Thomas J. Sargent and Francois R. Velde, The Big Problem of Small Change. Princeton, NJ: Princeton University Press, 2002. xxi + 405 pp. $39.50 (cloth), ISBN: 0-691-02932-6.

Reviewed for EH NET by Anna J. Schwartz, National Bureau of Economic Research.

When I mentioned to Levis Kochin that I had agreed to review Sargent and Velde's book for EH.Net, he told me that I had to read David Landes's (1982) Revolution in Time without explaining the connection. He forthwith sent me a paperback copy, which I've read. One book refers to the technology of manufacturing coins, the other to the technology of clocks and watches, but the only link between them obvious to me is that Carlo Cipolla (1967) Clocks and Culture inspired Landes and Carlo Cipolla (1956) Money, Prices, and Civilization in the Mediterranean World, Fifth to Seventeenth Century provided the title of the Sargent and Velde book: "the big problem of small change" as well as a name for the solution: "the standard formula."

What was the big problem? After 1200, when throughout Europe coins of larger denominations than the silver penny -- the sole constituent of Charlemagne's monetary system from 800 on -- became common, a puzzling phenomenon was the recurrence of shortages of small denomination coins, depreciations of small coins relative to large ones, and small coin debasements. Why would a shortage coincide with a fall in value of small coins?

According to the authors, initially, Sargent thought the problem arose because policy makers had the wrong model, but the standard formula provided a better model, making better policy possible; Velde thought the standard formula would not have worked absent improvements in technology. They finally decided that both poor economic theory and inadequate technology were responsible for past monetary difficulties, and that ideas about supplying small change contributed to modern monetary theory.

In a commodity monetary system, the value of a coin was based on its metal content, with an upper limit determined by the production cost and seigniorage charge for minting a coin from the raw metal, and a lower limit determined by the price level at which it paid to melt the coin and use the metal for payments. At a price level below the lower bound, the coin would be minted. At a price level above the upper bound, the coin would be melted. The government set the limits by choosing the metal content of each denomination and the price the mint would pay as measured by the number of coins it offered for the metal brought to it.

To explain the puzzling behavior of small change, Sargent and Velde present a model, with the special feature that it focuses on the denomination structure of money. Small denominations have a special role. They can be used to purchase expensive items, but large denominations cannot be used to purchase cheap items. During shortages of small coins, liquidity services of small coins exceed those of large coins, with a resulting appreciation of large coins relative to small ones. The capital loss on small coins offsets their liquidity services and equalizes the total yield of small and large coins inclusive of liquidity services.

When small and large coins yield the same rates of return, currency-holders are indifferent to the ratio each category bears to the other. During small coin shortages, however, the rate of return on large coins exceeds that on small coins, a signal to holders to hold on to small coins. The model predicts that a shortage may not have price level effects leading to coin production increases, but perversely may encourage the melting of coins. Debasements occurred as a cure for small change shortages.

The remedy for the problem was only dimly perceived until the nineteenth century. The standard formula prescribed the issue by government of small coins with a commodity value lower than their monetary value, limited legal tender for small coins, limitation of the quantity of small coins in circulation, and a commitment to provide convertibility between large and small coins.

The model guided the historical search by Sargent and Velde for evidence on small change shortages in different European locations during the centuries after 1200, how governments coped with the problem, and the slow growth of understanding of how to manage fiat money. The effort could not be crowned by success until minting technology had progressed to the point that made counterfeiting of coins difficult.

The book thus investigates a triad of subjects: history of doctrines, technologies, and experiments. Sargent and Velde regard history as showing how past monetary experts learned the elements of the correct model through a long process of trial and error.

Although the scholarship the book embodies is impressive, a challenge has been mounted to the argument underlying one of the triads. The authors accept Angela Redish's conclusion that the installation of Watt's steam-driven minting presses in Boulton's Soho Mint facilitated the implementation of the standard formula. In an exhaustive study, George Selgin has shown that manual labor and manual screw presses remained the norm among commercial coin-makers until beyond the middle of the nineteenth century, and that the invention of crucible steel for making dies capable of withstanding multiple blows without fracturing enabled coin manufacturers to afford superior engravers of master dies. Counterfeiters were stymied by these coins. Selgin contends that the Soho Mint, which obtained an exclusive contract to mint copper coin for the government in 1797, was a marginal operation that would have been forced out of business by its more efficient rivals, and that its coins were not particularly counterfeit resistant. It made coins with plain rather than milled or otherwise marked edges. According to Selgin, the short-change problem was solved by the employment of paper currency, which made counterfeiting less lucrative. As a libertarian, he complains that economists are too ready to accept the position of the standard formula in assigning to government a monopoly of the mint.

To conclude, Sargent and Velde have written a book with more detail than this review can cover. The model is introduced in a preliminary form in part I, studied in connection with the historical episodes in parts III and IV, and fully presented in part V. Pedagogically this probably makes sense. A reader, however, may sense that the same ground is being explored over and over again. If one cannot spend the time to study the book as a whole, Chapter 19 that concludes part IV is a good summary.

Anna J. Schwartz is a research associate of the National Bureau of Economic Research and the author of "Earmarks of a Lender of Last Resort," in Financial Crises, Contagion, and the Lender of Last Resort, C.A.E. Goodhart and Gerhard Illing, editors, Oxford University Press, 2002.