Inverse Limits and Models with Ill-Defined Forward Dynamics

Judy Kennedy

 David R. Stockman

and James A. Yorke

Some economic models like the cash-in-advance model of money have the property that the dynamics are ill-defined going forward in time, but well-defined going backward in time. In this paper, we apply the theory of inverse limits to characterize topologically all possible solutions to a dynamic economic model with this property. We show that such techniques are particularly well-suited for analyzing the dynamics going forward in time even though the dynamics are ill-defined in this direction. In particular, we analyze the inverse limit of the cash-in-advance model of money and illustrate how information about the inverse limit is useful for detecting or ruling out complex dynamics.

Keywords: cash-in-advance, chaos, inverse limits, continuum theory.

JEL: C6, E3, and E4.