This chapter is dedicated to Ragnar Frisch and his economic approach to business cycles developed from the late 1920s to the early 1930s. Initially derived from an initial concern for the effect of capital depreciation on the investment activity, this approach has been discussed with many economists and most publicly with John Maurice Clark, who build a propagation mechanism which encapsulated the latest research on the accelerator and reinvestment cycles and to propose a model of fluctuations that were truly economic. His concern for empirical and statistical work also led him to address economic fluctuations through the harmonic decomposition of time series into components with different periods and
through the concept of changing harmonics.

These works had a small impact, but they conduct Frisch to adopt a new perspective on the mechanisms behind the business cycles: from then on, instead of looking for a decomposition of time series, he looked for a mechanism able to produce component cycles which, once aggregated, could have the properties of a changing harmonic.

These ideas were put together through the use of mixed differential–difference equations, which had been pioneered in the work of Tinbergen (see chapter 2). Tinbergen had clearly shown that those equations could yield an infinity of cyclical components with different periods and degrees of damping, although he was interested only with one solution with the longest period. Frisch pushed the idea much further and used the different components to obtain an analogue of the harmonic decomposition. Because he built a strongly damped propagation mechanism, he was also led to give a central role to shocks, who made sure that the equilibrium would never be obtained and that the cycle would continue to fluctuate. Going back on the mathematical properties of his model, and the result of the superimposition of shocks on his propagation mechanism, it was eventually possible to show that the model could fluctuate even though the propagation mechanism was not oscillating, a property which was known to Frisch.

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