Heertje, Heemeijer, and Samuelson on the Origin of Samuelson's Multiplier-Accelerator Model

Who were the “fathers” of Paul Samuelson's (1939) famous business-cycle model built on the interaction between the multiplier and the accelerator? Arnold Heertje and Peter Heemeijer (2002, 207–8) draw the conclusion that “there is little factual support for Samuelson's suggestion ascribing the model mainly to Alvin Hansen, his mentor in the days of the creation of the model. Instead, the evidence indicates that Roy Harrod played the major role in the development of research leading to the multiplier-accelerator model.” In a reply, Samuelson (2002, 221) stressed Harrod's importance but underlined that “I reaffirm now, from clear memory, that my 1939 difference equation(s) came directly from the numerical sequence on which Hansen based his thesis.”

Below I will argue that the roots of the accelerator-multiplier model are more likely to be found in the work of Bertil Ohlin (1934) and Erik Lundberg (1937) but that Alvin Hansen might have transmitted Lundberg's ideas to Samuelson. However, my argument does not necessarily contradict the thesis of Heertje and Heemeijer concerning the importance of Harrod. The same idea may come from different sources.

Ohlin's Verbal Combination of the Accelerator and the Multiplier

In 1934 Bertil Ohlin delivered a 176-page report to the Swedish unemployment commission. In it he investigated various means of fighting unemployment. In order to evaluate the effects of different policies, he also discussed how the economy reacts to disturbances. His “model” might be described as a simple version of the Keynesian macroeconomics of the 1950s. More specifically, Ohlin used multiplier analysis to determine national income and the accelerator to determine investments. In the former case he started from Kahn 1931; in the latter case, probably ultimately from Clark 1917.

The following passage from Ohlin's report indicates that he verbally sensed that the interaction between the multiplier and the accelerator might produce oscillations:

1) The volume of investment is as discussed above related to the actual and calculated rate of change of production of consumption goods. 2) The latter is via the propensity to save related to total income, which is based on total production . . . . These circumstances also explain to some extent why in the absence of further disturbances an upturn of production in a normal business situation tends to continue and when the top of the business cycle has been reached after a while turns down again. (1934, 52)

Some caveats are necessary. First, Ohlin did not explicitly mention the multiplier in this connection. A discussion of the multiplier first appears on pages 102–3 in connection with a discussion of the effects of public works. However, the citation (and general reading of the text) makes it probable that he had an implicit model in which effective demand plays a decisive role in the business cycle.¹ Second, in his discussion on pages 52–53, Ohlin also discussed the effects of price changes on investments.

Ohlin's discussion was probably inspired by the debate between Ragnar Frisch and J. M. Clark in the Journal of Political Economy about the role of the accelerator mechanism in generating business cycles.² Here, Frisch (1932, 255) had pointed out that “this turning-point [of the business cycle] can only be proved by taking account of some additional fact [besides the accelerator] which explains why the slackening of consumer-taking [consumption] takes place in such particular manner as to call forth the decline in capital production.”³

Clark's (1932, 692) suggested “additional fact” was that “actual movements of consumer demand depend on the movements of purchasing power; and these in turn are governed by the rate of production in general, including that of capital equipment, and also that of durable consumption goods, such as housing and automobiles, to which the same essential principle [the accelerator] applies.”

Lundberg's Numerical Analysis of the Interaction between the...