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Isotone Recursive Methods: the Case of Homogeneous Agents

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  • Manjira Datta

    ()
    (Arizona State University)

  • Kevin L. Reffett

    ()
    (Arizona State University)

Abstract

Over the last decade, isotone recursive methods have provided unified catalog of results on existence, characterization, and computation of Markovian Equilibrium Decision Processes (MEDPs) in infinite horizon economies where the second welfare theorem fails. Such economies include models with production nonconvexities, taxes, valued fiat money, models with monopolistic competition, behavioral heterogeneity, and incomplete markets. In this paper, we survey this emerging class of methods. Our methods use a qualitative approach to economic equilibria first introduced in the work in operations research by Veinott and Topkis. As the methods emphasize the role of order, they are amenable for obtaining conditions for monotone comparison theorems on the space of economies. We are also able to describe monotone iterative procedures that provide the needed foundations for a theory of numerical solutions for MEDPs and stationary Markov equilibrium (SME). One interesting additional result of independent interest is we construct sufficient conditions for the existence of a new class of envelope theorems for nonconcave programming problems.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-012/2.

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Date of creation: 27 Jan 2005
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Handle: RePEc:dgr:uvatin:20050012

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Related research

Keywords: Isotone recursive mappings; Markovian Equilibrium Decisions Processes; Homogeneous agents;

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  1. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, Econometric Society, vol. 60(6), pages 1387-406, November.
  2. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer, Springer, vol. 29(3), pages 505-523, November.
  3. Jianjun Miao, 2003. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," Macroeconomics, EconWPA 0310001, EconWPA.
  4. Coleman, Wilbur II, 2000. "Uniqueness of an Equilibrium in Infinite-Horizon Economies Subject to Taxes and Externalities," Journal of Economic Theory, Elsevier, Elsevier, vol. 95(1), pages 71-78, November.
  5. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  6. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 409-426, March.
  7. Olivier F. Morand & Kevin L. Reffett, 2002. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Tinbergen Institute Discussion Papers, Tinbergen Institute 02-085/2, Tinbergen Institute.
  8. Greenwood Jeremy & Huffman Gregory W., 1995. "On the Existence of Nonoptimal Equilibria in Dynamic Stochastic Economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 65(2), pages 611-623, April.
  9. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, Econometric Society, vol. 62(1), pages 157-80, January.
  10. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 1091-1104, July.
  11. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 106(5), pages 867-896, October.
  12. Tom Krebs, 2002. "Non-Existence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete," Working Papers 2002-17, Brown University, Department of Economics.
  13. Donaldson, John B. & Mehra, Rajnish, 1983. "Stochastic growth with correlated production shocks," Journal of Economic Theory, Elsevier, Elsevier, vol. 29(2), pages 282-312, April.
  14. Aiyagari, S Rao, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 109(3), pages 659-84, August.
  15. 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.
  16. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods, EconWPA 0509001, EconWPA.
  17. Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 75(1), pages 122-140, July.
  18. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 329-339, December.
  19. Becker, R.A. & Foias, C., 1998. "Implicit Programming and the Invariant Manifold for Ramsey Equilibria," Papers, Indiana - Center for Econometric Model Research 98-006, Indiana - Center for Econometric Model Research.
  20. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(1), pages 27-29, January.
  21. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Working Papers, Department of Economics, W. P. Carey School of Business, Arizona State University 2132846, Department of Economics, W. P. Carey School of Business, Arizona State University.
  22. Bizer, David S & Judd, Kenneth L, 1989. "Taxation and Uncertainty," American Economic Review, American Economic Association, American Economic Association, vol. 79(2), pages 331-36, May.
  23. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, Elsevier, vol. 7(2), pages 295-300, September.
  24. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(3), pages 479-513, June.
  25. S. Illeris & G. Akehurst, 2002. "Introduction," The Service Industries Journal, Taylor & Francis Journals, Taylor & Francis Journals, vol. 22(1), pages 1-3, January.
  26. Prescott, Edward C & Mehra, Rajnish, 1980. "Recursive Competitive Equilibrium: The Case of Homogeneous Households," Econometrica, Econometric Society, Econometric Society, vol. 48(6), pages 1365-79, September.
  27. 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, Tinbergen Institute 05-013/2, Tinbergen Institute.
  28. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, Springer, vol. 5(2), pages 209-27, March.
  29. Coleman, Wilbur II, 1997. "Equilibria in Distorted Infinite-Horizon Economies with Capital and Labor," Journal of Economic Theory, Elsevier, Elsevier, vol. 72(2), pages 446-461, February.
  30. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(2), pages 410-452, December.
  31. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
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Cited by:
  1. Woźny, Łukasz & Growiec, Jakub, 2008. "Intergenerational interactions in human capital accumulation," MPRA Paper 10308, University Library of Munich, Germany.

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