Big Problem of Small Change

Thomas J. Sargent is Donald Lucas Professor of Economics at Stanford University and Senior Fellow at the Hoover Institution. A pioneer of the rational expectations school of macroeconomics, he is the author of "The Conquest of American Inflation" (Princeton), "Bounded Rationality in Macroeconomics", and "Dynamic Macroeconomic Theory". Francois R. Velde is Senior Economist at the Federal Reserve Bank in Chicago and Lecturer in Economics at the University of Chicago.

• List of Illustrations xiii List of Tables xv Preface xvii Acknowledgments xxi Part I: A Problem and Its Cure Chapter 1. Introduction 3 Paper and gold. The enduring problem of small change. A model. Supply side: the mint. Demand side: the coin owner. Shortages. Price level determination. Remedies. A history. Structure of subsequent chapters. Chapter 2. A Theory 15 Valuation by weight or tale. A basic one-denomination theory. Multiple denominations. Supply. Demand. Interactions of supply and demand. Economics of interval alignments. Perverse dynamics. Spontaneous debasements: invasions of foreign coins. Costs and Temptations. Opportunity cost. An open market operation from Castile. An open market operation for the standard formula. Transparency of opportunity cost. Trusting the government with bi = 0. Chapter 3. Our Philosophy of History 37 History and theory. Clues identified by our model. Cures. Our history. Part II: Ideas and Technologies Chapter 4. Technology 45 Small coins in the Middle Ages. The purchasing power of a small coin. The medieval technology: hammer and pile. Production costs and seigniorage. Mechanization. The screw press. The cylinder press. Other inventions. The steam engine. Counterfeiting, duplicating, imitating. Technologies and ideas. Chapter 5. Medieval Ideas about Coins and Money 69 Medieval jurists as advocates of Arrow-Debreu. Romanists and Canonists. Construction of the medieval common doctrine. Sources and methods of the romanists. Money in a legal doctrine of loans. Tests in a one-coin environment. Multiple currencies and denominations. Multiple denominations. Multiple metals. Fluctuating exchange rates: the stationary case. Multiple units of accounts. Demonetization. Overdue payments and extrinsic value. Trends in exchange rates. Debasements and currency reforms. A question from public law: setting seigniorage rates. Sources of the canonists. Debasements and seigniorage rates. Qualifications, exceptions, and discoveries. Early statement of double coincidence. Romanists repair the breach. Canonists versus romanists on seigniorage. Another breach. Philosophers help. The cracks widen: debasements and deficit financing. Concluding remarks. Chapter 6. Monetary Theory in the Renaissance 100 Precursors of Adam Smith. Debt repayment, legal tender, and nominalism. Dumoulin the revolutionary. Dumoulin's impact. Dumoulin the conservative. Fiat money. Fiat money in theory: Butigella. Double coincidence of wants revisited. Other formulations. Fiat money in practice. The conditions for valued fiat money. Restrictions on fiat money. Limited legal tender. Quantity theory. Lessons from the Castilian experience: fiat money. In Spain: Juan de Mariana (1609). Forecasting inflation. In France: Henri Poullain (1612). Concluding remarks. Part III: Endemic Shortages and "Natural Experiments" Chapter 7. Clues 123 Shortages of small change and bullion famine. Shortages and invasions of coins. Ghost monies and units of account. Free minting. The evidence. Chapter 8. Medieval Coin Shortages 131 England. France. Shortages elsewhere. Concluding remarks. Chapter 9. Medieval Florence 139 Turbulent debut of large coins in Tuscany. The Quattrini affair. Ghost monies as legal tender and unit of account. Florentine ghost monies: details. Concluding remarks. Appendix A: mint equivalents and mint prices. Minting. Appendix B: a price index for fourteenth-century Florence. Chapter 10. Medieval Venice 160 Four episodes. Piccolo and grosso, 1250 to 1320. Evolving units of account. Silver and gold, 1285 to 1353. Adaptation of units of account. Soldino and ducat, 1360 to 1440. Rehearsing fiat money. The torneselli in Greece. Expansion near Venice. Concluding remarks. Appendix: mint equivalents and mint prices. Chapter 11. The Price Revolution in France 186 Relative price change as inflation. Disturbances to coin denominations. A three-coin model. Supply: movements in the relative prices of metals. Demand: within the intervals shortages. Anatomy of money and inflation. Types of coins and units of account. The price level. Supply: the relative price of gold and silver. Debasement of billon coins. Mysterious movements in exchange rates. Evidence of small coins shortages. Policy responses. Perception of the problem by the authorities. Unit of account and legal tender. Units of account and international trade: the fairs of Lyon. The reform of 1577. Collapse of the reform. Concluding remarks. Appendix: mint equivalents and mint prices. Chapter 12. Token and Siege Monies 216 Precursors of the standard formula. Medieval tokens. Siege money. Convertible token currency: an early experiment. First attempt at standard formula. Part IV: Cures and Side-effects Chapter 13. The Age of Copper 227 The coinage of pure copper. Experiments in many countries. Chapter 14. Inflation in Spain 230 Elements of the standard formula. The Castilian experiment. Monetary manipulations. Restamping. Crying down coins. Theory of the Castilian tokens. Additional notation. Multiple regimes. More learning: aspects of indeterminacy. The evidence. The end of the token coin experiment. Comparison with inflation during the French Revolution. Unintended consequence for Sweden. Concluding remarks. Appendix: money stocks and prices. Chapter 15. Copycat Inflations in Seventeenth-Century Europe 254 France: flirting with inflation. Catalonia. Germany. Russia. The Ottoman empire. Chapter 16. England Stumbles toward the Solution 261 Free-token and other regimes. Laissez-faire or monopoly: England's hesitations. Private monopoly (1613-44). Laissez-faire. The Slingsby doctrine. Government monopoly. The Great Recoinage of 1696. The monetary system under the Restoration (1660-88). The crisis. A model with underweight coins. The Locke-Lowndes debate. The Great Recoinage. Locke: genius or idiot? Chapter 17. Britain, the Gold Standard, and the Standard Formula 291 The accidental standard. Laws and ceilings. The guinea and legal tender laws. Newton's forecasts. Gold becomes the unit of account. Underweight coins. Neglect the pence. Implementation of the standard formula. Chapter 18. The Triumph of the Standard Formula 306 Germany's monetary union of 1838. Bimetallism versus the gold standard. Bimetallism in a small country. Worldwide bimetallism. Passage to gold. The United States. The Latin Monetary Union. Free riders in monetary unions. The accident of 1873. The standard formula limps into place. Chapter 19. Ideas, Policies, and Outcomes 320 Evolutions of ideas and institutions. Our history. Experiments. Major themes. Beliefs and interests. Units of account and nominal contracts. Small change and monetary theory. Currency boards, dollarization, and the standard formula. Learning by markets and by governments. Part V: A Formal Theory Chapter 20. A Theory of Full-Bodied Small Change 335 Chapter 21. The Model 337 The household. Production. Production of goods. Production of coins. Government. Timing. Equilibrium. Analytical strategy. The firm's problem. Implications of the arbitrage conditions for monetary policy. Interpretations of o2. Full-weight and underweight coins. The household's problem. Chapter 22. Shortages: Causes and Symptoms 350 Equilibria with neither melting nor minting. Stationary equilibria with no minting or melting. Small coin shortages. Small coin shortage, no minting or melting. Permanent and transitory increases in 6. Logarithmic example. Money shortages bring inflation. Shortages of small coins through minting of large coins. Shortages through melting of full-weight small coins. Perverse effects and their palliatives. Chapter 23. Arrangements to Eliminate Coin Shortages 366 A standard formula regime. Variants of the standard formula. The standard formula without convertibility: the Castilian experience. Fiat currency. Chapter 24. Our Model and Our History 373 Glossary 375 References 377 Legal Citations Index 393 Author Index 395 Subject Index 399

Winner of the 2003 for Best Professional/Scholarly Book in Business Management & Accounting, Association of American Publishers "The core of [the] story is a mathematical model, in this case one that captures possible solutions to the small-change puzzle, including the correct one... For centuries, authorities sensed that economic health depended on the steady, predictable availability of currency. But they did not understand how to realize this goal. Messrs. Sargent and Velde deserve credit for revealing how the correct model came into being... More than a penny for their thoughts."--Paul Podolsky, The Wall Street Journal "This fascinating new history of money shows that the key ingredients of a sound currency were identified in Europe hundreds of years ago. The mystery is why, even today, so many governments fail to put this knowledge to work."--The Economist "This elegantly written, scholarly work will appeal to those interested in financial history or monetary theory."--Publishers Weekly "[The authors'] design serves as a temple for the conduct of research in economics as an empirical science. They have done it just right. Their book is strongly recommended."--Choice "This is an important and wide-ranging book, which will reshape the way in which we think of the origins of modern money and modern monetary theory. It is ... so well organized that the lay reader can get the message simply by reading the fascinating narrative and taking for granted the mathematical account of the standard formula, presented in two chapters at the conclusion. It is also splendidly illustrated and beautifully produced."--Harold James, Times Literary Supplement "A remarkable book... The Big Problem of Small Change is an impressive piece of scholarship that should be of interest to most economists, not just to economic historians. It offers a coherent model of money that helps explain a recurring problem that can arise with a commodity of money system and that provides the basis for understanding a solution to this problem."--Arthur J. Rolnick and Warren E. Weber, Journal of Political Economy "[H]istorically-minded readers will have traversed an insightful and entertaining exploration of European monetary history and of the writings of early monetary thinkers ... with as much enjoyment in the reading as the authors seem to have taken in the research and writing."--Robert W. Dimand, History of Economic Ideas