Fluctuations and growth in Ragnar Frisch’s rocking horse model

Abstract

Ragnar Frisch's famous "rocking horse" model has been the object of much praise and even controversy since its publication in 1933. This paper offers a new simulation of the model to show that there exists cyclical trajectories in the propagation mechanism. By building an analytical solution taking the same form as Frisch's original solution, we can provide new insights into the ideas encapsulated in his model, in particular the fact that the author constructed a model combining cycles and growth. The exploration of Frisch's formal construction of the model leads us to link his statistical work on the decomposition of time series with his economic insights on investment cycles, which both led to the 1933 model. We contrast Frisch’s approach to that of other econometricians who used similar equations, showing that their different mathematical solutions were the product of what they wanted to show with their models.

Breaking Free From the Stability Dogma: Samuelson and the Multiplier-Accelerator Model Over the Years

“…The dependence of the quantitative behaviour of Samuelson's 1939 model upon the values of the coefficients of the variables deployed in the equations became increasingly seen as problematic. It indicated to Kydland and Prescott (1991: 165), for instance, that "pure theory was not providing sufficient discipline", which brought into the picture the statistics discipline provided by Tjalling Koopmans 5 See Carret (2021) for a detailed account of the mathematical properties of Frisch's 1933 macrodynamic model. At about the same time, Tinbergen had developed a nonlinear macrodynamic model which he used to shed new light on several policy problems: wage changes, government expenditure and its relation to pump-priming, and the regulation of purchasing power.…”