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Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy

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  • Manjira Datta

    ()
    (Arizona State University)

  • Leonard J. Mirman

    (University of Virginia)

  • Olivier F. Morand

    (University of Connecticut)

  • Kevin L. Reffett

    ()
    (Arizona State University)

Abstract

We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitizian Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitzian (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact non-linear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-013/2.

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Date of creation: 27 Jan 2005
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Handle: RePEc:dgr:uvatin:20050013

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Keywords: Markovian equilibrium; isotone iterative fixed point constructions;

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Cited by:
  1. Cuong Le Van & Manh-Hung Nguyen & Yiannis Vailakis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101237, HAL.
  2. repec:hal:journl:halshs-00101237 is not listed on IDEAS
  3. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer, Springer, vol. 29(3), pages 505-523, November.
  4. Alexander W. Richter & Nathaniel A. Throckmorton, 2013. "The Zero Lower Bound: Frequency, Duration, and Determinacy," Auburn Economics Working Paper Series, Department of Economics, Auburn University auwp2013-16, Department of Economics, Auburn University.
  5. Todd B. Walker & Alexander W. Richter & Nathaniel A. Throckmorton, 2014. "Accuracy, Speed and Robustness of Policy Function Iteration," Auburn Economics Working Paper Series, Department of Economics, Auburn University auwp2014-08, Department of Economics, Auburn University.
  6. 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, Elsevier, vol. 139(1), pages 75-98, March.
  7. 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.
  8. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers, Tinbergen Institute 05-012/2, Tinbergen Institute.
  9. 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.
  10. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Nonclassical Brock-Mirman Economies," Working Papers, Department of Economics, W. P. Carey School of Business, Arizona State University 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.

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