Department of Economics

Inverse Limits and Models with Backward Dynamics

Department of Economics

University of Delaware

Working Paper #2006-12

Inverse Limits and Models with Backward Dynamics

Judy Kennedy, David R. Stockman, and James A. Yorke

ABSTRACT

Some economic models like the cash-in-advance model of money have the property that the dynamical system characterizing equilibria is multi-valued going forward in time, but single-valued going backward in time, i.e., the model has backward dynamics. In this paper, we apply the theory of inverse limits to characterize topologically the set of equilibria in 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 multi-valued 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 complicated dynamics.

 

JEL CODES: C6, E3, and E4

KEY WORDS: backward dynamics, chaos, inverse limits, continuum theory, cash-in advance

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