Indeterminacy of equilibrium in stochastic OLG models |
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Authors: | Michael Magill Martine Quinzii |
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Institution: | (1) Department of Economics, University of Southern California, Los Angeles, CA 90089-0253, USA (e-mail: magill@usc.edu) , US;(2) Department of Economics, University of California, Davis, CA 95616-8578, USA (e-mail: mmquinzii@ucdavis.edu) , US |
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Abstract: | Summary. This paper studies the equilibria of a stochastic OLG exchange economies consisting of identical agents living for two periods,
and having the opportunity to trade a single infinitely-lived asset in constant supply. The agents have uncertain endowments
and the stochastic process determining the endowments is Markovian. For such economies, the literature has focused on studying
strongly stationary equilibria in which quantities and prices are functions of the exogenous states of nature which describe
the uncertainty: such equilibria are generalizations of deterministic steady states, and this paper investigates if they have
the same special status as asymptotic limits of other equilibrium paths. The difficulty in extending the analysis of equilibria
beyond the class of strongly stationary equilibria comes from the presence of indeterminacy: we propose a procedure for overcoming
this difficulty which can be decomposed into two steps. First backward induction arguments are used to restrict the domain
of possible prices; then if some indeterminacy is left, expectation functions are introduced to make the forward equilibrium
equations determinate. The properties of the resulting trajectories, in particular their asymptotic properties, can then be
studied. For the class of models that we study this procedure provides a justification for focusing on strongly stationary
equilibria. For the model with positive dividends (equity or land) the justification is complete, since we show that the strongly
stationary equilibrium is the unique equilibrium. For the model with zero dividends (money) there is a continuum of self-fulfilling
expectation functions resulting in a continuum of equilibrium paths starting from any admissible initial condition: under
conditions given in the paper, these equilibrium paths converge almost surely to one of the strongly stationary equilibria-either
autarchy or the stochastic analogue of the Golden Rule.
Received: November 19, 2001; revised version: March 22, 2002
RID="*"
ID="*" We are grateful for the stimulating environment and research support provided by the Cowles Foundation at Yale University
during the Fall 2000 when this paper was first conceived. We are also grateful to the participants of the SITE Workshop at
Stanford University and the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001 for helpful discussions.
Correspondence to: M. Magill |
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Keywords: | and Phrases: Stochastic overlapping generations model Stationary rational expectations equilibrium Indeterminacy Expectation functions Martingale convergence theorem |
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