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Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies

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  • Olivier F. Morand

    ()
    (University of Connecticut)

  • Kevin L. Reffett

    ()
    (Arizona State University)

Abstract

In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in which the state-space is unbounded. Important examples of such economies are single-sector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are weIl known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and presents a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 02-085/2.

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Date of creation: 04 Sep 2002
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Handle: RePEc:dgr:uvatin:20020085

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Web page: http://www.tinbergen.nl

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Keywords: Equilibrium; Dynamic Models; Unbounded; Nonoptimal;

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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. 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.
  3. Robert E. Lucas Jr. & Nancy L. Stokey, 1984. "Money and Interest in Cash-In-Advance Economy," Discussion Papers 628, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  6. Jovanovic, Boyan & Rosenthal, Robert W., 1986. "Anonymous Sequential Games," Working Papers 86-12, C.V. Starr Center for Applied Economics, New York University.
  7. 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.
  8. Fernando Alvarez & Andrew Atkeson & Patrick J. Kehoe, 2000. "Money, interest rates, and exchange rates with endogenously segmented asset markets," Working Papers 605, Federal Reserve Bank of Minneapolis.
  9. 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.
  10. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
  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. James Bergin & Dan Bernhardt, 1989. "Anonymous Sequential Games with Aggregate Uncertainty," Working Papers 760, Queen's University, Department of Economics.
  13. 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.
  14. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1008-38, October.
  15. Greenwood, J. & Huffman, G.W., 1993. "On the Existence of Nonoptimal Equilibria," RCER Working Papers 370, University of Rochester - Center for Economic Research (RCER).
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Citations

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Cited by:
  1. Kevin Reffett & Olivier Morand, . "On the Existence and Characterization of Markovian Equilibrium in Models with Simple Non-paternalistic Altruism," Working Papers 2133478, Department of Economics, W. P. Carey School of Business, Arizona State University.
  2. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00294828, HAL.
  3. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer, vol. 29(3), pages 505-523, November.
  4. 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.
  5. 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.
  6. 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.
  7. Crettez, Bertrand & Morhaim, Lisa, 2012. "Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 197-206.
  8. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
  9. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation," Working Papers hal-00294828, HAL.
  10. 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.
  11. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Nonclassical Brock-Mirman Economies," Working Papers 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.

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