Cycles and Chaos in Economic Equilibrium

by Jess Benhabib

Book Overview

In recent years economists have begun to use the techniques of non-linear dynamics to show that some apparently erratic and turbulent economic phenomena reflect subtle underlying patterns. How do cyclic and chaotic dynamics arise in economic models of equilibrium? How can empirical methods be used to detect nonlinearities and cyclic and chaotic structures in economic models? In examining these questions, this book brings together the most significant...

• Format: Paperback
• Language: English
• ISBN: 0691003920
• ISBN13: 9780691003924
• Release Date: March 1992
• Publisher: Princeton University Press
• Length: 488 Pages
• Weight: 1.46 lbs.
• Dimensions: 1.0" x 6.1" x 9.2"

Customer Reviews

Good introduction to the theory

It was perhaps inevitable that the theory of chaotic dynamical systems would be applied to economics. In an intuitive, everyday sense, economic phenomena is usually perceived as being "chaotic", this notion being equated with a random behavior of sorts. Whether or not economic systems are really random (from a rigorous mathematical standpoint) is the subject of other books. This one addresses the question as to whether chaos does indeed exist in economic systems. Chaos and randomness are of course distinct concepts, and this is brought out clearly by the authors of the articles in the book, the specific theme of which is to shed light on the role of oscillatory dynamics in economic fluctuations. The oscillations are put in the context of chaotic dynamical systems, which, as is well known, have a very rich orbit structure. The emphasis is on theory, but there are some articles that discuss empirical validation of chaotic dynamical system models of time series. What is most interesting about the results in the book is that chaos is a deterministic explanation of the erratic behavior of economic behavior. This is to be contrasted with the situation in financial modeling, where randonmess is thought to be essential because of arbitrage opportunities. It is fascinating to compare the ideas in this book with the ones that are very entrenched in financial modeling. The authors of the articles have been heavily involved in the research of chaotic dynamical systems in economics. Space here permits only a limited review of the contents of the book. . Before the advent of research in chaos in economics, the complexity of economic phenomena was modeled by linear equations subjected to exogenous shocks. The approach taken in one of the articles discusses to what extent aggregate fluctuations represent endogenous phenomena that are persistent even when there are no random shocks to the economy. Recognizing that chaotic dynamical systems can generate time series that appear irregular or random, discussion is given on the models based on chaos that exhibit the persistence phenomena. Since chaotic systems have countably many periodic orbits, it is natural to ask to what extent these orbits play in models of economic phenomena. One of these considered is the overlapping generations model. A class of robust utility functions, assumed to be constant from one generation to another, are shown to give the existence of bounded trajectories that do not converge to periodic orbits or fixed points, but are also, because of the time scales involved, indistinguishable from periodic orbits of arbitrarily long period, the latter also existing in the model. The existence of these trajectories is interesting, particularly when considering the mechanism by which the trades between generations occur. This mechanism involves the introduction of a central credit authority, and even when the nominal credit expands at a constant rate, the model still exhibits erratic trajectories in