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Markovian equilibrium in infinite horizon economies with incomplete markets and public policy

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  • Datta, Manjira
  • Mirman, Leonard J.
  • Morand, Olivier F.
  • Reffett, Kevin L.

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

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 41 (2005)
Issue (Month): 4-5 (August)
Pages: 505-544

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Handle: RePEc:eee:mateco:v:41:y:2005:i:4-5:p:505-544

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, Econometric Society, vol. 73(6), pages 1939-1976, November.
  2. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 1(01), pages 45-75, January.
  3. Felix Kubler & Karl Schmedders, 2001. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1319, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. 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.
  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. Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 75(1), pages 122-140, July.
  8. 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.
  9. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, Econometric Society, vol. 62(1), pages 157-80, January.
  10. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(2), pages 410-452, December.
  11. Wilbur John Coleman II, 1989. "Equilibrium in a production economy with an income tax," International Finance Discussion Papers, Board of Governors of the Federal Reserve System (U.S.) 366, Board of Governors of the Federal Reserve System (U.S.).
  12. Santos, Manuel S., 2002. "On Non-existence of Markov Equilibria in Competitive-Market Economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 105(1), pages 73-98, July.
  13. Bergin, James & Bernhardt, Dan, 1992. "Anonymous sequential games with aggregate uncertainty," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 21(6), pages 543-562.
  14. 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.
  15. Jianjun Miao, 2004. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," CEMA Working Papers, China Economics and Management Academy, Central University of Finance and Economics 460, China Economics and Management Academy, Central University of Finance and Economics.
  16. Judd, Kenneth L. & Kubler, Felix & Schmedders, Karl, 2000. "Computing equilibria in infinite-horizon finance economies: The case of one asset," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(5-7), pages 1047-1078, June.
  17. Paul M Romer, 1999. "Increasing Returns and Long-Run Growth," Levine's Working Paper Archive 2232, David K. Levine.
  18. 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.
  19. Kevin Reffett & Manjira Datta & Leonard Mirman & Olivier Morand, . "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Working Papers, Department of Economics, W. P. Carey School of Business, Arizona State University 2133476, Department of Economics, W. P. Carey School of Business, Arizona State University.
  20. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer, Springer, vol. 29(3), pages 505-523, November.
  21. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 329-339, December.
  22. Jeremy Greenwood & Gregory W. Huffman, 1993. "On the existence of nonoptimal equilibria in dynamic stochastic economies," Research Paper, Federal Reserve Bank of Dallas 9330, Federal Reserve Bank of Dallas.
  23. Jorge DurÂn, 2000. "On dynamic programming with unbounded returns," Economic Theory, Springer, Springer, vol. 15(2), pages 339-352.
  24. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 16(3), pages 259-273, June.
  25. Olivier F. Morand & Kevin L. Reffett, 2001. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Working papers, University of Connecticut, Department of Economics 2001-02, University of Connecticut, Department of Economics.
  26. 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.
  27. 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, Elsevier, vol. 103(2), pages 377-410, April.
  28. Schechtman, Jack & Escudero, Vera L. S., 1977. "Some results on "an income fluctuation problem"," Journal of Economic Theory, Elsevier, Elsevier, vol. 16(2), pages 151-166, December.
  29. 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.
  30. 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.
  31. Kenneth L. Judd & Felix Kubler & Karl Schmedders, 2003. "Asset Trading Volume with Dynamically Complete Markets and Heterogeneous Agents," Journal of Finance, American Finance Association, American Finance Association, vol. 58(5), pages 2203-2218, October.
  32. Becker, Robert A, 1985. "Comparative Dynamics in Aggregate Models of Optimal Capital Accumulation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 100(4), pages 1235-56, November.
  33. Tom Krebs, 2002. "Non-Existence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete," Working Papers, Brown University, Department of Economics 2002-17, Brown University, Department of Economics.
  34. Scheinkman, Jose A & Weiss, Laurence, 1986. "Borrowing Constraints and Aggregate Economic Activity," Econometrica, Econometric Society, Econometric Society, vol. 54(1), pages 23-45, January.
  35. 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.
  36. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 62(4), pages 745-81, July.
  37. Becker, Robert A, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 95(2), pages 375-82, September.
  38. Mark Huggett, 1995. "The one-sector growth model with idiosyncratic shocks," Discussion Paper / Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis 105, Federal Reserve Bank of Minneapolis.
  39. Santos, M.S., 1989. "Differentiability And Comparative Analysis In Discrete-Time Infinite-Horizon Optimization Problems," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 127-89, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  40. Becker, Robert A., 1985. "Capital income taxation and perfect foresight," Journal of Public Economics, Elsevier, Elsevier, vol. 26(2), pages 147-167, March.
  41. Tom Krebs, 2003. "Human Capital Risk And Economic Growth," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 118(2), pages 709-744, May.
  42. Danthine, Jean-Pierre & Donaldson, John B, 1981. "Stochastic Properties of Fast vs. Slow Growing Economies," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1007-33, June.
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Cited by:
  1. Alexander W. Richter & Nathaniel A. Throckmorton, 2014. "The Zero Lower Bound: Frequency, Duration, and Numerical Convergence," Auburn Economics Working Paper Series, Department of Economics, Auburn University auwp2014-09, Department of Economics, Auburn University.
  2. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 43(3-4), pages 287-317, April.
  3. 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.
  4. 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.
  5. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer, Springer, vol. 29(3), pages 505-523, November.
  6. 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, Elsevier, vol. 43(3-4), pages 501-522, April.
  7. repec:hal:journl:halshs-00101237 is not listed on IDEAS
  8. Kevin Reffett & Olivier Morand, 2008. "Isotone recursive methods for Stationary Markov Equilibra in OLG models with stochastic nonclassical production," 2008 Meeting Papers, Society for Economic Dynamics 470, Society for Economic Dynamics.
  9. 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.
  10. 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.

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