Dossier: Business Cycles, Money and Economic Policy. Essays Dedicated to Pascal Bridel


Drawing on H. L. Moore’s reflections on method, and in particular the place of pure economics in relation to dynamics and statistics, this paper focuses on Moore’s last attempt at the end of the 1920s to analyze economic dynamics within a general equilibrium framework. Moore suggests abandoning Walras’s conception of a static and hypothetical general equilibrium state based on free competition, and adopting a concrete and dynamic approach. In this perspective, Moore conceives a tentative dynamic and potentially computable general equilibrium framework that specifically introduces relative deviations in the data on services, commodities, and capital, from their trend values.
S’appuyant sur les réflexions de H. L Moore sur la méthode, et en particulier la place de l’économie pure par rapport à la dynamique et les statistiques, cet article se concentre sur la dernière tentative de Moore, à la fin des années 1920, pour analyser la dynamique économique dans un cadre d’équilibre général. Moore suggère l’abandon de la conception de Walras d’un état d’équilibre général statique et hypothétique fondé sur la libre concurrence, en faveur d’une approche concrète et dynamique. Dans cette perspective, Moore conçoit un cadre d’équilibre général dynamique et potentiellement quantifiable pour analyser les fluctuations économiques à partir des déviations par rapport aux tendances des prix et quantités des services, des marchandises et des capitaux.
Keywords:economic dynamics; pure economics; statistics; equilibrium business cycle theories
Mots clés :dynamique économique; économie pure; statistique; théories des cycles d’équilibre
JEL:B13; B16; B22; B31; E31
The author thanks two anonymous referees. The usual caveat applies.
Figure 1 Varieties of Economic Equilibria (Source : Moore, 1926b, 1)
Jaffé, in his presentation of the unpublished manuscripts and letters of Walras during the 1934 Walras centennial program, recalls that Walras’s autobiography was written “mainly at the instance of one of our pioneer mathematical economists, Henry Ludwell Moore”.^{1} Moore made in the first part of his life numerous trips to Europe notably meeting Walras in the summer of 1903 with whom he maintained a regular correspondence, and Pareto in 1908. In the last period of his life, Walras wrote “touching letters to Henry Ludwell Moore, whom he looked upon as a spiritual child to whom he might well in trust the task of carrying on his work.” (Jaffé, 1935, 205). Moore received a copy of Walras’s autobiographic notes and copies of the Abrégé and the two books published by his father. Walras was convinced that Moore would have all these works translated into English which would ensure their wide diffusion. However, his hopes were disappointed.
Other parts of the correspondence indicate Moore’s reservations about translations. First, he argues that graphic treatment of the Abrégé would not make it accessible at secondary school level and that Walras was underestimating the complexities of his method and theory. Second, he feels anxious to use these materials in an article showing the nature and genesis of Walras’s system as suggested by Walras, and mentions his university duties as intervening to “make such [an] article impossible” (Jaffé, 1965, Vol. III, Letter 1609). Finally, Moore is clear that he will never translate the Abrégé, confessing that his limited available time is being absorbed by other investigations.^{2}
The letters also contain an interesting digression on the relations between pure economics and the statistical tests where Moore adopts a methodological stance characteristic of his future research agenda. He notes that the science of pure economics does not attract enough students “because of the absence of inductive demonstrations of its fundamental tenets” (ibid.) Moore argues that it is the task in particular of the present generation of scholars to use inductive methods to investigate problems which “[Walras] and others have treated so brilliantly in a deductive manner” (ibid.) and he concludes that it is precisely these reasons that motivated his empirical inquiries into wages which started in 1907. At that time Moore’s interest in the history of mathematical economics was dissipating and he was launching a research program of his own into the statistical and dynamic complements of pure economics, which marked the beginning of a twenty year period of creative investigation.^{3}
These exchanges provide more than anecdotal evidence of the profound differences between Walras and Moore regarding their conception of equilibrium, dynamics and methods.
Bridel (2009) compares the approaches of Walras, Pareto and Juglar and argues that Walras’s theory without measurement clearly contrasts with Juglar’s indisputable measurement without theory. Bridel recalls that Walras’s metaphysical conception of general equilibrium as an ideal state differs from the first approximation of Pareto which needs to be completed by empirical and concrete advances, notably as regards dynamic issues.^{4} This point reveals “the widely conflicting epistemologies Walras and Pareto attributed to their yet very similar versions of the general equilibrium model.” (Bridel and Mornati, 2009, 1). From this one can infer that Moore plays here the role of Juglar. However, as this paper tries to show, Moore adopts a more complex position than Juglar’s measurement without theory, which owes much to Pareto.
Several modern commentators focus mainly on Moore’s pioneering empirical contributions to statistics and partial estimation of demand functions (see e.g. Christ, 1985; Mirowski, 1990; Morgan, 1990; Wulwick, 1992 and 1995; Le Gall, 1996; Biddle, 1999). They point to his controversial results and the flaws in his econometric attempts, on the methodological side pointing to his quest for statistical tools and his emphasis on aggregate data and laws derived independently of individual choice (Teira, 2006). According to Morgan (1990, 141) whose judgement is particularly severe, “Moore’s approach was a mixture. As its worst, it involved both the unthinking application of theory to data and the adoption of empirically derived relationships without reference to theory.” However, examination of Moore’s specific reflections on method and his final contributions to economic dynamics at the end of the 1920s are interesting—especially about the status of pure economics in relation to dynamics and statistics. These general conceptions were discussed first in “Statistical complement of pure economics” published in 1908 and also in his last book, Synthetic Economics, which was published in 1929. Referring to some contemporaneous advances by Jevons, Edgeworth, Lexis and Pareto, Moore developed a thorough discussion on probability distributions and statistical tools in social science, completed by considerations on truth and scientific laws inspired notably by pragmatism and evolutionism. He also defined his position on free competition, general equilibrium, dynamics and the role of statistics, which differed from that of Walras and was an original approach. Drawing on these insights, we focus on Moore’s reflections on how to analyze actual economic dynamics within a general equilibrium framework, which were developed in “Theory of economic oscillations” and Synthetic Economics.^{5} Moore suggests abandoning the concept of a static and hypothetical general equilibrium based on free competition and adopting a concrete and dynamic approach. In this perspective, Moore conceives a tentative moving and potentially computable general equilibrium framework, notably introducing relative deviations of the data from their trend values for services, commodities and capital.
The present paper is organized as follows. Section 1 is devoted to Moore’s general views on method. Section 2 discusses his last contributions to economic dynamics and section 3 provides a few concluding remarks.
1. The Statistical Complement of Pure Economics 
The guidelines of Moore’s research agenda were developed in an article published in 1908, “The statistical complement of pure economics.” Moore begins by recalling that leading scholars in the elaboration of pure economics, such as Cournot, Jevons, Edgeworth, and Pareto, had in mind a complementary statistical science. He writes that:
They have all proceeded on the assumption that the greatest need, at the time of their writings, was a correct theory of economics, in order to afford a first approximation to reality and to show what is required to solve concrete problems. But they have likewise made fundamental contributions to inductive statistical complement of the pure science. (Moore, 1908, 2)
This quote encapsulates Moore’s general idea of the relationship between pure economics and statistics. Moore recalls the specific contributions of each of these authors on this topic (see Moore, 1908, Part 1, 48). Cournot believed in the power of statistical method and made a great contribution to the development of the theory of probability “as the foundation of all induction” (Moore, 1908, 4). Jevons shared his conceptions of the relation between induction and probability theory and applied the statistical method most notably to the value of gold and the coal question. Edgeworth was interested in the methodology of inductive natural and social sciences and contributed to the development of the materials and instruments in the theory of social statistics.^{6} Finally, Moore discusses the investigations conducted by Pareto, most notably the development of methods of interpolation, and his findings on the skewed distribution of income. Moore (1908, 7) states that “it will be granted that Professor Pareto has reached the most general a priori treatment of the whole problem of production and distribution, and I therefore regard as of great value his opinion as to the most promising direction of investigation in economics.” Moore recalls that Pareto had recently asserted that the most promising direction would depend in great part upon the investigation of the empirical laws derived from statistics, which should be compared with known theoretical laws or should become the basis for new laws.^{7}
In this perspective, Moore discusses the notions of laws, continuity, and truth in economics and statistics more specifically in relation to applications of the theory of probability to social science. For him, this theory is “not a body of concrete doctrine, but rather a machinery of general application in the study of the massphenomena upon which the social sciences rest” (Moore, 1908, 8).^{8} The theory of probability is helpful first to evaluate the most probable values in the data. Therefore, it is important to delineate the conditions of reliability of a mean and of the functions of a mean in relation to the type of distribution. Second, he discusses the problem of “the description and discovery of the type amid variety.” (op. cit., 12) which refers to attempts to test evolutionary hypotheses using statistical methods which for Moore are related to the leading developments by Galton and Pearson. Moore had visited Pearson’s laboratory in London and was greatly influenced by his views on causation and laws (Teira, 2006).^{9} In discussing the problem of interpolation and the derivation of continuous functions from discontinuous observations, Moore refers to the pragmatic philosophy of James and Dewey. The problem of truth and method handled by the pragmatists “are the same problems with which mathematical statisticians have been concerned” (Moore, 1908, 16). Thus, Moore endorses the view that truth is a form of social valuation and that the selection between rival truths of the appropriate theory, “which we call the true theory” (Moore, 1908, 17), should be grounded in their relative utility and relative simplicity.
In the rest of the article Moore discusses at length which statistical techniques would be best to improve statistical economics. A specific question related to change is to determine “under what conditions may statistical ratios be assumed to be empirical functions of a probability which is determined by the nature of things and which either remains constant or varies according to law” (Moore, 1908, 14). Here, Moore finds the distinction made by Lexis^{10} between normal and nonnormal series or evolutionary series particularly interesting, “the latter indicating a progressive change in the fundamental conditions of the phenomena under observation” (ibid., 16).
Next, referring in particular to Marshall, Clark, and Pareto he calls for development of a dynamical approach: “Nearly everyone who has dealt with the science as a whole assumes that the static aspect of our work is relatively complete, and that the investigation of dynamic problems should be entered upon.” (Moore, 1929, 32) Moore contends that there are two main issues to be considered with particular attention. The first concerns problems related to the theory of population.^{11} The second refers to the theory of crises. Both have achieved “an approximately satisfactory scientific form” (ibid.) based on the application of recent statistical methods, and therefore should serve as models for the treatment of other economic questions which “had remained in the realm of pure theory” (ibid.).
In relation to the theory of crises, in 1908 Moore refers explicitly to Juglar. For Moore, as mentioned by Bridel (2009) in his specific discussion of Juglar’s approach, Juglar “in his classical work on commercial crises” (Moore, 1908, 28) establishes statistically “the universality of crises, their periodic return and their general resemblance” (ibid.) But Moore also sees clear limits to (in Bridel’s words) Juglar’s “measurement without theory.” The same argument applies to the investigations made by Des Essars, who like Juglar “made no attempt to isolate the cause of crises” (Moore, 1908, 30) and only supplies “a barometer for this form of métérologie sociale” (ibid.). A crucial step forward was made by Pareto who considered that dynamic issues should be analyzed by introducing some hypothesis about actual change, and then making the necessary modifications to the initial static theory. Accordingly, unlike Juglar, Pareto “at once [provides] a hypothesis as to the general cause of crises, and then attempts to show how his dynamic assumption would affect the simultaneous equations to which he has reduced economic statics.” (ibid.)^{12} For Moore, these developments to the theory of crises illustrate “the attempt to establish deductively results which have at first been reached empirically” (Moore, 1908, 31) but he considers that the inverse direction “of establishing statistically results that have been reached in an a priori manner” (ibid.) must also be considered carefully. He concludes by saying that this is the route he takes in his own attempts on the theory of wages.
After twenty years of systematic application of this agenda to wages, demand functions, and his wellknown explanation of business cycles by exogenous weather conditions, Moore returns to the subject of his early methodological reflections in the first chapter of his last book, Synthetic Economics, published in 1929, in which he revisits Walras’s general equilibrium. Moore explains that early works on mathematical economy took two directions. The first involved practical scholars and produced “practical, but unrelated results” (Moore, 1929, 1). The second involved “mainly… philosophers with primary interest in causes and relations” (ibid.) and “ascended to picturesque heights affording distant views of the ensemble of economic activity, but has stopped short amid the enchanting scene and left the explorers in doubts as to what might be the real destination of so promising a beginning” (ibid.). For Moore, the works of Cournot and Walras respectively represent these two directions. Moore explains how both develop a mathematical method. However Cournot, as Moore highlighted in his 1908 article, makes use of the theory of probabilities which opens the road to numerical applications, while Walras “makes no effort whatever to obtain an empirical test of the adequacy of his theoretical construction in the interpretation of the world of economic realities” (Moore, 1929, 2).^{13} Moore understands that the central issue on which Walras focuses is the need to formulate a system of simultaneous equations expressing the interdependence among economic quantities and the conditions of equilibrium in a static hypothetical or ideal state. He also argues that Cournot had “a clear conception of the interdependence of the parts of the economic system and he stated very compactly the difficulties with which the economist is confronted.” (Moore, 1929, 3).^{14}
Moore recalls that Cournot’s mastery of the theory of probability had been very great but that, conscious of the difficulties of the task, he had abandoned “the forbidding task of determining concretely the conditions of general equilibrium and sought… to reach approximate solutions of special problems affecting the general economic system” (ibid.) According to Moore, Cournot—and not Walras—was right. Since Cournot’s work, improvements have been made to the theory of probabilities supported by abundant statistical data from recognized sources. In this perspective several advances were made by Moore himself, on the demand and supply functions for particular commodities.^{15} Moore believed that it was time to investigate more deeply “the idea that economic theory may be fruitfully approached through the conception of the equilibrium of the interdependent parts that has made such headway since the publication of Walras’ epochal essays” (Moore, 1929, 4).
2. The Scope of Dynamic and Synthetic Economics 
According to Moore, the theory of pure economics achieved precise mathematical form with the work of Walras and then Pareto. But pure economics provides only a theory of an ideal and static state and this framework does not allow investigation of actual dynamics. Moore (1929, 180) adds that “when we definitively put this question with regard to the static theory of general equilibrium we regretfully confess we seem to have been pursuing a mirage.” Accordingly “pure economics is intended as a first approximation to reality. Its primary functions are to supply carefully defined concepts, to trace out the nature of interdependent causes, and to invent a technique for detecting, describing and measuring the interplay of many causes.” (Moore, 1929, 184) The sole test for pure economics is its logical consistency. For a concrete analysis of economic change it is necessary go a step further and build a dynamic system of simultaneous measurable equations. This was the aim in Moore’s last contributions on dynamics where he analyzes economic oscillations and secular change using a method “[that] transforms a plurality of discontinuous facts into a network of continuous relations describing the solidarity of exchange, production capitalization and distribution as a moving equilibrium.” (Moore, 1929, 92). In other words, in line with the conclusions in his 1908 article, the objective is to leave the domain of pure theory to its concrete expression in a dynamic society with the help of the advances made in statistical economics.
Indeed, the logic of equilibrium for Moore is “absolutely indispensable to any form of quantitative work” (Moore, 1929, 5). However, until his last book, Synthetic Economics, this assessment was illustrated by partial equilibria or remained almost implicit rather than being developed in a systematic general equilibrium framework. The first such illustration can be found in the Laws of Wages (1911).^{16} The second is his first and wellknown explanation of business cycles. Using Fourier’s series analysis and trigonometric functions, Moore asserts that an eightyear rainfall cycle is caused by the passage of Venus around the sun. This rainfall cycle induces crop cycles which explain the cyclical pattern of general business conditions.^{17} As noted by Cox (1962), in the light of these two examples the reader feels that while many fruitful lines of investigation have been opened, particularly in the use of mathematics and statistics, Moore was long away from a dynamic complement to pure economics. His Forecasting the Yield and the Price of Cotton (1917) is more convincing and addresses the problem of finding the dynamic law of the demand for cotton.^{18} This book is the beginning of Moore’s pioneering work on the statistical estimation of economic functions.^{19} Notwithstanding its many shortcomings, notably the neglect of temporal shifts in curves,^{20} Schultz describes “the statistical study of demand” as “a new field in economics and may be said to be the creation of only one man, Professor Henry L. Moore” (Schultz, 1938, 63). Besides the influence of prices on demand, Moore for the first time combines economic theory and data to analyze the influence of supply on price, and the effect of price on subsequent production and storage. In addition, the treatment of time elements (“secular change”) and the possibility of a simultaneous determination of the effect of changes in price levels on the price of a particular commodity are recognized. Moore’s interest in the Walrasian system was still present “for the purpose of completely surveying the interrelated factors in the problems of exchange, production and distribution”.^{21} However, he refined his tools over more than a decade between the publication of Forecasting the Yield and the Price of Cotton (1917) and Synthetic Economics (1929).
His investigation of demand elasticity is a clear illustration of this. Moore begins by recalling that in the development of the deductive theory of economic equilibrium a distinction is drawn between particular equilibria and general equilibrium. The first are concerned with demand and supply functions relating to single commodities.^{22} The second “describe[s] the conditions of a state of rest in the economic system as a whole, and the functions descriptive of demand and supply of single commodities have been assumed to be functions either of the prices of or of the quantities of all commodities” (Moore, 1926a, 393). Referring again to Cournot and Marshall, Moore considers the simplest case of particular equilibria. He then develops a general formalization of the partial elasticity of demand and derives a typical equation for the general demand functions which can be statistically estimated. He provides here a method “by means of which the theory of particular equilibria may be given a concrete statistical form, but have so stated the laws of demand and supply as to connect them, respectively, with the theory of elasticity of demand and the laws of cost.” (Moore, 1926a, 394). Moore notes that the chief difficulty in making the transition from analysis of particular equilibria to general equilibrium is the need to work simultaneously with different types of functions with numerous variables. However he believes that his partial results help to overcome this difficulty by extending the theory to more complex systems. Accordingly, Moore observes that “the concrete derivation of the general demand function gives hope of the possibility of passing from a concrete treatment of particular equilibria to a concrete treatment of general equilibrium.” (Moore, 1926a, 401) In the pursuit of this goal, Moore wrote his article “A theory of economic oscillations” (1926b) and his extended version, Synthetic Economics (1929), the culmination of his work on dynamics.
Moore begins by recalling that particular equilibria may be static or dynamic, i.e. moving. Therefore, he gives the following classification:
Figure 1  
Figure 1 Varieties of Economic Equilibria (Source : Moore, 1926b, 1)  
Low resolution version High resolution version 
He goes on to discuss on the law of supply and demand in the history of economic theory which primarily is concerned with the theory of static particular equilibrium, saying that “no mathematical economist, as far I am aware, has ever attempted to pass from this or any similar presentation of a static, hypothetical equilibrium to a realistic treatment of an actual, moving general equilibrium.” (Moore, 1929, 106) Consequently, “Synthetic economics,” as defined by Moore involves three dimensions. The first is the use of simultaneous equations to express the interrelations among economic data in exchange, production, capitalization, and distribution as theorized by Walras. The second refers to the extension of this system into dynamic equations by treating all variables as a function of time. The third is giving a concrete measurable statistical form to each equation. Based on these three dimensions, Moore (1929, 5) contends that “Synthetic economics is both deductive and inductive; dynamic, positive, and concrete.” Neither Walras nor Pareto uses the expression synthetic economics; Moore explains that he borrowed the term from Barone who used it to describe the methods of Walras and Pareto “as a presentation of the whole of static economics in a series of simultaneous equations” (ibid.).
Moore begins by considering a theoretical system of (2m + 2n1) equations defining the conditions of general equilibrium in exchange and production. In this perspective, it seems preferable “for personal loyalty, to adhere as far as possible not only to Walras’ terms but also to his symbols” (Moore 1929, 17). However, Walras’s reasoning is limited to a static and ideal state. Indeed, “his quantities of commodities and prices are such as would prevail in his hypothetical construction under a regime of perfect competition. To carry his reasoning into the sphere of economic realities, a method must be found for obtaining the concrete, complex functions of demand in a constantly changing society where perfect competition does not generally exist, and where equilibrium is incessantly perturbed.” (Moore, 1929, 53) So Moore introduces several innovations to make Walras’s framework dynamics, i.e. as understood by Moore, to achieve a moving and statistically quantifiable equilibrium.
First, Moore recalls the importance of the hypothesis of free competition in Walras’s construction. For Moore this assumption “cannot be made to describe the moving equilibrium in a perpetually changing economy where free competition, in the technical sense of that term does not exist” (Moore, 1929, 181). Accordingly, we cannot change reality, but “we can change ad libitum the axioms, postulates and conventions that lies the basis of our rational construction.” (ibid.) Consequently, in Synthetic Economics Moore abandons the axioms of la libre concurrence absolue, for the principle stated by Cournot that “business men go in the direction in which the greatest profit can be made” (Moore, 1929, 182). In contrast to Walras, his general equilibrium is the equilibrium “which the forces actually at work in our perpetually changing economy tend to bring about” (ibid).
Second, Moore puts great emphasis on the elasticity of demand, whose coefficient is the key to Moore’s mathematical formulation of the Law of Demand.^{23} He notes that in Marshall’s definition the elasticity of a commodity is function of only one price, that of the commodity in question. Consequently, he introduces the notion of partial elasticity of demand.^{24} If demand for commodity C is a function of all prices, D_{c = }F_{c}(p_{t}, p_{p}, p_{k}, … p_{b}, p_{c}, p_{d}, …), the partial elasticity of demand for C with respect to p_{t} can be written (using Moore’s notation) as
Three typical assumptions are made concerning the demand functions and the subsequent partial elasticity which can be constant, linear, or quadratic,^{25} the Law of Supply is developed by an exactly parallel approach in which elasticity of supply is defined in the same way as elasticity of demand (see above).
Third, Moore (1929, 88) notes that “one of the greatest difficulties in dealing with moving equilibrium is the problem of the determination of the coefficients of production”. In this perspective, he chooses to replace Walras’s fixed coefficient of production by production functions. If the total cost of commodity C is made up of services of land T_{c}, services of persons P_{c} and services of capital K_{c}, the general expression of the production function is Q_{c} = Y_{c}(T_{c}, P_{c}, K_{c}, …). But as a “consequence of the ceaseless change in the conditions of business, a representative entrepreneur is constantly asking, and constantly answering, the question whether he shall increase or diminish the quantity of his physical output” (Moore, 1929, 76). His decisions are made according to the given probable movements of demand and “from the point of view of the efficiency of his own organization which he is capable of modifying” (ibid.). Then the key concept of “relative efficiency of organisation” (Moore, 1926b, 17; 1929, 76), e, defined as the ratio of the relative change in total production to relative changes in total cost^{26} plays the same role in production as partial elasticity of demand. Three types of typical production functions are then considered by Moore with constant, linear, or quadratic relative efficiency of organization, in the same way as applied to demand functions. Since these partial efficiencies can be computed empirically, the problem of production can be solved “dynamically and practically” (Moore, 1929, 91).
Finally, Walras’s general equilibrium conditions are made dynamic by introducing relative deviations from trends for all prices and quantities of services and commodities, caused by different perturbations in the data. The trend in each price and quantity is determined statistically after some manipulations, by fitting the time series of the data applying least squares. Using a bar over a symbol to represent the trend value, Moore obtains dynamic demand and supply functions. For instance, the demand function for commodity C can be written as:
The trends are supposed to represent normal yearly production and prices, and the ratios of the observed variables to their normal values indicate the shape of the dynamics induced by the law of demand.^{27} Accordingly for Moore, the introduction of this formula for the three types of functions mentioned above allows statistical evaluation of all the general functions once their algebraic forms are known. Moore mentions that raw data on prices and quantities have to be selected according to the problem in question. Indeed, “they may be of as many individual commodities as desired” (Moore, 1929, 64), or they may be “of representative commodities of various categories” (ibid.) or they may be price and corresponding quantity index numbers.
After some tedious presentations of different formal treatments, Moore provides four groups of three equations that can be statistically evaluated. They apply to “the actual changing economy” (Moore, 1929, 123) and replace the general functions used by Walras. For simplicity, we consider only the first among the three configurations proposed by Moore.^{28} The meaning and notation are the same as in Walras, with the modifications mentioned above: the bar refers to a trend value; are the partial elasticity of demand and the partial elasticity of supply of commodity C with respect to price of t, p, k, b, c, d; e_{at}, e_{bt}, e_{ct}, e_{cp}, e_{c} , …, are the partial relative efficiency of the organization measuring the sensitivity of total cost of a, b, c, t, p, k with respect to the price of t, p, k.
In this simplest case, we have, the following “concrete” demand equations for a representative commodity, C:
Walras’s supply equations are replaced by the following relation:
In place of Walras’s constant coefficient of production, Moore substitutes the following equation:
Finally, instead of Walras’s equations of cost and price, we have:
Moore concludes that these groups of equations (like Walras’s) determine a general equilibrium, but “the equilibrium with which they are concerned is real and not hypothetic, is moving and not static. It is a moving equilibrium about the lines of trend” (Moore, 1929, 126). He completes his model in a second approximation with the theory of capitalization which introduces new complications into the problem, but “will bring the mathematical description into more complete accord with economic facts” (Moore, 1929, 128).^{29}
The book’s final chapter highlights some implications for the study of economic fluctuations and business cycle theory. Referring to Walras’s lake metaphor,^{30} Moore recalls that Walras refers to the possible diffusion of perturbations throughout the system setting up oscillations which vanish progressively until equilibrium is restored. But the Walrasian scheme is purely virtual and abstract and concerns an ideal state. In particular, it “raises the question of the legitimacy of the implied assumption that the functions remain constant during the period of perturbation and adjustment” (Moore, 1929, 152). Thus when Moore’s concrete dynamic functions are substituted into Walras’s reasoning, the analysis of oscillations about a static general equilibrium is replaced by “a description of concrete oscillations about a moving, real, general equilibrium” (Moore, 1929, 153). Then Moore explains how his theory of a moving real general equilibrium provides an adequate framework to analyze actual fluctuations in real time.^{31} Economic oscillations are defined by Moore as fluctuations in quantities or prices from their normal position of equilibrium (trend values).
Accordingly, the empirical functions suggested in Synthetic Economics may be computed in order to take account of their changes over time; the method “enables us to arrive not only at average forms of these functions for any desired period of time, but also, at variants about their average forms” (Moore, 1929, 152). In addition, a global index number of oscillations in prices is derived by Moore as a linear function of the sum of the logarithms of the respective partial flexibilities of prices. With n commodities, we have, following Moore’s notation, that:
Moore contends that his synthesis “with its mathematical description of the industrial organism, reveals in its fidelity and completeness the critical, sensitive spots of the organism” (Moore, 1929, 166). Indeed, economic oscillations, periodic or non periodic, are the result of diverse disturbing factors which affect the “sensitive spots” i.e. the different equations defining the conditions of general equilibrium. They are “the source of the oscillations the nature of which is apprehended through the mathematical description of the mechanical functioning of the organism” (Moore, 1929, 167). Moore reviews the role played by natural phenomena, monetary or real factors which have been characterized and seized upon in traditional business cycle theories, and discusses the mechanism of their diffusion throughout the economic system.^{32} For instance, recurrent changes in the weather may affect the price of land services, inducing cumulative effects in the whole system. The variations in the supply and demand functions may also produce cumulative and recurrent effects, especially in the case of variations in all the empirical functions of supply and demand, which is particularly true for the supply of credit function. Hence, Moore notes that all the explanations of the trade and credit cycle based on waves of optimism or pessimism “have, in the variation of the empirical function, a foundation for the partial truth they contains” (Moore, 1929, 170). One of the main “sensitive spots” can be found in the group of equations defining the conditions of equality between costs and prices and the coefficients of production, since “any change in the coefficients of production affects not only the prices of both consumers’ and producers’ goods, but also the incomes of all factors in production” (Moore, 1929, 172). Moore considers this a reference to business cycle theories based on technological changes and “maladjustment of income” (ibid.). Finally, with regard to the relations associated with the production of new capital goods and determination of the rate of interest, time is the source of the main recurrent and cumulative effects. Indeed, “while it is true that in equilibrium, the value of new capital goods is equal to the volume of credit, and the volume of credit is equal to the amount of saving, it is also true that at no other time is the volume of credit identical with savings.” (Moore, 1929, 173). The divergence between the two is obviously a source of cumulative and recurrent effects and refers to all those theories of economic cycles that emphasize “the capitalistic or roundabout process of production, the excessive accumulation of capital, and the lag in the adjustment of the rate of interest” (ibid.). However, “the sum of partial truths does not constitute the whole truth” (Moore, 1929, 174).
In order to develop a fullfledged statistical analysis of economic fluctuations, it would be necessary to estimate empirically the relative contribution of each type of perturbation. But this task was definitely beyond Moore’s capacity at that time, and in Synthetic Economics he does not go further in the econometric direction, proposing only simple calculable forms for the different groups of his dynamic equations. Nevertheless, he concludes rather naively that one of the main advantages of his synthetic method, which relies on both qualitative and quantitative knowledge, is elimination of the endless controversies over the causes of the fluctuations observed in economic data, since the main factors typically discussed in the business cycles literature can be computed in the same model.
3. Concluding Remarks 
Henry Ludwell Moore is generally associated with the emergence of statistical economics in the US. His pioneering work on quantitative methods, his use of data to analyze cotton crop and his estimations of demand functions, have retained their power of fascination for scholars. Despite several flaws, as Stigler puts it in his obituary of Moore, “the econometric estimation of economic functions is the area of Moore’s work which was of permanent scientific importance.” (Stigler, 1962, 12) However, the use of data and statistical tests characteristic of his earlier empirical investigations are mostly absent from Synthetic Economics. Cox (1962) notes that “one is left with the feeling that here Moore’s ambition outran the capacity of his calculator.” (Cox, 1962, 12) This observation might explain Stigler’s severe judgment on Synthetic Economics. He noted that the statistical element consisted merely of defining simple computable equations, and felt that in Synthetic Economics “Moore’s creativity had been exhausted.” (Stigler, 1962, 16) This assessment contrasts with Schumpeter’s view. For him, it was clear that Moore does not go beyond comparative statics and that this incomplete work presents several shortcomings. However, he considered it an important contribution to the making of a dynamic economics rooted in equilibrium analysis. For Schumpeter (1954, 876) “this venture, embodied in a series of papers that he worked out into Synthetic Economics published in 1929, is one of those landmark achievements that are bound to stand out irrespective of whether or not we make use of them.” Moore’s early work and also Synthetic Economics have been internationally recognized, but for Schumpeter, Moore’s reputation is not as great as it should have been because of the nature of his project. Indeed, “to try to make the Walrasian system statistically operative is something that was altogether beyond that epoch’s scientific horizon. The route this book chalks out is, however, not only difficult, but, in the age of developing alternatives, also unpopular. All modern analysts should study this book with care, though it is quite possible that by so doing they will become admirers of Moore rather than followers” (Schumpeter, 1954, 877). The scientific horizon has now changed and certainly Moore would have dreamt of reaching the degree of connection between theory and quantitative advances characteristic of modern equilibrium analysis of economic dynamics.^{33}
References 
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1 Indeed, in May 1903 Moore wrote to Walras as follows: “You yourself have realized how essential it is for the progress of the social sciences that the man should be known as well as his work, and you have, consequently, told the world what little it knows about Gossen. The memoirs of Jevons exist, and as you know, I have discovered the Souvenir of Cournot. We must have the autobiography of Walras” (Jaffé, 1935, 188). While Walras, in a letter to Gustave Maugin, explains that, “Ce Moore, excité par son succès, s’est mis en tête de faire connaître les vies des fondateurs de l’économie mathématique. J’ai écrit celle de mon père et la mienne. (....) Je suis disposé à donner tout cela à Moore, mais à la condition que son Université se chargera de traduire en anglais et de publier aux EtatsUnis l’Abrégé que j’ai extrait de mes Éléments par la substitution de la méthode géométrique à la méthode analytique” (Jaffé, 1965, Vol. III, Letter 1604).
2 Moore published two articles on the subject in this period: “The differential law of wages”, Journal of the Royal Statistical Society, vol. 70 (Dec. 1907) and “The efficiency theory of wages”, Economic Journal, 17(68) (Dec. 1907). In 1911 Law of Wages: an essay in statistical economics, McMillan, NewYork was published.
3 Walras was very disappointed by Moore’s attitude. He informed Moore that the biography of his (Walras’s) father was being published in France by Émile Borel, and contacted Henry W. Farnam to manage the English translation and publication in the US. Farnam immediately wrote to Irving Fisher to ask Moore for information about the Abrégé.
4 For a detailed comparison of the epistemologies of Walras and Pareto, see also Bridel and Mornati (2009).
5 Moore (18691958) was trained in Vienna and at Johns Hopkins University in the US. He became interested in mathematics and in 1896 taught what at the time was a rare course in mathematical economics and, in 1906, accepted a long tenure at Columbia (19061929) where he developed his major research program on the construction of a statistical complement to pure economics. For a biographical note and the list of Moore’s publications, see Stigler (1962). Stigler notes that Moore was an extremely nervous and sensitive man, who “unfailingly avoided all of the minor entanglements of professional life, and the story of his books is the essential story of his life” (Stigler, 1962, 1). Moore’s scientific production ceased in 1930. He contracted a nervous illness and retired from Columbia in April 1929. He died in 1958. Stigler (1962, 3) stressed that “the pathos of this long twentynine years was a poor payment by Providence for services rendered”.
6 Moore mentions that without any knowledge of Edgeworth’s work on this topics, in his 1907 study of wage efficiency, he provided a peculiar illustration of the advantages of dealing with skewed distributions that originated in disturbed normal distributions. See Moore (1908, 7).
7 Moore refers in particular to an article by Pareto published in May 1907 in the Giornale degli economisti.
8 This statement according to Moore directly echoes Marshall’s point in the Principles (4th ed., Book I, chap V) where he develops the idea that the measurable motives of human action can be investigated by economists in so far as they are manifested in large groups.
9 Accordingly, Moore quotes the Grammar of Science (1908 edition, 372) highlighting its methodological warnings.
10 Moore refers to Lexis’s advances in “combinatorial precision” and the distinction made between normally distributed series with normal, supernormal, or infranormal dispersion and non normal distributions or symptomatic series or evolutionary series (see Moore, 1908, 1416).
11 In relation to population theory, Moore considered that the correlation with economic factors had been extensively investigated and that the nature and the causes of the changes were being properly investigated in the English evolutionary school of eugenics (Moore, 1908, 33).
12 Moore recalled that for Pareto these causes referred to the rhythmic changes in demand, “which [are] simply one form of a general law of rhythm characteristic of organic life” (Moore, 1908, 30).
13 Here, Moore quotes the 1874 letter from Walras to Cournot in which he explains the divergence between the two conceptions of economic theory: “Notre méthode est la même, car la mienne est la votre, seulement vous vous placez immédiatement au bénéfice de la loi des grands nombres et sur le chemin qui mène aux applications numériques. Et moi, je demeure en deçà de cette loi sur le terrain des données rigoureuses et de la pure théorie.“ (quoted in Moore, 1929, 2)
14 Moore quotes a long passage of the Recherches (Bacon English translation, 127).
15 In particular, his controversial result on the increasing pigiron demand curve. (See e.g. Wulwick, 1992 and 1995)
16 In this book, Moore uses data on French coal miners and tries to substantiate “in a rather unconvincing manner” Clark’s marginal productivity theory (Stigler, 1962, 4). For a detailed presentation and appraisal of this empirical example see also Cox (1962).
17 This approach is developed in Economic Cycles. Their Law their Cause (1914) and Generating Economic Cycles (1923). For critical comments on this explanation see notably, Mitchell (1927), Schumpeter (1939) and for a modern appraisal Le Gall (1999).
18 For a detailed presentation see Cox (1962).
19 Preliminary investigation of the statistical laws of demand for various crops and pigiron was made in his Economic cycles. Their Law their Cause (1914). For a thorough and critical appraisal of Moore’s work on identification and statistical estimation of demand and supply curves see especially Stigler (1962), Christ (1985), Biddle (1999), Morgan (1991), Wulwick (1992), and Le Gall (1996).
20 The estimations also neglect income and substitution effects, but Slutsky’s paper was published only in 1915 in an Italian journal and went unnoticed until the 1930s. On this point see Chipman and Lenfant (2002).
21 Forecasting the Yield and the Price of Cotton (Moore, 1917, 172).
22 See also “A Theory of Economic Oscillations.” (Moore, 1926b, 8)
23 As noticed by Ezekiel (1930) in his review of the book in the Quarterly Journal of Economics.
24 On the basis of his article, “Partial elasticity of demand” (Moore, 1926a), and the work of his student Henry Schultz.
25 E.g. we have:
26 E.g.
27 In fact, Moore’s method consists of deriving demand and supply curves from the same data through the mere artifice of lagging the price data when seeking the supply curve. This artifice was noted by Schultz, and by Wright (1930) in his review of Moore’s book in the Journal of Political Economy. Using this method, Moore shows that supply and demand elasticities have approximately the same numerical values but with opposite signs.
28 Indeed, Moore’s developments in Synthetic Economics are not always simple, brief, or direct. In this small (186 pages) book he includes 164 equations, many of which take up almost half a page.
29 On the one hand, the ratio of the rate of interest i to its normal
30 He quotes Walras’s lake metaphor, “De même que le lac est parfois profondément troublé par l’orage, de même aussi le marché est parfois violemment agité par des crises, qui sont des troubles subits et généraux de l’équilibre. Et l’on pourrait d’autant mieux réprimer ou prévenir ces crises qu’on connaîtrait mieux les conditions idéales de l’équilibre” (quoted in Moore, 1929, 146).
31 For a detailed presentation and appraisal of this approach in line with the development of modern equilibrium business cycles theory, see Raybaut (1991) and Le Gall (1999).
32 Contrary to his previous works, Moore does not give in Synthetic Economics any more details or references concerning these traditional business cycle theories.
33 As noticed by an anonymous referee, Moore is not a sort of unknown forerunner of computable general equilibrium modelling. First, computable general equilibrium modelling has not initially developed along dynamic lines. Second, Moore did not consider welfare and distribution issues or economic policy recommendations (for a review of this tradition see e.g.: Schubert, 1993). Accordingly, Moore’s dream on the statistical complement of economic dynamics seems more in line with equilibrium business cycle theories and DGSE modelling, even though we are very far with Moore’s from the analytical setting of these approaches. In particular, one of their most distinguishing features, the idea that modelling should be based on optimization, is alien to Moore (on this point see Terra, 2006).