3. Revitalizing the Quantity Theory of Money: From the Fisher Relation to the Fisher Equation

Milton Friedman (1992) gave high marks to Walker’s analysis, noting that even if international bimetallism proved to be in practice an alternating monometallic standard, that would result in a more stable price level than either a gold standard or a silver standard. The problem of alternating monometallic standards, resulting from trying to peg the relative price of two metals (whether one ounce of gold to sixteen ounces of silver or another ratio) would be avoided by the symmetallism tentatively suggested by Alfred Marshall in 1886 testimony and an 1887 article. Joseph Dorfman (1949, p. 19) discovered that symmetallism was proposed, a few years before Marshall, in New Haven, Connecticut, in 1879, when Walker was teaching at Yale’s Sheffield Scientific School and Sumner at Yale College and just five years before Fisher became a Yale undergraduate: “John Philip Phillips, wealthy New Haven physician and lawyer and former Greenbacker, advanced in A Primer of Political Economy (1879) the idea that the principle of the bimetallic standard be obtained by requiring that in all future contracts gold and silver be made semi-legal tenders; that is, coin debts should be legally payable only by delivering one-half their amount in gold dollars and one-half in silver dollars.” Phillips’s 80-page 1879 pamphlet is available at the Yale University Library (as is Phillips [1878], a 32-page pamphlet of which it is an expanded revision) but is not in the Library of Congress catalogue, which does, however, list Phillips (1888, 1896).

Specifically, John D. Rockefeller, benefactor of the University of Chicago, had not volunteered a large donation to Brown even though his son was a member of that year’s graduating class.

The other three issues of that year’s volume were, regrettably, devoted to “Race Traits and Tendencies of the American Negro” by Frederick L. Hoffman (1896), a 330-page work of racist pseudo-science by the statistician to the Prudential Insurance Company of America. Fisher was also a strident eugenicist (see Fisher [1997], Vol. 13, pp. 160–207; Cot 2005; Dimand 2005), and Fisher’s Rate of Interest (1907) expressed strong views on racial and ethnic differences in rates of time preference, which he considerably toned down in The Theory of Interest (1930).

More than a quarter of a century later, John Maynard Keynes (1923) added the covered interest parity condition that the spread between forward and spot exchange rates equals the difference between interest rates in the two currencies.

Fisher (1896) did not consider the effect of risk, other than riskiness of price changes, on the term structure of interest rates. His main contribution to analysis of risk in financial markets came a decade later, in Fisher (1906).

While Fisher, like Newcomb before him and Norton and Kemmerer afterwards, presented the quantity theory of money in terms of the velocity of circulation (V in the transactions version of the equation of exchange MV = PTor in the income version of the equation of exchange, MV = PY), the Cambridge monetary theorists Marshall, Pigou and Keynes used variants of the equation M = kPY, which related desired cash balances M to nominal income. The income version of the equation of exchange is equivalent to the Cambridge cash balance equation, with velocity of circulation V as the inverse of the Cambridge cash balance coefficient k, with the differences between the two approaches being more of exposition than of substance (see Patinkin 1965; Laidler 1991; Dimand 1995). Fisher and Marshall are appropriately pictured together (along with Knut Wicksell) on the cover of David Laidler’s Golden Age of the Quantity Theory (1991).

Sarah McLean Hardy, one of the first female graduate students in economics in the United States, published as S. McLean Hardy.