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September 22, 1997 | Humphrey, Thomas M. | Copyright

COPYRIGHT 1999 Federal Reserve Bank of Richmond. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights or concerns about this content should be directed to Customer Service.

The quantity theory of money, dating back at least to the mid-sixteenth-century Spanish Scholastic writers of the Salamanca School, is one of the oldest theories in economics. Modern students know it as the proposition stating that an exogenously given one-time change in the stock of money has no lasting effect on real variables but leads ultimately to a proportionate change in the money price of goods. More simply, it declares that, all else being equal, money's value or purchasing power varies inversely with its quantity.

There is nothing mysterious about the quantity theory. Classical and neoclassical economists never tired of stressing that it is but an application of the ordinary theory of demand and supply to money. Demand-and-supply theory, of course, predicts that a good's equilibrium value, or market price, will fall as the good becomes more abundant relative to the demand for it. In the same way, the quantity theory predicts that an increase in the nominal supply of money will, given the real demand for it, lower the value of each unit of money in terms of the goods it commands. Since the inverse of the general price level measures money's value in terms of goods, general prices must rise.

In the late nineteenth and early twentieth centuries, two versions of the theory competed. One, advanced by the American economist Irving Fisher (1867-1947), treated the theory as a complete and self-contained explanation of the price level. The other, propounded by the Swedish economist Knut Wicksell (1851-1926), saw it as part of a broader model in which the difference, or spread, between market and natural rates of interest jointly determine bank money and price level changes.

The contrasts between the two approaches could hardly have been more pronounced. Fisher's version was consistently quantity theoretic throughout and indeed focused explicitly on the received classical propositions of neutrality, equiproportionality, money-to-price causality, and independence of money supply and demand. By contrast, Wicksell's version contained certain elements seemingly at odds with the theory. These included (1) a real shock explanation of monetary and price movements, (2) the complete absence of money (currency) in the hypothetical extreme case of a pure credit economy, and (3) the identity between deposit supply and demand at all price levels in that same pure credit case rendering prices indeterminate.

Despite these anomalies, Wicksell was able to derive from his analysis essentially the same conclusion Fisher reached. Both concluded that the monetary authority bears the ultimate responsibility for price level stability, a responsibility it fulfills either by determining some nominal variable - such as dollar price of gold, monetary base, bank reserves - under its control or by adjusting its lending rate in response to price level deviations from target.

The story of how Fisher and Wicksell reached identical policy conclusions from seemingly distinct models is instructive. It reveals that models appearing to be substantially different may be only superficially so. In the case of Fisher and Wicksell, it reveals that their models may not have been as dissimilar as often thought. Indeed, the alleged non-quantity-theory elements in Wicksell's work prove, upon careful examination, to be entirely consistent with the theory. In an effort to document these assertions and to establish Wicksell's position in the front rank of neoclassical quantity theorists with Fisher, the paragraphs below identify the two men's contributions to the theory and show how their policy conclusions derived from it.

1. FISHER'S VERSION OF THE QUANTITY THEORY

In his 1911 book The Purchasing Power of Money, Fisher gave the quantity theory, as inherited from his classical and pre-classical predecessors, its definitive modern formulation. In so doing, he accomplished two tasks. First, he expressed the theory rigorously in a form amenable to empirical measurement and verification. Indeed, he himself fitted the theory with statistical data series, many of them of his own construction, to demonstrate its predictive accuracy.

Second, he spelled out explicitly what was often merely implicit in the work of John Locke, David Hume, Richard Cantillon, David Ricardo, John Wheatley, and other early quantity theorists, namely the five interrelated propositions absolutely central to the theory. These referred to (1) equiproportionality of money and prices, (2) money-to-price causality, (3) short-run nonneutrality and long-run neutrality of money, (4) independence of money supply and demand, and (5) relative-price/absolute-price dichotomy attributing relative price movements to real causes and absolute price movements to monetary causes in a stationary fully employed economy.(1)

Fisher enunciated these propositions with the aid of the equation of exchange P = (MV + M[prime]V[prime])/T, which he attributed to Simon Newcomb even though Joseph Lang, Karl Rau, John Lubbock, and E. Levasseur had formulated it even earlier. Here P is the price level, M is the stock of hard or metallic money consisting of gold coin and convertible bank notes, V is the turnover velocity of circulation of that stock, M[prime] is the stock of bank money consisting of demand deposits transferable by check, V[prime] is its turnover velocity, and T is the physical volume of trade. Fisher's assumption that metallic money divides in fixed proportions between currency and bank reserves and that reserves are a fixed fraction of deposits allowed him to treat checkbook money as a constant multiple c of hard money. His assumption allows one to simplify his expression to P = M[V.sup.*]/T, where [V.sup.*] = V + cV[prime].

Of the equation's components, Fisher ([1911] 1963, p. 155) assumed that, in long-run equilibrium, the volume of trade is determined at its full-capacity level by real forces including the quantity and quality of the labor force, the size of the capital stock, and the level of technology. Save for transition adjustment periods in which the variables interact, these real forces and so the level of trade itself are independent of the other variables in the equation. Likewise, institutions and habits determine aggregate velocity, whose magnitude is fixed by the underlying velocity turnover rates of individual cash-holders, each of whom has adjusted his turnover to suit his convenience (Fisher [1911] 1963, p. 152). Like the volume of trade, velocity is independent of the other variables in the equation of exchange. And with trade and velocity independent of each other and of everything else in the equation, it follows that equilibrium changes in the price level must be due to changes in the money stock.

Classical Propositions

All the fundamental classical quantity theory propositions follow from Fisher's demonstration. Regarding proportionality, he writes that "a change in the quantity of money must normally cause a proportional change in the price level" ([1911] 1963, p. 157). For, with trade and velocity independent of the money stock and fixed at their long-run equilibrium levels, it follows that a doubling of the money stock will double the price level.

Fisher realized, of course, that proportionality holds only for the ceteris paribus thought experiment in which trade and velocity are provisionally held fixed. In actual historical time, however, trade and velocity undergo secular changes of their own independent of the money stock. In that case, proportionality refers to the partial effect of money on prices. To this partial effect must be added the parallel effects of coincidental changes in velocity and trade (see Niehans [1990], p. 277). The sum of these separate effects shows the influence of all on the price level. Thus if M, [V.sup.*], and T evolve secularly at the percentage rates of change denoted by the lowercase letters m, [v.sup.*], and t, respectively, then the price level P evolves at the percentage rate p = m + [v.sup.*] - t. Fisher ([1911] 1963, pp. 246-47) himself expressed the matter precisely when he declared that the history of the price level is a history of the race between increases in the money stock and increases in the volume of trade. …

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