Irving Fisher (1867-1947), American economist, had originally intended to become a mathematician. He studied at Yale with the eminent mathematician J. Willard Gibbs but was drawn toward economics under the influence of William Graham Sumner. As Fisher himself reported, he was fascinated by Sumner. He was also deeply influenced by the astronomer Simon Newcomb, who had published a number of economic texts, including the remarkable Principles of Political Economy.
From 1892 to 1895 Fisher taught mathematics at Yale, with an interval in 1893 and 1894, when he visited Europe, spending time in Berlin and Paris. After 1895 he transferred from the mathematics to the economics department, remaining at Yale until his retirement in 1935.
A prolific writer, gifted in the most varied subjects, active as a mathematician, statistician, demographer, economist, businessman, reformer, and teacher, Fisher left behind him some thirty books and hundreds of papers and theoretical studies, as well as many popular articles dealing with a wide spectrum of subjects, ranging from economic theory to public health.
Fisher made a fortune from his invention of a visible card index file system, which he marketed in 1910. The corporation he founded merged with others in 1926 to form Remington Rand, Inc., of which he was a director until his death. He was also a founder and director of several agencies for economic analysis and forecasting, and a director of a considerable number of other companies. Part of Fisher’s fortune was lost in the 1929 stock-market crash.
He was connected with a large number of associations and interested in many public causes. He was concerned with the problems of world peace and campaigned for six months throughout the United States in favor of U.S. participation in the League of Nations. He published two books (1923; 1924) and many articles on the subject. He was an ardent proponent of prohibition (see 1926; 1928o). His objectivity in selecting statistical data for these books has been questioned by some of his opponents.
Fisher also devoted a good deal of his time to campaigning for improved hygienic, sanitary, and eugenic practices. These crusades were an outcome of his own severe attack of tuberculosis in 1898, which interrupted his work for four years and gave him an interest in problems of health. In 1913, together with H. A. Ley and ex-President Taft, he founded the Life Extension Institute, with a view to generating public awareness of the contribution that sound living and periodic medical examinations can make to good health. He published How to Live (see Fisher et al. 1915), which has run into 90 editions and sold more than 400,000 copies in the United States; it has also been translated into ten languages. None of Fisher’s economic writings was as successful.
His deep concern with problems of eugenics arose from his belief that civilization could be saved only if the trends of physiological decadence of the superior elements and excessive reproduction of the inferior were reversed. Fisher served as president of the Eugenics Research Association, the American Eugenics Society, the Life Extension Institute, and the Vitality Records Office.
Like Walras, and like Pareto in the earlier part of his life, Fisher was always actively concerned with public policy, trying to modify the existing situation and to protect the organization of the economic system. He saw clearly that economic difficulties are very often monetary difficulties, and he constantly recommended active intervention by the public authorities in monetary affairs. He was an apostle of managed currency and of stabilization of the purchasing power of money. In his book on stable money he related that between 1912 and 1934 he prepared no less than 99 speeches, 37 letters to newspapers, 161 special articles, 9 submissions to appropriate governmental bodies, 12 circulars, and 13 books, a total of 331 documents intended to disseminate his ideas on monetary stabilization. Fisher was founder and president of the Stable Money League, a body whose aim was to make propaganda in favor of the “compensated” dollar.
The very lucidity of Fisher’s thought may have led superficial minds to undervalue its true worth. Since no effort is necessary to comprehend his meaning, there is a tendency to underestimate the complexity and, in many instances, the originality of his thinking. In contrast to Marx and Keynes, he could develop his ideas fully, specify them, and so strip them of their obscurities and contradictions that the formulas which emerged were extraordinarily plain and clear. Whatever the difficulty of the subject, Fisher excelled at distinguishing the theoretical from the practical, at using only perfectly defined concepts, at identifying problems, treating each in a concise, clear paragraph, and at relegating to appendixes elements that were accessory to the main theme. His essential contribution lay, first, in his reduction of the copious accumulation of inconsistent notions in earlier writings to a contradiction-free synthesis that made full use of their valid elements and, second, in his lucid presentation of this synthesis.
The remarkable characteristic of Fisher’s work is that it contains no basic error. Taken as a whole, and aside from a few minor errors of detail, it offers only valid ideas. His work is characterized by the ability to clarify, whether analytically or synthetically, rather than by the power of creative imagination. This is where Fisher’s true originality is to be found.
Use of mathematics . Fisher must be considered one of those who laid the foundations of modern economics, particularly of econometrics. He contributed more than any other scholar to the introduction into economics of scientific methodology and mathematical thinking, and he played an essential role in the development of specific concepts and theories which lie at the base of today’s economics.
Even as a student, Fisher perceived the immense potential that a scientific approach offered in the field of economics, and he became one of the most brilliant pioneers in the cause of mathematical economics. He believed that sooner or later every science tends to become mathematical and that the social sciences are therefore only more backward than astronomy, physics, and mathematics. He was convinced that all those who, like Gibbs, systematically relied on mathematics as a working tool would find their reward in the form of important discoveries. But he was also aware of the need to limit the use of mathematics. He was an economist; while mathematics was one of his tools, he never fell into the trap of mere formalism, characteristic of so much of the work done today. His work, like that of Pareto, teems with judicious comments on the scope and nature of theories, on the power and limits of the application of mathematical techniques, and on scientific method in general.
In 1929 two young mathematical economists, Charles Roos and Ragnar Frisch, proposed to Fisher that he join them in founding a society aimed at disseminating mathematical thinking in economics. He welcomed the suggestion with enthusiasm. The international Econometric Society was founded the next year, with Fisher as its first president. By now this society has several thousand members, including many of the most distinguished economists. [See ECONOMETRICS.] This may serve to indicate how much the atmosphere has changed since the young Fisher noted, in 1891, that mathematical economics was still almost as much on the defensive as it was during the 1870s and 1880s, when Jevons and Walras were pleading for it so ardently, and so vainly.
Theory of value and prices . In the Mathematical Investigations in the Theory of Value and Prices (1892), a work of his youth, Fisher’s aim was to present a general mathematical model of the determination of value and prices. He claimed to have specified the equations of general economic equilibrium for the case of independent goods (chapter 4, sec. 10), although the only mathematical economist whose work he had consulted was Jevons. With commendable honesty he recognized the priority of Walras’s Éléments d’économie politique pure (1874) as far as the equations of the general equilibrium are concerned and likewise the priority of Edgeworth’s Mathematical Psychics (1881) as regards the concept of utility surfaces. It appears that, although only a student, Fisher had independently developed a theory of general economic equilibrium that was identical to part of Walras’s and included the concept of the indifference surface, one of the fundamental bases of modern economic theory [See the biography of WALRAS].
Given the existence of these earlier formulations, the truly new elements in the Investigations were its clarity of presentation, its illustration of the general theory of equilibrium by a mechanical model in the case of independent goods, and its generalization of equilibrium theory to the case in which the utility of each good depends on the quantities of other goods consumed. A comparison of Fisher’s text with Walras’s will show how much more clear and concise Fisher’s exposition is. Fisher, however, apparently did not perceive the distinction between ordinal and cardinal utility; it was Pareto who emphasized the concept of ordinal utility and used it systematically. Although the Investigations does have a valuable appendix on utility and the history of the mathematical method in economics, on balance, the assessment made by Ragnar Frisch (see Schumpeter 1948), that the Investigations is a work of monumental importance, seems exaggerated and unjustified.
Capital and income . Fisher’s study of capital and income (1906) was intended to place the fundamental concepts in this field on a rational and rigorous basis and to develop the theorems flowing from these concepts. According to Fisher, his aim was to supply the long-missing link between the ideas and habits that govern business management and the theories of abstract economics.
This aim was satisfactorily realized. The Nature of Capital and Income contains the theoretical foundations of accounting science, both at the enterprise level and for the economy as a whole, as well as of actuarial science. Moreover, it presents these fundamentals in the framework of a general economic theory. Thus, Fisher prepared a rigorous foundation for the subsequent work on national income and wealth.
With this book Fisher apparently became the first economist to develop a theory of capital (including human capital) on an actuarial and accounting basis; both disciplines are essential parts of any economic calculus. His theoretical constructions issued from a concrete examination of accountancy and actuarial operations; this is the only valid approach, and many economists (even including Keynes, in the Treatise on Money as well as in the General Theory ) have erred by postulating a priori relationships between economic aggregates.
Also in The Nature of Capital and Income Fisher presented a systematization of the two concepts of capital and income, both rigorously defined. He showed very clearly how these two concepts are linked through the rate of interest. Capital consists of a stock of goods; income is a flow of services. The value of capital is given by the present value of the future flow of income from it. The direction of the causal relation is not from capital to income but from income to capital; it is not from the present to the future but from the future to the present. In other words, the value of capital is the discounted value of expected income. [See CAPITAL.]
He saw with unprecedented clarity that the economic present is no more than the capitalization of the future and that therefore the economic present is only a synthetic projection of the anticipated future. Fisher demonstrated convincingly that in economics only the future counts, and that past costs have no direct relevance to value. In point of fact, his research resulted in a rigorous definition of the bases on which it is possible to ground a valid theory of interest.
The only notable omission in this work is Fisher’s failure to give the mathematical relations between capital and income in continuous notation. Such a formulation, which could well have found a place in an appendix, would have shown even more clearly the link between capital and income (see Allais 1965a).
The analysis of capital and income in this book is so satisfactory that it is hardly possible to go beyond it, and it retains all its relevance today. Curiously enough, The Nature of Capital and Income —which is Fisher’s masterpiece, in my opinion—was not duly appreciated, and Pareto and Schumpeter are among the few economists who have recognized its value.
Monetary theory . In The Purchasing Power of Money (1911) Fisher completely recast the theory of money, giving a full demonstration of the principles that determine the purchasing power of money in the formal framework of the equation of exchange
(1) MV + M’V’ = PQ
and applying these principles to the study of historical changes in purchasing power.
It is impossible, without doing grave injustice to the author, to analyze or even summarize this book, which is powerfully original in its close association of theory and econometric analysis with factual data. For Fisher, the purchasing power of money (or its reciprocal, the general price level) depends wholly on five well-defined factors: (1) the stock of money in circulation, M; (2) its velocity of circulation, V; (3) the volume of deposits, M′; (4) their velocity of circulation, V′; and (5) the over-all volume of transactions.
In his preface Fisher stated that, fundamentally, his ambition was only to renovate and amplify the old “quantity theory” of money. He claimed that if the previously presented version is modified appropriately, it must be accepted as a basically correct theory.
Although Fisher is all too widely believed to have been an intransigent quantity theorist, he specified in many places the limiting conditions on the quantity theory’s validity. A few quotations should dissipate any doubt as to his real position:
. . . the theory is correct in the sense that the level of prices varies directly with the quantity of money in circulation, provided the velocity of circulation of that money and the volume of trade which it is obliged to perform are not changed. . . . ( 1920, p. 14) The strictly proportional effect on prices of an increase in M is only the normal or ultimate effect after transition periods are over. The proposition that prices vary with money holds true only in comparing two imaginary periods for each of which prices are stationary or are moving alike upward or downward and at the same rate. . . . (ibid., p. 159)
Therefore the “quantity theory” will not hold true strictly and absolutely during transition periods. . . . (ibid., p. 161)
There is no doubt that the weak point in Fisher’s theory is his inability to free himself from the trammels of the ceteris paribus assumption, which Bishop Berkeley had introduced in the eighteenth century. In his attempt to show the correctness of the quantity theory, Fisher shed fresh light on a significant number of questions, but in a sense he wanted to prove too much and was led into giving insufficient weight to short-term transitional phenomena.
Long before The Purchasing Power of Money first appeared in 1911, Walras had attempted to escape from this blind alley by defining the concept of “real wanted cash balances.” The Cambridge school, including Pigou and Keynes, did no more than take up Walras’s idea, but nobody was able to develop an operational formulation of the theory of money, and the coefficients that were defined could not be rendered determinate. An operational formulation has only been developed in the recent past, for example, by the present author (Allais 1965b). The equation of exchange MV = PQ had already been used by Newcomb in his Principles of Political Economy, and indeed it was to Newcomb that Fisher dedicated his book on money.
From a monetary viewpoint, the main contributions of Fisher’s work seem to be a notable clarification of the significance of the formal framework of the equation of exchange; the definition of statistical methods for estimating the different parameters of this equation, in particular the velocities of circulation of notes and coin and of deposit money, and for estimating the over-all volume of transactions; the estimates themselves; and finally, a definitive clarification of the influence of demand deposits on prices and of the need to include them in the definition of the supply of money.
Although Fisher was responsible for remarkable progress in monetary theory, he was not exempt from errors of judgment. Thus, chapters 11 and 12 are devoted to the verification of the equations of exchange. But an equation of this kind, which is the definition of the velocity of circulation, cannot be verified; all that the statistics can demonstrate is the compatibility of the different estimates of the velocity of circulation.
Whatever its limitations, The Purchasing Power of Money clarified much that had been confused. Fisher did not use the fertile Walrasian concept of desired cash balance explicitly, nor did he attain the fruitful Keynesian concept of liquidity preference. And it is true that he did not reach a satisfactory synthesis of the theory of money with price theory (although taking his work as a whole, he came nearer to such a synthesis than did Keynes). Nevertheless, he produced analyses of monetary questions—in particular of the velocity of circulation and of the equation of exchange—that in many respects are definitive. [See MONEY, articles On QUANTITY THEORY and VELOCITY OF CIRCULATION.]
Theory of interest . For Fisher, the rate of interest is governed by the balance between the supply of capital, as determined by the psychology of savers, and the demand for capital, as determined by the possibilities of, and the outlook for, investment.
As with some of his other works, the major contribution of The Theory of Interest (1930a) is not so much the presentation of major new ideas as the clarity and rigor of exposition of an extremely complex subject. The fundamental theses of the book had already been developed before Fisher by John Rae (1834) and, above all, by Bohm-Bawerk (1884-1912). Fisher, indeed, underlined his debt in the dedication of his book: “To the memory of John Rae and of Eugen Bohm-Bawerk, who laid the foundations upon which I have endeavored to build.”
At the outset, Fisher made the distinction between nominal interest and real interest. The major part of the book (chapters 4-18) is devoted to the theory of the determination of the real rate of interest. Then follows a special chapter, 19, on the relation of interest to money and prices. Fisher’s theory of the real rate of interest is a synthesis of psychological theories, such as the theory of abstinence, and physical theories, such as the theory of productivity. The objectivity with which he accomplished this synthesis enabled him to give due weight to the significance of each of the different aspects. While the central themes of the book are all to be found in greater or lesser measure in Bohm-Bawerk’s work, the clarity of Fisher’s presentation and the rigor of his analysis are incomparably greater.
Throughout his analysis, Fisher quite correctly distinguished two problems, namely, how the interest rate is determined and why it is always positive. He contended correctly, and in contrast to the approach taken by many earlier writers, that the determination problem should be the one studied first. He stressed, again quite correctly (chapter 8, sees. 4, 5), that from a psychological or technical viewpoint there is nothing in the nature of men or things that should lead one to expect that the rate of interest, expressed in terms of whatever good is chosen as unit, will be positive rather than negative. Long before Keynes, Fisher showed clearly that the rate of interest in terms of a given good cannot become negative if the good can be stocked without significant expense, a condition that is met by money (chapter 2, sec. 3, chapter 11, sec. 9). In his discussion of the case of the interest on unredeemable bonds (chapter 13, sec. 10), he also pointed out the impossibility of a zero or negative interest rate. But since he does not appear to have seen that land rents, like unredeemable bonds, are in practice a kind of perpetual income, he failed to realize that in a social organization based on private land ownership the rate of interest cannot be zero or negative (see Allais 1947, vol. 2, pp. 479-499).
Fisher’s theory of interest, like that of Bohm-Bawerk, is a capitalistic theory springing from an examination of the nature of capital. In a sense, it is the opposite pole to a theory such as that of Keynes, which is essentially a monetary theory of the rate of interest. (The present author has discussed this point: Allais 1947, vol. 1, p. 27.) Neither Fisher nor Keynes succeeded in approaching the indispensable synthesis of the two points of view. In discussing the repercussions of the theory of interest on monetary problems, Fisher showed conclusively that when prices are at peak levels, interest rates are high, not because the price level is high but because it has risen; and that when prices are low, interest levels are low, not because the price level is low but because it has declined (chapter 19, sec. 10).
Fisher’s Theory of Interest is not entirely free of error. For example, in the discussion of the optimum date for tree felling (chapter 7, sec. 6), Fisher stated that the date is given by the equality of the marginal growth rate of the forest and the rate of interest. This result is wrong and leads to an overestimation of the optimum length of the interval between two fellings—for no account is taken of the fact that the earlier the trees are felled, the earlier will it be possible to repeat the cycle. The quantity to be maximized is not the present value of a single felling, but the present value of all the income from successive fellings. Elsewhere, Fisher appears to have considered that the reason for the difference between long-term and short-term interest rates reflects the nearness or distance of the redemption date (chapter 13, sec. 11). He failed to observe what Keynes saw clearly, namely, that short-term loans have the advantage of being relatively more liquid and are therefore remunerated at a lower rate. Finally, Fisher stated that the productivity of nature is a factor tending to support the interest rate (chapter 8, sec. 6). Counterexamples showing that this point of view is untenable can be found (see, among others, Allais 1947, vol. 2, p. 721).
Nevertheless, in an over-all view allowing for these minor criticisms, Fisher’s analysis of interest represents a successful attack on one of the most difficult problems of economic theory, one that such men as Walras, Pareto, and Marshall had not fully grasped and for whose first deep analysis the credit goes to Bohm-Bawerk.
While it is true that Fisher did not completely resolve the issues of the basis of interest and the relation between the physical productivity and the value productivity of capital, he was responsible for a remarkable growth of understanding in this field. His analyses, particularly of the propensities to save and invest and of the interdependence of the rate of interest with other components of the economic system, prepared the way for his followers. [See INTEREST.]
Monetary policy . Three of Fisher’s works are devoted to projects for monetary reform: Stabilizing the Dollar (1920), Stamp Scrip (1933b), and 100% Money (1935). It is not unfair to say that throughout his life he was absorbed, even obsessed, by concern for the maintenance of a stable purchasing power of money—in other words, the avoidance of both inflation and deflation.
Stabilization of purchasing power. Fisher’s first book on monetary policy (1920) contains a plan for a reform of the gold standard, intended to stabilize purchasing power. Its principle, which was stated as early as 1911 in The Purchasing Power of Money (chapter 13, sec. 5), is very simple. If prices in terms of gold rise by one per cent, the official price of gold should be lowered by one per cent in order to maintain the purchasing power of the dollar; conversely, if prices in terms of gold decline by one per cent, the official price of gold should be raised by one per cent. In this system, the increase (or decrease) of the official price of gold must apply to all currencies if the principle of fixed exchange parities is to be respected. But a single country can also apply the system, as long as it is prepared to accept variations in its currency exchange rate in line with the price fixed for gold in terms of national currency. Stabilizing the Dollar also contains a systematic bibliography on the stabilization of the purchasing power of money, in which Fisher cited many authors (e.g., Rooke 1824; Newcomb 1879; Marshall 1887) whose ideas corresponded closely to his own.
Despite Fisher’s assertions to the contrary (appendix 2, ID) the cogency of his propositions is based on the quantity principle, which is valid only over the long term. Although his plan therefore applies only to long-term price movements, it would have been entirely viable and effective during the nineteenth century. Certainly, if the system had been in operation in that period, the long-run increases and declines in the price level, which actually occurred and whose drawbacks are evident, could have been avoided. It is also certain that it would have enabled full internal and external currency convertibility to be maintained after World War I. One might even claim that the introduction of this system would have been a necessary condition for the maintenance of convertibility. Indeed, as Fisher himself stressed, the link with gold is not strictly indispensable, and under a system of paper money, price stability can be underpinned by appropriate limitation of the volume of newly issued means of payment. He himself stated that the operation of his plan would be facilitated rather than hindered by the internal demonetization of gold, the sole essential feature of his scheme being the full convertibility of paper money into gold ingots (chapter 4, sec. 6). These ideas still have some potential value. In point of fact, they had been applied during the Middle Ages to prevent nominal prices from declining, and the fixed price of gold, introduced in the nineteenth century, was in a way a regression of practice.
Stamped money plan. The objective of Fisher’s stamped money plan of 1932 and 1933 was to furnish an efficient method of combating the hoarding of money, which has extremely injurious effects in a period of depression, the more so as the rate of hoarding tends to accelerate. Here again, the original idea was not Fisher’s own but was first suggested by Silvio Gesell in his book The Natural Economic Order (1906-1911, part 2) as a means of lowering the rate of interest.
In the system advocated by Gesell, notes in circulation would retain their value only if validated each month by a stamp sold through the post office network. The price of the stamp could be fixed in the light of circumstances; Gesell proposed a figure equivalent to a depreciation of the order of 5 per cent per annum. Gesell’s aim was not so much to combat depression as to lower the rate of interest toward zero in order to suppress all unearned income in a market economy.
In Booms and Depressions Fisher took up the idea with his customary clarity, pointing out that it constitutes a method of discouraging hoarding. He wrote:
Let one hundred of these dollars be given to each citizen. . . . This “gift” would be to all of us from all of us (and so no gift at all). . . . After all the 12 stamp spaces have been filled, the dollar could be redeemed either by another of the same kind or by an ordinary dollar, at the option of the government. If the stamped dollar, renewed, runs for nine years (108 months), the funds for this redemption will have already been provided to the government by the public. . . . This strange-appearing plan will not seem so strange if we think of it as a loan to the public from the government, to be repaid in monthly installments of one per cent. (1932, pp. 227-229)
Gesell’s suggestion was taken up by Keynes also, who pointed out that it would permit the level of interest rates to be lowered (1936, chapter 23, sec. 6).
There is no doubt that a scheme of this kind is a valid antidepression weapon, provided it is extended also to cover bank deposits—which is feasible. Fisher believed that in normal times there would be no need to have recourse to this system but that if the need for it became evident, it could be introduced with beneficial effect. It has been objected that anyone wishing to hoard would not be prevented from hoarding land, precious stones, or precious metals, but from a monetary viewpoint this is not a valid objection: what is at issue is how to avoid generalized overproduction by rendering it undesirable to hoard money.
The proposals for monetary reform by Gesell, Keynes, and Fisher have not been understood. The idea of stamped money has been derided as an economic absurdity. Yet the only objection that may validly be raised is that in normal circumstances, i.e., when monetary policy is implemented reasonably, hoarding is moderate and the stamping of money is unnecessary. So far as the monetary aspect is concerned, the policy of validation of money through stamps is recommended by Fisher only in case of need. As for Keynes’s notion that lower interest rates would increase the real national income, it can be shown that losses are wholly negligible by comparison with the capitalistic optimum situation with an interest rate of a few per cent (see Allais 1962).
Today the danger is not deflation but inflation, and the current interest in the stamped money plan is quite limited, if it exists at all. But from a theoretical point of view, this system—as well as that of the stable dollar—has many features that merit reflection.
The aim of Stamp Scrip, which was published in 1933, a few months after Booms and Depressions, was to describe the stamped-money experiments made in the Austrian towns of Schwanen-kirchen and Wbrgl and in a score of American cities in 1932, to assess the merits of these experiments, and to reply to certain objections that had been put forward. In Fisher’s own words, the book was prepared “in a few days of fast and furious work”; the speed with which it was written had, to say the least, unfortunate consequences for its quality.
Hundred per cent reserve. Fisher’s aim in 100% Money was to show that economic fluctuations can be largely eliminated if demand deposits are totally backed by a corresponding amount of cash, thus depriving the banking system of its right—more or less erratically exercised—to create money; and to show that a system of this kind “would actually stop the irresponsible creation and destruction of circulating medium by our thousands of commercial banks which now act like so many private mints” (1935, p. xi).
The fact is that the degree of potential instability of a banking system becomes greater as the coverage ratio departs farther from unity. Credit is generally the process in which a banker makes a loan of money he does not possess to a client who nevertheless considers the money as available. The system can continue to operate as long as depositors as a whole have sufficient confidence in its stability. But once confidence is shaken, the banks are unable to honor demands for withdrawals. In its basic conception this system is irrational, and its only justifications are its historical acceptance and the savings of gold that it permitted in the nineteenth century, when the price of gold was fixed—the possible consequence of this fixity under a gold standard being long-term decreases of the price level. Fisher’s 100% Money sets forth a valid plan to rationalize the monetary system. Some of the aims of the plan have been implemented since 1934, when the Federal Deposit Insurance Corporation was founded: since then a bank failure caused by depositors withdrawing funds from the banking system has become a practical impossibility. However, the present system has the drawback that the management of the over-all money supply is less easy than it would have been under a “100 per cent money” system.
Again, the original idea was not Fisher’s, as he acknowledged in his preface. He himself gave the credit for the suggestion to a group of economists from the University of Chicago, including, among others, Henry C. Simons, Aaron Director, Frank H. Knight, Henry Schultz, Paul H. Douglas, and A. G. Hart. In November 1933 this group circulated an unsigned 26-page mimeographed paper entitled “Banking and Currency Reform” (see Walker 1935; Hart 1935). However, the credit for the original idea should not go to the Chicago school. Much earlier, in 1898, Walras was stressing the unstable nature of the system of issue of banknotes and was proposing a 100 per cent coverage ratio (1898, pp. 348, 365, 374, 375 of the 1936 French edition). Ludwig von Mises adopted much the same position in 1928 in his book Geldwertstabilisierung und Konjunkturpolitik.
A system of 100 per cent money is perfectly feasible providing that banking activity is split into two clearly separated branches, deposits and lending. Depositors would pay charges to cover the cost of managing their accounts, and banks would make loans with funds they had borrowed for that purpose. Introducing the system would involve certain transitional problems, but they could easily be overcome, and their resolution would give governments a much greater mastery of monetary policy than could be acquired in any other way. The idea of this reform has generally been abandoned today; its only proponents are a few economists such as Milton Friedman in the United States (1959) and Maurice Allais in France (1947).
Other works on monetary policy. Three other books written for the lay public should be mentioned among Fisher’s published works on monetary reform. These are The Money Illusion (1928k), Booms and Depressions (1932), and Inflation”? (1933a). The first and last of these are, by comparison with his other works on the subject, of limited interest.
Booms and Depressions is of more importance. It has three parts, dealing with theories, facts, and remedies, respectively. Nine main factors are considered: overindebtedness, volume of currency, price level, net worth, profit, production, psychological factors, currency turnover, and rates of interest. Most stress is placed on the factor of over-indebtedness.
When the 1929 slump occurred, Fisher was over 60 years old; yet he tackled the very difficult theory of economic fluctuations. He finally reached the conclusion—which contains a large element of truth—that business cycles are due on the one hand to the existence in the banking system of uncovered demand deposits and on the other to the opportunities for hoarding offered by the circulating monetary media. These views led him to recommend regulation of the demand for and supply of money through steadily depreciating circulating money and 100 per cent coverage of demand deposits as a cure for business cycle ills (see 1933b; 1935).
Appraisal of monetary policy. Nowhere in his writings did Fisher really take up the central problem of variations in the demand for money with the level of economic activity, and despite the reservations he himself made, his approach was too narrowly oriented toward quantity theory. As Schump-eter aptly put it, “the scholar was misled by the crusader.” His propaganda in favor of the compensated dollar resulted in his misinterpretation of the price stability that ruled up to 1929 and, correspondingly, his total unawareness of the gravity of the situation. He was one of the most optimistic supporters of the doctrine of the “new economic era.” Although he had done quite well from his investments in the 1920s, he had to absorb large losses in the 1929 crisis. But as soon as he assessed its scope properly, he became an indefatigable proponent of the various plans for the restoration of prosperity that have been summarized above. Together with George Frederick Warren, he persuaded President Roosevelt to devalue the dollar in order to stimulate a rise in the price level in the United States.
Fisher’s work on money and prices, in particular his propositions for stabilization of the dollar, led him to considerable advances in two branches of statistical science: price indices and distributed lags.
Index numbers . The aim of Fisher’s book The Making of Index Numbers (1922) is to identify the characteristics of the best feasible index of prices for use in measuring changes in the purchasing power of money. This book, in which he tried to systematize and rationalize index number theory by defining a certain number of criteria, is in fact an extension of chapter 10 of his Purchasing Power of Money and of the appendix to that book. His research into the qualities of a satisfactory price index was a by-product of his general analysis of the equation of exchange.
Whereas Fisher’s approach in The Purchasing Power of Money was deductive, in The Making of Index Numbers it was inductive and empirical: he compared the results of using different formulas on the same historical data. He used two principal criteria of evaluation, the “time reversal test” and the “factor reversal test,” and recommended use of the “ideal” index, the geometric mean of the Paasche and Laspeyre indices.
There can be no doubt that Fisher’s study, which was the most extensive at that time in the field of index numbers, was a fruitful springboard for much of the progress made subsequently [See INDEX NUMBERS].
Distributed lags . Fisher was the first to envisage a systematic dependence of the present on the past in economics, and thus he opened up a whole new area. The existence of systematic effects explains why it has been possible successfully to analyze economic and geophysical time series using autoregressive equations
which when inverted can be written formally as
in which yt is the cumulative effect of earlier actions, εt-p, weighted by coefficients ap, which decline with distance in time. The accepted English term for this formulation, “distributed lags,” was coined by Fisher. This term is intended to convey that each εt-p acts with a certain delay, so that lags of different length must be taken into account when studying the influence of the past.
In his study “Our Unstable Dollar and the So-called Business Cycle” (1925) Fisher proposed a formulation of the type
in which the weights α(θ) are distributed lognormally, for study of the interdependence of the level of economic activity y(t) and past values p(t—0) of the general level of prices.
Later, in his Theory of Interest (chapter 19, sec. 6), he used weights a, which declined linearly with time, to study the relationship between the rate of interest and earlier rates of increase of the price level.
The line of approach initiated by Fisher was later to prove particularly fertile in econometric thought. [SeeDISTRIBUTED LAGS .]
Unlike Adam Smith, John Stuart Mill, and Alfred Marshall, Fisher wrote no systematic treatise. The reason for this is doubtless that Fisher was preoccupied above all with research and that his manifold practical activities took much time. In Schumpeter’s well-chosen words, Fisher’s works “are the pillars and arches of a temple that was never built. They belong to an imposing structure that the architect never presented as a tectonic unit” ( 1960, p. 237). But these foundations are solid.
Fisher was not an eminent philosopher, like Cournot, and he did not have a universal mind, like Pareto; he did not share Walras’s preoccupation with social problems or try to study the philosophy of the social and economic organization of the time, as did Keynes and Schumpeter. But the fact remains that he made major contributions to the fundamental problems of capital, interest, and money.
As Schumpeter observed in his remarkable biographical article, Fisher, unlike Marx, Marshall, and Keynes, did not found a school. He had many pupils, but few disciples. In his crusades he joined forces with many other groups and individuals, but he remained almost alone in his scientific work. Perhaps it was the derision aroused by his crusading activity that led to his isolation; one of his critics has written: “His career was marked by neglect at its inception and ridicule at its close” (Lekachman 1959, p. 293).
For many years, Fisher’s influence was nonetheless considerable. He was president of the American Statistical Association, of the international Econometric Society, of the National Institute of the Social Sciences, and of the American Association for Labor Legislation. The appearance of a book by Fisher was invariably an event, and it would be reviewed widely, though the reception might be favorable or hostile. In the case of both Stamp Scrip and 100% Money, the reaction among Fisher’s fellow economists and in official circles was unfavorable. In fact, Fisher was often considered prone to draw too rapid conclusions from abstract conceptions and therefore inclined to suggest measures whose chances of success were correspondingly uncertain.
Although there has never been a Fisher school in the sense that there has been a Keynesian school, Fisher’s influence on a great number of young economists was nevertheless profound (see Sasuly 1947). As a disciple of Fisher, the author of the present article is among those who have recently produced systematizations, generalizations, or extensions of Fisher’s theoretical and econometric work on capital, income, interest, and money (see Allais 1943; 1947; 1954; 1965a; 1965b).
The opinion of Fisher’s work has not generally been as high as its merit warrants, especially in the United States, where its value has been grossly underestimated.
To a remarkable extent Fisher combined within himself the eminently Anglo-Saxon preoccupation with facts and practical action and the essentially Latin quality of clarity of conception and exposition. He was at one and the same time theorist and practitioner, having the characteristics, therefore, of a great engineer.
Fisher had, above all, an extraordinary feeling for things concrete, and the whole body of his work is permeated by an unceasing search for numerical applications. For him no theory was of use unless it led to applied work and the quantitative analysis of factual data. Fisher always maintained close contact with businessmen and tried to familiarize himself with their reactions and preoccupations, so as to analyze them and compare them with the theoretical models of economic science. He was deeply interested in practical action. Economic science, as he saw it, was not merely pure philosophical speculation; it should be used, as engineering is, to achieve practical ends.
Fisher’s normative approach tended to lower the esteem in which he might otherwise have been held. This unfortunate fate he shares with Marx, whose remarkable sociological accomplishments have been partially discredited by his political attitude and with Walras, whose normative propositions have been considered by many as unsophisticated or even downright infantile.
Men who are accepted as geniuses have been known to spout nonsense on certain issues. As Pareto wrote: “It is somewhat hard to believe, although it is no more than the truth, that the great Newton wrote a book which proved that the prophecies of the Apocalypse had come to pass.” No one would conclude from this that Newton’s Mechanics is not a first-level achievement of the human spirit.
Fisher marks a decisive stage in the history of economic science. He was the first economist to combine profound theory and authoritative observation. He contributed powerfully to the construction of theoretical mathematical models aimed at the explanation of reality, and at the same time, whether in working out his assumptions or interpreting his results, he never lost his extraordinary preoccupation with reality, which he observed and analyzed with a refined sense of the concrete.
Simultaneously a theorist and a practitioner, Fisher combined to the highest degree two supposedly incompatible characteristics: an esprit de geometric and an esprit de raffinement; these are, despite Pascal’s opinion, but two sides of one and the same medal—intelligence. Because of these qualities, Fisher ranks with the greatest contributors to economic science. Like physics, economics calls for the study of abstract constructions at the same time that it requires the observation and analysis of facts. When Fisher died in 1947, the present author wrote (Allais 1947) that it was because of the combination of these two qualities that Fisher had to be given a place in the hall of fame of modern economics. A year later Schumpeter described him as America’s greatest scientific economist. The future will certainly confirm this judgment. Fisher opened up a new horizon. Others will go beyond the point he reached; they have done so already, for it is easier to progress when the way is posted with signs.
(1892) 1961 Mathematical Investigations in the Theory of Value and Prices. New Haven: Yale Univ. Press.
(1896) 1925 Elements of Geometry. New York: American Book Co. ⇒ In collaboration with Andrew W. Phillips.
(1897a) 1960 A Bibliography of Mathematical Economics. Pages 173-209 in Antoine A. Cournot, Researches Into the Mathematical Principles of the Theory of Wealth. New York: Kelley.
(1897b) 1943 A Brief Introduction to the Infinitesimal Calculus. New York: Macmillan.
(1906) 1927 The Nature of Capital and Income. New York and London: Macmillan.
1907 The Rate of Interest: Its Nature, Determination and Relation to Economic Phenomena. New York: Macmillan.
(1910a) 1912 Elementary Principles of Economics. New York: Macmillan. ⇒ First published as Introduction to Economic Science,
1910b National Vitality: Its Wastes and Conservation. U.S. 61st Congress, 2d Session, Senate Document No. 419. Washington: Government Printing Office.
(1911) 1920 The Purchasing Power of Money: Its Determination and Relation to Credit, Interest and Crises. New ed., rev. New York: Macmillan.
1914 Why the Dollar Is Shrinking? A Study in the High Cost of Living. New York: Macmillan.
(1915) 1946 FISHER, IRVING et al. How to Live: Rules for Healthful Living Based on Modern Science. 21st ed., rev. New York: Funk & Wagnalls.
1920 Stabilizing the Dollar: A Plan to Stabilize the General Price Level Without Fixing Individual Prices. New York: Macmillan.
(1922) 1927 The Making of Index Numbers: A Study of Their Varieties, Tests, and Reliability. 3d ed., rev. Boston: Houghton Mifflin.
1923 League or War? New York: Harper.
(1924) 1926 America’s Interest in Worid Peace. Rev. ed. New York: Funk & Wagnalls. ⇒ A revised edition and condensation of League or War?
1925 Our Unstable Dollar and the So-called Business Cycle. Journal of the American Statistical Association 20:179-202.
(1926) 1927 Prohibition at Its Worst. 5th ed. New York: Alcohol Information Committee.
1928a Prohibition Still at Its Worst. New York: Alcohol Information Committee.
1928b The Money Illusion. New York: Adelphi. ⇒ Contains a systematic bibliography.
(1930a) 1961 The Theory of Interest. New York: Kelley. ⇒ Revision of The Rate of Interest 1907.
1930b The Stock Market Crash—and After. New York: Macmillan.
1932 Booms and Depressions: Some First Principles. New York: Adelphi. ⇒ Contains a systematic bibliography.
1933a Inflation? New York: Adelphi.
1933b Stamp Scrip. New York: Adelphi.
1933c After Reflation, What? New York: Adelphi.
1934 FISHER, IRVING; and COHRSSEN, HANS R. L. Stable Money: A History of the Movement. New York: Adelphi.
(1935) 1945 100% Money: Designed to Keep Checking Banks 100% Liquid; to Prevent Inflation and Deflation; Largely to Cure or Prevent Depressions; and to Wipe Out Much of the National Debt. 3d ed. New Haven: City Printing.
1937 Note on a Short-cut Method for Calculating Distributed Lags. International Statistical Institute, Bulletin 29, no. 3:323-328.
1942 Constructive Income Taxation: A Proposal for Reform. New York: Harper.
ALLAIS, MAURICE (1943) 1952 Traité d’économie pure. 2d ed. Paris: Imprimerie Nationale. ⇒ First published in 1943 as Économie pure.
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ALLAIS, MAURICE 1954 Les fondements comptables de la macro-économique: Les équations comptables entre quantités globales et leurs applications. Paris: Presses Universitaires de France.
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ALLAIS, MAURICE 1965b Reformulation de la theorie quantitative de la monnaie: La formulation heredi-taire, relativiste et logistique de la dentande de monnaie. Paris: SEDEIS. ⇒ An abridged version was published in the December 1966 issue of the American Economic Review.
BÖHM-BAWERK, EUGEN VON (1884-1912) 1959 Capital and Interest. 3 vols. South Holland, 111.: Libertarian Press. ⇒ First published as Kapital und Kapitalzins. See especially Volume 1: History and Critique of Interest Theories, 1884; and Volume 2: Positive Theory of Capital, 1889.
CAGAN, PHILLIP 1956 The Monetary Dynamics of Hyperinflation. Pages 25-117 in Milton Friedman (editor), Studies in the Quantity Theory of Money. Univ. of Chicago Press.
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HART, ALBERT G. 1935 The “Chicago Plan” of Banking Reform. Review of Economic Studies 2:104-116.
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WESTERFIELD, RAY B. 1947 Irving Fisher. American Economic Review 37:656-661.
Fisher, Irving 1867-1947
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 life-cycle 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 Bőhm-Bawerk’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.
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.
Robert W. Dimand
The American economist Irving Fisher (1867-1947) made significant and original contributions in the fields of economics, mathematics, statistics, demography, public health and sanitation, and public affairs.
Irving Fisher was born in Saugerties, N. Y., on Feb. 27, 1867. He received his doctoral degree in mathematics at Yale in 1891. From 1892 until 1895 he taught mathematics at Yale; in 1895 he joined the faculty of political economy, where he remained until his retirement as professor emeritus in 1935.
It is virtually impossible to do justice to Fisher's many contributions to economics and statistics, but his writings on monetary theory and policy and index numbers have earned special acclaim. He brought to his writings the lucidity, analytical precision, and rigor of an accomplished mathematician. In The Purchasing Power of Money (1911) Fisher completely recast the theory of money into his classical quantity-theory-of-money equation MV + M'V' = PQ,which made the purchasing power of money (or its reciprocal, the general price level P) completely determined by the stock of money in circulation M, its velocity of circulation V, the volume of bank deposits M', their velocity of circulation V', and the total volume of transactions Q. Fisher translated his theory into a policy prescription of "100 percent money" (all bank deposits should be backed by 100 percent reserves rather than fractional reserves, used then and now by virtually all banking systems) on the grounds that such a policy would control large business cycles. He spent a large part of his private fortune promoting (unsuccessfully) the policy.
Fisher's The Theory of Interest, which draws heavily from John Rae and Eugen von Böhm-Bawerk, added clarity and rigor to one of the most complex concepts in economics. In his theory the rate of interest is based on the supply of savings and on the demand for capital as determined by the present and future outlook for investment opportunities. He also distinguished between the nominal and real rates of interest and developed the concepts of positive, negative, and neutral time preferences. Fisher's theory anticipated the later works of members of the Cambridge school.
Fisher made significant and original contributions in statistical theory, econometrics, and index number theory. The Making of Index Numbers (1922) became a standard reference on the subject. After a methodical and quantitative analysis of various index number formulations, he developed his "ideal" index, the geometric mean of the Paasche and Laspeyre indexes. He considered this formulation "ideal" because it met his "time reversal" and "factor reversal" tests.
It has been said of Fisher's contributions to economics and statistics that he built grand columns and arches but he never quite completed the intellectual edifice that could be designated the Fisher theory or the Fisher economic system. It can also be said that he laid solid foundations on which others built their edifices.
The monumental variety and quantity of Fisher's writings defy description. His son, Irving Norton Fisher, compiled a 4,300-page bibliography of his known writings, A Bibliography of the Writings of Irving Fisher (1961); he also wrote a creditable biography, My Father, Irving Fisher (1956), that covers the essentials of his father's career. A valuable introduction to Fisher's many activities is William Fellner and others, Ten Economic Studies in the Tradition of Irving Fisher (1967).
Allen, Robert Loring., Irving Fisher: a biography, Cambridge, Mass.: Blackwell Publishers, 1993. □