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Stationary Markov equilibria for overlapping generations


  • Felix Kubler


  • Herakles Polemarchakis



At a stationary Markov equilibrium of a Markovian economy of overlapping generations, prices at a date-event are determined by the realization of the shock, the distribution of wealth and, with production, the stock of capital. Stationary Markov equilibria may not exist; this is the case with intra-generational heterogeneity and multiple commodities or long life spans. Generalized Markov equilibria exist if prices are allowed to vary also with the realization of the shock, prices and the allocation of consumption and production at the predecessor date-event. (Stationary) Markov $ \epsilon $ -equilibria always exist; as $ \epsilon \rightarrow 0, $ allocations and prices converge to equilibrium prices and allocations that, however, need not be stationary. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:24:y:2004:i:3:p:623-643
    DOI: 10.1007/s00199-004-0523-3

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    References listed on IDEAS

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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. P. Siconolfi & A. Citanna, 2007. "Recursive equilibrium in stochastic OLG economies," 2007 Meeting Papers 777, Society for Economic Dynamics.
    3. Citanna, Alessandro & Siconolfi, Paolo, 2012. "Recursive equilibrium in stochastic OLG economies: Incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 322-337.
    4. Rodrigo Raad, 2016. "Recursive equilibrium with Price Perfect Foresight and a minimal state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 1-54, January.
    5. Hillebrand, Marten, 2014. "Uniqueness of Markov equilibrium in stochastic OLG models with nonclassical production," Economics Letters, Elsevier, vol. 123(2), pages 171-176.
    6. Drèze, Jacques H. & Herings, P. Jean-Jacques, 2008. "Sequentially complete markets remain incomplete," Economics Letters, Elsevier, vol. 100(3), pages 445-447, September.
    7. Junjian Miao & Manuel Santos, 2005. "Numerical Solution of Dynamic Non-Optimal Economies," Boston University - Department of Economics - Working Papers Series WP2005-003, Boston University - Department of Economics.
    8. Felix Kubler & Karl Schmedders, 2003. "Approximate Versus Exact Equilibria," Discussion Papers 1382, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
    10. Paul Gomme & Richard Rogerson & Peter Rupert & Randall Wright, 2005. "The Business Cycle and the Life Cycle," NBER Chapters,in: NBER Macroeconomics Annual 2004, Volume 19, pages 415-592 National Bureau of Economic Research, Inc.
    11. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 83-110, February.
    12. Adrian Peralta-Alva & Manuel S. Santos, 2010. "Problems in the Numerical Simulation of Models with Heterogeneous Agents and Economic Distortions," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 617-625, 04-05.
    13. 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.
    14. 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.
    15. Sonia Giannatale, 2008. "Sunspot-like equilibria in an overlapping generations economy with strategic interactions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 191-199, April.
    16. Stepanchuk, Serhiy & Tsyrennikov, Viktor, 2015. "Portfolio and welfare consequences of debt market dominance," Journal of Monetary Economics, Elsevier, vol. 74(C), pages 89-101.
    17. Kevin Reffett & Olivier Morand, 2008. "Isotone recursive methods for Stationary Markov Equilibra in OLG models with stochastic nonclassical production," 2008 Meeting Papers 470, Society for Economic Dynamics.
    18. Costas Xiouros, 2006. "Asset price volatilities and trading volumes in heterogeneous agent economies," Computing in Economics and Finance 2006 466, Society for Computational Economics.
    19. Alessandro Citanna & Paolo Siconolfi, 2008. "On the nonexistence of recursive equilibrium in stochastic OLG economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 417-437, December.


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