The origins, development, and fate of Clower's “stock-flow” general-equilibrium programme

ABSTRACT

Before becoming the hallmark of macroeconomics à la Wynne Godley, the “stock-flow” analysis was already developed in microeconomics and general-equilibrium theory. The goal was to study the formation of economic plans and the determination of market prices when individuals were supposed to consume, produce, and hold commodities. I show that since the early 1950s, Robert W. Clower used the “stock-flow” price theory to offer microfoundations to a Keynesian business cycle model. I analyse the origins of this microfoundation programme, trace its development, and discuss its fate.

KEYWORDS:

• Microfoundations of macroeconomics
• trade cycle
• stock-flow analysis
• Bushaw and Clower

JEL CODES:

• B2
• E12
• E32
• D4

Acknowledgments

I would like to thank Alain Béraud, Mauro Boianovsky, Kevin D. Hoover, Jean-Sébastien Lenfant, Goulven Rubin, Stéphane Vigeant, and two anonymous reviewers for their helpful remarks on earlier drafts of this essay. I am also grateful to the staff of the David M. Rubenstein Rare Book and Manuscript Library of Duke University for their help with the Robert Clower Papers. I am also indebted to Simon Bailey (Oxford University Archives) who helped me to obtain the report of Clower's thesis defence.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Godley is often considered as one of the founding fathers of the “stock-flow consistent models” (Claudio H. Dos Santos and Gennaro Zezza, 2004).

² The expression “general equilibrium program” was coined by Kevin D. Hoover (2012) to characterize the way Hicks and his followers addressed the microfoundations of macroeconomics.

³ For an exhaustive presentation of Hicks’ method, see Weintraub (1979). For a short presentation, see Hoover (2012).

⁴ In fairness to Keynes, the exclusion of the propensity to consume was suggested by its formalisation. Since it depended partly on realised income, it could not be considered as a cause of fluctuations. With regard to the liquidity preference, Keynes maintained that its modifications would necessarily be the consequence of a previous variation of entrepreneurs’ long-term expectations (1936, 316). Accordingly, this component could not be viewed as a cause of fluctuations: “Liquidity preference […] does not increase until after the collapse in the marginal efficiency of capital” (1936, 316). Yet, it could be a factor prolonging the slump (1936, 316).

⁵ In the short run, entrepreneurs had to anticipate the price at which output would be sold as well as the capacity of absorption of the economy during a given market period; in the long-run, they had to anticipate the future proceeds of an additional unity of capital taking into account the potential modifications of the taste of consumers, of the effective demand, and of the variations of nominal wages.

⁶ Clower indicated that “the models of Mr. Harrod and Professor Hicks are only two of many possible mechanical theories of capital accumulation [references to Metzler (1941) and Samuelson (1939)], but since the results and shortcomings of these two models are broadly characteristic of mechanical analyses, generally, we need not consider other theories” (1952a, 53).

⁷ In the dissertation, Clower referred to the Foundations but not directly to Moore. Yet the principle of generalization by abstraction later became a clear reference, used to justify his second line of research, developed in the 1950s (see “On the existence of a general theory of price determination” (c.1954a, 49) Box 4).

⁸ Clower also modified the standard theory of the consumer to ground his business cycle model. He started with James S. Duesenberry's (1949) idea that the preferences were interdependent. This meant that in addition with absolute income, the relative position in the society mattered in patterns of consumption. Typically, individuals would increase their consumption expenditures with increasing consumption expenditures in their social network. This micromodel was intended to endogenize the trend and the “floor” of his theory of the trade cycle. The maintenance of the consumption, to keep up with the Joneses, would underpin the minimum limit of investment at which the economy would rebound. And since this “floor” was supposed to depend on the stock of capital assets accumulated and that this stock was likely to increase over time (1952a, 43), a rising trend would be described. Clower presented in details his modifications of the standard theory of the consumer in an article titled: “Professor Duesenberry and Traditional Theory” (1952b).

⁹ These two economists were the main references of Clower, both in his dissertation and in the paper that he devoted to the “producer-consumer” theory of the firm (1952c). Yet, it is important to note that in the early 1950s, there was a general concern for the economic effects of the interactions between stocks and flows. The proposals of Hurwicz, De Graaff, and Clower were part of a broader reflection on the incorporation of wealth (i.e., assets and debts) into standard microeconomics, in order to explain the influences of stocks on economic behaviours and vice versa (See Lawrence Klein's paper “Assets, Debt and Economic Behavior” (1951) for a review). In another way, these preoccupations underlined the proposals of Morris A. Copeland (1949) to broaden social accounting to monetary flows.

¹⁰ Clower did not formalise explicitly the expectations. He thought that the introduction of D would be sufficient to account for entrepreneurs’ degree of uncertainty. Thus, unlike Hicks (1939 [1946]), he did not resort to intertemporal optimisation and expectations to address decision making in a context of uncertainty. This may be explained by Hicks's (1939 [1946]) own difficulty to elaborate a theory of expectations rooted in individuals choices.

¹¹ Because of the absence of market models, it is also difficult to understand the kind of theory of the trade cycle contemplated by Clower. Did he have in mind an equilibrium model of the business cycle? Or did he consider that the trade cycle had to be thought by means of derivations with regard to equilibria, like in the models of Harrod (1939) and Hicks (1950)? Whether markets were supposed to clear or not in various stages of the trade cycle modified fundamentally the understanding of this phenomenon.

¹² The quotations are taken from the jury's report. Oxford University Archives: FA4/18/3/1, SS. R (52)16.

¹³ Although Kennedy and Little “considered asking [Clower to revise his dissertation, they came] to the conclusion that, on the more theoretical side, [Clower had] not enough of importance to say to make a satisfactory D. Phil thesis; while any great elaboration of the more practical side would result in a new thesis, rather than an improvement of this one”.

¹⁴ The quotations are taken from a resume written by Clower in 1964. R. W Clower Papers, Box 1-2001-0088, Rubenstein Rare Book and Manuscript Library.

¹⁵ In the mathematical appendix of “An Investigation into the dynamics of investment” (1954a), it is indicated that “this note was prepared by R.W. Clower and D.W. Bushaw, who is instructor in mathematics at the State College of Washington, Pullman” (1954a, 78).

¹⁶ This is the mathematical expression offered by Bushaw and Clower (1954c, 328). They considered a continuous-time model. A discrete-time model required using a sum instead of an integral.

¹⁷ ) was a vertical line which indicated that at a given moment of time, the quantity held by individuals could not change and was independent of current market prices.

¹⁸ From 1953 to 1957, the terminology changed. The expression “non-stationary equilibrium” was substituted to the expression “temporary equilibrium” in Introduction to Mathematical Economy.

¹⁹ Note the modification of the formalisation of the “temporary” equilibrium. There is no inconsistency with the general case expounded in 2.1. Here, Clower assumed that the price at which individuals wanted to hold stocks was independent of the variations of stocks (cf. the mathematical appendix (1954b, 78)).

²⁰ This quotation is from “A Suggestion for Generalizing the Pure Theory of Production” (c.1954b). R. W. Clower Papers, Box 4, Rubenstein Rare Book and Manuscript Library.

²¹ This “short-term” dynamic feature of ‘stock-flow’ models did not imply that the stationary equilibrium was unstable. Rather, Clower demonstrated that if the excess-flow-demand curve was both flat and had the same sign of the excess-stock-demand curve, the stationary equilibrium was stable (1954b, 113). Nonetheless, this would pave the way for such a result once uncertainty would be taken into account (1954b, 114).

²² There is only one equation instead of two, to express the equilibrium on the capital market. This is not consistent with the standard treatment of stock-flow markets. Yet, Bushaw and Clower (1957) argued that this reflected an assumption made by Keynes in the General Theory, namely that the variations of the stock of capital assets were not taken into account in the determination of equilibrium prices (1957: p. 44).

²³ Clower formulated his first disequilibrium interpretation of the General Theory in “Keynes and the Classics: A Reinterpretation” (1958). In this unpublished manuscript (which turns out to be the preliminary version of “Keynes and the Classics: A Dynamical Perspective” (1960)), Clower's goal was to lay the foundations to a general-equilibrium model able to account for the market adjustment processes occurring in disequilibrium situations such as involuntary unemployment and inflation. This constituted the basic idea underlying his disequilibrium programme of microfoundations. For more details, see Plassard (2017c).

²⁴ For an explanation of how and why Clower came to formulate his disequilibrium programme of microfoundations, see Plassard (2017a).

²⁵ This quotation is taken from a research proposal probably written in 1965. R. W. Clower Papers, Box 5, Rubenstein Rare Book and Manuscript Library.

²⁶ As evidenced of that, neither the concept of involuntary unemployment nor the concept of unemployment is listed in the index of Introduction to Mathematical Economics.

²⁷ According to Clower, a dichotomous model was inappropriate for analysing the formation of the temporary equilibrium but appropriate for analysing the properties of the stationary equilibrium. This explains why he kept using “stock-flow” models (without real-balance effect) in debates over the integration of monetary and value theory. His article with Meyer Burstein, in 1960, is an example. Burstein and Clower considered a “stock-flow” economic system ideally situated at the stationary equilibrium to demonstrate the quantity theory (1960, 36). See Plassard (2017b) for a detailed presentation of Clower's strategy to integrate monetary and value theory.

²⁸ George Horwitch (1957) also proposed to use the “stock-flow” price theory to analyse the dynamics of the rate of interest under various scenarios (open-market policy, disturbance of saving or investment…). But his analysis is here omitted since he was not really concerned with the derivation of Keynes's theory of interest from the “stock-flow” market models. Instead, he was involved in an assessment of the existing positions regarding the determinant factors of the rate of interest.

²⁹ For a review of these debates, and in particular of the role played by the distinction between stocks and flows in this context, see Harry G. Johnson (1962).

³⁰ Patinkin (1958) particularly showed that the interest rate was the same whether one assumed a stock demand for money instead of a flow demand for money, and a stock supply of money instead of a flow supply of money. This was because market prices were determined by the system of excess-demand equations, and that the excess-stock-demand for money and the excess-flow-demand for money were identical (1958, 304). While making this point, Patinkin claimed that “the excess demand for money as a stock [had] the dimension of a flow” (1958, 303), a claim that prompted a reaction from Clower. In “Stock and Flow: A Common Fallacy” (1959), Clower pointed out that stocks were measured at points of time while flows were measured over a period of time. Consequently, the excess-stock-demand for money and the excess-flow-demand for money could not have the same dimensions (1959, 251).

³¹ This approach was closed to Clower's (1954b). The difference was that Clower led a partial equilibrium analysis (see 3.1).

³² Clower failed to manage the complexity of his “stock-flow” disequilibrium model. His problem lay in the number of variables that had to be considered. In an unpublished manuscript written in 1971 (“The Keynesian Paradigm: An Attempt at Reconstruction”), Clower stressed that in situations of disequilibrium, undesired variations of stocks would have implied that individuals’ plans included a “set of additional side constraints relating changes in actual stocks of various commodities to realized purchases and sales” (10). This resulted in “an extremely complex theory of individual behavior”, one which made the interactions with markets and the resulting effects on the dynamic path of the economic system hard to formally capture (12).