Introduction
Paper and gold
A century ago few would have foretold the kind of money we use today. In 1873, the U.S. Congress had passed a law, section 14 of which states: “the gold coins of the U.S. shall be a one-dollar piece, which, at the standard weight of 25.8 grains, shall be the unit of value” (Statutes at Large of USA 17:427). Section 14 thus defined the American unit of account,1 the dollar, as a specified quantity of a particular metal. In doing so, it embodied a shared wisdom accumulated from centuries of experience. And, while some countries did not adhere to the gold standard in 1900, relying instead on some type of inconvertible paper money, they were regarded as backward by the “advanced nations.” Today, the definition of the dollar as an amount of gold is gone and long forgotten. The “advanced nations” now all rely on inconvertible paper money.2
How can we explain this remarkable reversal? With hindsight, can we detect groundwork laid in earlier times for the universal replacement of gold by fiat?
On closer inspection, ancillary sections of the 1873 U.S. law portend the monetary developments of the twentieth century. Sections 15 and 16 prescribed that smaller denominations, from 50¢ to 1¢, were to be made in metals other than gold. An act of 1879 (Statutes at Large 1879, 7) made these subsidiary coins convertible, in sums of $20 or more, into “lawful money” (i.e., gold) on demand at the Treasury. Subsidiary coins were tokens: their value came not from metal within but from trust in the government’s promise to convert them into gold (dollars) upon demand.
In 1900, sections 15 and 16 were thought unremarkable, dealing as they did with a matter of subsidiary importance, a technical issue much like minting charges or employee salaries. Indeed, similar provisions for small change could be found in the monetary laws of other advanced countries, and monetary textbooks of the time routinely described what had become by then a “standard formula” for managing the supply of small change.
Yet it took centuries to devise the formula. And until it was devised, the supply of small change was an important and persistent problem. Furthermore, from our vantage one hundred and twenty-five years later, the more enduring features of the act of 1873 are sections 15 and 16: for today all parts of our money, not just small change, have now become “tokens,” convertible only into other tokens.
This book is about the “big problem of small change”: what the problem was, how it was solved and why it took so long, and what was learned in the process about broader monetary and fiscal affairs. A long struggle with the problem of small change eventually produced a practical solution. It also produced a monetary theory that was able to extend token coinage to the entire denomination structure and found the comprehensive fiat money system that prevails today.3
The enduring problem of small change
Western Europeans long struggled to sustain a proper mix of large and small denomination coins, and to free themselves of the belief that coins of all denominations should be full-bodied.
The monetary system begun by Charlemagne about A.D. 800 had only one coin, the silver penny. From the end of the twelfth century, various states introduced larger denominations. To do so, they established a monetary system that embodied the prevailing views about money. At the time, European monetary authorities did not think of money as something whose value emerges from its role as medium of exchange. Instead, they shared a conception of money that ignored its moneyness and focused solely on the substance it contained, namely silver. Therefore, in their view, coins of all denominations should be full-bodied, and rates of exchange of coins of different denominations should reflect their relative metal contents. They understood how a commodity money anchored nominal prices, and they sought to maintain that anchor throughout the denomination structure. So they set up a system in which supplies of coins of all denominations were chosen by private citizens, who decided if and when to use metal to purchase new coins from the mint at prices set by the government.
In the following centuries, that system produced intermittent shortages of small denomination coins, persistent depreciations of small coins relative to large ones, and recurrent debasements of the small coins. Cipolla (1956, 31) stated that “Mediterranean Europe failed to discover a good and automatic device to control the quantity of petty coins to be left in circulation,” a failure that extended across Europe. He called this failure the “big problem of small change.”
By the middle of the nineteenth century, the mechanics of a sound system were well understood, thoroughly accepted, and widely implemented. According to Cipolla (1956, 27):
Every elementary textbook of economics gives the standard formula for maintaining a sound system of fractional money: to issue on government account small coins having a commodity value lower than their monetary value; to limit the quantity of these small coins in circulation; to provide convertibility with unit money.… Simple as this formula may seem, it took centuries to work it out. In England it was not applied until 1816, and in the United States it was not accepted before 1853.
The standard formula avoided shortages and depreciations of small denomination coins without causing inflation. It retained a commodity money anchor but did not impose it coin by coin. Instead, it made the smaller denominations into token coins, convertible into gold.
In 1900, J. Laurence Laughlin (1900, 113–14) described the standard formula and added: “As a matter of course, countries have not always had clear conceptions regarding this kind of money, so that the principles just enumerated have come forth only by a process of evolution out of experience.”
Thus, Cipolla, Laughlin, and others4 have highlighted the discrepancy between the formula’s simplicity and the time required to devise it. The aim of our book is to understand the sources of this discrepancy. We retrace events from 1200 to 1850, following three strands.
First, important ideas about money had to be discovered and others discarded. It took a long time before theorists recognized the superiority of tokens over full bodied coins. 5 Second, technologies that made it possible to issue token coinage had to be developed. Third, by trial and error, policy makers had to learn the properties of new institutions.
The long process of evolution out of experience provides a fascinating perspective on the growth of monetary theories and institutions, with many interactions among the three strands of theories, technologies, and experiments. Commentators tried to make sense of their observations, building monetary theory in the process. Governments ran diverse experiments, sometimes in response to commentators’ advice. Technical innovations in metal working altered the relative costs of legal and illegal suppliers of small change, and made new monetary policies feasible.
Governments had long experimented with issuing token coinage themselves and sometimes allowed private agents to issue it, before they discovered, or accepted, that, as in Cipolla’s standard formula, small change should be tokens backed by a government standing ready to exchange them for full-bodied large denomination coins or currency. In the process, they discovered the two main ideas that underlie the twentieth century concept of a “well-managed fiat” system: the quantity theory of money, and the need to restrain the suppliers of token money from creating inflation.
A model
We use a model to guide our narrative. The “big problem of small change” took a long time to solve, in part because it is in truth technically complicated. The only way we have been able to understand the problem, as well as the decisions made over the centuries by monetary authorities, is to construct a model that highlights the problem and that isolates alternative potential solutions, including, among others, the standard formula. We created our model by modifying and extending a more or less standard model of fiat money that does not differentiate the supply or demand for money by denominations. 6 While that model has performed well in describing various twentieth-century experiences with fiat money, we have to modify the demand side to accommodate diverse denominations of coins and the supply side to account both for different denominations and the fact that money was based on a commodity, not on government fiat. We believe that our model illuminates a variety of problems that stalked monetary authorities for centuries.
We need a model because the facts don’t speak for themselves. To understand economic phenomena we have to appreciate the views that guided historical decision makers, that is, their models. To judge when they chose well and when they chose poorly, we measure their models against ours.
Our model explains why the medieval money supply mechanism was prone to shortages of small coins. It shows why debasements or reinforcements of parts of the denomination structure would temporarily cure those shortages. The model also explains why shortages and depreciations of small coins happened simultaneously.
Our model uses the concepts of supply and demand to sort the forces operating on the market for coins of different denominations into two mutually exclusive categories. The supply and demand sides of the model both have unusual features designed to focus on the denomination structure of money.
Supply side: the mint
The supply side of our model represents the arrangements by which coins were provided in medieval times. The mint stands ready to convert gold or silver into specified coins at fixed prices. People choose the quantities of coins to be produced at any point in time. If they want to convert coins into silver or gold, people can either melt them or use them to purchase silver or gold from metal merchants. The supply side determines intervals bounded by “silver points,” one interval for each denomination of coin, within which the price level (the price of goods in terms of coins) must reside if coins of all denominations are to circulate. Were the price level to fall below the lower bound of the interval for a particular coin, that coin would be minted; were it to exceed the upper bound, the coin would be melted. Thus, whether a particular coin exists depends on the position of the price level with respect to that coin’s interval. The size of the interval for each coin depends on the production costs and the seigniorage taxes (or subsidies) for that coin. The model asserts that coin shortages can be avoided only if costs and seigniorage rates imply a nonempty intersection of all of the intervals.
In the model, the government sets the limits of the intervals, the silver points. The lower limit is called the “mint equivalent” and the upper limit is called the “mint price.” The government sets these limits by choosing the metal content of each coin and the price that the mint will pay, in each coin, for gold or silver. In making these choices, the government is constrained by its own production costs and those of its competitors, counterfeiters and foreign mints. Technological developments in the minting process can provide the government with a cost advantage over its competitors and give it more freedom to adjust the intervals, at least for a while. But even if a government finds it feasible initially to set the intervals properly, the demand side can separately generate shortages.
Demand side: the coin owner
To understand shortages of small coins, we need a model that grants them a special role in transactions. The standard model of the demand for money, for example Lucas (1982), assigns a special transactions role to the aggregate stock of currency, but does not distinguish among denominations. The special role assigned to the aggregate stock of currency permits nominal interest rates to be positive, thereby letting currency, which bears no interest, be dominated in rate of return by other assets. The positive nominal interest rate reflects the extra “liquidity services” provided only by currency.
The demand side of our model extends the standard model by distinguishing among denominations and assigning to small denominations a further special role. This allows small coins to be dominated in rate of return by large coins during shortages of small coins. At such times, small coins render more liquidity services than large coins. Then large coins appreciate relative to small coins, so that the resulting capital loss on small coins exactly offsets their special liquidity services, and equalizes the total yield of large and small coins, inclusive of liquidity services.
Our model extends Lucas’s model to incorporate two cash-in-advance constraints, one like Lucas’s that constrains all consumption purchases, and a second that constrains only small purchases. These constraints represent the idea that small denomination coins can be used to purchase expensive items, but large denomination coins cannot be used to buy cheap items. The second cash-in-advance constraint (denoted the penny-in-advance or p.i.a. constraint) embodies a demand for small change and adds an occasionally binding constraint and an associated Lagrange multiplier that plays a decisive role in characterizing “shortages” of small change. The Lagrange multiplier measures the extra liquidity services of small denomination coins. When the p.i.a. constraint is not binding, the model exhibits a version of penny-versus-dollar exchange rate indeterminacy, a feature of many models with inconvertible currencies. 7 So long as pennies and dollars bear the same rates of return, holders of currency are indifferent to the ratio in which they hold pennies and dollars. Exchange rate indeterminacy stops during small change shortages, manifested in a binding p.i.a. constraint and a rate of return on dollars that exceeds that on pennies. This rate of return dominance manifests itself in an appreciation of dollars when measured in pennies. It is the market signal that causes money holders to conserve pennies.
Shortages
How can shortages occur when people can always use silver to purchase new coins from the mint? The answer is that people want to convert metal into coins only if it is profitable to do so. Whether it is depends on the price level. Most of the time, movements in the price level are determined by the aggregate stock of currency, not just the stock of small denominations.
A novel prediction of our model is that, within the medieval system, shortages can occur away from the bounds of the intervals constraining the price level, and that a shortage may fail to induce the price level movements necessary to trigger production of more coins. Moreover, the price signals induced by shortages of small change perversely hasten the day when small coins will eventually be melted. Since they depreciate as currency, they ultimately become more valuable as metal than as coins, unless the government makes appropriate adjustments in the parameters governing the melting point for small coins. This feature of the model explains the widely observed persistent depreciation of small coins, inspires our interpretation of debasements of small coins as a cure for shortages of small change within the medieval money supply mechanism, and suggests how that mechanism needed to be reformed. 8
Price level determination
An ideal commodity money system is designed to equate the price level to a relative price of a metal for consumption goods, and, by making stocks of coins endogenous, to prevent effects on the price level coming from exogenous fluctuations in the quantities of coins. As in the medieval monetary system, that ideal is imperfectly realized in our model because seigniorage and other production costs induce a spread between the minting and melting points. Within those silver points, there is scope for exogenous movements in the quantities of coins to influence the price level. The interval between the silver points thus makes room for influences on the price level conforming to the quantity theory of money.9
Because there are silver points for each denomination of coin, our model embodies various forms of the quantity theory of money, depending on how those different silver points are aligned and on whether the penny-in-advance constraint is binding. The intervals between the minting and melting points for large and small denomination coins identify a price level band within which the ordinary quantity theory operates, cast in terms of the total quantity of coins. The price level is inside this band during periods in which coins of both denominations circulate and neither is being melted or minted. However, when the p.i.a. constraint binds but neither coin is melted or minted and both circulate, the quantity theory breaks in two, with one holding for “dollars,” another for “pennies.” Yet another more standard version of the quantity theory holds in a regime in which the parameters of supply have been set to cause large denomination coins to disappear because they have been expelled by token small coins.
These features of the model explain how a system designed to anchor the price level to the value of gold or silver nevertheless allowed observers to learn about the quantity theory. The intervals between minting and melting points could be wide enough occasionally to provide a glimpse of the quantity theoretic mechanism for price level determination that controls the price level under today’s pure fiat money regime.
Remedies
The model formalizes the contributions of various parts of Cipolla’s standard formula, including the roles of token coinage, costless to produce upon demand; of convertibility at a pegged exchange rate between large and small coins; of limited legal tender for smaller coins, to modify the cash-in-advance constraints. The model produces elements to seek in the historical record. Was a technology available to produce a token coinage? Could institutions be trusted to guarantee convertibility? When and how was the belief discarded that coins of all denominations should be full-bodied?10
A history
Armed with our model, we sift through the historical record. Our story begins in Carolingian times,11 when money came in one simple form: a coin called the penny, produced by a crude technology, and thought of as a commodity like wheat or wine. The growing needs of trade led to the introduction of larger denominations, silver and gold coins. From then on, a variety of puzzling phenomena occurred, including chronic coin shortages, flows of small coins across borders, varying exchange rates between coins, and correlations between the quantity of coins and the price level, suggesting a “quantity theory.” Governments sometimes used debasements to alleviate these problems. Lawyers grappled with these observations as they confronted related legal issues, refined their views of money as a commodity, and ultimately recognized the concept of fiat money. In the late fifteenth century, isolated experiments with convertible token coinage were carried out, but they floundered on technological constraints and undisciplined governments.12
The sixteenth century brought mechanization of minting. Coins of higher quality, more immune to counterfeiting, could be produced, but at a high fixed cost. This tempted Castile into an experiment to reap some of the efficiency gains from a well-managed fiat currency system based on token copper coins. But deficit finance ultimately created unprecedented inflation. Other countries across seventeenth-century Europe confronted the same temptation, with a range of outcomes. Monetary doctrine responded to these experiments with an understanding of when fiat money might be desirable, how to manage it, and why the quantity theory of money might recommend limiting the role of small coins as legal tender. In England in 1661, Sir Henry Slingsby proposed a version of the standard formula.
It took another century and a half before England implemented Slingsby’s recommendations. We close our story by endorsing Angela Redish’s (1990) account of how the application of the steam engine opened the way for the first de facto implementation of the standard formula in Britain in 1816. It took more decades before the formula was to be adopted in the United States, France, and Germany, providing an important element of the Classical Gold Standard.
After this long learning process, societies emerged with a well-functioning commodity money system, and also with the theoretical tools and the collective experience to prepare a fiat money system with stable prices. Nevertheless, the twentieth century brought many prolonged inflation experiments with fiat money that resemble ones described in this book, with paper replacing copper as the handmaiden of inflation. So learning continued well into the last quarter of the twentieth century.
Structure of subsequent chapters
We have used our model to organize our history of doctrines, technologies, and experiments. Our historical account refers to our model so often that sometimes we may seem to be writing a history of how past monetary experts learned our model, piece by piece through a long process of trial and error.
We have structured our exposition as follows. The remainder of part I describes our model in an informal way, and conveys enough intuition about its workings to guide the reader as the model has guided us. Part II presents histories of technologies and ideas, while parts III and IV describe shortages and experiments. Chapter 19 summarizes and interprets our historical observations. Finally, part V presents our model formally. Mutual influences among technologies, ideas, and events will prompt frequent references across parts.
1 This and other terms are defined in the glossary.
2 Few countries even define their unit of value as a particular quantity of another country’s paper money, i.e., peg exchange rates.
3 The gold standard finally ended when President Nixon closed the gold window on August 15, 1971.
4 Feavearyear (1963, 169–70) writes of England in the eighteenth century: “The failure for the better part of a century to make adequate provision for fractional payments in spite of all the profound discussion of economic matters which went on may seem to us somewhat remarkable, accustomed as we are to a well-managed token currency which, while being useful, and indeed indispensable, to the public, brings in the long run a good profit to the state. From the earliest times there had been great difficulty in getting an adequate supply of small coins into circulation.”
5 “Monetary policy would have faced fewer difficulties if the commodity money concept of money had commanded less respect. Its persistence as an ideal obstructed and delayed the development of a workable system of redeemable token money” (Usher 1943, 196).
6 Versions of this model appear in Lucas (1982) and Sargent and Wallace (1973) and are used in Sargent (1993, ch. 3).
7 See Kareken and Wallace (1981).
8 See also Sargent and Smith (1997). Glassman and Redish (1988) also interpret debasements in early modern Europe as a cure.
9 See Sargent and Wallace (1983, 172) for a similar result. If our model abstracted from seigniorage, the silver points would coincide and no such room would be left for the quantity theory (as in Niehans 1978, 147–48).
10 Though sophisticated analysts had long before articulated a coherent theory of convertible token subsidiary coins, John Locke’s position in 1695 was that full-bodied coins should be maintained throughout the denomination structure. His views prevailed in Parliament. Even after England had embraced the standard formula, Macaulay ([1855] 1967, ch. 22) lauded Locke’s analysis and belittled Locke’s opponents for advocating token small coins (see chapter 16).
11 Further back, Burns (1927, ch. 12) found evidence of token coinage for small denominations in Greek and Roman times, and Reekmans (1949) discussed copper inflation in Ptolemaic Egypt.
12 See Kohn (2001, ch. 7) for another account of coin shortages during medieval times. Kohn alludes to some of the same mechanisms that are captured in our model. Schmoller (1900) briefly surveys the development of monetary policy with respect to small coins from the Middle Ages to the early 19th century, with emphasis on the emergence of overvalued small denominations with limited legal tender; he does not, however, mention convertibility.