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Irving Fisher, the outstanding American neoclassical economist of the first half of the twentieth century, was born in Saugerties, New York, on February 27, 1867, and was living in New Haven, Connecticut, when he died on April 29, 1947. Fisher graduated with an A.B. in 1888 and a Ph.D. in economics and mathematics in 1891 from Yale University (from which his father, a Congregational clergyman, had also graduated). He taught at Yale until his retirement in 1937, initially in mathematics and then, from 1895, in political economy, and was promoted to full professor in 1898. A student of both the mathematical physicist Josiah Willard Gibbs and the political economist, sociologist, and social Darwinist William Graham Sumner, Fisher combined his interests in mathematics and economics in his dissertation and his first book, *Mathematical Investigations in the Theory of Value and Prices *(1892; Fisher 1997, vol. 1). This remarkable work made Fisher, along with John Bates Clark and Stuart Wood, a pioneer in introducing marginal utility and marginal product analysis into U.S. economics. Fisher’s (re)discovery of both general equilibrium analysis and indifference curves (requiring only a preference ordering, not cardinally measurable utility) was an independent breakthrough because he did not read either Léon Walras or F. Y. Edgeworth until his thesis was almost finished. But modern opinion is consequently divided between Paul Samuelson’s modest description of Fisher’s thesis as the greatest doctoral dissertation by an American economist, and Robert Dorfman’s belief that it should have been rejected for unnecessary reinvention of existing theory. The unique contribution of Fisher’s thesis was his construction, in an age before electronic computers, of a hydraulic model simulating the determination of equilibrium prices and quantities (William Brainard and Herbert Scarf in Dimand and Geanakoplos 2005). In an article in 1896 Fisher used a simplified hydraulic model to analyze the bimetallic controversy in monetary economics (Fisher 1997, vol. 1).

Fisher’s 1896 American Economic Association monograph *Appreciation and Interest *(Fisher 1997, vol. 1) attributed the difference between interest rates expressed in two standards (gold, silver, paper currencies, or commodities) to the expected rate of appreciation of one standard against the other. The Fisher equation, now expressed as equating nominal interest to the sum of real interest and expected inflation, formalized an insight briefly remarked upon by John Stuart Mill and Alfred Marshall. Fisher’s monograph introduced uncovered interest parity for exchange rates and the expectations theory of the term structure of interest rates—that is, differences in interest rates for different lending periods reflect expected changes in the purchasing power of money. In *The Theory of Interest *(1930; Fisher 1997, vol. 9), Fisher tested his equation empirically by correlating nominal interest with a distributed lag of past price level changes (adaptive expectations), finding considerably less than perfect correlation. Having shown in *Appreciation and Interest *that correctly anticipated inflation would affect only nominal interest, leaving real interest unaltered, Fisher and Harry G. Brown argued in *The Purchasing Power of Money *(1911; Fisher 1997, vol. 4) that, in the long run, a change in the quantity of money would change the price level in the same proportion, with no lasting effect on real variables. Fisher thus defended the quantity theory of money against both bimetallists who held that monetizing silver would have lasting real benefits and some of their hardmoney opponents, notably J. Laurence Laughlin of the University of Chicago, who denied that changes in the quantity of money could explain observed changes in prices. While insisting on the long-run neutrality of money, Fisher viewed monetary shocks as the force driving short-run fluctuations in real output and unemployment: his 1926 *International Labour Review *article, “A Statistical Relation Between Unemployment and Price Changes,” was reprinted in the *Journal of Political* *Economy *in 1973 as “Lost and Found: I Discovered the Phillips Curve—Irving Fisher” (also in Fisher 1997, vol. 8). Fisher’s monetary theory of economic fluctuations depended on the slow adjustment of expected inflation, and hence of nominal interest, to monetary shocks.

If changes in the purchasing power of money were correctly perceived and expected, there would be no booms or depressions, so Fisher campaigned to educate the public against the “money illusion,” which provided the title of his 1928 book (Fisher 1997, vol. 8). He also wished to neutralize price changes through indexation, and persuaded Rand Kardex to issue an indexed bond in 1925. Alternatively, fluctuations could be eliminated by avoiding changes in the purchasing power of money, so Fisher proposed a monetary policy rule (the compensated dollar) to peg the price level by varying the exchange rate (the dollar price of gold) to counteract any change in a price index. This monetary policy rule, eradication of money illusion, and statistical verification of the quantity theory of money and of the monetary theory of fluctuations all required an appropriate price index. When prices rise, a Laspeyres index with base-year quantity weights overestimates the price increase, which a Paasche index with current-year weights underestimates. In *The Making of Index Numbers *(1922; Fisher 1997, vol. 7) Fisher advocated, as an “ideal index” suitable for all purposes, the geometric mean of the Laspeyres and Paasche indexes, the formula that came closest to satisfying a list of seven criteria he proposed as desirable for an index number. (Ragnar Frisch and Subramanian Swamy later determined that no formula could satisfy all seven of Fisher’s criteria.) In the 1990s several governments including the United States adopted Fisher’s ideal index and issued some indexed bonds.

In *The Rate of Interest *(1907; Fisher 1997, vol. 3) and *The Theory of Interest*, Fisher systematized the neoclassical theory of how the equilibrium real rate of interest is determined by the interaction of impatience (time preference) and opportunity to invest (the expected rate of return over costs on new investments). The Fisher diagram, showing utility-maximizing consumption-smoothing over two periods, illustrated the Fisher separation theorem between the time-pattern of income and that of consumption: given perfect credit markets, consumption in any period depends only on the present discounted value of expected lifetime income, not on income in that period. Not only was this insight the basis for the later permanent-income and lifecycle theories of consumption and saving, but the Fisher diagram also proved useful in applications ranging from international trade to insurance (allocation across possible states of the world). Ironically, Fisher’s 1907 numerical example of the possibility of multiple solutions for BöhmBawerk’s average period of production prefigured criticisms of neoclassical capital and interest theory advanced in the Cambridge capital controversies of the 1960s (and Fisher’s own concept of rate of return over costs was subject to the same possibility of multiple solutions).

From 1898 to 1904 Fisher battled successfully to recover from tuberculosis, which had killed his father. His heightened sensitivity to the value of health and longevity led him to advocate health insurance, a federal department of health, and prohibition of alcohol; to coauthor the best-seller *How To Live *; and to estimate the nation’s human capital at five times the value of its physical capital. It also motivated Fisher’s involvement with the dietary reforms proposed by Dr. Kellogg of Battle Creek and with the “race betterment” schemes of the eugenics movement, including support for the Immigration Restriction Act of 1924 (Fisher 1997, vol. 13). Fisher invented and patented a tent for tuberculosis patients.

Among Fisher’s many subsequent inventions, the Index Visible (precursor of the rolodex) made him wealthy, temporarily, when it was absorbed by Rand Kardex. An enthusiastic “new economy” advocate of the permanence of the 1920s stock boom based on technological breakthroughs, Fisher had a net worth of ten million dollars before losing all of it, and more, in the Wall Street crash that began in October 1929. Fisher’s memorable statement that month that “stock prices appear to have reached a permanently high plateau” continues to haunt his reputation with the general public. Among economists, however, after a period of eclipse by the rise of Keynesian macroeconomics, Fisher is now once again celebrated as America’s outstanding scientific economist of the first half of the twentieth century, and perhaps of any time.

**Bibliography:**

- Allen, Robert Loring. 1993.
*Irving Fisher: A Biography*. Malden, MA, and Oxford: Blackwell. - Dimand, Robert W., and John Geanakoplos, eds. 2005.
*Celebrating Irving Fisher: The Legacy of a Great Economist*. Malden, MA, and Oxford: Blackwell. Also published as*American Journal of Economics and Sociology*64 (1): 1–456. - Fisher, Irving. 1997.
*The Works of Irving Fisher*. 14 volumes. Ed. William J. Barber assisted by Robert W. Dimand and Kevin Foster, consulting ed. James Tobin. London: Pickering and Chatto. - Fisher, Irving Norton. 1956.
*My Father Irving Fisher*. New York: Comet. - Loef, Hans-E., and Hans G. Monissen, eds. 1999.
*The Economics of Irving Fisher*. Cheltenham, U.K., and Northampton, MA: Edward Elgar.

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