Department of Economics
University of Delaware
Working Paper #2006-03
Chaotic Equilibria in Models with Ill-Defined Forward Dynamics
Judy Kennedy and David R. StockmanABSTRACT
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.