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 exist 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.

Letter to the Editors: Solving Vincent Carret’s Puzzle: A Rebuttal of Carret’s Fallacies and Errors

“…Unlike Carret, we worked within Frisch's framework, and strictly followed Frisch's demonstration step by step without introducing any new mathematical tools or economic reasoning, as Carret does. In so doing, we proved that Frisch's model fluctuates with its original values (Ginoux and Jovanovic 2023, 2022a, 2022b. Indeed, while Frisch did not provide the value of the coefficients k j (because he did not give an explicit general solution of his model), we provide a general solution by choosing a set of coefficients that respect Frisch's closure relation and for which his propagation model fluctuates.…”

“…In his criticism of our work, Vincent Carret (2022a) states that we made a mistaken interpretation of Ragnar Frisch's paragraph in which he expressed a condition that must be respected in order to obtain the general solution. Frisch called it a "proviso."…”

“…In his criticism of our work, Vincent Carret (2022a) states that we made a mistaken interpretation of Ragnar Frisch’s paragraph in which he expressed a condition that must be respected in order to obtain the general solution. Frisch called it a “proviso.” According to the Cambridge Dictionary , a proviso is “a statement in an agreement, saying that a particular thing must happen before another can.” In modern terms, Frisch’s proviso is a closure relation, according to which the sum of the coefficients k j , which are the weight of each cycle, must be equal to unity.…”

“…What business cycle did Carret try to replicate with his model? Because Carret (2022a) ignored Frisch’s closure relation, which ensures that Frisch’s system oscillates, he was obliged to change the value of the parameters to obtain oscillations (Ginoux and Jovanovic 2022b). The problem here is that Carret dismisses the consequences of his choice too easily.…”

Letter to the Editors: The Emperor Has No Clothes: A Reply to Ginoux and Jovanovic

“…Given the subsequent separation of growth and cycles in the literature, I came to see this as one of Frisch's most original contributions, and the main point of my paper, hence the title I chose: "Fluctuations and Growth in Ragnar Frisch's Rocking Horse Model. " This was the point elaborated in section III of my paper (Carret 2022a), where I presented the results I had worked out and coded in the programming language R. The mathematical reasoning on which it is based can be found in my working paper on Frisch's model (Carret 2020, pp. 19-25), and the code is available online (the link was given in my original working paper, Carret 2020, pp.…”