Department of Economics

Chaotic Equilibria in Models with Ill-Defined Forward Dynamics

Department of Economics

University of Delaware

Working Paper #2006-03

Chaotic Equilibria in Models with Ill-Defined Forward Dynamics

Judy Kennedy and David R. Stockman

ABSTRACT

Some economic models like the cash-in-advance model of money or overlapping generations model have the property that the dynamics are ill-defined going forward in time, but well-defined going backward in time. In such instances, what does it mean for an ill-defined dynamical system to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, we provide a definition of chaotic that is in the spirit of Devaney for a dynamical system with ill-defined forward dynamics. We utilize the theory of inverse limits to provide necessary and sufficient conditions for such a dynamical system to be chaotic.

Keywords: cash-in-advance, overlapping generations, chaos, inverse limits.

JEL: C6, E3, and E4.

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