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Indeterminacy of equilibrium in stochastic OLG models

Author

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  • Michael Magill
  • Martine Quinzii

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Michael Magill & Martine Quinzii, 2003. "Indeterminacy of equilibrium in stochastic OLG models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 435-454, March.
    • Handle: RePEc:spr:joecth:v:21:y:2003:i:2:p:435-454
    DOI: 10.1007/s00199-002-0287-6
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    Citations

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    Cited by:

    1. Zhigang Feng & Matthew Hoelle, 2017. "Indeterminacy in stochastic overlapping generations models: real effects in the long run," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 559-585, February.
    2. Chatterji, Shurojit & Chattopadhyay, Subir, 2006. "Functional sunspot equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 22-35, February.
    3. Eisei Ohtaki & Hiroyuki Ozaki, 2014. "Optimality in a Stochastic OLG Model with Ambiguity," Working Papers e069, Tokyo Center for Economic Research.
    4. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    5. Martin Barbie & Marten Hillebrand, 2018. "Bubbly Markov equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 627-679, October.
    6. Takeoka, Norio, 2006. "Stationary Markov equilibria on a non-compact self-justified set," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 269-290, June.
    7. Eisei Ohtaki, 2023. "Optimality in an OLG model with nonsmooth preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 611-659, September.
    8. Eisei Ohtaki & Hiroyuki Ozaki, 2015. "Monetary equilibria and Knightian uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 435-459, August.
    9. Ohtaki, Eisei, 2014. "Tractable graphical device for analyzing stationary stochastic OLG economies," Journal of Macroeconomics, Elsevier, vol. 40(C), pages 16-26.

    More about this item

    Keywords

    Keywords and Phrases: Stochastic overlapping generations model; Stationary rational expectations equilibrium; Indeterminacy; Expectation functions; Martingale convergence theorem.; JEL Classification Numbers: D50; D84; C62.;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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