Work
Fisher’s Mathematical Investigations in the Theory of Value and Prices (1892) brought general equilibrium analysis to North America. Stimulated by Jevons’s Theory of Political Economy (1871) and the recent book by Auspitz and Lieben, Fisher had largely invented the masterly exposition of general equilibrium theory for himself.
He came to know the works of Walras and Edgeworth only when he had finished his book. In his generalized mathematical formulation of utility functions and their maximization Fisher treats the utility of every commodity as a function of the quantities consumed of all commodities. This differs from the analysis of Walras who made the quantity consumed of every commodity a function of prices. Fisher constructed indifference curves as Edgeworth (1881) had done before him, but in contrast to Edgeworth refused the penetration of psychology into economics as dangerous and inappropriate. In his early renouncing of utility as a psychic entity he “anticipated in substance the line of argument that then runs on from Pareto to Barone, Johnson, Slutsky, Allen and Hicks, Georgescu, and finally to Samuelson” (Schumpeter 1948 [1951]: 225). He points out that for the determination of equilibrium neither an interpersonal comparison of utility nor a cardinal measurement of utility for each individual would be necessary. Although Fisher thus can be considered as having pioneered the idea of ordinal theory of utility, which had been elaborated a decade later by Pareto, unlike Pareto, Fisher did not give up “Measuring marginal utility” (1927) empirically.In his general equilibrium system Fisher (1892) also drew attention to two types of interdependent goods, in modern utility theory later distinguished as substitutes and complements. However, the supply side, including technology and available factors of production, is not elaborated.
Furthermore, Fisher’s early model of general equilibrium does not contain capital and interest. This should change with his later works, beginning with Appreciation and Interest. In this work, with which he also intervened into the bimetallic controversy, the focus is on the connection between monetary appreciation and the rate of interest. It is here that in the discussion of a redistribution of wealth between creditors and debtors, he makes the important distinction between expected and unexpected changes in the value of money. Expected changes have no real effects because they are neutralized by interest rates adjustments through arbitrage. Fisher (1896 [1961]: ch. II) develops the interest parity formula in which the difference in interest between two commodities is exactly matched by the expected change in their relative price. If i is the interest rate for gold and j is the interest rate for wheat, and a is the rate at which gold appreciates relatively to wheat in one interest interval, then the equilibrium condition is 1 + j = (1 + i)(1 + a) or j = i + a + ia.The rate of interest in the (relatively) depreciating standard is equal to the sum of three terms, namely, the rate of interest in the appreciating standard, the rate of appreciation itself, and the product of these two elements (1896: 9) Each commodity has its own rate of interest depending on the expectations of the development of its price in the future. As long as future changes in the purchasing power of money are anticipated, there would be no real effects since they are neutralized by adjustments in interest rates. Contrary to a widespread view, a growing scarcity of gold, resulting in falling wheat prices relative to gold, need not necessarily harm farmers who have taken a credit in gold. “[T]he farmer who contracts a mortgage in gold is, if the interest is properly adjusted, no worse and no better off than if his contract were in a ‘wheat’ standard or a ‘multiple’ standard” (ibid.: 16, original emphasis).
The problem of non-neutrality, however, arises with unexpected changes in the purchasing power of money. Fisher considered wrong expectations mainly as a short-run phenomenon since people would learn from experience and adjust their expectations, although with a lag. Fisher became a pioneer of the statistical analysis of distributed lags. Fisher (1926) correlates unemployment with a distributed lag of inflation. However, it has to be pointed out that in this article, which had been reprinted in 1973 as “I discovered the Phillips curve” in a leading journal, causality runs from changes in the value of money to unemployment, whereas in the Phillips curve it is the unemployment rate which affects changes in the wage (inflation) rate.
Modern monetary macroeconomics started with Wicksell’s Interest and Prices (1898 [1936]) and Fisher’s The Purchasing Power of Money; whereas Humphrey in his thorough comparative analysis of Fisher’s and Wicksell’s different interpretations of the quantity theory comes to the conclusion “that Wicksell was... every bit as much a quantity theorist as Fisher. Evidence reveals that he, like Fisher, understood and indeed enriched the theory’s postulates” (Humphrey 1999: 73), it must not be overlooked that there is a direct line from Fisher’s forceful restatement and statistical verification of the quantity theory of money, to Milton Friedman’s modern revival of quantity theory (the “Fisher connection”). Wicksell’s critical, although respectful, re-examination of quantity theory, on the other hand, gave much stimulus to various savings-investment businesscycle theories in the interwar debates, as shown in Leijonhufvud’s famous diagram of the “Wicksell Connection” (1981: 133).
Schumpeter (1954: 1096) as well as most other contemporary economists considered Fisher’s Purchasing Power of Money as an “outstanding achievement”, as “quantity theory analysis at its highest”, that is, as the best and most complete explanation in the entire economic literature before the modern revival by Friedman et al.
However, it is interesting to note that Friedman’s version is in fact based on the Cambridge approach which Keynes so strongly opposed to Fisher’s. Fisher generalized the quantity theory to a long-run or equilibrium theory of price level/inflation determination, taking up the classical propositions of neutrality, equiproportionality, causality running from the quantity of money to prices, and independence of the supply and demand of money. Fisher extended the equation of exchange, as had been formulated by Simon Newcomb to whom he dedicated the book, to, in obvious notation, MV + M'V' = PT, which soon became Fisher’s equation of exchange or Yale equation, in contrast to the Cambridge version of the quantity equation (based on the demand for money) as formulated by Marshall and Pigou, who wrote the equation in terms of income, whereas Fisher preferred to write it in terms of transactions.If the principles here advocated are correct, the purchasing power of money - or its reciprocal, the level of prices - depends exclusively on five definite factors: (1) the volume of money in circulation [M]; (2) its velocity of circulation [V]; (3) the volume of bank deposits subject to check [M']; (4) its velocity [V']; and (5) the volume of trade [T]. (Fisher 1911a: vii)
Fisher extended Newton’s equation by taking into account the rising importance of bank deposits. While the equation of exchange in itself is a “truism”, asserting no causal relationship between the quantity of money and the price level, nevertheless it holds empirically that after the transition period “a change in M produces a proportional change in M', and no changes in V, V', or the Q’s [T], there is no possible escape from the conclusion that a change in the quantity of money (M) must normally cause a proportional change in the price level (the p’s)” (ibid.: 157), where the p’s and Q’s are individual prices and quantities.
After the transition period, that is, in long-run equilibrium the “Fisher equation” holds, according to which the nominal interest rate i fully reflects a change in the inflation rate p, leaving the real interest rate r unaltered, that is, i = r + p.
Like the equation of exchange the Fisher equation is an identity in the sense that an unobservable real interest rate can be calculated as the difference of the other two variables. More interesting is the application of the equation as an equilibrium condition for financial markets for which the expected rate of inflation pe has to be included. Whereas in long-run equilibrium it holds that p = pe, it is a characteristic of adjustment processes that changes in the inflation rate are only imperfectly anticipated in the nominal rate of interest. The real rate of interest which matters for investment decisions very often is too low in the upswing and too high in the downswing. This was particularly the case in the Great Depression of the early 1930s with its strong deflation.These short-run deviations implying a non-neutrality of money were considered by Fisher as the principal causes of booms and depressions. For Schumpeter the most important insights of Fisher’s analysis are contained in chapters IV to VI of The Purchasing Power of Money where Fisher deals with transition periods, explicitly recognizing changes in the velocity of money - which Wicksell regarded as one of the flimsiest variables in the economy so that an elaborated quantity theory in particular has to analyze the factors which cause changes in the velocity of circulation of money - and the tardiness (lags) of interest adjustment to price movements. While conceding that the quantity theory is not strictly true during transition periods, Fisher (1911a: 159-62), however, is downplaying these temporary disturbances and “bent all his forces to the task of arriving actually at a quantity-theory result... I cannot help thinking that the scholar was misled by the crusader” (Schumpeter 1948 [1951]: 234-5). Whereas the equation of exchange first of all is an identity, the causal content is injected by propositions such as making the velocity an institutional constant independent of the quantity of money, assuming that the volume of bank deposits varies proportionally with legal-tender money, and the independence of the volume of trade from the quantity of money.
The outcome of the analysis of this “essentially ‘mechanistic’ mind” (ibid.: 235) is “that one of the normal effects of an increase in the quantity of money is an exactly proportional increase in the general level of prices” (Fisher 1911a: 157, original emphasis). Fisher’s restatement of the quantity theory of money has survived more than a century of monetary debates without major revisions. This is best indicated by the formula for the reference value for the growth of the monetary aggregate M3 by the European Central Bank.Fisher was convinced that fluctuations in the purchasing power of money were the main cause of most severe macroeconomic problems. This belief explains his life-long crusade for stable money and a stable managed currency. His various proposals for stabilizing the general price level induced him to engage in a persistent quest of the best index for measuring the value of money. Whereas in 1911 he had opted for the Paasche price index, and also seemed to favour the idea of chain indexes, in his later The Making of Index Numbers (1922), he postulated various criteria for a successful price index formula and elaborated a host of formulas of which he favoured the geometric mean of the Laspeyres (base-year weighted) and the Paasche (current-year weighted) formulas as coming closest to an “ideal index”. In January 1923 Fisher also founded the Index Number Institute.
Fisher’s masterpiece is The Theory of Interest (1930), a revised and elaborated version of his earlier The Rate of Interest (1907a), which he dedicated to the memory of John Rae and Eugen von Bohm-Bawerk. “[T]he book is a wonderful performance, the peak achievement... of the literature of interest” (Schumpeter 1948 [1951]: 230). Owing to its clear exposition “it is hard to imagine a better book to take with you to a desert island than this 1930 classic” (Samuelson 1967: 18). The core of Fishers’s theory of interest comes out best in the subtitle “As determined by impatience to spend income and opportunity to invest it”. It is central for Fisher’s thought that the present value of the capital stock equals the discounted value of the flow of future net incomes derived from an investment project, at the going rate of interest. Fisher held the view that “income is the alpha and omega of economics” (1930: 13) and controversially insisted that income consists solely of consumption (1906, 1930: ch. I). It is a basic idea of his interest theory that a trade-off exists between current and future consumption. In this sense investment is not a part of income but acts only as a means for the distribution of consumption over time, i.e. saving (investment) implies the sacrifice of current for the benefit of future consumption. The dated quantities of consumption goods are the only object of choice.
Thereby a two-stage decision rule applies (Fisher separation theorem). First, on the investment opportunity side the decision-maker chooses that technique of production which maximizes the expected marginal rate of return over cost ri of all available real investment projects (production optimum). Second, intertemporal consumption is maximized by comparison of the rate of time preference δ and the market rate of interest i which decides whether an individual becomes a borrower or a lender (consumption optimum). Fisher makes a clear distinction between production and exchange opportunities. His graphical illustration of the two sub-decisions which nicely shows the interplay of investment opportunities, time-preference (impatience) and the market rate of interest (which is a given data for the individual) for the simple case of two time periods has entered many textbooks.
In equilibrium the marginal rate of return over cost and the marginal rate of time preference equal the market rate of interest, that is, r = i = δ. Fisher’s main aim “is to show how the rate of interest is caused or determined” (1930: 13, original emphasis). Here the interplay between the rates of return on investment and rates of time preferences of all individuals is decisive. But most of his considerations are made from the perspective of an individual for whom the rate of interest is given within a partial equilibrium framework. In oscillating from the level of an individual investor (for whom the price system and interest rate are given) to the economy as a whole, a dilemma of Fisher’s theory of interest becomes apparent. The connection between the interest rate and the price system, which can only be treated simultaneously, is dissolved into two allegedly isolated subsystems, so that on the one hand in his price theory he assumes a given interest rate whereas in his theory of interest he assumes given prices (1930: 131). Owing to this fixed- price assumption Fisher can express all variables in money terms and operate with the investment of value sums. Alas, this is not possible because commodity prices and the wage rate have to be determined simultaneously with the interest rate. Fisher’s partial analysis and the associated fixed-price assumption are inadequate since a theory of interest has to be elaborated within a general equilibrium analysis. In such a framework interest rates affect the flow of net incomes of alternative investment projects via changes in the wage rate and product prices.
Fisher himself recognizes this “complication”, that is, the interdependence between the interest rate and prices which is most clearly visible in his discussion of the ranking of alternative investment projects (1930: 170 ff.). There he expresses that not only the choice of the investment project but even the range of choice depends upon the rate of interest, because “[i]f the rate of interest is changed, a change is produced not only in the present values of the income items but in the income items themselves” (ibid.: 171). However, he downplays this complication as “more intricate than important”, and therefore refrains from drawing consequences for his theory of capital and interest. Although Fisher, besides Walras, can be regarded as the second ancestor of a modern version of a general equilibrium theory, to which he gave decisive impulses with regard to the temporal disaggregation, he remained engrained in a partial equilibrium framework in his theory of interest.