It is probably not unfair to say that Nonlinear Dynamics (NLD) has not had a major impact on the development of modern economic theory. In fact one may even be tempted to add that, until very recently, it was either an unfamiliar tool for the mathematical economist or one whose implications were often disregarded as nonrelevant to the purposes of the research. Dynamical Systems theory appeared for a while in the background of the studies on the stability of the tâtonnement process (see Hahn [1982]) and on optimal growth and turnpike (see McKenzie [1986]), but never really got on the stage.
During the 1950s and 1960s the only well developed effort to use nonlinear techniques in the study of dynamic economic processes is associated to the name of Richard Goodwin (see Goodwin [1982] for a collection of the relevant essays). He put forward the idea of illustrating persistent, deterministic oscillations within a multiplier-accelerator setup by means of a limit cycle for a nonlinear, two-dimensional flow. His research effort toward an endogenous explanation of economic fluctuations motivated a few others contributions within the Keynesian and Cambridge (UK) tradition, but was never able to take off and influence the whole of the profession. In fact the late 1960s and 1970s witnessed an almost complete unanimity on the use of linear stochastic models in order to understand business cycles.
The causes of this historical process are complex and they will not concern us in this place. Similarly, I will not try to list the motivations for the sudden revival of interest in NLD which is characteristic of the last few years, but simply try to provide a (cursory) description of the problems that have been considered and of the results achieved. At the end I will also take a timid look at the "mare magnum" of issues that are still open to investigation.
Let me make clear, at the outset, that the revival of interest in NLD to which I refer is not widespread among economists and that, as a matter of fact, the great majority of applied and theoretical researchers still look at it with doubtful eyes and believe it will not help much in understanding what is going on in the real economic world. They may, indeed, be right.
In spite of this a group of scholars have taken the opposite perspective and have started to look at economic fluctuations under the hypothesis that a relevant portion of them can be explained as a deterministic phenomenon, endogenously created by the interaction of market forces, technologies and preferences. In particular it is conjectured that deterministic periodic cycles affected by small stochastic forces and/or "noisy" chaotic paths generated by dynamical systems of relatively small dimensionality, can account for a relevant portion of the observed fluctuations of most of the important macroeconomic variables.
Download
PDF Ebook Persistent Oscillations And Chaos In Dynamic Economic Models: Notes For A Survey
