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A Rational Route to Randomness

William A. Brock and Cars H. Hommes
Econometrica
Vol. 65, No. 5 (Sep., 1997), pp. 1059-1095
Published by: The Econometric Society
DOI: 10.2307/2171879
Stable URL: http://www.jstor.org/stable/2171879
Page Count: 37
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A Rational Route to Randomness
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Abstract

The concept of adaptively rational equilibrium (A.R.E.) is introduced. Agents adapt their beliefs over time by choosing from a finite set of different predictor or expectations functions. Each predictor is a function of past observations and has a performance or fitness measure which is publicly available. Agents make a rational choice concerning the predictors based upon their past performance. This results in a dynamics across predictor choice which is coupled to the equilibrium dynamics of the endogenous variables. As a simple, but 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.

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