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Uniqueness of Markov equilibrium in stochastic OLG models with nonclassical production

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  • Hillebrand, Marten

Abstract

This paper studies Markov Equilibria (ME) corresponding to recursive equilibria on natural state space in the stochastic OLG model extended to include non-additive utility, nonclassical production, and Markovian production shocks. Specifically, we provide sufficient conditions under which the ME in unique. It turns out that uniqueness for a large class of economies and that restrictions either on the consumption side or the production side alone are sufficient to garantuee this result. We also discuss additional properties such as continuity or smoothness of the equilibrium mappings and whether additional recursive or non-recursive euilibria exist.

Suggested Citation

  • Hillebrand, Marten, 2012. "Uniqueness of Markov equilibrium in stochastic OLG models with nonclassical production," Working Paper Series in Economics 46, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    • Handle: RePEc:zbw:kitwps:46
    DOI: 10.5445/IR/1000031128
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    References listed on IDEAS

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    1. Greenwood Jeremy & Huffman Gregory W., 1995. "On the Existence of Nonoptimal Equilibria in Dynamic Stochastic Economies," Journal of Economic Theory, Elsevier, vol. 65(2), pages 611-623, April.
    2. Wang, Yong, 1994. "Stationary Markov Equilibria in an OLG Model with Correlated Production Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 731-744, August.
    3. Wang Yong, 1993. "Stationary Equilibria in an Overlapping Generations Economy with Stochastic Production," Journal of Economic Theory, Elsevier, vol. 61(2), pages 423-435, December.
    4. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521001151.
    5. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    6. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 623-674, November.
    7. Morand, Olivier F. & Reffett, Kevin L., 2007. "Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 501-522, April.
    8. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 623-643, October.
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    Citations

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    Cited by:

    1. Hillebrand, Marten & Kikuchi, Tomoo, 2015. "A mechanism for booms and busts in housing prices," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 204-217.
    2. Shi, Lisi & Suen, Richard M. H., 2014. "The Macroeconomic Consequences of Asset Bubbles and Crashes," MPRA Paper 57045, University Library of Munich, Germany.
    3. 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.

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    More about this item

    Keywords

    Markov equilibrium : Uniqueness; Overlapping generations; Nonclassical production; Markovian production shocks;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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