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

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Author Info

  • Kevin Reffett

    (Arizona State University)

  • Olivier Morand

    (University of Connecticut)

Abstract

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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Bibliographic Info

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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Postal: Society for Economic Dynamics Christian Zimmermann Economic Research Federal Reserve Bank of St. Louis PO Box 442 St. Louis MO 63166-0442 USA
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References

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  1. Olivier F. Morand & Kevin L. Reffett, 2002. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Tinbergen Institute Discussion Papers 02-085/2, Tinbergen Institute.
  2. 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.
  3. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer, vol. 24(3), pages 623-643, October.
  4. Carl Futia, 2010. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Levine's Working Paper Archive 497, David K. Levine.
  5. Piero Gottardi & Subir Chattopadhyay, 1999. "- Stochastic Olg Models, Market Structure And Optimality," Working Papers. Serie AD 1999-15, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. 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.
  7. 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.
  8. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Tinbergen Institute Discussion Papers 02-086/2, Tinbergen Institute.
  9. 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.
  10. 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.
  11. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-42, March.
  12. 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.
  13. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2005. "Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy," Tinbergen Institute Discussion Papers 05-013/2, Tinbergen Institute.
  14. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  15. 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.
  16. Gabrielle Demange & Guy Laroque, 1999. "Social Security and Demographic Shocks," Econometrica, Econometric Society, vol. 67(3), pages 527-542, May.
  17. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
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