This Master Thesis was written with the supervision of Professor Olav Bjerkholt and is part of a project for the organization and the improvement of the catalogue for the Ragnar Frisch Archive. The subject of this thesis was chosen for its relevance to Economic history and for the history of methodology in Economic theory. The overall goal of the thesis is to revisit and analyse Ragnar Frisch’s Macrodynamic model as published in ’Economic essays in honour of Gustav Cassel’, London, George Allen and Unwin Ltd., 171-205 under the name: Propagation problems and impulse problems in dynamic economics (which will be referred to as PPIP throughout the paper). An added goal to the thesis was to inspect the economist Stefano Zambelli’s criticism of PPIP in his two papers.The Wooden Horse that Wouldn’t Rock: Reconsidering Frisch. UCLA Economics Working Papers 623, UCLA Department of Economics - 1991 and A Rocking Horse That Never Rocked: Frisch’s ”Propagation Problems and Impulse Problems” History of Political Economy, Spring 2007. The result of this paper is a challenge of Zambelli’s conclusions regarding the oscillatory nature of the model, as well as a new development in adding new analysis in Frisch’s impulse mechanism. The conclusions drawn from this thesis are that Zambelli’s assertions that PPIP is overall a non-oscillatory model across the board are wrong, and that an analysis of the nature of the impulse mechanism allows for no doubt to be lifted as to the oscillatory qualities of the model. It is also a conclusion in this manuscript that Zambelli’s criticism of the propagation mechanism are correct, but that more rigour ought to have been applied when producing the criticism accorded to Frisch. The Thesis is divided into 6 sections.
The first section contains a most brief introduction into the subject of Econonomic and Scientific thought and is to be received as an appetizer for the development ahead. The second section contains a short description of the historical context regarding the application of mathematics, or more importantly: the application of mathematical and statistical tools to the development of economics and specifically to the theory of business cycles. The relevance of the economists chosen was based firstly due to their impact on business cycle theory in the eyes of economic historians and secondly on the effect these had on Ragnar Frisch upon his development of PPIP.
As a third section one finds a thorough description of Frisch’s model as written in PPIP. Fullexplanations as well as a complete development of the model are included here. Reproduction1of results for the sake of information and reference are created here as well as a few historicalnotes that will prove useful regarding the understanding of the model and how it came to be.
An entire section is assigned to Zambelli’s reviews and opinions on PPIP as expressed inhis two articles and this constitutes the main body of section four. In this section, a full reproductionof Zambelli’s criticism regarding the trends for the general solutions for the variablesutilized by Frisch are developed, as well as new judgement regarding Zambelli’s attempts.
The fifth section is entirely the contribution of the author and attempts to enlighten twoparticular aspects of the problems proposed on PPIP. Firstly, the finding of the zeroes andits relevance to the final solution of the characteristic equation Frisch finds in his search for asolution to his ’Macro-Dynamic system giving rise to oscillations’ are evaluated and expanded.Secondly, an in-depth analysis is done regarding the as-of-yet untouched perspective from PPIP regarding the origin of what Frisch referred to as the Impulse Mechanism. This is a mechanism Frisch barely touched in his article despite its paramount importance for the entirety of the model, and the inspection carried out in this thesis would go on to reveal that Frisch’s discussion on the possible look of these impulse structures were not only relevant and applicable to his model, but ultimately adequate to generate the oscillations that PPIP claimed the model was capable of creating.
The last section contains closing arguments regarding Zambelli’s articles and critics as well as the conclusions drawn from the discussions contained in the earlier sections. Lastly, one finds bibliographical reference.
The software used for this paper are the following privately owned programmes: Microsoft Office 2007, Matlab, Mathematica 7 and Texmaker for the generation of LaTex.