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Monotone Methods for Markovian Equilibrium in Dynamic Economies

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In this paper, we provide an overview of an emerging class of "monotone map methods" in analyzing distorted equilibrium in dynamic economies. In particular, we focus on proving the existence and characterization of competitive equilibrium in nonoptimal versions of the optimal growth models. We suggest two alternative methods: an Euler equation method for a smooth, strongly concave environment, and a value function method for a non-smooth supermodular environment. We are able to extend this analysis to study models that allow for unbounded growth or a labor-leisure choice.

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Paper provided by Department of Economics, W. P. Carey School of Business, Arizona State University in its series Working Papers with number 2133476.

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Handle: RePEc:asu:wpaper:2133476

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  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. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
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  16. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
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  23. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  24. 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.
  25. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  26. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  27. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
  28. 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.
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Citations

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Cited by:
  1. 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.
  2. Takashi Kamihigashi & John Stachurski, 2012. "Existence, Uniqueness and Stability of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2012-27, Research Institute for Economics & Business Administration, Kobe University.
  3. 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.
  4. 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.
  5. Morand, Olivier F. & Reffett, Kevin L., 2003. "Existence and uniqueness of equilibrium in nonoptimal unbounded infinite horizon economies," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1351-1373, September.
  6. Leonard J Mirman & Olivier F. Morand & Kevin L. Reffett, 2004. "A Qualitative Approach to Markovian Equilibrium in Infinite Horizon Economies with Capital," Levine's Bibliography 122247000000000224, UCLA Department of Economics.
  7. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.
  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. repec:hal:wpaper:hal-00294828 is not listed on IDEAS
  10. 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.
  11. Takashi Kamihigashi & John Stachurski, 2011. "Stability of Stationary Distributions in Monotone Economies," ANU Working Papers in Economics and Econometrics 2011-561, Australian National University, College of Business and Economics, School of Economics.

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