A Rational Route to Randomness

William A. Brock
Department of Economics and Social Research Institute, University of Wisconsin

Cars H. Hommes
Department of Economics and Tinbergen Institute, University of Amsterdam

Abstract

We introduce the concept of Adaptively Rational Equilibrium (A.R.E) where agents base decisions upon predictions of future values of endogenous variables whose actual values are determined by equilibration. Predictors are chosen from a finite set. Each predictor is a function of past observations and has a performance measure attached to it which is publically available. Agents use a discrete choice model and make a rational choice concerning the predictor based upon the performance measure. This results in a dynamics across predictor choice with is coupled to the equilibrium dynamics of the endogenous variables.

As a typical example we consider a cobweb type demand-supply model where agents can choose between rational and naive expectations. In an unstable market with (small) positive information costs for rational expectations, a high intensity of choice to switch predictors leads to highly irregular equilibrium prices converging to a strange attractor. The irregularity of the equilibrium time paths is explained by the existence of a so-called homoclinic orbit and its associated complicated dynamical phenomena. Thus local instability and global complicated dynamics may be a feature of a fully rational notion of equilibrium.