Cycles and Chaos in Economic Equilibrium.

• Author: Jaditz, Ted

This book contains 21 papers on the subject of nonlinear determinism and chaos in economics. Fifteen of the 21 have appeared in print in one venue or another, and a number of these would have to be considered among the more important articles on nonlinear determinism in economics. The remaining papers elaborate on or extend themes developed in the published work.

The papers in this book utilize tools originally developed in the natural sciences for the study of complex deterministic dynamical systems. Most economists have had some exposure to deterministic dynamics at one time or another during their graduate studies, perhaps taking a course from a book like Kamien and Schwartz's Dynamic Optimization |2~ or Stokey and Lucas's Recursive Methods in Economic Dynamics |3~. The usual approach is to develop conditions under which the underlying dynamic optimization problem has a unique solution. Typically, one then studies the asymptotic behavior of a general system by linearizing within a neighborhood of the equilibrium and studying the stability properties of the corresponding linear system. Linear systems are easy to work with, and exhibit only a limited range of behaviors: they are stable or explosive, periodic oscillatory or monotonic. The student takes away from the course the subliminal message that economically relevant deterministic dynamical systems are too simple to be empirically interesting. Deterministic systems are quickly discarded in favor of stochastic systems, which appear to generate time series that more closely resemble economic data sets.

The French mathematician Henri Poincare, writing around the turn of the century, is generally credited with the discovery that nonlinear deterministic dynamical systems can exhibit strange, erratic behaviors. These results were mainly of intellectual interest until the '60s and '70s, when researchers in the hard sciences discovered that systems in meteorology, biology, and physics exhibited complex behaviors that could be usefully modeled with simple, nonlinear systems. Where physicists go, economists soon follow, and by the mid '80s came a flood of papers on nonlinear deterministic models of economic systems.

Two features of nonlinear systems captured the attention of economists working in the area. First, it is easy to design a simple nonlinear system that can generate aperiodic, irregular cycles. Second, there are some nice examples of nonlinear systems that appear to be random to many...