Fifteen years after the Global Financial Crisis: Recessions and Business Cycles in the History of Economic Thought

Business cycle nonlinear models: From Kalecki to Allais

Bismans Francis Bismans, BETA, University of Lorraine

During the Great Depression, Michał Kalecki (1933,1935a,b) developed a model that used the Keynesian multiplier, but above all proposed an original nonlinear investment function. Finally, our author ended up with a system of four equations, which, after substitutions, resulted in a mixed difference-differential equation. He then calibrates his model and comes to the conclusion: “The actual duration of the business cycle being (…) 8-12 years, one can safely say that (…) the conclusions of our theory do not differ very much from the reality”. After the Second World War, Goodwin (1951) proposed a model which combines a dynamic multiplier and a nonlinear accelerator. As with Kalecki, there is a fixed-time delay in the accelerator and Goodwin's model also results in a mixed difference-differential equation. The resolution of the latter leads to a stable limit-cycle, but not of sinusoidal shape. The future Nobel Prize-winner Maurice Allais (1953, 1955, 1956) also conceives a very original nonlinear model of the cycle. It differs from Kalecki’s or Goodwin’s in that it is founded on essentially monetary dynamics. In fact, the effort of the French theorist consists of explaining stable cycles’autogeneration on the basis of interactions between preferences for cash defined as the opposite of money’s circulation, and the quantity of bank money. Allais’ model formalizes the fact that from one period to another, the variation in overall expenditure is proportional to the excess of the money supply over the corresponding demand. Ultimately, Allais arrives at a mixed differential-integral equation, which depends exclusively on the demand for money.

Area: Eshet Conference

Keywords: Business cycles, calibration, econometric estimation, investment, mixed equations, nonlinear models, phases of the cycle

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