AN INSTITUTIONALIST'S JOURNEY INTO THE YEARS OF HIGH THEORY: JOHN MAURICE CLARK ON THE ACCELERATOR-MULTIPLIER INTERACTION

Abstract

I am myself enough of an institutionalist (whatever that may mean) to have more than a lurking distrust of formulas and equations! But not enough of an institutionalist to ignore their importance. (J. M. Clark to J. M. Keynes, July 24, 1941)1

¹Quoted in Dorfman (1970, p. 13).

Acknowledgments

The research for this paper made use of the Wesley C. Mitchell and John Maurice Papers at the Rare book and Manuscipt Library, Columbia University. Thanks to Pier Francesco Asso, Daniele Besomi, Malcolm Rutherford, Warren Samuels, and an anonymous referee for helpful comments.

Notes

¹Quoted in Dorfman (1970, p. 13).

²See the papers contained in the 2003 Summer issue of History of Political Economy.

³A third contestant, the Swedish economist Erik Lundberg, was introduced by Siven (2003).

⁴A. Aftalion, C.F. Bickerdike, M. Bouniatian, T.N. Carver, and R. Hawtrey, just to name a few.

⁵John Maurice Clark to Wesley Clair Mitchell: January 24, 1915. Wesley C. Mitchell Papers, Rare books and Manuscript Library, Columbia University. The letter is reproduced in the appendix.

⁶Later in his life, Clark discussed “the psychological genesis of the theory of the accelerator principle” in his correspondence with Paul Samuelson, reaffirming what he had stated in 1917. See John M. Clark to Paul A. Samuelson: April 21, 1953. The letter is reproduced in the appendix.

⁷In particular, there are some important parallels between Aftalion and Clark's versions of the accelerator, especially in their illustrative examples of the actual functioning of the mechanism. A careful assessment of Clark's 1917 contribution in relation to earlier versions of the accelerator, however, is well beyond the aim of this paper. See Fisher (1952) for a brief comparative discussion of Aftalion, Bickerdike, Carver, and Clark.

⁸The explicit hypothesis of a time-lag between the fluctuations in demand for producers' goods and the fluctuations in demand for consumers' goods can also be found in Aftalion (1909, p. 209).

⁹The applicability of these results for a typical industry to aggregate business cycle analysis was accomplished by a generalization of a particular instance to the general case on the basis of the implicit assumption that most of the firms face generally similar conditions at each stage of the business cycle.

¹⁰See Knox (1952) for an excellent survey on the literature concerning the accelerator and the theory of derived demand.

¹¹See Frisch (1931, 1932a, 1932b) and Clark (1931b, 1932).

¹²Clark's passage quoted by Samuelson is actually longer than the one reproduced here.

¹³In this connection, it should be noted that Clark's rejoinder to Frisch, albeit published in 1932, was actually written and submitted to the JPE in 1931.

¹⁶John M. Clark to Joseph Dorfman: May 12, 1956. Dorfman Papers, Rare Book and Manuscript Library, Columbia University. See also John M. Clark to Paul A. Samuelson: April 21, 1953. John Maurice Clark Papers, Rare Book and Manuscript Library, Columbia University. The letter is reproduced in the appendix. Nonetheless, some have argued, not without cause, that the highly individual, personal perspective of later recollections, tend to overstate individual agency and obscure the constructive influence of the general intellectual environment or of other thinkers. For these reasons, Clark's statements in his correspondence with Dorfman and Samuelson concerning his independent discovery of the multiplier must be taken with the necessary caution.

¹⁴As argued elsewhere (Fiorito 2001), an earlier discussion of the multiplier, albeit intuitive and phrased in non-rigorous terms, can be traced in Clark's The Cost of the World War to the American People (1931a). See Dimand (2000) for a contrasting point of view.

¹⁵Clark's reference to Kahn (1933) is somewhat puzzling since Kahn version of the multiplier was first expounded in 1931. Curiously, in the Economics of Planning Public Works (1935c) Clark correctly refers to Kahn (1931). It should be also noted that Clark does not mention Keynes's Means to Prosperity (1933).

¹⁷In sending his comments on an early draft of chapter IX of the Economics of Planning Public Works, Hansen observed: “In general I have the impression that your analysis still follows too much along the Keynes lines.” See A. H. Hansen to J. M. Clark, August 8, 1934, reprinted in Fiorito (2001).

¹⁸In a 1928 Treasury memorandum (quoted in Davis 1983, appendix; and Dimand 1988, p. 108), Hawtrey had reached similar results, working through a numerical example of the multiplier analysis, adding up successive rounds of reductions in spending to obtain a finite value for the total change in equilibrium income and expenditure. See Dimand (1997).

¹⁹It should be noted, however, that Keynes never thought of an instantaneous multiplier. In The Means to Prosperity he clearly recognized the problem involved by the existence of time-lags but underplayed it on the following ground: “[t]he amount of time which it takes for current income to be spent will separate each repercussion from the next one. But it will be seen that seven-eights of the total effects come from the primary expenditure and the first two repercussions, so that the time-lags involved are not unduly serious” (Keynes 1933, p. 343).

²⁰Clark's analysis of the “non-instantaneous” multiplier has also some important monetary implications, which are discussed in Fiorito (2001, 2004).

²¹At that time Kuznets was part of NBER staff. On Kuznets's relationship with Mitchell and American institutionalism see Rutherford (2004).

²²It should be stressed that the lags described by Clark are not a “one-off lags,” during which nothing visible happens and at the end of which something all of a sudden occurs—such as a Robertsonian expenditure lag, or an accelerator lag in which induced investment in period t is proportional to the change in national income between period t – 1 and t – 2. The lags Clark had in mind are more properly “periods” during which things continuously happen and the relevant economic variables interact among them. Lags so conceived are not amenable to a discrete treatment such as Samuelson's (difference equation, where X at time t is a function of X at time (t–1), and were probably beyond Clark's mathematical capability.

²³Clark had explicitly mentioned these exogenous factors in his Studies in the Economics of Overhead Costs (1924, pp. 393–94).

²⁴See the exhaustive discussion in Besomi (2003).

²⁵Clark's reference to “modernization” is quite problematic. When firms replace machines, they usually install larger or “better” ones. New equipment is always both modernization and replacement. As observed by Knox (1952, p. 284) “even if it were possible to determine ex post what part of investment is net and what part replacement, the distinction would be artificial.” It should be pointed out, however, that Clark's 1940 notes were merely suggestive and devoid of analytical precision. The relevant passages are reproduced below in their full length:

Restate the basic mathematical relation in terms of the relation between productive capacity and additions thereto (plus or minus). Also between net additions and gross output of equipment (new). The latter relationship is modified by changes in the rate of retirements, which may be a rather indefinite thing when one takes account of the element of stand-by capacity, retired from regular service, but not scrapped. This is a function not merely of age, but of functional obsolescence and modernization, taking effect in an increase of retirements from regular service, with or without scrapping. Productive capacity in service may be increased, temporarily and within limits, by reducing retirements as well as by increasing output of new equipment. Financial hard-upness may cause it to take the former form, temporarily … Modernization may the basis for another purely mathematical relation between amount of modern equipment in service and rate of output of new equipment. Here it is obvious that not all the equipment can be modernized at once. What is a normal rate? Does it vary from case to case, and with what conditions? The relation between demand current for the end-product or service and the supply of means of production then becomes a separate question. It would presumably work differently in different industries—competitive—perfect, pure, oligopolistic, monopolistic-competitive; private monopolies, public service industries. Cf. Abramovitz's [1939] thesis on the most profitable timing of addition to capacity: just before a revival of demand for the end-product. The above leaves lots of room for the rate of profits, as distinct from the rate of physical demand for the end-product, to influence rate of acquisition of new equipment (Clark 1940).

²⁶Rendings T. Fels, later at Vanderbilt University, is the author of several contributions on business cycle theory which appeared in major academic journals during the 1950s and 1960s.

²⁷Although skepticism towards the abuse of formalism was one of the distinguishing marks of American institutionalism, it was by no means exclusive to it. See for instance Besomi's (2003) remarks on Harrod's treatment of the accelerator-multiplier interaction which, in some respects, bears strict resemblance to Clark's.

Additional information

Notes on contributors

Luca Fiorito

Università di Palermo, [email protected].