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Isotone recursive methods for Stationary Markov Equilibra in OLG models with stochastic nonclassical production

  • Kevin Reffett

    (Arizona State University)

  • Olivier Morand

    (University of Connecticut)

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of minimal state space Markovian equilibrium decision processes (MEDPs) and stationary Markov equilibrium (SME) for a large class of stochastic overlapping generations models. In contrast to previous work, our focus is exclusively on constructive fixed point methods. In addition, we extend results obtained in earlier work to the case of more general reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods provide monotone iterative algorithms the uniformly converge to extremal Markovian equilibrium decision proceesses. Further, those methods can be tied to the computation of extremal equilibrium invariant distributions. Our methods select equilibrium that avoid many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We study cases where MEDPs are unique continuous functions, as well as provide the first results in the literature on the existence and computation of minimal state space MEDPS and SME for the case where capital income is not monotone. We show that our results on minimal state space MEDPs extend to the case of n-period stochastic OLG models. Finally, we conclude with examples common in macroeconomics such as models with social security, we provide a brief discussion of equilibrium comparative statics, and show how some of our results extend to settings with unbounded state spaces.

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Paper provided by Society for Economic Dynamics in its series 2008 Meeting Papers with number 470.

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Date of creation: 2008
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Handle: RePEc:red:sed008:470
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  1. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Working Papers 2132846, Department of Economics, W. P. Carey School of Business, Arizona State University.
  2. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  3. 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 731-44, August.
  4. Gabrielle Demange & Guy Laroque, 1999. "Social Security and Demographic Shocks," Econometrica, Econometric Society, vol. 67(3), pages 527-542, May.
  5. Kevin Reffett & Manjira Datta & Leonard Mirman & Olivier Morand, . "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Working Papers 2133476, Department of Economics, W. P. Carey School of Business, Arizona State University.
  6. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-37, October.
  7. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
  8. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
  9. Olivier F. Morand & Kevin L. Reffett, 2001. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Working papers 2001-02, University of Connecticut, Department of Economics.
  10. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
  11. Wilbur John Coleman II, 1989. "Equilibrium in a production economy with an income tax," International Finance Discussion Papers 366, Board of Governors of the Federal Reserve System (U.S.).
  12. Chattopadhyay, Subir & Gottardi, Piero, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Journal of Economic Theory, Elsevier, vol. 89(1), pages 21-67, November.
  13. 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.
  14. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
  15. Hauenschild, Nils, 2002. "Capital Accumulation in a Stochastic Overlapping Generations Model with Social Security," Journal of Economic Theory, Elsevier, vol. 106(1), pages 201-216, September.
  16. Carl Futia, 2010. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Levine's Working Paper Archive 497, David K. Levine.
  17. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-42, March.
  18. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  19. Olivier F. Morand & Kevin L. Reffett, 2005. "Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production," Working papers 2005-52, University of Connecticut, Department of Economics.
  20. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer, vol. 24(3), pages 623-643, October.
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