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. YorkeABSTRACT
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