Regularity in overlapping generations exchange economies |
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Authors: | Timothy J. Kehoe David K. Levine |
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Affiliation: | Clare College, Cambridge CB2 1TL, UK;University of California, Los Angeles, CA 90024, USA |
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Abstract: | In this paper we develop a regularity theory for stationary overlapping generations economies. We show that generically there is an odd number of steady states in which a non-zero amount of nominal debt (fiat money) is passed from generation to generation and an odd number in which there is no nominal debt. We are also interested in non-steady state perfect foresight paths. As a first step in this direction we analyze the behavior of paths near a steady state. We show that generically they are given by a second order difference equation that satisfies strong regularity properties. Economic theory alone imposes little restriction on those paths: With n goods and consumers who live for m periods, for example, the only restriction on the set of paths converging to the steady state is that they form a manifold of dimension no less than one, no more than 2nm. |
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