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History of Political Economy 35.2 (2003) 329-331

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Further Evidence on the Origin of Samuelson's Multiplier-Accelerator Model

Arnold Heertje

I highly welcome the reactions by Claes-Henric Siven and Daniele Besomi to our article on the origin of Paul Samuelson's multiplier-accelerator model (Heertje and Heemeijer 2002). Both contributions indicate that the development of new ideas is full of complexities and may come from different sources and places, and may be linked to a specific time-pattern. Briefly, I shall first deal with the observations put forward by Siven and then move on to Besomi's contribution.

Contribution by Siven

On the basis of Siven's quotation from Bertil Ohlin's paper of 1934, I hesitate to draw the conclusion that Ohlin “had an implicit model” in mind. In my view, using the term “model” implies a clear and explicit picture of the relationship between a specific set of assumptions and conclusions, often phrased in terms of a mathematical approach. Ohlin seemed to be far away from that position in 1934. Recently, Björn Hansson (2002, 319) concluded after a thorough discussion of Ohlin's contributions in the 1930s, that Ohlin “made no significant contribution to the development of a dynamic method.” Erik Lundberg is much more a case in point, but, as Siven himself observes, at the time Lundberg was [End Page 329] not able to solve his second-order difference equation in general terms. In other words, he had no explicit idea of the sensitivity of his conclusions for changes in the parameters of his model (Lundberg 1937).

Did Lundberg inspire Samuelson through Alvin Hansen? It seems highly improbable. I quote Lundberg in full on his meeting with Hansen in 1932: “Together with Mr. Tout he (Hansen, A.H.) was at this time preparing a paper on the theories of Keynes and Hayek, so it was a good opportunity to discuss my problems. However, we did not get very far. We agreed upon some of the fundamental points: that Hayek was wrong and that Keynes did not push his analysis far enough. But, otherwise, our points of view were rather different, and we did not become interested in each others' problems” (Lundberg 1994, 52). Lundberg's book came out five years later. In view of Hansen's indifference with respect to Lundberg's analysis in 1932, it is very doubtful that Hansen derived a numerical example from Lundberg's book in 1937.

Contribution by Besomi

Besomi raises a number of interesting points within the general framework of global macroeconomic relationships that, in a rather verbal and sometimes vague way, can be linked to Samuelson's model, but not in the sense of a precise understanding of what Samuelson really accomplished. In Besomi's paper, not only real business cycle theory but also growth theory along Harrodian lines is part of the story. This is fine, but it creates the danger of deviating too much from the issue at stake: the multiplier-accelerator model as a dynamic version of the simple Keynes\-ian model. Of course, I realize that it is easy to make use of the same formal structure to derive Harrod's growth model. And also the other way round, one may translate Harrod's growth model into a multiplier-accelerator model, using the same set of equations. But this is nothing more than pointing out that the same formal structure allows different interpretations with respect to content. Our point is that Harrod in 1936 did not see that, for certain given values of the marginal propensity to consume and the accelerator, a second-order differential model could produce cyclical movements of national income from within. This is exactly what Samuelson proved for the first time. Besomi's remarks on the causes of changes in the coefficients of the equation system are irrelevant. Therefore, I avoid arguing about the question of whether exogenous or endogenous causes are involved. The point is that, with another [End Page 330] set of values of the coefficients, there may be one-sided movements of...


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