor β is less than one, u(c) and v MP are twice differentiable, strictly increasing, and strictly concave,11 and E 0 is the expectation operator conditional on time-0 information. The sources of uncertainty are described in Sect. 3.2.3. The maximization of the objective  function (3.1) is subject to Bt+1 + Mt+1 = Pt+1 (yt+1 − τt+1 − ct+1 )− R1,t − 1 Mt + R1,t (Bt + Mt ), where yt is a real endowment stream in terms of consumption goods, ct is the real amount of consumption goods, τt is a real lump-sum tax, Pt is the price of consumption goods, Mt is the nominal money balance, Bt is the nominal amount of public bonds, both of which are defined at the beginning of time t.12 R1,t is the one-period nominal gross rate of interest.   The following functional forms are applied to u(c) and v MP : u(c) = ln(c),

(3.2)

with a unit elasticity of intertemporal substitution, and: 

M v P



λ = 1−

 1 σ

M χ+ P

1− σ1

,

(3.3)

11 As discussed in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy and Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?”, money demand never saturates at any finite level of real money stocks   the assumption that   M (v  M > 0 for a finite ) is crucial in the discussion in this chapter. On the other hand, if v  M P P P reaches zero at the upper limit of M P and money demand saturates, then strong money demand never emerges. 12 In Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy and Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?”, bond and money stocks are defined at the end of period.

3 Behavior of the Price Level in the Fiscally Sustainable …

131

where σ > 0 is interpreted as part of the interest and income elasticities of money demand, as discussed in Sect. 4. Both λ and χ are positive. Here, a positive χ represents the existence of an alternative means of exchange to central banknotes M, and assists in setting an upper bound on nominal interest rates R1,t .

3.2.2

Two Fiscal Policies and Two Fiscal Regimes

In the FU regime, fiscal policy always lacks discipline, and the fiscal surplus is never responsive to the outstanding public bonds, that is:   PtFU τtFU − gt = PtFU ε − (Mt − Mt−1 ), where PtFU is the price level prevailing in the FU regime, and ε is a constant real primary balance. In the context of the FTPL, the above fiscal policy is called nonRicardian, in the sense that any disturbance in the fiscal surplus is not neutralized. However, in contrast with standard FTPL models, ε may be zero or negative in the current setup. Any seigniorage Mt − Mt−1 is reimbursed to households as a lump-sum subsidy.13 Thus, the nominal balance of the public bonds evolves according to:  FU  FU FU ε. τt+1 − gt − (Mt+1 − Mt ) = R1,t Bt − Pt+1 Bt+1 = R1,t Bt − Pt+1

(3.4)

The nominal value of the public bonds may be unstable if ε is quite small, or negative. Turning to the FS regime, it is assumed that the government commits to a disciplined fiscal policy upon switching, but fiscal reforms may actually be implemented only after the catastrophic shocks disappear completely. A major reason for this assumption is that it is difficult to imagine fiscal reforms being successfully implemented during catastrophic periods in the real world. Given a drastic reduction in the debt–GDP ratio caused by the price surges, any fiscal reform in the FS regime may not be extremely strict. Under a disciplined fiscal policy, the surplus responds positively to the outstanding public bonds as follows. If γBt−1 > B > 0 with 0 < γ < 1, then:     PtF S τtF S − gt = R1,t−1 − γ Bt−1 − (Mt − Mt−1 ), and otherwise:     PtF S τtF S − gt = R1,t−1 B t−1 − B − (Mt − Mt−1 ), 13 The assumption of reimbursing seigniorage to households follows the tradition of the FTPL in the

sense that the public bonds are redeemed only by real fiscal surpluses. In a related study, Sargent and Wallace (1981) include seigniorage in the government’s budget constraint in determining the price process.

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Long-Run Mild Deflation Under Fiscal Unsustainability …

where PtF S is the price level prevailing in the FS regime. The above fiscal policy is called Ricardian in the sense that the outstanding public bonds are stabilized in nominal terms. A disciplined fiscal policy is called ‘strict’ if γ is close to zero or B is set low. Again, any seigniorage revenue is reimbursed to households. Thus, the outstanding public bonds evolve according to:  FS  FS τt+1 − gt − (Mt+1 − Mt ) = γBt , Bt+1 = R1,t Bt − Pt+1

(3.5)

if γBt > B > 0, and otherwise according to:  FS  FS τt+1 − gt − (Mt+1 − Mt ) = B. Bt+1 = R1,t Bt − Pt+1

(3.6)

Under the above fiscal policy, the nominal balance of the public bonds converges to its lower bound B. In terms of monetary policy, the money stocks grow at a constant rate of μ > 0 in both regimes: Mt+1 = (1 + μ)Mt .

3.2.3

A Discontinuous Price Jump as a Rare and Catastrophic Event

A price surge takes place with probability π, which is quite low and probably less than 5% per year, and is accompanied by catastrophic endowment shocks in the years that follow. Thus, the regime remains fiscally unsustainable in the next year with probability 1 − π, but fiscal sustainability is restored at a regime switch with probability π. As t years pass, the regime will remain fiscally unsustainable with probability (1 − π )t , and will become fiscally sustainable with probability 1 − (1 − π )t . Thus, the FS regime is regarded as an absorbing state. As discussed in Sect. 3.2.2, a government commits to future fiscal reforms when the economy switches to the FS regime, but a disciplined (Ricardian) fiscal policy is not actually implemented upon switching. At first, an undisciplined fiscal policy is maintained under the FS regime, with the introduction of a disciplined policy occurring only several years after the price surge. During the FU regime, an endowment stream of consumption goods yt is constant, and real consumption is time-invariant at constant y, net of constant real government expenditure g: ct = c = y − g. As a rare event, a price surge has catastrophic impacts on endowments in the following years. The endowment available for consumption declines substantially,

3 Behavior of the Price Level in the Fiscally Sustainable …

133

partly because of the negative endowment shocks (yt < y) and partly because of the extra public expenditures required to deal with catastrophic events (gt > g). When the economy switches regimes at time s, consumption declines from c to: cs = c(1 − d) L ,

(3.7)

where 0 < d < 1 and L is a natural number. Even after switching, consumption remains stagnant at: cs+l = c(1 − d) L−l ,

(3.8)

at time s + l (l = 1, 2, . . . , L − 1). That is, it takes L + 1 years for consumption to recover to c.

3.3 The QTM in the FS Regime 3.3.1

Maximization After Switching to the FS Regime

Let us begin by solving the maximization problem when the economy switches to the FS regime at time s: ∞  t=s

β

t−s

λ ln(ct ) + 1−

 1 σ

Mt χ+ Pt

1− σ1

,

  FS subject to Bt+1 + Mt+1 = Pt+1 (y − τt+1 − ct+1 ) − R1,t − 1 Mt + R1,t (Bt + Mt ). In the FS regime, every variable is deterministic. Focusing on time t and t + 1 consumption, the above maximization problem is reformulated as:    1

Mt+1 1− σ λ χ+ max β ln(ct+1 ) + ct ,ct+1 ,Mt Pt+1 1 − σ1  1− σ1 Mt λ + ln(ct ) + χ+ , Pt 1 − σ1 FS subject to Bt+1 = P t+1 + (yt+1 − τt+1 − ct+1 )  − (Mt+1 − Mt )

R1,t (yt+1 − τt+1 − ct+1 ) − (Mt+1 − Mt ) + R1,t−1 Bt−1 . Together with Eqs. (3.7) and (3.8), the first-order conditions with respect to consumption (c) and the money stocks (Mt ) are obtained as follows:

134

Long-Run Mild Deflation Under Fiscal Unsustainability …

βR1,t

PtF S (1 − d0 ) = 1, FS Pt+1

(3.9)

where d0 = d for t = s, s + 1, s + 2, . . . , s + L − 1, and d0 = 0 for t ≥ s + L, and:  1    1 Mt − σ 1 1− . λ χ + FS = ct R1,t Pt

(3.10)

Substituting Eq. (3.10) into Eq. (3.9) leads to:  1

 PtF S 1 1 Mt − σ = = ct . 1 − λ χ + FS FS β R1,t (1 − d0 ) β(1 − d0 ) Pt+1 Pt

(3.11)

When a disciplined fiscal policy (3.5) or (3.6) is implemented at time s  > s + L, a period-by-period budget constraint can be solved as the following GIBC:   ∞      Bs  t−s R T −s BT β . β = − g τ + lim t t T →∞ PsF S PTF S  t=s

Then, the terminal condition associated with the public bonds is:    B T β T −s F S = 0. T →∞ PT lim

3.3.2

(3.12)

The QTM Without Any Catastrophic Endowment Shock (d = 0)

Which price path does difference Eq. (3.11) yield? For the moment, suppose that catastrophic shocks are absent, or that d = 0. Fig. 5a, b depict the relationship between the current real money balance and the next-period deflation rate ( PMFtS on t

P FS

the x-axis and PtF S on the y-axis). There are three cases, as follows: t+1 First, the economy stays at point A in Fig. 5a forever. There, the price level is completely proportional to the money stocks and the inflation rate is constant at the monetary growth rate μ. Hence, the QTM holds with the constant real money stocks. When d = 0, PtQT (d=0) is obtained as follows: PtQT (d=0)

=

1 , 1+μ

(3.13)

QT (d=0) R1,t =

1+μ , β

(3.14)

QT (d=0) Pt+1

3 Behavior of the Price Level in the Fiscally Sustainable …

135

a

b

Fig. 5 a Dynamics of

Pt Pt+1

1

implied by Eq. (3.11) when 0 < λχ − σ c < 1. b Dynamics of

implied by Eq. (3.11) when 1 < λχ

− σ1

c

Pt Pt+1

136

Long-Run Mild Deflation Under Fiscal Unsustainability …

PtQT (d=0) = 

1 λ(1+μ) 1− σ1 c 1+μ−β

σ

−

χ c

Mt . c

(3.15)

The below choice of λ is consistent with a constant Marshallian k, or constant relative money stocks (κ = P M QT c ): λ=

χ c

+κ

 σ1 1 + μ − β 1 c σ −1 > 0. 1+μ

(3.16)

Equation (3.16) implies that Friedman’s (1969) rule is not feasible because λ turns out to be zero given that μ = β − 1 with R1,t = 1.14 Given Eqs. (3.5), (3.6), (3.13), (3.14), and (3.15), the terminal condition (3.12) in the GIBC holds for the QTM: lim β

T −s

T →∞

Note that

β 1+μ



B





QT

(1 + μ)T −s P s

 = lim

T →∞

β 1+μ

T −s 



B PsQT

= 0.

< 1.

Second, the economy approaches an asymptotic line at

PtF S FS Pt+1

=

1 β

in Fig. 5a as the

real money balance goes to infinity. Immediately after switching, PsF S < PsQT (d=0) P FS 1 or PsF S > 1+μ ; then, the deflationary process is initiated. The real money balance s+1

P FS

goes to infinity, and PtF S converges to β1 from Eq. (3.11). Accordingly, the terminal t+1 condition converges to a positive constant, as below, and Eq. (3.12) fails to hold: 0 < lim β

T −s

 β T −s

T →∞



B



FS Ps

=

B < ∞. PsF S

Therefore, the deflationary process is ruled out from the possible equilibrium paths. 1 Third, when 0 < λχ − σ c < 1, the economy converges to point B in Fig. 5a as the P FS 1 real money balance degenerates to zero. At the start PsF S > PsQT (d=0) or PsF S < 1+μ . s+1 Then, immediately after switching, the inflationary process is accelerated and the real 1 money balance degenerates to zero. As Eq. (3.11) implies, if 0 < λχ − σ c < 1, then PtF S Fs Pt+1

1

converges to a positive

1−λχ − σ c 15 . β

Consequently, the terminal condition (3.12)

14 Buiter and Sibert (2007) prove that Friedman’s rule is not available in standard monetary models, in which real money demand never saturates. 15 If a means of exchange alternative to central bank money is more readily available and χ is larger, 1 then 0 < λχ − σ c < 1 is more likely to be satisfied with a lower upper limit on the inflation rate

(

FS Pt+1 ). PtF S

3 Behavior of the Price Level in the Fiscally Sustainable …

137

in the GIBC holds:



lim

T →∞ 

β

β T −s B T −s 

1 1−λχ − σ

c

FS

 T −s  − σ1 1 − λχ c = lim B = 0. T →∞

P s

In this case, the accelerating inflationary (hyperinflationary) process cannot be ruled out from the possible equilibrium paths, as pointed out by Brock (1975) and Obstfeld and Rogoff (1983), and a continuum of equilibria emerges with an arbitrary initial value for PsF S > PsQT (d=0) . 1 However, as shown in Fig. 5b, Eq. (3.11) with 1 < λχ − σ c implies that positive prices cannot be supported eventually because point C in Fig. 5b is not located in the first quadrant. Hence, in this case, the accelerating inflationary process is not feasible. In what follows, it is assumed that: 1 < λχ − σ c, 1

(3.17)

thereby eliminating the possibility of the accelerating inflationary (hyperinflationary) process. Accordingly, only the QTM price (PtQT (d=0) ) is justifiable as a legitimate equilibrium path in the FS regime. As shown in Sect. 4, if c is standardized to one, χ is set at one, and κ in Eq. (3.16) is chosen by the long-run average of the relative 1 money stocks (the Marshallian k) of the Japanese economy. Then, λχ − σ c (= λ in this case) is indeed greater than one.

3.3.3

The QTM with Catastrophic Endowment Shocks (d > 0)

How does the QTM price (PtQT ) behave in the presence of catastrophic endowment shocks (d > 0)?16 As discussed in detail in the appendix to this chapter, the price level is higher at switching because money demand falls with a decline in output, and interest rates are higher owing to the economic recovery after switching. More QT QT QT (d=0) ) overshoots PsQT (d=0) and R1,s jumps beyond R1,s at the specifically, (P1,s QT (d=0) time of switching, s. Then, the price level grows more slowly than Ps+l and QT (d=0) at time s + L. On the other hand, the nominal interest rate coincides with Ps+L QT (d=0) up to time s + L − 1. continues to be above R1,s As shown in the appendix to this chapter, PtQT is determined in relation to QT (d=0) by a positive parameter η as follows: Pt

d > 0, a disciplined fiscal policy (3.5) or (3.6) is assumed to be implemented at time s  > s + L , that is, only after the catastrophic shocks disappear completely. 16 When

138

Long-Run Mild Deflation Under Fiscal Unsustainability …



QT Ps+l

1 = (1 − d)η

 L−l

QT (d=0) QT (d=0) Ps+l > Ps+q ,

(3.18)

for l = 0, 1, 2, . . . , L − 1. Here, η is determined by Eq. (3.19) in the appendix to this chapter: ⎤ ⎡ Ms  QT (d=0) QT (d=0) − 1 R Ps QT (d=0) ⎦>0 ⎣1 + 1,s η = R1,s s σ χ + QTM(d=0)

(3.19)

Ps

 QT (d=0) s Given Eqs. (3.14) and (3.15), R1,s and QTM(d=0) / χ+ Ps In what follows, it is assumed that:   Ms Ms χ + > σ. PsQT (d=0) PsQT (d=0)

Ms PsQT (d=0)

 are constant.

(3.20)

QT QT (d=0) Then, 0 < η < 1 from Eq. (3.19) and R1,s > R1,s from Eq. (A.4).

3.4 Possible Deflationary Processes in the FU Regime 3.4.1

The FU Regime with d = 0

Let us move to the FU regime with an undisciplined fiscal policy (Eq. (3.4)), which commences at time 0. This regime is called fiscally unsustainable because the terminal condition may not hold, and the bubbles that back the unfunded component may emerge in the GIBC. Given inequality (3.17), the accelerating inflationary process is infeasible in the FU regime. However, the deflationary process can occur once we relax the assumption that the terminal condition holds, and admit the temporal presence of the bubble supporting the unfunded component. Accordingly, the bubble bursts at the time of the regime switch. Then, a discontinuous jump in the price level occurs, which rises from the deflationary trend in the FU regime up to the QTM price in the FS regime. Detailed descriptions follow.  1− σ1  ∞ t Mt λ is subject to The maximization of t=0 β E 0 ln(ct ) + 1− 1 χ + Pt σ  FU Bt+1 + Mt+1 = Pt+1 (y − τt+1 − ct+1 ) − R1,t − 1 Mt + R1,t (Bt + Mt ). The first-order conditions with respect to consumption and the money stock lead to:  FU   1

 Pt 1 c 1 Mt − σ = = c , (3.21) 1 − λ χ + FU Et Pt+1 ct+1 β R1,t β Pt

3 Behavior of the Price Level in the Fiscally Sustainable …

139

where Pt+1 and ct+1 are random variables, the realization of which depends on FU and ct+1 = c), or whether the regime remains fiscally unsustainable (Pt+1 = P t+1 QT = whether there is a switch to the FS regime (Pt+1 = P t+1

QT (d=0) Pt+1 (1−d)ηL

and ct+1 =

(1 − d) c). Let us begin with a case endowment shock  FUin which there is no catastrophic Pt PtFU PtFU P FU c (d = 0). Substituting E t Pt+1 c = E t Pt+1 = (1 − π ) P FU + π QTt (d=0) into Eq. L

Pt+1

t+1

(3.21) leads to: PtFU 1 = FU 1−π Pt+1

  1

 1 PtFU Mt − σ c − π QT (d=0) . 1 − λ χ + FU β Pt Pt+1

(3.22a)

Before exploring the price behavior implied by Eq. (3.22a), we derive the GIBC. FU ε. Even after Given an undisciplined fiscal policy (Eq. (3.4)), Bt+1 = R1,t Bt − Pt+1 the economy switches to the FS regime at time s, the undisciplined fiscal policy QT ε holds at time continues for at least one period (s  > s), and Bs+1 = R1,s Bs − Ps+1 s + 1. Using the first equality of Eq. (3.21), Eq. (3.4) is further rewritten as:     Bt+1 Bt + ε , = β E t Pt+1 PtFU

(3.23)

where both Pt+1 and Bt+1 are random variables. Equation (3.23) may be interpreted as an arbitrage condition for the public bond pricing, in which the return consists of the real appreciation of the public bonds as capital gains, and the real fiscal surplus as income gains.   QT (d=0) R1,t B t −Pt+1 ε Bt+1 Bt+1 t+1 = (1 − π ) PBt+1 Substituting E t BPt+1 FU + π QT (d=0) = (1 − π ) FU + π QT (d=0) P t+1

Pt+1

t+1

Pt+1

into Eq. (3.23) leads to: R1,t B t Bt Bt+1 = β(1 − π ) FU + β(1 − π )ε + βπ QT (d=0) . PtFU Pt+1 Pt+1 The above difference equation is solved in a recursive manner as follows: 

∞  B0 R1,t Bt t t = β (1 − π ) β(1 − π )ε + βπ QT (d=0) P0FU Pt+1 t=0   β(1 − π )ε B T + lim β T (1 − π )T FU = T →∞ 1 − β(1 − π ) PT     ∞  BT R1,t Bt t t + β (1 − π ) βπ QT (d=0) + lim β T (1 − π )T FU . T →∞ PT Pt+1 t=0

(3.24)

140

Long-Run Mild Deflation Under Fiscal Unsustainability …

Instandard models of the FTPL, the terminal condition is strictly respected, and T = 0 must hold in equilibrium. However, during the FU lim β T (1 − π )T PBFU

T →∞

T

T →∞

T

regime  in the current setup,  the terminal condition is relaxed, and a positive but finite T is admitted on the equilibrium path as long as the FU regime lim β T (1 − π )T PBFU continues. When the inequality below holds:   BT 0 ≤ lim β T (1 − π )T FU < ∞, T →∞ PT the regime is indeed fiscally unsustainable in the sense that the bubbles that back the unfunded component of the GIBC are present. Equation (3.24) can serve as an instrument to determine the initial price P0FU . Here, the initial price is determined according to (1) the present value of the fiscal surpluses [the first term on the right-hand side of Eq. (3.24)] as in the FTPL, (2) the real valuation of nominal public bonds at a regime switch (the second term), and (3) in contrast to the situation under the FTPL, the component  that is unfunded  by the T BT T future fiscal surpluses (the third term), if any (0 < lim β (1 − π ) P FU < ∞). T →∞

T

The bubbles that back the unfunded component of the GIBC burst on switching to the FS regime, under which the terminal condition is satisfied strictly by Eq. (3.12). The case in which the initial price level is determined according to Eq. (3.24) may be called the MFTPL as in Chapters “Introduction: Toward a Monetary and Fiscal Theory of the Price Level and Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy”, in the 0 ) is augmented by the temporal sense that the real valuation of public bonds ( PBFU 0 presence of the bubbles coexisting with near-zero interest rates. t−1 R1,i B 0 with ε = 0 Equation (3.24) can be simplified as follows. When Bt = i=0 in the FU regime, the last two terms on the right-hand side of Eq. (3.24) amount to: ∞ 

β (1 − π ) βπ t

t

R1,t

t=0

t−1

i=0 R1,i B 0 QT (d=0) Pt+1



+ lim β (1 − π ) T

T −1 T

T →∞

i=0

R1,i B0

PTFU

.

If ε is not equal to zero, then the above value decreases with the present value of β(1−π)ε the fiscal surpluses, or 1−β(1−π) . Hence, Eq. (3.24) is rewritten as follows: B0 β(1 − π)ε + = 1 − β(1 − π ) P0FU

 ∞ 

+ lim β (1 − π ) T

t=0

T −1 T

i=0

T →∞

=

∞  t=0

β (1 − π ) βπ t



β t (1 − π )t βπ

R1,t

R1,i B0

PTFU t−1

t



i=0 R1,i B0 QT (d=0) Pt+1

R1,t

t−1

i=0 R1,i B0 QT (d=0) Pt+1

β(1 − π )ε − 1 − β(1 − π )





3 Behavior of the Price Level in the Fiscally Sustainable …

+ lim β (1 − π ) T

T −1 T

i=0

R1,i B0

.

PTFU

T →∞

141

(3.25)

Now, the relaxed terminal condition is rewritten as:

T −1 i=0 R1,i B0 T T 0 ≤ lim β (1 − π ) < ∞. T →∞ PTFU

(3.26)

An interesting feature of Eq. (3.25) is that, because B0 is cancelled out on both sides, the initial price (P0FU ) is independent not only of the real primary balance (ε), but also of the initial nominal balance of the public bonds (B0 ). Thus, Ricardian equivalence holds even during the FU regime. A reason for this equivalence result is that the public bonds, which accumulate as a result of the undisciplined fiscal policy in the FU regime, are repaid by the devaluation of nominal bonds that occurs because of the price jump at switching, as well as by fiscal reforms, which are implemented later in the FS regime. It is easy to prove that the initial price can be the QTM price (P0QT (d=0) ) from Eq. P FU 1 (3.25). Substituting PtFU = 1+μ and R1,t = 1+μ into Eq. (3.25) leads to: β t+1

B0 P0FU

⎡ ∞  ⎢ t t = ⎣β (1 − π) βπ t=0



(1 + μ)

⎡



⎢ + lim ⎣β T (1 − π )T

=

t=0

(1 − π )t π

+ lim (1 − π )T T →∞

B0

1+μ β

P0QT (d=0) B0 P0QT (d=0)

⎤

t+1

t+1

(1 + μ)

B0

T →∞

∞ 

1+μ β

T

⎥

⎦ P0QT (d=0) ⎤

T B0

⎥

⎦ P0QT (d=0)

=

B0 . QT (d=0) P0

Hence, P0FU = P0QT (d=0) . In this case, there is no discontinuity in the price level at switching. As in the FS regime, there are potentially two more scenarios. When the initial price starts from P0FU > P0QT (d=0) given inequality (3.17), positive prices cannot be supported as the real money balance ( PMFUt ) converges to zero. However, in this case, even before

Mt PtFU

t

converges to zero, the inflationary price may fall to the QTM price

at switching, and a large

PtN R QT (d=0) Pt+1

may make positive prices infeasible in Eq. (3.22a).

In any case, the accelerating inflationary process is not feasible at all.

142

Long-Run Mild Deflation Under Fiscal Unsustainability …

When the initial price starts from P0FU < P0QT (d=0) , the deflationary process is 1 t ) converges to β(1−π) with initiated. As Eq. (3.22a) implies, the deflation rate ( PPt+1 growing real money balances. Thus, the terminal condition (3.26) converges to a positive constant17 : 0 < lim β (1 − π ) T

T →∞



B0

T

β T (1

− π)

T

=

NR P0

B0 < ∞. P0N R

Here, the relaxed terminal condition (3.26) is still satisfied. Thus, the initial price in the FU regime could be not only the QTM price (P0QT (d=0) ) but also P0FU ≤ P0QT (d=0) . If P0FU = P0QT (d=0) , then there is no discontinuous price jump at switching. However, if P0FU < P0QT (d=0) , then the price level surges from the deflationary trend to the QTM price at switching. In the latter case, the deflationary process is determined by Eq. (3.22a) or:    1

 PtFU 1 PtFU PtFU Mt − σ = c +π − QT (d=0) . 1 − λ χ + FU FU FU β Pt+1 Pt Pt+1 Pt+1

(3.22b)

One interesting feature of Eq. (3.22b) is that with faster monetary expansion (a higher μ), the price process is more deflationary in the FU regime. Given an upward P FU P FU P FU P FU price jump at switching at time t + 1, PtFU > 1 > QTt (d=0) , and PtFU − QTt (d=0) in Eq. t+1

Pt+1

t+1

Pt+1

(3.22b) is positive. Because the QTM price is proportional to existing money stocks, P FU QT (d=0) Pt+1 is higher with a faster monetary expansion. Then, PtFU is higher from Eq. t+1 (3.22b). Accordingly, rapid monetary growth makes ongoing deflation severe. With price surges being more likely (a higher π ), the price process is also more deflationary in the FU regime. In addition, the first term on the right-hand side of Eq. (3.22b) implies that higher discount rates β1 (lower discount factors) add to deflationary pressures during the FU regime. A final remark in this subsection regards Eq. (3.25). This equation is rewritten as: ⎡ ⎢ Bh ⎢ t−h = ⎢β (1 − π)t−h βπ FU ⎣ Ph t=h ∞

⎡ ⎢ ⎢ + lim ⎢β T −h (1 − π )T −h T →∞⎣

⎤ R1,i Bh ⎥ ⎥ i=h ⎥ QT (d=0) ⎦ Pt+1 t−1 

R1,t

T −1

⎤

R1,i Bh ⎥ ⎥ ⎥. PTFU ⎦

i=h

17 The unfunded component, or the non-zero terminal condition, has the same structure as the rational bubble proposed by Blanchard and Watson (1982), Weil (1987), and others, in the sense that its real value grows at a discount rate (1 − β) plus a bursting probability (π).

3 Behavior of the Price Level in the Fiscally Sustainable …

143

QT (d=0) As time goes by, the price surge (a jump from PtFU to Pt+1 ) becomes sharper with growing money stocks. Thus, the first term on the right-hand side of the above equation is devalued more heavily, and the share of the unfunded component in the real valuation of the public bonds is larger.

3.4.2

The FU Regime with d > 0

Let us turn to the case with catastrophic endowment shocks (d > 0). Given aversion to catastrophic risks, the magnitude of endowment shocks d is adjusted by the degree of relative risk aversion γ > 1, or δ = γd. Then, if d is relatively small18 : 1 − δ ≈ (1 − d)γ .

(3.27)

If the actual magnitude of shocks d is replaced by the risk-adjusted magnitude γd, then a heavier weight is put on the γ expected marginal utility γ  at switching   L 1 1 1 1  π ≈ π u (1 − d) c = (1−γ d)L c π ≈ (1−d)L c π ; that is, (1−d)L c π < (1−d) L c 1 π (1−γ d) L c

with γ > 1. Note that the functional form of u(c) remains logarithmic, and that the intertemporal elasticity of substitution is still one, as in Eq. (3.2). That is, by introducing the risk-adjusted magnitude of shocks (γd) instead of d, the degree of relative risk aversion can be determined independently of the unit intertemporal elasticity of substitution, as in the preference proposed by Epstein and Zin (1989). In the presence of endowment shocks, Eq. (3.23) is replaced by:    c Bt+1 Bt = β E + ε . t ct+1 Pt+1 PtN R c ). On the Here, the discount factor is not deterministic (β) but stochastic (β ct+1 other hand, Eq. (3.24) is replaced by:



∞  B0 β(1 − π )ε 1 R1,t Bt t t + = π QT β (1 − π ) β 1 − β(1 − π) t=0 P0FU (1 − γ d) L Pt+1   T T BT . + lim β (1 − π ) T →∞ PTFU From Eqs. (3.18) and (3.27):  Et

18 If d

PtFU c Pt+1 ct+1

 = (1 − π )

PtFU +π FU Pt+1

c PtFU  1 ηL QT (d=0) (1 − d)γ L c Pt+1 1−d

(the size of the catastrophic damage per period) is small, but L (the length of the catastrophic period) is long, then the initial catastrophic shock is large.

144

Long-Run Mild Deflation Under Fiscal Unsustainability …

= (1 − π )

PtFU PtFU 1 +π . FU L(γ −η) QT (d=0) Pt+1 (1 − d) Pt+1

Then, Eq. (3.22b) is rewritten as:

 1

L   PtFU PtFU PtFU 1 1 Mt − σ = c +π − , 1 − λ χ + FU FU FU QT (d=0) β 1− Pt+1 Pt Pt+1 Pt+1 (3.22c)  where

1 (1−d)γ −η

L

π≈



L 1 π, 1−

and: = (γ − η)d.

(3.28)

Note that is always positive given that γ > 1, and 0 < η < 1 from inequality (3.20). A that with a larger   comparison betweenEqs. (3.22b) and (3.22c) indicates  1  L PtFU PtFU PtFU P FU in Eq. (3.22) is smaller than P FU − QTt (d=0) in Eq. , P FU − 1− QT (d=0) t+1

Pt+1

t+1

Pt+1

(3.22b). This implies that the deflationary pressure is mitigated by either a larger d (larger shocks) or a higher γ (greater risk aversion). A reason for this implication is that, as Rietz (1988) and others demonstrate, real interest rates decline substantially with aversion to catastrophic risks. Accordingly, the expected deflation also decreases because it is approximately equal to the real rate of interest at a nominal interest rate of zero. Another interesting implication is that an inflationary phase may even emerge in the FU regime if is large, either as a result of high-risk aversion or large catastrophic QT (d=0) , but the former shocks. If PtFU is smaller than Pt+1  from  does not differ much  1  L PtFU PtFU in Eq. the latter just after the economy starts at time 0, then P FU − 1− QT (d=0) t+1

Pt+1

(3.22c) may be negative with a larger . Thus, mild inflationary pressures could be created initially in the FU regime. Note that if P0FU starts from P0QT (d=0) , then the price level behaves as if catastrophic shocks were absent (d = 0).19

3.5 On the Term Structures of Interest Rates During the FU Regime Let us derive the term structures of interest rates that emerge during the deflationary FU regime. From the Euler equation appearing in the first equality of Eq. (3.21), an QT (d=0)

P0N R is equal to P0 QTM without any catastrophic shocks.

19 If the initial price

, then it is assumed that the price process follows the

3 Behavior of the Price Level in the Fiscally Sustainable …

145

n-period nominal yield (Rn,t ) is obtainable as follows20 : 

1 Rn,t

n

 = β Et n

 PtFU ct . Pt+n ct+n

Using notation defined by Eq. (3.28), the above Euler equation is developed as 

1 Rn,t

n

 FU  n n Pt = β (1 − π ) FU Pt+n    L−n+i n FU  1 P + β n QTt (d=0) π (1 − π )i−1 , 1− Pt+n i=1

(3.29a)

for n = 1, 2, . . . , L + 1, and 

1 Rn,t

n

  FU  P FU n n Pt = β (1 − π ) FU β n QTt (d=0) 1 − (1 − π )n−L−1 Pt+n Pt+n  i−1

L+1  1 n−L−1 i−1 +(1 − π ) π (1 − π ) 1− i=1

(3.29b)

for n ≥ L + 2. With d = 0 or = 0 

1 Rn,t

n

  FU   PtFU n Pt n n n = β (1 − π ) FU + β QT (d=0) 1 − (1 − π ) . Pt+n Pt+n

(3.29c)

The first term on the right-hand sides of Eqs. (3.29a), (3.29b), and (3.29c) represents the negative impact on yields, which is caused by the ongoing deflationary expectations, whereas the second term on the right-hand sides represents the positive impact on yields, which results from the expectation of future price surges. Thus, the yield curves are determined by these competing expectations. On the one hand, as discussed in Sects. 3.4.1 and 3.4.2, a higher switching probability generates stronger deflationary pressures and helps to flatten yield curves. On the other hand, lower discount rates, larger catastrophic shocks, and greater risk aversion mitigate deflationary pressures and work to steepen yield curves. In addition, higher monetary growth contributes to larger price surges in the future and increases the dominance of inflationary expectations, thereby resulting in steeper yield curves.

20 Here,

longer-term public bonds are redundant assets and can be replicated from the one-period public bonds. Thus, the yield curve is neutral with respect to the maturity structure of the public bonds. In this regard, our model differs from that of Cochrane (2001), where the maturity structure of the public debt has effects on current and future inflation.

146

Long-Run Mild Deflation Under Fiscal Unsustainability …

Figure 6 illustrates the above competing effects on yield curves. In the absence of catastrophic endowment shocks ( = 0), a downward-sloping line (PtFU B) depicts the deflationary path in the FU regime, and a steeper upward-sloping line (PtQT A) depicts the QTM price path in the FS regime. At some point in the future (for example, time s1 or s2 ), the price level jumps from the deflationary to the QTM price path. Reflecting the possibility of such a price surge, the expected price line (PtFU C) is drawn as a less steep but still upward-sloping line between the deflationary and QTM price path lines. The resulting expected price path makes the yield curve upward sloping. Given catastrophic endowment shocks together with strong risk aversion ( > 0), the price level overshoots line PtQT A at some point in the future (for example, time s3 ), thereby increasing inflationary expectations. At the same time, deflationary pressures are mitigated to some extent in the FU regime, and the deflationary path becomes less downward sloping (from line PtFU B to PtFU B  ). Consequently, the expected price path, as well as the yield curve, is even more upward sloping (shifting from line PtFU C to PtFU C  ).

Logarithmic price

Price path consistent with money stock

′

Impacts by catastrophic shocks

Expected price path implicit in yield curves ′

Deflationary price path

Current (t)

Time

1

Time

3

Time

2

Time

Fig. 6 Interpretations of switching possibilities from the FU regime to the FS regime

3 Behavior of the Price Level in the Fiscally Sustainable …

147

3.6 Real Risk-Free and Real Growth Rates Finally, real risk-free rates are compared with real growth rates in the deflationary FU regime. As Blanchard (2019) emphasizes, debt rollovers may be feasible even in an economy with much public debt, when interest rates continue to be below growth rates. However, the current model suggests that the feasibility of debt rollovers differs from fiscal sustainability. As shown below, interest rates may be below growth rates in real and nominal terms in the FU regime, and the public bonds are valued highly owing to the bubbles. However, fiscal sustainability is restored only at the cost of bursting bubbles, price surges, and interest rate hikes at switching. That is, fiscal sustainability and debt rollover feasibility are exclusive in the current model. Let us demonstrate that the real safe rate of interest is quite low in the deflationary FU regime, and that it may even be below the real growth rate. In the current setup, the real rates of growth and interest are never influenced by fiscal or monetary policies. The real growth rate in the FU regime is determined by (1 − π ) + π(1 − d) L , and its net rate is approximated by −πd L. The real safe one-period rate r1,t satisfies the following Euler equation:   1 + r1,t β E t



ct ct+1



   = 1 + r1,t β (1 − π ) + π

1 (1 − γ d) L

 = 1.

Then, r1,t is approximated by 1 − β − γ πd L. If (γ − 1)π d L exceeds the discount rate 1 − β, then the real safe rate is short of the real economic growth rate. Consistent with Rietz (1988), the real risk-free rate is lowered more in the case of stronger risk aversion (γ higher than one) and larger catastrophic risks (larger d L). Given the expected inflation, the relative size of interest rates and growth rates does not change much in real or nominal terms.

4 Calibration Exercises for Japan’s Long-Run Deflation In this section, several calibration exercises are presented to mimic Japan’s long-run mild deflation. As discussed in Sect. 1, there is no price surge event observed during the previous decades, and it is virtually impossible to specify an occurrence probability (π ) or the size of catastrophic shocks (d and L). Here, instead of considering a price surge as a catastrophic event, a large-scale inland earthquake in Tokyo is regarded as triggering a regime switch and causing price surges.21 The goal of this 21 A

large-scale inland earthquake in Tokyo may be one of the most likely trigger events, because it might immediately cause interest hikes upon completely exhausting domestic private savings. As shown in the next footnote, its estimated economic damage (around 20% of nominal GDP) would be equivalent to about three years’ worth of private savings. As shown in Fig. 9 in Chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, the annual private saving ranged from 7 to 8% of nominal GDP in the 2010s.

148

Long-Run Mild Deflation Under Fiscal Unsustainability …

section is to describe not only the mild deflation with near-zero rates that occurred from the mid-1990s, but also the price stagnation that commenced in the mid-1980s, the drastic decline in short-term yields that occurred in the first half of the 1990s, and the slowly flattening yield curves observed in the twenty first century. According to the Earthquake Research Committee (2014), there is a 4% chance of an inland earthquake occurring in Tokyo in any coming year, and around a 70% chance of one occurring in the next three decades (1 − (1 − 0.04)30 ≈ 0.706). The Disaster Management Department (2013) indicates that possible damage from such an earthquake would amount to around 20% of GDP in the initial year, and that complete recovery would take several years.22 Based on such a catastrophic event, in our model, π ≤ 0.04, L = 3, and d = 0.072, where (1 − d)3 ≈ 1 − 0.2. Here, normal consumption c is detrended at one. It is assumed that the economy starts from 1980 with a switching probability (π > 0), and the catastrophic possibility ( > 0) is introduced from 1986 onwards. The timing for this setup accords with the observed stagnation of the price level that commenced from the mid-1980s, despite rapid monetary expansion, as demonstrated in Sect. 2. A set of parameters associated with money demand is chosen, as explained below. Given that c is detrended at one, a sequence of monetary growth μt for the years 1980–2017 is computed from the growth rate of the outstanding BOJ notes, which are adjusted by a real economic scale or divided by real GDP. In addition, μ is set at 0.02 from 2018 onwards, given that the long-run inflation target is 2%. In the FS regime, the money stock relative to a nominal economic scale ( PMt ct ) is constant; accordingly, it is set at the 1955–1970 average of the Marshallian k (the ratio of the BOJ notes relative to nominal GDP), or κ = 0.078. In this context, Japan’s fiscal policy was considered Ricardian before the early 1970s. λ is determined by Eq. (3.16) together with β = 0.98, χ = 1, μ = 0.02, c = 1, and κ = 0.078. PtQT (d=0) is approximated by Eq. (3.15) with a constant μ (= 0.02), and a time-varying Mt up to 2017, and an Mt growing at 2% from 2018. How should σ in Eq. (3.3) be determined? Given the preference specification in Eqs. (3.2) and (3.3), the money demand function is linearized as follows: χ + Mt−1 /Pt−1 ct . (Mt /Pt ) χ + Mt−1 /Pt−1 Rt +σ = −σ . Mt−1 /Pt−1 Mt−1 /Pt−1 R1,t−1 − 1 Mt−1 /Pt−1 ct−1 t−1 /Pt−1 Thus, σ χ+M can be interpreted as either interest elasticity or income Mt−1 /Pt−1 elasticity. In terms of interest elasticity, σ may be set at a rather low value. More concretely, we choose a value of σ = 0.01, as we explain below. Above, it is assumed that χ = 1 and MPtt = PMt ct = 0.078 for the FS regime.23 Thus, interest elasticity is computed as

22 The Disaster Management Department (2013) does not estimate initial and subsequent effects on GDP, but predicts that direct and indirect losses would be 47.4 trillion yen (around 10% of nominal GDP at FY2012), and 47.9 trillion yen (around 10%), respectively. We assume that the initial impact on real GDP is approximated by the sum of the estimated direct and indirect losses (9.8% + 9.9%). 23 Even in the FU regime, Mt initially remains close to the level that holds in the FS regime. Pt c

4 Calibration Exercises for Japan’s Long-Run Deflation

149

−0.13, given σ = 0.01. This interest elasticity value is quite comparable with the estimates of interest elasticity in the existing empirical literature, with estimates of −0.174by Nakashima and Saito (2012), −0.107 to −0.115by Fujiki and Nakashima (2019), and −0.0466 to −0.0999by Watanabe and Yabu (2018). In the case of income elasticity, on the other hand, our estimate differs from those in the literature. Fujiki and Watanabe (2004), Fujiki and Nakashima (2019), and others t−1 /Pt−1 is much less than estimate that it is close to one, but the above elasticity σ χ+M Mt−1 /Pt−1 one. However, in the current context, income elasticity is associated with temporary deviations from the detrended level c = 1. Thus, lower short-run elasticity may not be inconsistent with long-run unit elasticity. In addition, the property whereby t−1 /Pt−1 decreases in a liquidity trap when MPtt increases is empirically consistent σ χ+M Mt−1 /Pt−1 with the finding that money demand became less responsive to aggregate output as the real money balance grew (Nakashima and Saito 2012; Fujiki and Nakashima 2019). With inequality (3.21) satisfied in all the exercises,24 the accelerating inflationary (hyperinflationary) process is not feasible in either of the two regimes. Thus, the QTM price of 1980 is considered the only legitimate equilibrium price prevailing in the FS regime. The initial money stock M0 is set at 100.25 The initial price is set at a QT (d=0) FU level slightly less than the QTM price (P1980 = 1280 < P 1980 ≈ 1282), thereby initiating the deflationary process. In sum, the evolution of the price level and the yield curves, which is observed for the years 1986–2017, is simulated by assuming only three time-specific exogenous components: (1) the realized monetary growth from 1980 to 2017 (μt ), (2) a slight downward deviation of the initial price from the QTM price in 1980 QT (d=0) FU (P1980 < P 1980 ), and (iii) the small possibility of a catastrophic event, such as a Tokyo inland earthquake (π ≤ 0.04, L = 3, and d = 0.072). As discussed in Sect. 3.4.1, the price level prevailing during the FU regime is independent of the fiscal surplus (ε) and the initial holdings of public bonds (B0 ). Thus, no assumption is made for ε or B0 . As a baseline case (Case 1), we assume that is 0.144, given = (γ − η)d = 2 × 0.072 by Eq. (3.28), where γ denotes the degree of relative risk aversion, and η is determined by Eq. (3.19).26 As shown in Fig. 7a, the predicted price level is more deflationary than the observed level. In the absence of catastrophic shocks ( = 0 or d = 0 in Case 2), it is even more deflationary. Conversely, it is relatively inflationary with a higher σ (σ = 0.02 > 0.01 in Case 3). More empirically plausible cases are presented later. As demonstrated in Fig. 7b, the one-year yield predicted in Case 1 can capture the downward trend in short-term yields that appeared between the mid-1980s and 1

the above set of parameters, λχ − σ c (= λ in this case) is greater than one; it is 71.7 in Cases 1 and 2, 1.67 in Case 3, and 53.8 in Cases 4–7. 25 As implied by Eq. (3.25), the initial price level P N R is independent of the initial balance of the 1980 public bonds B1980 . 26 As we assume a low value for σ, inequality (3.20) and 0 < η < 1 are satisfied in all cases. Concretely, η is computed as 0.8035 in Cases 1 and 2, 0.9069 in Case 3, and 0.8450 in Cases 4–6. 24 Given

150

Long-Run Mild Deflation Under Fiscal Unsustainability …

a 350 300 250 200 150 100 50 0

QTM prices

Observed prices (private consumption deflator)

Case 1: β = 0.98, π = 0.04, Δ = 0.144

Case 2: β = 0.98, π = 0.04, Δ = 0.000

Case 3: β = 0.98, π = 0.04, Δ = 0.144, σ = 0.02

b 10%

8%

6%

4%

2%

0%

-2% Observed 1-year yield

Case 1: β = 0.98, π = 0.04, Δ = 0.144

Case 2: β = 0.98, π = 0.04, Δ = 0.000

Case 3: β = 0.98, π = 0.04, Δ = 0.144, σ = 0.02

Fig. 7 a Predicted price path for Cases 1, 2, and 3. b Predicted 1-year interest rates for Cases 1, 2, and 3

4 Calibration Exercises for Japan’s Long-Run Deflation

151

the mid-1990s, and the near-zero interest rate situation that commenced from the mid-1990s. In the early 1990s, the one-year yield temporarily increased owing to a temporary decrease in the money stock per unit of output. Comparing Case 1 ( > 0) and Case 2 ( = 0), such a downward trend in short-term yields is driven not by endowment shocks, but by a switching possibility (π > 0). In comparison with Case 3 (σ = 0.02 > 0.01), an extremely low value for σ is necessary to generate near-zero interest rates in the mid-1990s. Note that the assumption of a constant discount factor β may limit our ability to trace the observed one-year yield. With a lower β ( 0.02), the price process is even less deflationary, as shown in Fig. 8a, and short-term yields decline much more slowly, as shown in Fig. 8b. However, Case 7 produces more realistic upward-sloping yield curves, as shown below. How do the term structures of interest rates behave in each case? In Fig. 9a–d, the predicted yield curves are compared with the observed one; that is, the observed one-year yield is replaced by the predicted one, on which the observed term spreads are added. As shown in Fig. 9a,28 the predicted yield curves are all upward sloping in Case 1, reflecting more inflationary pressure from future price surges, and less deflationary pressure caused by catastrophic endowment shocks ( = 0.144). The predicted yield curve in Case 2 is much less upward sloping, with the deflationary expectations dominating in the absence of the catastrophic endowment shock (see Fig. 9b). Conversely, in Case 6, the yield curve is more upward sloping with the deflationary expectations being less dominant as a result of the larger endowment shocks (see Fig. 9c). However, even in Case 6, the predicted yield curves are less upward sloping than the observed yield curves. In particular, the predicted ten-year over one-year yield (0.5%) is much smaller than the observed one (2.5%) in 1996. In Case 7, increasing inflationary pressures through a higher π (π = 0.03 > 0.02), as shown in Fig. 9d, generate the predicted upward-sloping yield curves that are

27 According to Okazaki and Sudo (2018), the natural rate of interest was 4% in the 1980s, but it decreased to 0.3% in the 2010s. 28 For the yield curve starting from 1981, we assume that endowment shocks are absent ( = 0) because we assume that catastrophic endowment shocks are present from 1986 onwards.

152

Long-Run Mild Deflation Under Fiscal Unsustainability …

a 350 300 250 200 150 100 50 0

QTM prices

Observed prices (private consumption deflator)

Case 1: β = 0.98, π = 0.04, Δ = 0.144

Case 4: β = 0.99, π = 0.04, Δ = 0.144

Case 5: β = 0.99, π = 0.02, Δ = 0.144

Case 6: β = 0.99, π = 0.02, Δ = 0.216

Case 7: β = 0.99, π = 0.03, Δ = 0.216

b 10%

8%

6%

4%

2%

0%

-2% Observed 1-year yield

Case 1: β = 0.98, π = 0.04, Δ = 0.144

Case 4: β = 0.99, π = 0.04, Δ = 0.144

Case 5: β = 0.99, π = 0.02, Δ = 0.144

Case 6: β = 0.99, π = 0.02, Δ = 0.216

Case 7: β = 0.99, π = 0.03, Δ = 0.216

Fig. 8 a Predicted price path for Cases 1, 4, 5, 6, and 7. b Predicted 1-year interest rates for Cases 1, 4, 5, 6, and 7

4 Calibration Exercises for Japan’s Long-Run Deflation

153

a 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0%

One-year interest rates

1986

1991

1996

2001

2006

2011

2016

1986 (observation)

1991 (observation)

1996 (observation)

2001 (observation)

2006 (observation)

2011 (observation)

2016 (observation)

b 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0%

One-year interest rates

1986

1991

1996

2001

2006

2011

2016

1986 (observation)

1991 (observation)

1996 (observation)

2001 (observation)

2006 (observation)

2011 (observation)

2016 (observation)

Fig. 9 a Predicted yield curves for Case 1 (β = 0.98, π = 0.04, = 0.144). b Predicted yield curves for Case 2 (β = 0.98, π = 0.04, = 0.000). c Predicted yield curves for Case 6 (β = 0.99, π = 0.02, = 0.216). d Predicted yield curves for Case 7 (β = 0.99, π = 0.03, = 0.216)

154

Long-Run Mild Deflation Under Fiscal Unsustainability …

c 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0%

One-year interest rates

1986

1991

1996

2001

2006

2011

2016 2001 (observation)

1986 (observation)

1991 (observation)

1996 (observation)

2006 (observation)

2011 (observation)

2016 (observation)

One-year interest rates

1986

1991

1996

2001

2006

2011

2016

1986 (observation)

1991 (observation)

1996 (observation)

2001 (observation)

2006 (observation)

2011 (observation)

2016 (observation)

d 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0%

Fig. 9 (continued)

4 Calibration Exercises for Japan’s Long-Run Deflation

155

500 450 400 350 300 250 200 150 100 50 0

Observed prices

Predicted prices before price surge

Predicted prices after price surge

Fig. 10 Predicted prices before and after a price surge in 2025 for Case 6 (β = 0.99, π = 0.02, = 0.216)

more consistent with the observed curves in the 2000s and 2010s. Nevertheless, the predicted yield curve is still flatter than the observed one in 1996. In either case, a discontinuous nominal adjustment following a catastrophic event would be immense. As an example, as Fig. 10 demonstrates for Case 6, if a switch occurred in 2025, then the price level would be multiplied by 5.2 from 2024 to 2025, decline at a rate of 6.1% from 2025 to 2028 [from Eq. (3.18) or (A.3)], and then commence on a 2% inflation path in 2028. Thus, the price level would be multiplied by 4.3 in terms of the long-run trend (5.2 × (1 − 0.061)3 ≈ 4.3). In the same case, one-year yields would immediately leave the zero level and then overshoot a long-run rate of 3% by 1.2% from 2025 to 2027, based on Eq. (A.4). Then, to what extent would a government commit to future fiscal reforms upon the price surge? To answer this question, the share of the unfunded (bubble) component in the real valuation of public bonds needs to be computed. In all seven cases, the share of the unfunded component in the real valuation of the public bonds, which is computed from Eq. (3.25), is significant during the FU regime.29 As reported for Case 6 in Table 1, for example, the share of the unfunded component amounts to 34.2% in 1980, 58.4% in 2000, 69.9% in 2010, 77.2% in 2017, and 83.8% in 2025. As discussed in the final paragraph of Sect. 3.4.1, as time goes by, the price surge becomes steeper at switching, and the unfunded share is larger as a consequence of heavier devaluations. Compared with other cases, the unfunded share increases with 29 As

implied by Eq. (23), the share of the unfunded component is independent of the initial value of the public bonds (B1980 ).

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Long-Run Mild Deflation Under Fiscal Unsustainability …

Table 1 The share of the unfunded component relative to the real valuation of the public bonds during the FU regime 1980 (%) 2000 (%) 2010 (%) 2017 (%) 2025 (%) Case 1: β = 0.98, π = 0.04, = 0.144 26.7

64.8

80.3

87.9

93.3

Case 2: β = 0.98, π = 0.04, = 0.000 45.1

83.1

91.6

95.1

97.4

Case 3: β = 0.98, π = 0.04, = 0.144, 18.3 σ = 0.02

49.1

68.0

79.2

88.0

Case 4: β = 0.99, π = 0.04, = 0.144 19.1

49.4

66.3

76.6

85.3

Case 5: β = 0.99, π = 0.02, = 0.144 44.3

69.3

78.9

84.5

89.3

Case 6: β = 0.99, π = 0.02, = 0.216 34.2

58.4

69.9

77.2

83.8

Case 7: β = 0.99, π = 0.03, = 0.216 14.8

35.0

49.5

60.4

71.5

more deflationary pressure caused by either a lower β or a smaller , and it decreases with higher initial inflation caused by a combination of a higher π and a larger . As discussed above for Case 6, if the price surge took place in 2025, then the longrun price level would be multiplied by 4.3. The real valuation of public bonds would decline to 23.3% upon the price surge (1 ÷ 4.3). However, as demonstrated in Table 1, the funded component would amount to 16.2% in 2025 (1−0.838) and would thus be less than 23.3%. Accordingly, the difference of 7.1% (0.233 − 0.162) would be covered by future fiscal reforms. In this way, fiscal sustainability is recovered largely by immediate price surges, and partly by strict fiscal reforms in the future.

5 Conclusion One of the most important implications from this chapter is that the current mild deflation, or nearly stable prices, are tightly linked with a (far) future price surge. Thus, the present mild deflation with near-zero interest rates cannot be controlled completely independently of such a long-run equilibrium context. More concretely, mild deflation, or nearly stable prices, cannot be remedied by the current monetary/fiscal expansion. They can be dissolved only at the cost of one-off price surges. In this context, fiscal sustainability will be restored not by hyperinflation, or continuous mild inflation with near-zero interest rates, but largely through a heavy bond devaluation caused by such a one-off price surge together with strict fiscal reforms. One caveat of these implications is that those living in the pre-surge period are assumed to be identical to those living in the post-surge period in the current representative agent framework. However, intergenerational effects on the price level may emerge in an overlapping generations framework.30 Given that a one-off price surge is unprecedented by its nature, and is absent from any observations of the past decades, it is a type of Peso problem that raises 30 For example, Aiyagari and Gertler (1985) examine the intergenerational impacts on nominal variables in the context of overlapping generations models.

5 Conclusion

157

the following questions. Is any prediction based on the current model unrealistic or a mere theoretical abstraction? Is there any episode comparable with the one-off price surge phenomena in Japanese monetary history? Our answer is no for the first question, and yes for the second. As discussed in detail in Chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, the sharp price increase emerging immediately after the end of World War II in August 1945 is often interpreted as a typical hyperinflationary phenomenon, but this can be construed more consistently as a price surge event. If it were a hyperinflationary phenomenon, the real money balance, or the money balance adjusted by a nominal macroeconomic scale, would degenerate to zero quite rapidly. According to Fig. 1 in Chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, however, the relative outstanding BOJ notes (divided by nominal gross national expenditure [GNE]), or Marshallian k declined substantially after 1945, when they were close to 50%, but did not fall to 0%. Instead, by 1949, it declined to just below 10%, which was the prewar average. The price level ceased to surge abruptly once Marshallian k reached its prewar average in the late 1940s. Taking a closer look at the price behavior during the same period, GNE deflator multiplied 31.1 times,31 while the outstanding BOJ notes multiplied 6.4 times. Thus, the money-stock-adjusted price level multiplied only 4.9 times (31.1 over 6.4) for five years, far from a hyperinflationary phenomenon. As a result of this sharp price surge, the Japanese government could repay its public debt practically without any sovereign default; the debt–GNE ratio indeed declined from 174% in 1945 to 19% in 1949.32 Consistent with the setup of our model, fiscal discipline was finally established by the Dodge Line in 1949, four years after the war had ended. As discussed in Chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, the fiscal surplus indeed turned out to be positive from 1947 on. Of course, the sources of such strong money demand, which prevailed before the price surge, differ between the wartime and contemporary periods. Whereas the latter has been induced by near-zero interest rates as discussed intensively in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy” and this chapter, the former was driven partly by strong demand for BOJ notes from black markets for income concealment purposes as discussed in Chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, and accompanied by money demand for various kinds of banknotes 31 As discussed in detail in Chapter “Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, GNE deflator, which was estimated for the wartime and postwar periods by the Economic Planning Agency (1964), reflected transactions involving not only official (authorized) prices, but also (black) market prices. Thus, this is not a case in which the level of nominal GNE was heavily underestimated as a result of employing only officially regulated prices for the estimation. 32 See Chapters “Introduction: Toward a Monetary and Fiscal Theory of the Price Level and Central Banknotes and Black Markets: The Case of the Japanese Economy During and Immediately After World War II”, for the data sources.

158

Long-Run Mild Deflation Under Fiscal Unsustainability …

issued in the occupied territories as discussed in Chapter “On Large-Scale Monetary Operations in the Japanese Occupied Territories During the Pacific War”. Immediately after the end of the war in August 1945, however, strong money demand from black markets and in the occupied territories disappeared completely. As shown in Fig. 1 in Chapter “Introduction: Toward a Monetary and Fiscal Theory of the Price Level”, Marshallian k (the relative size of the outstanding proportion of BOJ notes) was quite stable during the pre- and postwar periods; it stayed at around 10% from 1890 to 1936, and at around 8% from 1950 to 1995. Given such a longrun trend in the relative money stocks, it is likely that the prediction demonstrated in Sect. 4 is not only theoretically consistent, but also empirically plausible. Based on the model, at some point in the future the relative proportion of outstanding BOJ notes, which was already greater than 20% in 2018, will revert to the postwar average (around 8%) as a result of a one-off price surge, whereby prices rise to a level probably several times as high as before. Then, the government could repay the public debt largely without any sovereign default if it committed to future fiscal reforms. Given the 1945–1949 experience, the above prediction is not as unrealistic as it may appear. As a final remark, it is again worth reminding readers that one-off price surges are totally different from hyperinflation33 ; that is, the real money balance is reduced from an excessively high level to a normal level in the former case, whereas it degenerates to zero under hyperinflation, resulting in an extremely chaotic monetary situation. As repeatedly emphasized throughout this book, it is crucially important to restore fiscal sustainability, thereby preventing a price surge from falling into genuine hyperinflation.

Appendix: Price Behavior During the FS Regime with d > 0 Suppose that the economy switches to the FS regime in time s. The price level QT (d=0) when catastrophic shocks disappear completely in time coincides with Ps+L s + L. From Eq. (3.11), the following holds between time s + L − 1 and s + L: QT Ps+L−1 QT (d=0) Ps+L

⎡ ⎤  − σ1 M 1 s+L−1 ⎣1 − λ χ + = (1 − d)c⎦. QT β(1 − d) Ps+L−1

QT (d=0) and Ms+L−1 as fixed, and marginally increasing d from zero and Taking Ps+L QT QT (d=0) Ps+L−1 from Ps+L−1 , the following total differential is obtainable by a first-order approximation:

33 Given a set of parameters for Japan’s economy, λχ − σ1

are ruled out in both the FU and FS regimes.

c > 1 holds, and hyperinflationary equilibria

Appendix: Price Behavior During the FS Regime with …

159

⎤ Ms QT (d=0) QT (d=0) R − 1 Ps 1,s QT (d=0) ⎣ ⎦ > 0, (A.1) η = QT (d=0) / d = R1,s / 1+ s σ χ + QTM(d=0) Ps+L−1 P ⎡

QT Ps+L−1

s

QT (d=0) where R1,s and (3.15). If:

Ms PsQT (d=0)

 / χ+

Ms PsQT (d=0)

 / χ+ QT (d=0) Ms

Ps

 are constant, given Eqs. (3.14) and 

Ms PsQT (d=0)

> σ,

(A.2)

then 0 < η < 1. Equation (A.1) is approximated as: QT Ps+L−1 =

1 P QT (d=0) . (1 − d)η s+L−1

Using the same approximation technique leads to:  QT Ps+l =

1 (1 − d)η

 L−l

QT (d=0) Ps+l ,

(A.3)

for l = 0, 1, 2, . . . , L − 1. From Eq. (3.9): QT R1,t =

QT Pt+1 1 . β(1 − d) PtQT

Together with Eq. (A.1), the total differential is derived by a first-order approximation: QT R1,t QT (d=0) R1,t

/ d = 1 − η.

QT (d=0) QT > R1,t . Thus, if 0 < η < 1, then R1,t

(A.4)

Central Bank Cryptocurrencies in a Competitive Equilibrium Environment: Can Strong Money Demand Survive in the Digital Age?

Abstract This chapter discusses the possible macroeconomic consequences of the introduction of cryptocurrencies by central banks (so-called central bank cryptocurrencies or CBCCs) in a competitive equilibrium environment. In this setup, central banks set not only the money supply, but also the interest rate on CBCCs, whereas bond interest rates, the price level, and the exchange rates between CBCCs are determined in competitive markets. We first resolve a severe confrontation between the quantity theory of money (QTM) and the fiscal theory of the price level (FTPL) in that, as long as the currency interest rate lies below the bond interest rate, the QTM is applicable in principle. However, once the bond interest rate (asymptotically) matches that of the currency, the QTM is replaced by the FTPL, or the monetary and fiscal theory of the price level (MFTPL), in which the government’s budget constraint as well as money market conditions jointly work to determine the price level as discussed in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy and Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”. We then investigate whether the introduction of CBCCs plays a role in the disappearance of strong money demand (currently present at near-zero interest rates in Japan) and its alternatives. We find that if a central bank sets the currency interest rate below a near-zero bond interest rate, then strong money demand disappears, and the massive issuance of long-term public bonds is no longer absorbed in currency markets. However, once the consolidated government succeeds in lowering the currency interest rate to be deeply negative, it can obtain immense seigniorage, allowing it to repay these public bonds. In addition, if the bond interest rate also falls, even below zero for long periods, then the government can exploit seigniorage from CBCC holders without limit.

1 Introduction Can strong money demand, which is currently present at near-zero interest rates in Japan, survive in the digital age? Does the emergence of central bank cryptocurrencies (CBCCs) expel strong money demand from the macroeconomy? We provide © Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9_6

161

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Central Bank Cryptocurrencies in a Competitive Equilibrium …

definitive responses to these questions by the end of this chapter. However, for this challenging purpose, we first require a long detour. Why do cryptocurrencies attract acute interest from those in the financial world in the first place? One of the most important reasons is that it is possible to transfer cryptocurrencies promptly in any amount to whoever transacts within a cryptocurrency system. That is, the electric delivery of cash from one peer to another may be just as convenient as the physical delivery of cash from one hand to another. As suggested by the title of Nakamoto (2008), cryptocurrencies may simply be in the form of peer-to-peer electric cash, as opposed to hand-to-hand physical cash. Nevertheless, cryptocurrencies, delivered on networks and not in person, still appear as something mysterious to many. In the case of physical cash, that one has a note in a wallet immediately guarantees one as the legitimate owner. If that owner as payer then delivers this by hand, the other receiving it as payee can rightly claim to be the new owner. That is why delivering cash from one person to another by hand immediately implies settlement between the payer and payee. However, in the case of electric cash, owners do not retain tokens, with ownership only recorded in electric ledgers. Why then among those participating in a cryptocurrency system do they believe that a certain token belongs to a particular person as the legitimate owner just by recording it? They believe so because ledgers are trusted to record this information with unrivaled accuracy, with a complete record of the changes in the ownership of tokens from the initial issue to the present. Any cryptocurrency system requires three kinds of cryptanalytic mechanisms to guarantee the extreme accuracy of the electric ledgers distributed among the system participants. First, owing to asymmetric cryptography, only the true owner of a token can transfer it to another, while only the one receiving it from its true owner can employ it for payment. While there is a pairing of public and secret keys in asymmetric cryptography, a public key identifies every participant in a cryptocurrency system. A legitimate owner of a token can then use this by placing his own secret key, unknown to others, into the system. In remitting cash, the owner as payer transfers a token to another identifiable person with a public key, such that only the payee can unlock a token-use restriction using the secret key, paired with the key publicly posted by the payee. Utilizing asymmetric cryptography in this way, the one receiving a token from its true owner can transfer it to another as the new legitimate owner. Second, a cryptanalytic mechanism prevents double payments in an effective manner. With physical cash such as coins and banknotes, the transfer of a token to a particular person immediately implies that it is not possible to transfer it to anyone other than this recipient. With physical cash, unless counterfeited at considerable cost, it is almost impossible to make double payments. In the case of electric cash, however, it is relatively easy to duplicate tokens on distributed ledgers. Nevertheless, while even a true owner may counterfeit a token, and then transfer false tokens to multiple peers, any cryptocurrency system will involve sophisticated devices to prevent double payments. As an example, with Bitcoin, a representative private cryptocurrency system (described in Sect. 2), special participants, known as miners, have an incentive to check rigorously for double payments every ten minutes.

1 Introduction

163

Third, a cryptanalytic mechanism also prevents the falsification of any record in the distributed ledgers. A brief explanation of this mechanism is that a distributed ledger records for each token its transaction history from the initial issue to the present using a long sequence of binary numbers, zero or one. In most cryptocurrency systems, a hash function seals this binary sequence at some time interval, say every ten minutes. This transforms the binary sequence into a particular 256-digit binary sequence. Importantly, once a hash function seals a token’s transaction history, a vestige of broken seals easily detects any record falsification; that is, the hash function yields a very different number from any falsified sequence, even if slightly altered. Combined, these three mechanisms ensure that the recorded transaction history of each token entails extreme accuracy, thereby preventing double payments and record falsification in an effective manner. International remittances can exploit these conveniences provided by cryptocurrency systems to the maximum degree. In the existing currency system, fund transfers over national borders operate in a complicated manner, that is, via bucket brigades among multiple private banks and through the intermediation of several central banks. As shown in Fig. 1, for example, a money transfer from Firm A in Country I to Firm B in Country II involves two central banks (located in Country I and Country II), and Private Banks a, b, and c. In the actual remittance system, Private Bank c, which has branches in both countries, may not necessarily intermediate over national borders, if Private Bank a and Private Bank b establish correspondent accounts with each other, and they are connected via SWIFT (Society for Worldwide Interbank Financial Telecommunication). In any case, international money transfers are quite time-consuming and costly because of the involvement of multiple private banks

Country I’s CB Reserves

Bank a

Country II’s CB Reserves

Bank c

Firm A

Bank b

Firm B

Cryptocurrencies

Fig. 1 Comparison of conventional currencies and cryptocurrencies in sending money

164

Central Bank Cryptocurrencies in a Competitive Equilibrium …

and several central banks. However, as Fig. 1 also illustrates, it is possible in a cryptocurrency system to transfer tokens directly from Firm A in Country I to Firm B in Country II without any intermediation by private or central banks. Accordingly, cryptocurrency systems achieve quick and cheap international transfers. Given the highly convenient functions described, cryptocurrencies are likely to substitute for or complement existing central bank (CB) currencies such as reserves and notes. In fact, not a few central banks have begun large-scale experiments to test the validity of CBCCs and conduct practical trials. For example, the Bank of Canada (BOC) and the Monetary Authority of Singapore (MAS), both of which were among the first central banks to trial CBCCs, are jointly pursuing the Jasper–Ubin project (BOC and MAS 2019). Elsewhere, the European Central Bank (ECB) and the Bank of Japan (BOJ) are also undertaking a joint project known as STELLA (ECB and BOJ 2017, 2018). In this chapter, we demonstrate that CBCCs make for a possibly significant impact on the nominal pricing system, consisting of the price level and the nominal rates of interest, owing to the following two features, either of which is practically impossible using traditional banknotes or coins, but quite possible with the newly introduced CBCCs. First, it is difficult to remunerate conventional banknotes or coins regularly. In the case of a banknote, it is challenging to determine how long a legitimate owner precisely holds it before handing it to another because there is no transaction record on either its face or reverse side. Thus, according to the holding period, there may not be any positive (or negative) interest on banknotes or coins. If instead positive interest is forced on a banknote, the banknote owner needs to go to a bank’s offices to collect the positive coupons, and have their receipt recorded on either side of the banknote itself. In the case of negative interest, banknote owners will have to stick stamps on notes at a fixed interval to validate their own notes. In contrast, in the case of cryptocurrencies, it is quite easy to remunerate tokens with either positive or negative interest because the electric ledgers correctly record the holding period for each owner of a particular token. Second, it is physically inconvenient to hold different kinds of banknotes with flexible exchange rates. For example, it is much easier to pay using yen notes only than a combination of yen and dollar notes. Once selected for daily use, one also does not need to worry about the exchange rate between and among yen notes and coins as the exchange rates between different yen currency notes and coins are fixed at one-toone rates. For example, it is always possible to exchange a ¥1000 note for two ¥500 coins. However, if CB currencies are transacted not hand-to-hand physically but peerto-peer electronically, flexible exchange rates among the various cryptocurrencies issued by the same central bank will not sacrifice any currency convenience. For example, it is convenient for consumers and retailers to use different CBCCs with flexible exchange rates at the same time once electric wallets have money-changing functions installed for the various kinds of electronic tokens. In sum, unlike conventional banknotes or coins, it is easy to remunerate CBCCs with either positive or negative interest, and exchange them at flexible rates among

1 Introduction

165

various kinds of tokens. This is likely to change the current currency system drastically in which CB currencies such as banknotes, coins, and reserves are not in principle remunerated,1 and with a one-to-one exchange rate legally established among the different CB currencies.2 In this chapter, we demonstrate that this revolutionary reform in currency systems also revises conventional monetary theory fundamentally. More concretely, the introduction of CBCCs with remuneration and flexible exchange rates will change how central banks operate in a competitive equilibrium environment. In most existing monetary models, a central bank is intended to directly control short-term interest rates as in actual policy practice, despite a common theoretical setup in which all agents, including a central bank and a government, behave as price-takers in competitive markets. However, such a combination of policy practice and theoretical setup often generates serious logical inconsistencies. As one of the best-known examples, Sargent and Wallace (1975) argue that if a central bank directly controls shortterm interest rates, the price level is indeterminate, and inflation rates fluctuate via self-fulfilling expectations without any exogenous shocks. The fiscal theory of the price level (FTPL), which assumes that a government and a central bank behave as a consolidated government, is an alternative theoretical device used to determine a unique price level under interest-rate controls. However, the FTPL does not help resolve this logical inconsistency, but instead contributes to deepening it further. Under the FTPL, a consolidated government’s budget constraint, which states that the current real balance of public bonds is equal to the present value of future fiscal surpluses, needs only hold at the equilibrium price level. In other words, the budget constraint serves as an equilibrium condition for public bond markets in the FTPL. This setup of the FTPL is inconsistent with that of a competitive equilibrium environment, in which a budget constraint of any agent holds at not only on- but also at off-equilibrium prices. To overcome this logical inconsistency, Bassetto (2002) presents a new equilibrium concept as an alternative to a competitive equilibrium, and treats the consolidated government as a big player, who is no longer a price-taker. Here is yet another logical inconsistency. In the presence of interest-free CB notes, but in the absence of exchange markets for CB currencies, the introduction of interestbearing excess reserves creates opportunities for arbitrage. In particular, unconventional monetary policies accompanied by negative interest on excess reserves would trigger a large-scale shift from excess reserves to CB notes without any quantity control on currency holdings. The presence of arbitrage opportunities clearly jeopardizes the existence of competitive equilibria. Bassetto (2004) again proposes an alternative to a competitive equilibrium framework to justify negative interest rate policy. However, taking leave of a competitive equilibrium framework immediately 1 There are important exceptions in which it is possible to add positive or negative interest to excess

reserves held at a central bank. However, apart from some quantity restrictions, remunerated reserves continue to be one-to-one exchanged for unremunerated reserves. 2 As discussed in Sargent and Velde (1999), England, Continental Europe, and North America established the standard formula through which any CB currency is convertible at one-to-one exchange rates only in the nineteenth century. In this regard, the current currency system has a relatively short history.

166

Central Bank Cryptocurrencies in a Competitive Equilibrium …

implies that its analytical simplicity and lucidity are lost altogether. In Bassetto (2002, 2004), analysis indeed becomes extremely complicated, even for his admittedly simple setup. In the context of monetary theory, it may then be a better idea to stick to a competitive equilibrium framework instead of abandoning it completely. As discussed, the introduction of CBCCs is likely to expand greatly the set of available monetary policy instruments. For example, a central bank can set interest rates on currencies as well as a supply plan for each currency, and create exchange markets among CB currencies. Consequently, money market rates, exchange rates among CB currencies, and the price level in a core CB currency are determined in a competitive equilibrium manner. Unlike the current currency system, a central bank never exercises direct controls over money market rates, but instead sets only the currency interest rate.3 In this case, the currency interest rate serves only as the lower bound for market interest rates. In this chapter, we investigate in detail how to reformulate two major monetary theories, namely, the quantity theory of money (QTM) and the FTPL, in this competitive equilibrium setup. As discussed in Sect. 3, as long as the market interest rate lies above the currency interest rate in a core currency, the standard QTM in principle holds. That is, the price level is still proportional to the aggregate quantity of currencies after the conversion of currency exchange rates. Alternatively, if the market interest rate coincides with the currency interest rate in a core currency, and real money demand saturates at a certain level, then the standard FTPL holds. Because CB currencies do not yield any additional liquidity service, but carry the same interest rate as bonds, public bonds and CB currencies are now exactly equivalent. In this situation, the real balance of both public bonds and additional CB currencies should equal the present value of any future fiscal balances. However, if real money demand never saturates, and the market interest rate (asymptotically) matches the currency interest rate, then the monetary and fiscal theory of the price level (MFTPL) is applicable, as discussed in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy and Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”. The real balance of public bonds in excess of future fiscal surpluses is now supported by excess money demand (Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy”), or a bubble term coexisting with strong money demand (Chapter “Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”). In the MFTPL, excess money demand, which we may interpret as the bubble term in equilibrium analysis, generates deflationary pressures on the price level, despite the rapid expansion of currencies and public bonds. As discussed so far, we can clearly respond to the question posed at the beginning of this chapter, “Can strong money demand survive in the digital age?” If a central bank controls the currency interest rate below a near-zero market interest 3 Iwamura

(2016) distinguishes between currency and bond interest rates, treating the former as policy instruments and the latter as market rates.

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rate, strong money demand never emerges. That is, unless the lower bound for market interest rates, as imposed by the currency interest rate, is binding at any moment, the QTM always holds, and the price level is accordingly proportional to the aggregate quantity of currencies. At the same time, strong money demand never absorbs massively issued public bonds. As discussed in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy and Long-Run Mild Deflation Under Fiscal Unsustaina– Bility in Contemporary Japan”, the price level would experience a one-off jump immediately after strong money demand disappears. In this way, the introduction of CBCCs provides an opportunity to restore both the QTM in currency markets and fiscal sustainability in public bond markets, but also triggers a large-scale adjustment in the price level and market interest rates, particularly long-term rates, during the normalization process for currency markets. However, if the consolidated government can maintain a negative currency interest rate far below the near-zero market interest for a long period, the situation changes dramatically. In this case, it loses strong money demand as an instrument to support the massive issuance of public bonds, but instead may obtain immense seigniorage from currency holders. If not only the currency interest rate but also the market interest rate is negative in terms of some core currency, then the consolidated government can enjoy seigniorage without limit, thereby sustaining massively issued public bonds. However, double negative rates tax currency holders heavily, and they may forgo the use of CB currencies for everyday settlement. This chapter is organized as follows. In Sect. 2, we briefly explore how Bitcoin works as a representative private cryptocurrency, and then how CBCCs deliver convenience equivalent or even superior to existing CB reserves and notes. We also demonstrate that the system of CBCCs is much simpler than that of Bitcoin. A major reason for this is that with private cryptocurrencies, participants never trust each other, whereas with CBCCs, central banks and private banks authorized by central banks obtain the trust of participants in a currency system. In Sect. 3, we investigate how the QTM and the FTPL change in a competitive market equilibrium with multiple currency interest rates and currency exchange markets. Whether the QTM, the FTPL, or the MFTPL holds then depends on the difference between market and currency interest rates, while how the consolidated government obtains seigniorage is contingent on the signs of the market and currency interest rates in some core currency. Section 4 offers the final answer to the initial question, “Can strong money demand survive in the digital age?”

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2 An Overview of CBCCs 2.1 How Do Private Cryptocurrencies Work? We first describe how Bitcoin, a representative private cryptocurrency, works according to Nakamoto (2008), among others, and then compare it to CBCCs. The main reason for this is that Bitcoin is a private cryptocurrency in which system participants never trust each other, and thus exhibits a striking contrast with CBCCs in which participants place great confidence in a central bank as the system operator. Given such high confidence in a central bank, CBCCs have a much simpler structure for consensus building for transaction records in the electric ledgers distributed among system participants compared with those for private cryptocurrencies such as Bitcoin. For example, Bitcoin implements a special mechanism, called proof-of-work, to prevent remitters from making double payments. All transactions in electric tokens stay together in the one block every ten minutes, and multiple miners, engaged in closely examining each block, must present proof-of-work for their investigation by devoting a tremendous amount of computational resources. In the presence of such proof-of-work, it also costs substantially more to balance altered records whenever there is any falsification in the distributed ledgers. With Bitcoin, as anyone can access the online ledgers and participate in investigating each block, system participants never trust each other. Without such a proof-of-work mechanism, perfect strangers in a system never believe that miners have a proper incentive to check double payments thoroughly, and little inducement to alter open ledgers. Let us take a closer look at a distributed ledger system, referred to as a blockchain. With Bitcoin, the recording of token transfers is in chronological order, in series, and in binary sequences, with all recorded transactions organized in the one block every ten minutes. A new block, just examined for double payments by miners, is then stacked on these blocks. Thus, a distributed ledger system is a chain of blocks, or a blockchain. Bitcoin seals this chain of blocks as follows. To start, all transactions in the one block are summarized by a Merkle tree, and time-stamped by a hash function. More concretely, a long binary sequence, summarized by a Merkle tree, is returned as a 256-digit binary value by a hash function. Once a sealed transaction record is falsified, the hash value from any altered sequence differs completely from the hash value originally computed from the authentic sequence. In Bitcoin, as shown in Fig. 2a, a hash value is generated from not just the transaction sequence in one block, but also from the sequence extended by the hash value of the previous block. Consequently, if falsification is made in any past block, then the hash values for all of the blocks following this falsified block differ completely from the initially time-stamped values. In this way, any ledger falsification is immediately recognized by the participants concerned. In this blockchain system, proof-of-work works as follows. Miners, engaged in checking double payments, do not merely compute hash values from the summarized

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a Previous Hash

Transaction Information Summarized by a Merkel Tree

Previous Hash

Transaction Information Summarized by a Merkel Tree

Previous Hash

b Previous Hash

Nonce

Transaction Information Summarized by a Merkel Tree

Previous Hash

Nonce

Transaction Information Summarized by a Merkel Tree

Previous Hash

Fig. 2 a Blocks time-stamped by hash functions. b Blocks verified by proof-of-work

sequence plus the previous hash value, but have to satisfy demanding conditions for a newly generated hash value. As shown in Fig. 2b, a miner inserts a nonce, an arbitrary binary sequence, between the hash value from the previous block and the summarized sequence, and has to present a hash value with N digits initially equal to all zeros. As the Bitcoin system chooses a larger N, it takes more computational resources for a miner to find an appropriate nonce. For example, if N = 40, then the probability that the initial 40 digits are all zeros in the one trial is about one over 1.1 trillion (≈ 1/240 ). A miner finding an appropriate nonce before anyone else can receive a certain number of newly supplied tokens as a reward. In the Bitcoin system, the value of newly supplied tokens is equal to the value of the entire computational resources used, as devoted by all miners participating in proof-of-work.4 Suppose that I participants as miners have identical computational abilities. Each miner wins new tokens as a reward with probability 1I , and the expected value of this reward is equal to (l × PBC )/I , where l is the number of new tokens, and PBC is the price per token. Miners will participate in competition for proof-of-work as long as the expected reward exceeds the computation cost to find a nonce for a required N, or C(N ). That is, the following inequality is available for PBC : PBC ≥

I × C(N ) l

Given that the above inequality holds, increasingly more miners continue to participate in proof-of-work. Accordingly, PBC = [I × C(N )]/l is satisfied in equilibrium. That is, the value of Bitcoin is proportional to the total computational resources devoted by all participating miners (I × C(N )). The Bitcoin system controls N, such that the number of newly supplied tokens can be almost constant every ten minutes. That is, the token supply is nearly fixed per unit of time. As the demand for Bitcoin becomes stronger, more and more miners participate in proof-of-work with the anticipation of token appreciation. Then, given N, it takes less time for miners to find an appropriate nonce, and the token supply increases per unit of time. To maintain a fixed supply every ten minutes, the system 4 Iwamura

et al. (2019) provide a detailed discussion of the valuation of Bitcoin.

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raises N as a way to place tasks that are more difficult on the increasing number of miners. Conversely, with the anticipation of token depreciation accompanied by weaker demand, the system lowers N to make a decreasing number of miners find an appropriate nonce more easily. Given this fixed nature of token supply, the value of Bitcoin is quite sensitive to fluctuations in token demand; that is, the price of Bitcoin appreciates (depreciates) quickly with stronger (weaker) token demand. This proof-of-work mechanism, which disciplines miners for the examination of double payments, also contributes to discouraging ledger alteration. Given extremely costly proof-of-work, it is next to impossible for anyone to quickly balance falsified records in a completely sealed block by recomputing hash values for the following blocks consistently given the past series of N. However, this also works to sacrifice the convenience of Bitcoin as a currency. First, the major convenience of hand-tohand physical cash such as banknotes or coins comes from immediate settlement after handing it to someone. However, it takes a relatively long time for peer-to-peer electric cash such as Bitcoin to complete settlement. In the case of Bitcoin, it takes six blocks, or about one hour, to finalize ordinary transactions, while it takes 100 blocks, or more than 16 h, to activate the newly supplied tokens as reward. Second, all currency systems have evolved in such a way that operational costs may be economized, but Bitcoin runs counter to this history of currencies. For example, precious metals such as gold and silver have been common as coinage in the past, but this is mainly because these metals do not find ready use for production or consumption, other than as a means of currency. However, in undertaking proof-ofwork, Bitcoin exhausts an enormous amount of computational resources, which are rather useful for production and services. The fact that scarce computational resources are so wastefully used for a private cryptocurrency system may be interpreted as not the evolution of currency but rather its devolution.

2.2 How Do CBCCs Work? We now examine how a central bank introduces cryptocurrencies as substitutes or complements to CB reserves and notes. As outlined earlier, CBCCs have simpler structures in consensus building among system participants than private cryptocurrencies in the following respects. First, the most significant difference between private cryptocurrencies and CBCCs is that in the case of private cryptocurrencies an unspecified large number of agents can have access to distributed ledgers and may be engaged in making a close examination of ledgers. However, in CBCCs only a central bank, and private banks chartered by a central bank, can share transaction records on ledgers, and are then solely responsible for ledger examination. We refer to this as a permissioned system. Given the confidence placed in central banks and chartered private banks, a permissioned system can be constructed in a much simpler manner. Second, CBCCs never use resource-wasting and time-consuming mechanisms such as proof-of-work to build consensus among participants. For example, RS Coin, which was developed by cryptologists, employs two-phase commitment for a

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consensus-building mechanism, in which consensus is formed immediately after all designated participants (cohorts) as ledger checkers send an agreement to a coordinator (Danezis and Meiklejohn 2016). An earlier version of STELLA, which is the CBCC project being carried out jointly by the ECB and the BOJ, adopted Practical Byzantine Fault Tolerance (PBFT), in which, if more than two thirds of participants (permissioned banks) reach agreement in ledger examination, then settlement is finalized immediately (ECB and BOJ 2017). Third, another consensus-building mechanism, and one even simpler than the earlier mechanism, is in CBCC systems. In the previous mechanism, the central bank and designated private banks are on an equal footing in making a close examination of ledgers, and they share completely all transactions recorded in a blocked ledger. However, a second phase of Project Jasper, initiated by the BOC, adopted Corda5 as a distributed ledger system. In Corda, only a central bank (the BOC in this case) administers the entire ledger system, and makes final checks of all transactions (Chapman et al. 2017). Meanwhile, private banks share ledgers and check records only for transactions carried out as an interested party. Elsewhere, e-krona, a cryptocurrency investigated as a substitute for banknotes by Sweden’s central bank (the Riksbank), also employs Corda as a distributed ledger system. With e-krona, only an official third party, other than the central bank, can have access to the entire transaction information (Sveriges Riksbank 2017, 2018, 2020). In this alternative mechanism, not all transactions made at a certain time interval have to be organized in the one block for perusal purposes, while any financial institution participating in a CBCC system does not have to share the entire ledger. In a number of countries, serious consideration is being given to CBCC systems characterized by the above features as substitutes or complements to CB reserves and notes. Because consensus building concerning transactions and ledgers can be formed quickly among participants in CB systems, unlike with private cryptocurrencies, payments through CBCC systems can almost mimic real-time gross settlement.

2.2.1

CBCCs Substituting for CB Reserve Accounts

Let us present some examples in which a central bank introduces cryptocurrencies as alternatives to CB reserves. In this case, system participants consist of only private banks opening current accounts at the central bank. One of the earliest experiments testing this category of CBCCs is Project Jasper by the BOC.6 In Jasper, private banks exchange Canadian dollars (CAD) as legal tender for CAD-Coins issued as a cryptocurrency by the BOC. These CAD-Coins can then be used for large-order settlements between private banks. In the first phase of Project Jasper, proof-ofwork was employed as a consensus-building mechanism, but was abandoned because of the extremely time-consuming settlement process. As noted, in response, the second phase adopted Corda as a distributed ledger system, which enabled settlement 5 See 6 See

Brown (2018) and Hearn and Brown (2019) for detailed descriptions of Corda. Chapman et al. (2017) for an overview of Project Jasper.

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by CAD-Coin to almost mimic the finalization achieved through real-time gross settlement. In this second phase, the BOC conducted an experiment to test a liquiditysaving mechanism, in which designated-time net settlement was made feasible in a distributed ledger system. In this mechanism, a private bank temporarily places a large remittance order in a waiting queue when its holding of CAD-Coin is short of this remittance. At the same time, other banks place similarly large orders in queues. At a certain point of time, the BOC as the central clearinghouse provides net settlement for the large orders accumulated in queues by the private banks. The large-order CBCC system has since been extended to not only settlement between private banks, but also to delivery versus payment (DVP) for security settlement as well as international money transfers. As noted, the BOC and the MAS are undertaking joint work to develop a CBCC system in this direction (BOC and MAS, 2019), and using an early experiment in STELLA, the ECB and the BOJ have successfully achieved gross settlement in a relatively short time using PBFT. Later, they also adopted Corda and applied it to a liquidity-saving mechanism as well as DVP for security settlement (ECD and BOJ 2017, 2018).

2.2.2

CBCCs as Substitutes for CB Notes

While CBCCs as substitutes for or complements to CB reserves attract broad support among those in the financial world, CBCCs as substitutes for CB notes encounter fierce opposition from a number of economists and analysts. Berentsen and Schär (2018) and Bindseil (2020) oppose the introduction of CBCCs partly because CBCCs may be used for illegal transactions or money laundering given their anonymity, and partly because it is difficult for instantaneous settlement to be achieved given their time-consuming requirements for consensus building. Instead, they propose that individual households and firms should be allowed to directly open current accounts at a central bank, and recommend such simple and traditional CB current accounts as substitutes for CB notes. They believe that the rigorous and thorough administration of these accounts by the central bank effectively prevents illegal transactions and money laundering. However, small-order CBCCs, provided through the intermediation of private banks by a central bank, can achieve almost the same instantaneous settlement as CB notes and coins. As noted, in Sweden, e-krona as a CBCC for small-order settlements by the Riksbank allows for instantaneous settlement even among individuals and firms using Corda as a distributed ledger system. In Corda, consensus building is never time-consuming given that only an official third party administers the entire transaction records (Sveriges Riksbank 2017, 2018, 2020). In addition, with RS Coin, financial institutions called mintettes (which are not necessarily private banks) use a simple consensus-building mechanism (two-phase commitment) to avoid timeconsuming settlement (Danezis and Meiklejohn 2016). In addition, private banks, which intermediate the issuance of CBCCs between individual users and the central

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bank, are expected to install CBCCs for various kinds of financial services, such as useful electric wallets, thereby improving the convenience of CBCCs. In principle, anonymity in currency transactions can be eliminated completely in a CBCC system. Because a central bank or an official third party in CBCCs administers all transaction information, it is indeed next to impossible to use CBCCs for illegal transactions in either wholesale or retail settlement. However, those in the financial world remain deeply concerned that anonymous CBCC transactions are completely absent, particularly in retail settlement. With the digital euro, which has been considered for retail settlement by the ECB, the Anti-Money Laundering (AML) Authority is responsible for the prevention of illegal transactions, but allows for anonymous currency transactions in retail settlement (ECB 2019). Concretely, digital euro users receive anonymity vouchers from the AML Authority, and they attach the vouchers in remitting digital euros up to limited amounts to avoid inspection by the AML Authority. Viewed in this way, it may be better to issue CBCCs as substitutes for or complements to CB notes for retail settlement not directly through a central bank, but via the intermediation of private banks to improve currency convenience for individual users, while maintaining a moderate degree of anonymity for retail transactions.

3 CBCCs in a Competitive Equilibrium Environment 3.1 How to Formulate CBCCs in Macroeconomic Models As discussed in Sect. 1, it is possible to remunerate CBCCs with either positive or negative interest, but convert them at flexible market rates. Systems of CBCCs with these two features should have a drastic impact on the current currency system, in which CB currencies are interest-free, and any CB currency is converted in a one-to-one fashion. As explored in Sect. 2, it is difficult to imagine that CBCCs as substitutes for and complements to CB reserves and notes would sacrifice any currency convenience for private banks, firms, or individuals. On the contrary, we would expect currency convenience to improve with the financial services for CBCCs provided by private banks. In this section, we demonstrate that the introduction of such convenient CBCCs with these features indeed reformulates central theorems in conventional monetary theories, particularly, theories of the price level. Two research agendas concern the possible macroeconomic impact of the introduction of CBCCs. The first concerns the interest on CB currencies, with the conversion between CB currencies and private deposit currencies explored as policy instruments to control a large-scale shift between private deposits and CBCCs. In a broader macroeconomic context, Benes and Kumhof (2012), Raskin and Yermack (2016), and others discuss the introduction of CBCCs as an effective instrument to implement the Chicago Plan, in which private deposits backed by commercial loans are replaced entirely by those backed by CBCCs for financial stability.

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In a narrower macroeconomic context, Barrdear and Kumhof (2016) investigate the possible macroeconomic effects of a large-scale shift from private deposit currencies to CBCCs.7 Kumhof and Noone (2018) propose the following as controls in this currency shift: (1) negative interest is temporarily added to the CBCC; (2) conversion between CBCCs and conventional CB reserves is forbidden; (3) conversion from private deposits to CBCCs is not automatically guaranteed; and (4) CBCCs should be backed not by private deposits or bonds but by public bonds only. Bindseil (2020) makes a more moderate proposal in which CBCCs are remunerated with either positive or zero interest up to a certain limit, but the amount of CBCCs beyond this upper limit is remunerated with either negative or zero interest. According to Bindseil, such two-tier remuneration substantially reduces the attractiveness of holding large volumes of CBCCs, and works to prevent a large-scale currency shift to CBCCs. The second research agenda theoretically addresses the exchange market between interest-free CB notes and negative-interest-bearing CBCCs in detail. As surveyed by Rogoff (2016), the idea that negative interest was added to currencies, and that these then negative-interest-bearing currencies would be exchanged with interest-free currencies at market rates was originally proposed by Eisler (1933).8 In a modern macroeconomic context, Buiter and Panigirtzoglou (2003), Agarwal and Kimball (2015), and others rigorously investigate the exchange market between negativeinterest-bearing and interest-free currencies. In this section, we pursue this second agenda in a macroeconomic environment. That is, we investigate the possible macroeconomic consequences of the remuneration and conversion of CBCCs. At a more fundamental level, we attempt to resolve serious dilemmas that emerge in conventional monetary theories. In conventional monetary models, the central bank and the government directly control the shortterm interest rate and even the price level, but this assumption seriously contradicts that of competitive equilibrium, in which any agent, including the central bank and the government, behave as price-takers. However, such a contradiction can be resolved once we can remunerate and convert CBCCs at market rates. In this case, the central bank sets the currency interest rate, but the bond interest rate is determined in money markets. Owing to this separation between the currency and bond interest rates, the severe confrontation between the QTM and the FTPL can be resolved in a consistent manner. Given macroeconomic investigation of CBCCs, we will finally tackle the question we posed at the beginning of this chapter, “Can strong money demand survive in the digital age in which various kinds of CBCCs are issued?”

7 Barrdear and Kumhof (2016) do not analyze any substitution between traditional CB reserves/notes

and CBCCs. and Menner (2011) explore the historical contexts in which currencies have been remunerated with negative interest.

8 Ilgmann

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3.2 Basic Setup Let us present a basic setup of a monetary model with CBCCs introduced in a competitive equilibrium environment. In this model, utility at time t arises not only from consumption c(t), but also from a conventional interest-free CB note (currency 0), and an interest-bearing CBCC (currency 1), whose convenience may be equivalent to, or even superior to, existing CB reserves and notes, as described in Sect. 2. The interest rate on currency 1 (i 1 (t)), as well as the supply plans for currencies 0 and 1 are chosen by the central bank. In contrast, the price level (P1 (t)) and the short-term interest rate on public bonds (i B (t)), both of which are quoted in terms of currency 1, are determined in competitive markets. In addition, the exchange rate of currency 0 per unit of currency 1 (e(t)) is agreed to in markets. While some part of the consumption goods may be quoted in currency 0 in a more realistic setup, all consumption goods are assumed to be quoted in terms of currency 1 in the present setup. The representative household’s period utility is formulated as:  u(c(t)) + v0

M0 (t − 1) P0 (t − 1)



 + v1

 M1 (t − 1) , P1 (t − 1)

(3.1)

where P1 (t) (P0 (t)) is the price level in terms of currency 1 (0), and M1 (t) (M0 (t)) is the nominal balance of currency 1 (0) and u(c) is increasing, concave, and twice differentiable. The variables v1 (m) and v0 (m) are also increasing and concave, but differentiability takes any of the following three forms. First, as assumed in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy and Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”, both functions are twice   differentiable, and lim v1 (m) = 0 and lim v0 (m) = 0 hold. That is, the utility m→∞ m→∞ from real money balances asymptotically approaches its upper limit as shown in Fig. 3a. Second, money utility saturates at m, and its marginal utility from the right is   zero at m (v1 (m) = 0 and v0 (m) = 0) as in Fig. 3b. Third, money utility is constant for m ≥ m, and its marginal utility is zero for m > m as in Fig. 3c. A budget constraint for the representative household is derived as follows: B(t) + M1 (t) +

1 M0 (t) = P1 (t)[y(t) − c(t) − tax(t)] e(t) + [1 + i B (t)]B(t − 1) + [1 + i 1 (t)]M1 (t − 1)   1 e(t) M0 (t − 1), + 1− e(t − 1) e(t − 1)

where B(t), M1 (t), and M0 (t) are the end-of-period nominal balances of public bonds, currency 0, and currency 1, respectively. y(t) and tax(t) denote real household income and real tax at time t, respectively. The nominal interest rates on public bonds

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a Utility from money holding

0

Real money balance

b Utility from money holding

0

Real money balance

c Utility from money holding

0

Real money balance

Fig. 3 a Function of utility from money holding when utility asymptotically approaches its upper limit. b Function of utility from money holding when utility saturates at the upper limit of real money balance. c Function of utility from money holding when utility saturates, but without any limit on real money balance

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(i B (t)) and currency 1 (i 1 (t)) are determined at the beginning of the period, but the price level (P1 (t) and P0 (t)) and the exchange rate of currency 0 per unit of currency e(t) is approximated by 1 − e(t−1) . 1 (e(t)) are determined at the end of the period. e(t−1) e(t) M0 (t) (t) Given PB(t) + MP11(t) + e(t)P as a state variable at the end of the period, the above 1 (t) 1 (t) budget constraint can be rewritten as follows:

B(t − 1) M1 (t − 1) M0 (t − 1) + + P1 (t − 1) P1 (t − 1) e(t − 1)P1 (t − 1) 1 = [c(t) + tax(t) − y(t)] 1 + ρ(t)  1 M1 (t − 1) + [i B (t) − i 1 (t)] 1 + i B (t) P1 (t − 1)    M0 (t − 1) e(t) + i B (t) + e(t − 1) e(t − 1)P1 (t − 1)   B(t) M1 (t) M0 (t) 1 + + + 1 + ρ(t) P1 (t) P1 (t) e(t)P1 (t)

(3.2)

The real rate of interest ρ(t) is defined as: 1 + ρ(t) = (1 + i B (t))

P1 (t − 1) P1 (t) ≈ 1 + i B (t) − . P1 (t) P1 (t − 1)

Note that i B (t) is determined at the beginning of the period, but ρ(t) and P1 (t) are determined at the end of the  period. M1 (t−1) e(t) M0 (t−1) in Eq. (3.2) correspond to [i B (t) − i 1 (t)] P1 (t−1) and i B (t) + e(t−1) e(t−1)P1 (t−1) the holding cost of currencies 0 and 1 from the viewpoint of the representative household. For interest-bearing currency 1, i B (t) in excess of i 1 (t) is a holding cost per real unit, while for interest-free currency 0, i B (t) adjusted by exchange rates is a real holding cost. However, from the viewpoint of the consolidated government, consisting of the government and the central bank, these currency holding costs are equivalent to seigniorage from currency holders. As shown in Eq. (3.2), we discount one-period-ahead real consumption, income, and taxes by the real interest rate, but discount the one-period-ahead real holding costs associated with the two currencies by the nominal interest rate. Let us move to the budget constraint of the consolidated government. The government’s intertemporal budget constraint from time t − 1 to time t is written as follows: M0 (t) = P1 (t)[g(t) − tax(t)] e(t) + [1 + i B (t)]B(t − 1) + [1 + i 1 (t)]M1 (t − 1)   e(t) M0 (t − 1) + 1− e(t − 1) e(t − 1)

B(t) + M1 (t) +

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Because g(t) denotes real government consumption, tax(t) − g(t) represents a fiscal surplus or a primary fiscal balance. M0 (t) (t) + MP11(t) + e(t)P as a state variable at the end of the period, the above Given PB(t) 1 (t) 1 (t) intertemporal budget constraint can be rewritten as follows: B(t − 1) M1 (t − 1) M0 (t − 1) + + P1 (t − 1) P1 (t − 1) e(t − 1)P1 (t − 1)  1 M1 (t − 1) 1 = [tax(t) − g(t)] + [i B (t) − i 1 (t)] 1 + ρ(t) 1 + i B (t) P1 (t − 1)    M0 (t − 1) e(t) + i B (t) + e(t − 1) e(t − 1)P1 (t − 1)   B(t) M1 (t) M0 (t) 1 + + (3.3) + 1 + ρ(t) P1 (t) P1 (t) e(t)P1 (t)  e(t) M0 (t−1) (t−1) As discussed, [i B (t) − i 1 (t)] MP11(t−1) and i B (t) + e(t−1) correspond e(t−1)P1 (t−1) to seigniorage from the viewpoint of the consolidated government. Solving Eq. (3.3) leads to the consolidated government’s budget constraint. M1 (t − 1) M0 (t − 1) B(t − 1) + + P1 (t − 1) P1 (t − 1) e(t − 1)P1 (t − 1)  ∞ 

1 τ = [tax(τ ) − g(τ )] k=t (1 + ρ(k)) τ =t  ∞ 

1 M1 (τ − 1) τ + [i B (τ ) − i 1 (τ )] P1 (τ − 1) k=t (1 + i B (k)) τ =t    M0 (τ − 1) e(τ ) + i B (τ ) + e(τ − 1) e(τ − 1)P1 (τ − 1)    1 B(τ ) M1 (τ ) M0 (τ ) + + + lim τ τ →∞ P1 (τ ) e(τ )P1 (τ ) k=t (1 + ρ(k)) P1 (τ )

(3.4)

As shown in Eq. (3.4), the current real balances of public bonds and the two currencies are equal to the sum of the present value of future fiscal surpluses and seigniorage, and the terminal value of public bonds and the two currencies. In this section, we carefully consider the following four possibilities in a competitive equilibrium environment where CBCCs may be interest-bearing and exchanged at flexible rates. First, we investigate whether the standard QTM holds, that is, whether stable demand is present for the two currencies, and the two currency price levels P1 (t − 1) and P0 (t − 1) are proportional to the aggregate quantity of money. For example, monetary aggregation may be expressed by M1 (t − 1) + M0 (t − 1) or 0 (t−1) . M1 (t − 1) + Me(t−1) Second, the standard FTPL is usually where money demand is abstracted from the initial setup as in Woodford (1995, 1998) and others. Here, we explore whether

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there is room for the FTPL to hold even if money demand is present. As discussed in Sect. 3.5, if the bond and currency interest rates are equal, and money demand saturates at a certain real balance, then the standard FTPL holds. In this case, CB currencies are equivalent to public bonds in terms of interest as well as no additional liquidity service. Third, we investigate when public bonds serve as net wealth from the viewpoint of households as shown in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy and Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”. That is, the real balance of public bonds in excess of the future tax burdens  ∞ 

1 B(t − 1) τ > [tax(τ ) − g(τ )] P1 (t − 1) k=t (1 + ρ(k)) τ =t is supported by strong money demand as in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy” or the public bond price bubble as in Chapter “Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”. As shown in Sect. 3.5, if the bond and currency interest rates are again equal, and money demand never saturates, then part of the real balance of public bonds serves as net wealth for households. In this case, the government’s budget constraint, augmented by either strong money demand or the non-zero terminal condition, determines the price level. More concretely, the QTM cannot determine the current price level because demand deviates from supply in currency markets and is instead determined according to the MFTPL. Fourth, we investigate whether we can pay for the massive issuance of public bonds through immense seigniorage from currency holders by imposing negative currency interest rates or widening the spread between the bond and currency interest rates. In this case, strong money demand disappears as the bond interest rate exceeds the currency interest rate, and public bonds are no longer absorbed in currency markets. Instead, the negative interest rate set by the central bank may yield immense seigniorage. In addition, if not only the currency interest rate but also the bond interest rate falls below zero for a long period, the consolidated government can obtain seigniorage without limit. Immense seigniorage through negative currency interest rates may substitute for strong money demand in supporting massively issued public bonds, but differs fundamentally from strong money demand because public bonds no longer serve as net wealth for households, and have to be repaid through heavy tax burdens from currency holders.

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3.3 Optimality Conditions, Interest Parity, and Purchasing Power Parity M0 (t) (t) We now set PB(t) + MP11(t) + e(t)P as a state variable in the representative household’s 1 (t) 1 (t) budget constraint (3.2), and solve the problem to maximize the following life-time utility: ∞ 

τ =t

     1 M1 (τ ) M0 (τ ) u(c(τ )) + v1 + v0 , P1 (τ ) P0 (τ ) (1 + δ)τ −t+1

where δ > 0 is the rate of time preference. The Euler equation associated with the optimal allocation of consumption between time t and t + 1 is derived as:   1 u  (c(t + 1)) P1 (t) − 1 + i (t) B 1 + δ u  (c(t)) P1 (t − 1) 1 u  (c(t + 1)) (3.5) = [1 + ρ(t)] = 1. 1 + δ u  (c(t)) The optimal allocation between consumption and currency 1 or 2 is determined by the equality between marginal currency utility and currency holding costs in terms of marginal utility of consumption: 

 M1 (t − 1) = [i B (t) − i 1 (t)]u  (c(t)) v1 P1 (t − 1)     M0 (t − 1) e(t)  u  (c(t)) = i B (t) + v0 P0 (t − 1) e(t − 1) 

(3.6) (3.7)

Because the currency interest rate serves as the lower bound for the bond interest rate, the following inequalities hold: i B (t) ≥ i 1 (t) i B (t) ≥ −

e(t) e(t − 1)

(3.8) (3.9)

As to the interest parity between the two CB currencies, the marginal currency utility from investment in currency 1, and that from investment in currency 0 first, and conversion to currency 1 later, should be equal: i 1 (t)v1



M1 (t − 1) P1 (t − 1)



  e(t)  M1 (t − 1) v =− e(t − 1) 1 P1 (t − 1)

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Thus, the following interest rate parity relationship holds: i 1 (t) = −

e(t) e(t − 1)

(3.10)

Alternatively, the purchasing power from holding currency 1 should match that from currency 0 and converting it to currency 1 in terms of marginal consumption utility yields: 1  e(t)  u (c(t)) = u (c(t)). P1 (t) P0 (t) Thus, purchasing power parity holds: P1 (t) =1 e(t)P0 (t)

(3.11)

As policy instruments, the central bank sets interest rates on currency 1 (i 1 (t)), 1 (t) 0 (t) and MM ). and determines the money supply plans for the two currencies ( MM 1 (t−1) 0 (t−1) In this chapter, we consider the simplest case to illuminate the possible impacts of introducing CBCCs in a competitive equilibrium setup. First, we assume that consumption is constant over time; c(t) = c. Accordingly, the following relation is obtained from Eq. (3.5). i B (t) −

P1 (t) = ρ(t) = δ P1 (t − 1)

That is, the real interest rate on public bonds is always equal to the rate of time preference. 1 (t) = μ1 The central bank then sets a constant currency growth rate as follows: MM 1 (t−1)

0 (t) and MM = μ0 In this policy environment, the central bank never faces the choice 0 (t−1) between its nominal interest rate and money supply plans, but it is able to choose the currency interest rate and money supply plans simultaneously. In the current competitive equilibrium setup, given c, μ1 , μ0 , (t) (t) {i 1 (t − 1), i 1 (t), i 1 (t + 1), i 1 (t + 2) . . .}, real money balances ( MP11(t) and MP00(t) ), the

1 (t) 0 (t) price levels (P1 (t) and P0 (t)), inflation rates ( PP and PP ), and interest on 1 (t−1) 0 (t−1) public bonds (i B (t)) are determined. Note that the exchange rate between the two currencies is determined as the relative price levels from purchasing power parity relationship in Eq. (3.11), while its rate of change is determined by interest on currency 1 (i 1 (t)) from the interest parity relationship in Eq. (3.10).

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3.4 Extended QTM Under Fixed Interest on Currencies Let us first demonstrate how to reformulate the QTM in the presence of stable demand for the two CB currencies. For the moment, assume that the interest rate on currency 1 is fixed at some nonnegative value, while that on public bonds is above the currency interest rate, that is, i B (t) > i 1 ≥ 0. If i 1 = 0, then currency 1 is equivalent to currency 0 in terms of the currency interest rate, but they still differ in terms of currency convenience. (t) (t) = m 1 ( MP00(t) = Suppose that the real demand for currency 1 (0) is stable at MP11(t)     e    m 0 ). Then, v1 (m 1 ) = [i B − i 1 ]u (c) and v0 (m 0 ) = i B + e u (c) = [i B − i 1 ]u (c) 1 = μ1 hold. In this case, inflation rates are equal to the monetary growth rates, P P1 P0 and P0 = μ0 . The nominal rate of interest on public bonds is then equal to the real rate of interest plus the inflation rate of currency 1 (i B = δ + μ1 ). Given i B > i 1 , μ1 needs to be above i 1 − δ. Note that a low currency interest rate is compatible with low inflation but not with monetary expansion, but rather with monetary contraction in the current setup. Let us establish the proportionality between the price level and the quantity of money. We average the two currency prices with the weights of the real money balances: P(t) =

m0 m1 P1 (t) + P0 (t) m1 + m0 m1 + m0

Substituting P1 (t) = Mm1 (t) and P0 (t) = 1 following version of the QTM: P(t) =

M0 (t) m0

into the above equation leads to the

1 [M1 (t) + M0 (t)] m1 + m0

Two additional versions of the QTM are also available:   1 M0 (t) P1 (t) = M1 (t) + m1 + m0 e(t) P0 (t) =

1 [e(t)M1 (t) + M0 (t)] m1 + m0

As these three versions of the QTM imply, the price level is proportional to not only the simple sum of money supply (M1 (t) + M0 (t)), but also to the exchange rate0 (t) and e(t)M1 (t) + M0 (t)). We refer to these versions of weighted sum (M1 (t) + Me(t) the price–money relationship as the extended QTM. Given that the extended QTM holds under i B (t) > i 1 ≥ 0, the consolidated government’s budget constraint (3.4) is rewritten as follows.

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183

 ∞ 

1 B(t − 1) + m1 + m0 = [tax(τ ) − g(τ )] P1 (t − 1) (1 + δ)τ −t+1 τ =t ∞

i B − i1 (m 1 + m 0 ) + i B )τ −t+1 (1 τ =t    1 B(τ ) + lim + m + m 1 0 τ →∞ (1 + δ)τ −t+1 P1 (τ )  ∞ 

i B − i1 1 = [tax(τ ) − g(τ )] + (m 1 + m 0 ) τ −t+1 iB (1 + δ) τ =t +

+ lim

τ →∞

1 1 B(τ ) (m 1 + m 0 ) + lim τ →∞ (1 + δ)τ −t+1 P1 (τ ) (1 + δ)τ −t+1

For the two terminal conditions on the right-hand side of the above equation, the first condition lim (1+δ)1τ −t+1 (m 1 + m 0 ) definitely converges to zero, while the τ →∞

) also converges to zero under the assumption second condition lim (1+δ)1τ −t+1 PB(τ 1 (τ ) τ →∞ that the consolidated government adopts a Ricardian fiscal policy. Then, the above government’s budget constraint is simplified as:

 ∞ 

B(t − 1) 1 i1 + (m 1 + m 0 ) = [tax(τ ) − g(τ )] . P1 (t − 1) i B (1 + δ)τ −t+1 τ =t

(3.12)

As the above equation implies, if the consolidated government sets a positive currency interest rate (i 1 > 0), not only the outstanding public bonds ( PB(t−1) ), 1 (t−1) but also the payment of future currency interest ( iiB1 (m 1 + m 0 )) has to be covered by future fiscal surpluses. Accordingly, the consolidated government faces a much tighter budget constraint. Note that the current price level is determined according to the extended QTM, not by the consolidated government’s budget constraint (3.12) as in the FTPL. Equation (3.12) merely implies that the obligation of redeeming public bonds and paying currency interest requires financing by future fiscal surpluses at any price level determined by the extended QTM.

3.5 Standard FTPL and MFTPL Given Equivalence Between Currencies and Public Bonds Let us move to the case where the bond interest rate exactly matches the currency rate, consumers no longer pay currency-holding costs, while the government never receives seigniorage from currency holders. In terms of optimality conditions,   the (t−1) =0 marginal utility from holding the two currencies is equal to zero, or v1 MP11(t−1)

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Central Bank Cryptocurrencies in a Competitive Equilibrium …

  (t−1) = 0. Accordingly, the currencies are equivalent to public bonds in and v0 MP00(t−1) terms of not only interest, but also in that they provide no additional liquidity service. Given that the bond interest rate equals the currency interest rate, the following three cases are considered, depending on the functional forms of the utility from the real balance of currency. First, if currency utility saturates at the upper limit of real money balance, m 1 and m 0 , as shown in Fig. 3b, then the standard FTPL takes the place of the QTM in determining the initial price level. That is, the current price level is determined not by the aggregate money supply, but by future fiscal surpluses. The reasoning is as follows. For the moment, suppose that the consolidated government matches the real money supply with the satuM s (t−1) M s (t−1) ration level ( P11(t−1) = m 1 and P00(t−1) = m 0 ), and adopts a Ricardian fiscal   ∞  1 = − g(τ . In this case, the price levels, policy PB(t−1) [tax(τ ) )] τ −t+1 τ =t (1+δ) 1 (t−1) P1 (t − 1) and P0 (t − 1), are still determined by the aggregate quantity of M1s (t − 1) and M0s (t − 1). However, the situation changes if there is an additional increase in the supply of M s (t−1)+M currency 1 ( 1 P1 (t−1) 1 > m 1 ). Money supply beyond saturation earns the same return as the bond interest rate, but never yields any additional liquidity service. Thus, the additional currency supply (M1 ) is identical to public bonds, demanded as public bonds by consumers, and repaid by future fiscal surpluses. As to currency 0, its nominal supply is adjusted to make its real balance equal to m 0 . Then, given  the newly determined price level P1 (t − 1), the government’s budget constraint is rewritten as follows:  s  M1 (t − 1) + M1 B(t − 1) + − m 1 P1 (t − 1) P1 (t − 1)   ∞

1 (3.13) = [tax(τ ) − g(τ )] (1 + δ)τ −t+1 τ =t In the above, P1 (t − 1) cannot be determined according to the QTM, because the real money supply temporarily exceeds demand in the currency 1 market  M s (t−1)+M ( 1 P1 (t−1) 1 > m 1 ). Instead, P1 (t − 1) is governed by the government’s budget constraint, or Eq. (3.13), as in the standard FTPL. Accordingly, the change in the price P  (t−1)−P (t−1) M1 = B(t−1)+M < level is less than proportional to monetary growth 1 P1 (t−1)1 s (t−1) M1 . Then, the government M1s (t−1) P1 (t − 1)m 1 , and raises it at the



remains m 1 from then on. Given   B(t − 1) + M1s (t − 1) + M1 − P1 (t − 1)m 1 

=

∞ 

τ =t

1

resets the nominal money supply M1s (t − 1) at rate of μ1 . Consequently, the real money balance

P1 (t − 1)

 1 [tax(τ ) − g(τ )] , (1 + δ)τ −t+1

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185

a Ricardian fiscal policy is recovered at the newly determined price level  P1 (t − 1). The monetary rule proposed by Friedman (1969), or i B = i 1 = 0, is included in this case in which real money demand saturates. However, what we emphasize here is that there is room for the standard FTPL but not the QTM, to hold under Friedman’s rule. Second, as shown in Fig. 3c, if the utility from currencies also saturates at m 1 (m 0 ), but the real money balance may exceed m 1 (m 0 ), then the MFTPL takes over M s (t−1) the QTM in determining the initial price level. Again, suppose that P11(t−1) = m 1 , M0s (t−1) P0 (t−1)

= m 0 , and  ∞ 

1 B(t − 1) . = − g(τ [tax(τ ) )] P1 (t − 1) (1 + δ)τ −t+1 τ =t

So far, the QTM determines the price level, while a Ricardian fiscal policy is in place. Then, the real demand for currency 1 can increase to m 1 without any impact on utility. An additional increase in money demand can absorb public bonds, which are now equivalent to currencies. Again, the nominal supply of currency 0 is adjusted to make its real balance equal to m 0 . In contrast to the first case, the supply of public bonds in excess of the future fiscal surplus is now demanded as currencies. Thus, the government’s budget constraint is rewritten at the new price level P1 (t − 1) as follows:    ∞  1 B(t − 1)

M1s (t − 1)  = m (3.14) − − − g(τ [tax(τ ) )]  1 P1 (t − 1) τ =t (1 + δ)τ −t+1 P1 (t − 1) M s (t−1)

Given m 1 > P11(t−1) , M1s (t − 1) never determines P1 (t − 1) according to the QTM. Instead, the price level is given by Eq. (3.14), or the present value of future fiscal surpluses, augmented by the current excess demand in the currency 1 market. From then on, both currency 1 supply and the price level grow at the rate of μ1 , and real money demand m 1 (s − 1) is arbitrarily chosen such that  ∞  1 B(s − 1)

M1s (s − 1) = m − − g(τ − 1) − [tax(τ ) )] (s 1 P1 (s − 1) τ =s (1 + δ)τ −t+1 P1 (s − 1) may hold at the end of each time s − 1. Accordingly, the government can ignore a Ricardian fiscal policy as long as the bond and currency interest rates are equal. We may refer to the second case as the MFTPL as in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy”. However, note that once the bond interest rate i B (t) exceeds the currency interest rate i 1 , excess currency demand disappears, and the QTM again takes the place of the MFTPL. In addition, a Ricardian fiscal policy needs to be restored immediately.

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Third, as shown in Fig. 3a, currency utility asymptotically approaches its upper limit. In this case, money demand expands quickly as the bond interest rate i B (t) converges to the currency interest rate i 1 . As in Chapter “Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”, we assume that seigniorage   M1 (τ − 1) M0 (τ − 1) + [i B (τ ) − i 1 (τ )] P1 (τ − 1) P0 (τ − 1) is reimbursed to households, and that the consolidated government adopts a non-Ricardian fiscal policy. Then, the terminal condition or the bubble term  B(τ ) 1 ( lim τ (1+ρ(k)) P1 (τ ) ) in the following government’s budget constraint neither τ →∞ k=t degenerates to zero nor explodes, but rather converges to a positive finite:  ∞  B(t − 1)

1 τ 0< − [tax(τ ) − g(τ )] P1 (t − 1) τ =t k=t (1 + ρ(k))   B(τ ) 1 = lim τ 0. That is, the central bank adjusts the currency interest rate i 1 (t) with the bond interest rate i B (t). In this case, real demand for the two currencies (m 1 and m 2 ) is stabilized according to v1 (m 1 ) = v2 (m 2 ) = s B1 u  (c). Thus, the extended QTM holds as in Sect. 3.4. Given fixed monetary growth at μ1 , i B (t) is constant at δ + μ1 . In other words, the bond interest rate is controllable through monetary growth. Because the government ) = 0 always holds. adopts a Ricardian fiscal policy, lim (1+δ)1τ −t+1 PB(τ 1 (τ ) τ →∞ Given s B1 = i B (t) − i 1 (t) > 0, there are four cases: (1) i B > i 1 > 0, (2) i B > i 1 = 0, (3) i B > 0 > i 1 , and (4) 0 ≥ i B > i 1 . The first case with i B > i 1 > 0 is identical to that of Sect. 3.4. Only part of the interest burden i B (t) associated with the currency issue is covered by the interest spread s B1 (< i B (t)), and the remainder i 1 (t) (> 0) needs to be financed by future fiscal surpluses. The second case with i B > i 1 = 0 is identical to the current currency system where CB currencies are never remunerated. The interest burden associated with the currency issue is fully covered by seigniorage (i B = s B1 ), and the consolidated government does not have to pay the burden associated with the currency issue. Thus, its budget constraint (3.12) reduces to:  ∞ 

1 B(t − 1) = [tax(τ ) − g(τ )] . P1 (t − 1) (1 + δ)τ −t+1 τ =t The third case with i B > 0 > i 1 is quite interesting. Owing to negative currency interest rates, the government can raise more seigniorage not through i B as in the second case, but through s B1 > i B . Thus, the present value of the additional  B − 1 (m 1 + m 0 ) = − iiB1 (m 1 + m 0 ) > 0. With the seigniorage amounts to s B1i−i B additional seigniorage, the government’s budget constraint is relaxed as follows:  ∞ 

1 i1 B(t − 1) = − (m 1 + m 0 ) + [tax(τ ) − g(τ )] P1 (t − 1) iB (1 + δ)τ −t+1 τ =t With negative currency interest rates, however, households as currency holders are forced to pay additional taxes, proportional to their real currency holdings. The final case with 0 ≥ i B > i 1 is even more interesting. In this case, borrowing benefits not costs arise when the consolidated government issues currencies at i B ≤ 0. Consequently, the government enjoys triple seigniorage, that is negative currency interest (i 1 < 0), positive currency spreads (s B1 = i B − i 1 > 0), and borrowing benefits (i B ≤ 0). If both bond and currency interest rates are controlled below zero for a long period, the government can obtain seigniorage without limit. However, households are forced to pay triple costs for currency holding. Note that the issuance of public bonds is always discounted by not the nominal rate of interest, but by

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the real rate of interest, which equals the rate of time preference, and that negative interest on public bonds never helps to reduce the burden associated with the public bond issue.

4 Conclusion: Strong Money Demand or Immense Seigniorage in the Digital Age? Let us now return to our original policy question, “Can strong money demand survive in the digital age in which various kinds of CBCCs are issued?” If our response to this question is “No”, then we have to ask ourselves whether a certain macroeconomic mechanism can be substituted for strong money demand in supporting massively issued public bonds. As discussed in Sect. 3.5, strong money demand disappears immediately when the bond interest rate (i B (t)) exceeds the positive or zero currency interest rate (i B (t) > i 1 ≥ 0). Accordingly, the massive issuance of public bonds in excess of future fiscal surpluses can no longer be absorbed by excess money demand as in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy”, or the bubble term coexisting with strong money demand as in Chapter “Long-Run Mild Deflation Under Fiscal Unsustaina-Bility in Contemporary Japan”. In addition, the consolidated government faces a more serious budget constraint because of fiscal expenditures on positive currency interest. As discussed in Chapters “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Current and Future Japanese Economy and Long-Run Mild Deflation Under Fiscal Unsustaina– Bility in Contemporary Japan”, where the currency interest rate is set at zero the price level and bond interest rates, including the long-term rates, immediately jump after the bond interest rates deviate upward from the currency interest rate. However, the situation changes dramatically when the consolidated government can set a negative interest rate on currency (i 1 < 0). Given a positive spread between the bond and currency interest rates (i B (t) > 0 > i 1 ), strong money demand disappears, but the government can obtain immense seigniorage from both negative currency interest and positive interest spreads. If the bond interest rate is moved even below zero for a long period (0 > i B (t) > i 1 ), then the government can obtain seigniorage without limit. Thus, immense seigniorage resulting from deeply negative currency interest can be substituted for strong money demand in repaying the massive issuance of public bonds, whose value is currently far above the present value of future fiscal surpluses. We should emphasize here that strong money demand and immense seigniorage by negative currency interest can serve as firm support for the massive issuance of public bonds, but that they differ fundamentally from the viewpoint of households. For consumers as investors, public bonds in excess of tax burdens can serve as net assets as long as strong money demand is present. For households as taxpayers,

4 Conclusion: Strong Money Demand or Immense Seigniorage …

189

however, immense seigniorage in itself is equivalent to heavy tax burdens on currency holding. In a deflationary environment where bond interest has already been close to zero, the currency interest rate needs to be deeply negative to maintain a large interest spread (i B (t) − i 1 ). However, given deeply negative interest rates on currencies, CBCCs have to be extremely convenient relative to private deposits or currencies. If the marginal utility from holding CBCCs (v1 (m 1 ) and v2 (m 2 )) fails to be high at a moderate level of real money balances, then currency demand shifts dramatically from CBCCs to private deposit currencies. Consequently, not only strong money demand for CB currencies, but also ordinary money demand, may rapidly disappear. A common concern among those in the financial world is that financial and economic crises could trigger the large-scale shift from private deposit currencies to CB currencies. However, if the consolidated government attempts to finance enormous debt through immense seigniorage by imposing deeply negative interest rates on CBCCs, then a reverse shift from CB currencies to private deposit currencies may emerge as a new form of currency crisis.9

9 A currency competition between central and private banks was first investigated by Hayek (1978).

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Index

A Accelerating inflationary process, 137, 141, 149 Adams, F. G., 27 Agarwal, R., 174 Aiyagari, S. R., 156 Allied occupation, viii, 3 Anti-Money Laundering (AML) Authority, 173 Armstrong, S., 81, 122 Asakura, K., 5 As long as zero interest continues, viii, xii Asset price bubble, vii, 7 Asymmetric cryptography, 162 Austrian economics, 85

B Bank of Canada (BOC), 164 Bank of China, 61 Bank of Chosen (BOChs), 61 Bank of Communications, 61 Bank of Indochina (BOI), 58, 65 Bank of Japan (BOJ), 2, 33, 164 BOJ’s de facto direct refinancing, 85, 91, 113 BOJ’s de facto direct underwriting, 83, 91 BOJ’s direct underwriting, 33, 34 Bank of Japan (BOJ) note, 2, 25 old and new bills, 35, 54, 56 Bank of Taiwan (BOTw), 61 Bank of Thailand (BOTh), 58, 65 Barrdear, J., 174 Barter, 15, 28, 34, 39 Bassetto, M., 96, 124, 165

Benes, J., 173 Benhabib, J., 124 Berentsen, A., 172 Bhattacharyya, D. K., 27 Bianchi, F., 122, 124 Bilateral depositing contract (Azuke-ai), 63 Bindseil, U., 172 Bitcoin, 168 Black market, 25, 34 black marketeer, 6, 14, 28 black marketeers’ portfolios, 51 black market price, 4, 36 Blanchard, J. O., 80, 122, 142, 147 Blockchain, 168 Bloise, G., 124 Boldorf, M., 76 Braun, R. A., 122 Brock, W. A., 137 Brown, R. G., 171 Brunnermeier, M. K., 93, 124 Buiter, W. H., 96, 136, 174

C CAD-Coins, 171 Cagan, P., 27, 40 Call rate, 3, 7, 101 Capital levy, 35 Catastrophic event, 129, 132 Central Bank Cryptocurrency (CBCC), 24, 161, 170 flexible exchange rates among CBCCs, 164 interest-bearing CBCC, 164, 175 negative-interest-bearing CBCC, 174, 187, 188

© Springer Nature Singapore Pte Ltd. 2021 M. Saito, Strong Money Demand in Financing War and Peace, Advances in Japanese Business and Economics 28, https://doi.org/10.1007/978-981-16-2446-9

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200 Central banknote, 25, 39 Central Bank of China, 61 Central Bank of Manchuria (CBM), 58, 61, 65 Central Reserve Bank of China (CRBC), 57, 63 Chapman, J., 171 Chicago Plan, 173 Christiano, L., 122 Cochrane, J. H., 145 Collapse of Lehman Brothers, 102 Competitive equilibrium, 165 Consensus building, 168 Consolidated government, 18, 19, 81, 165, 177 Consumption tax, 8, 82, 125, 126 Continuum of equilibria, 124, 129, 137 Controlled economy, viii, 3, 29 Corda, 171 Costs of money holding, 7 Cui, W., 124

D Danezis, G., 171, 172 Davig, T., 124 Deflationary process, 136, 138, 142, 149 Deflationary spiral, 85 Deflator consumption deflator, 125 GDP deflator, 8 GNE deflator, 4, 37, 42, 46 GNI deflator, 37, 46 De Janosi, P. E., 27 Delivery versus payment, 172 Demand-siders, 122 Digital euro, 173 Disequilibrium analysis, 82, 85 Disequilibrium dynamics, 85 Distributed ledger, 162, 168 Dodge Line, 32, 157 Double payments, 162, 168

E Earmarked gold, 76 Earthquake Great East Japan Earthquake, 16 Great Hanshin–Awaji Earthquake, 16 Great Tokyo Earthquake, viii, 11 inland earthquake in Tokyo, 17, 125, 147 Economic blockades, 29

Index Economic Planning Agency (EPA), ix, 2–4, 13, 26, 29–31, 40, 41, 43–45, 47, 48, 50, 53, 54, 157 Editorial Office of History of Public Finance in Showa Era (EOHPF), 12, 35, 58, 67, 71, 73, 76 Efficiency and inequality, 28, 55 Eggertsson, G. B., 122 Eisler, R., 174 E-krona, 171 Emergency Financial Measures (EFM), 5, 35, 56 frozen deposits, 15, 35, 56 Emi, K., 58 Epstein, L., 143 European Central Bank (ECB), 164 Excess supply/demand excess demand in money markets, 23, 82, 89 excess demand in money/public bond markets, 83 excess supply in goods/labor markets, 23, 80, 89 excess supply in public bond markets, 23, 81, 90

F Face value, 59 Federal Reserve Bank of China (FRBC), 57, 63 Feige, E. L., 27 Financial surplus, 46 Fiscal dominance, 20 Fiscal Investment and Loan Program bonds (FILP bonds), 81 Fiscal policy active fiscal policy, 20 disciplined fiscal policy, 131 non-Ricardian fiscal policy, 124 Ricardian fiscal policy, 124 undisciplined fiscal policy, 20, 129, 138 Fiscal reformers, 122 Fiscal surplus, 19, 89 Fiscal sustainability, 23, 81, 122, 129 Fiscal Theory of the Price Level (FTPL), 18, 82, 124, 165 standard FTPL, 184 Fiscal unsustainability, 122, 129, 138 Floating exchange rate system, 12 Foley, K. D., 88 Forced saving, 13 Formal economy, 27

Index Frey, B. S., 27 Friedman, M., 136 Friedman’s rule, 136, 185 Fujiki, H., 149 Fujiwara, H., 43 Fukao, K., 42

G Gartaganis, A. J., 27 General Headquarters of the Allied Powers (GHQ), 29 Georgiou, G. M., 27 Gertler, M., 156 Global financial crisis of 2007–2008, 16 Goldberger, A. S., 27 Gold standard, 33 Government’s Intertemporal Budget Constraint (GIBC), 123, 124, 138 Gutmann, P. M., 27

H Hagedorn, M., 93, 124 Hand-to-hand physical cash, 162 Hara, A., 43 Hash function, 163 Hattori, T., 43 Hayek, F. A., 189 Hearn, M., 171 Hokkaido Colliery and Steamship Company, 32 Hong Kong and Shanghai Banking Corporation (HSBC), 63 Huff, G., 59, 65, 69, 73, 74, 76, 77 Hyperinflation, 4, 23, 84, 107, 137, 158

I Ilgmann, C., 174 Ilut, C., 124 Import restrictions, 29 Imrohoroglu, S., 81, 122 Income leakage, 26, 37 Inconsistency between the QTM and the FTPL, 96 Informal economy, 27 Interest currency interest, 24, 166 interest-bearing money, 95 interest-free CB note, 175 interest-free money, 95 money market interest, 166 negative currency interest, 167

201 negative interest on excess reserves, 165 negative interest on public bond, 188 public bond interest, 24 International remittance, 163 Intertemporal elasticity of substitution, 143 Ito, A., 4 Ito, M., 127 Iwai, K., 85 Iwamoto, Y., 44 Iwamura, M., ix, 166, 169 Iwatake, T., 78 J Japan Coal Company, 32 Japanese Government Bonds (JGBs), 81, 126 Jasper–Ubin project, 164 Jean-Pascal, B., 42 Joines, D. H., 122 Jung, T., 122 K Kawamoto, T., 80, 97 Kikuchi, K., 30 Kimball, M., 174 Kobayashi, K., 93, 124 Kocherlakota, N., 130 Koike, R., 13 Kojima, S., 62, 63 Kosai, Y., 55 Krugman, P. R., 122 Kumhof, M., 173 L Leeper, E. M., 20 Leff, N. H., 55 Legal tender, 61 LeRoy, S., 124 Liquidity-saving mechanism, 172 Liquidity trap, 109, 122, 124 Long-term interest rates, 102 Lost Decades, vii M Majima, S., 59, 65, 69, 73, 74, 76, 77 Makino, F., 69, 75 Manchurian Incident, 11 Marco Polo Bridge Incident, 5, 61 Market Operations Statistics (MOS), 113 Marshallian k, 3, 26, 49, 158 Material Mobilization Plans (MMP), 29

202 Meiklejohn, S., 171, 172 Melosi, L., 122, 124 Menner, M., 174 Merkle tree, 168 Mild deflation, 79, 85, 123, 125 Military scrip, 61, 62 Minami, R., 69, 75 Miner, 168 Miwa, Y., 30, 32, 45 Mizoguchi, T., 27, 30, 42, 44, 55 Modern Monetary Theory (MMT), 80 Monetary and Fiscal Theory of the Price Level (MFTPL), 18, 21–24, 24, 166, 185 Monetary Authority of Singapore (MAS), 164 Money demand, 148 income elasticity, 149 interest elasticity, 148 unit income elasticity, 40, 109 Money substitutes, 82, 90, 96 Morita indexes, 30, 42 Morita, Y., 30 Murase, H., 93, 124 N Nakamoto, S., 162, 168 Nakamura, T., viii, 29, 32 Nakashima, K., 149 Nakayama, T., 102 National City Bank, 63 National financial crisis of 1997–1998, 16 National Savings Promotion Bureau, 13 Natural rate of interest, 151 Near-zero interest rates, 79, 123 Negative Interest Rate Policy (NIRP), 102, 104 Neo-Fisherian model, 124 New normal, xii Nishida, Y., 30 Nishiyama, C., 5 Nixon Shock, 12 Noguchi, Y., viii Nojima, N., 27, 42, 44, 55 Nonce, 169 Noone, C., 174 O Obstfeld, M., 137 Occhino, F., 60 Official discount rate, 3, 7 Official price, 4, 36, 46

Index Ogawa, Y., 43 Oguro, K., 43 O’Higgins, M., 27 Ohkawa, K., ix, 2, 42, 58, 72, 74 Oi, H., 3 Oil shock, 12 Okazaki, T., viii, 76 Okazaki, Y., 151 Okimoto, T., 81, 122 Okuno-Fujiwara, M., viii Ono, H., 34 Ono, Y., 86 Orthodox monetarists, 85 Output gap, 80, 97 Overseas Funds Bank (OFB), 13, 59, 65 P Panigirtzoglou, N., 174 Peer-to-peer electric cash, 162 Permissioned system, 170 Peso problem, 125, 156 Phelan, C., 130 Pommerehne, W. W., 27 Practical Byzantine Fault Tolerance (PBFT), 171 Price control, 25, 29 Price Control Law, 30 Price Control Order (PCO), 29, 34 Price differentials, 30, 32 Price index consumer price index (CPI), 8 corporate goods price index (CGPI), 8 retail price index, 4, 5 wholesale price index, 4, 5 Price jump, 111, 123 Price surge, 124, 155 Primary fiscal balance, 81, 126 Priority Production System, 30 Private cryptocurrency, 162, 168 Private saving, 13, 16 Project Jasper, 171 Proof-of-work, 168 Public bond price bubble, 23, 83, 92, 94, 138, 140, 186 Public compensation (delivery) bonds, 61 Public Finance Act, 33, 83 Purchasing Power Parity (PPP), 59 Q Quantitative and Qualitative Easing (QQE), 81, 100, 101, 104 Quantitative Easing (QE), 16, 102

Index Quantity Theory of Money (QTM), 9, 82, 134, 166 extended QTM, 182 R Ramseyer, J. M., 32 Raskin, M., 173 Rationing, 29 Real risk-free rates, 147 Real-time gross settlement, 172 Reconstruction Finance Bank (RFB), 32, 33 Redemption-purchase operations, 117 Redenomination, 11 Regime switch, 124, 129 Reichlin, P., 124 Relative risk aversion, 143 Reserve/central banks in the occupied territories, 14, 59 Ricardian equivalence, 141 Ricardian fiscal policy, 185 Rietz, T. A., 144, 147 Rockoff, H., 25 Rogoff, K. S., 25, 137, 174 S Saito, M., 149 Sakuragawa, M., 93, 124 Sargent, T. J., 9, 20, 131, 165 Schär, F., 172 Scherner, J., 60 Schmitt-Grohe, S., 124 Schneider, F., 27 Seigniorage, 19, 24, 72, 187 Shibamoto, M., 33 Shima, K., 33 Shionoya, Y., 58 Shizume, M., 33 Showa depression, 11 Sibert, A. C., 136 Sims, C. A., 122 Southern Development Bank (SDB), 57, 64 Special account for Extraordinary Military Expenses (EME), 13, 58, 61 Special yen, 66 Standard formula, 165 Statistical discrepancy, 26, 36, 44 STELLA, 164 Strong money demand, 1, 82, 161 disappearance of strong money demand, 106 Sudo, N., 151 Sveriges Riksbank, 171

203 T Takahashi, K., 33 Takaishi, S., 62, 76, 77 Tanzi, V., 27 Tashiro, T., 80, 122 Tatai, Y., viii, 63 Terminal condition, 19, 23, 92, 140, 141, 186 Term structures of interest rates, 144, 151 Thomas, J., 27 Total National Mobilization Law, 29 Transversality condition, 92 Treasury bills (T-bills), 81 Treasury Funds Statistics (TFS), 116 Triple Zero, vii Two-phase commitment, 170

U Unconventional policy recommendations, 79 Underground economy, 14, 27 Unemployment, 80, 97 Unfunded component, 140 United States Strategic Bombing Survey (USSBS), 30, 45 Uribe, U., 124

V Velde, F. R., 165

W Wallace, N., 20, 131, 165 War interwar Europe, 9, 21 Pacific War, 25, 57 Russo-Japanese War, 11 Second Sino-Japanese War, viii, 3, 25, 61 World War I, 9 World War II, 3, 25 Watanabe, K., 149 Watanabe, T., 149 Watson, M. W., 142 Weil, P., 142 Wei Wah system, 62, 63 White, E. N., 60 Wicksellian case, 85 Williams, F. M., 25 Woodford, M., 122, 124 Wray, L. R., 80

204 Y Yabu, T., 149 Yamamoto, R., 43 Yamamoto, Y., 74 Yeager, L. B., 85 Yermack, D., 173 Yield curves, 127, 151 Yield spreads, 102 Yokohama Specie Bank (YSB), 63

Index Z Zahringer, K. A., 85 Zero Interest Rate Policy (ZIRP), 81, 101, 103 Zhaojin, J., 78 Zin, S., 143