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Stochastic optimal growth with a non-compact state space

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  • Yuzhe Zhang

Abstract

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [J. Econ. Theory 4 (1972)] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 639.

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Date of creation: 2005
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Handle: RePEc:fip:fedmwp:639

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  1. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  2. Takashi Kamihigashi, 2005. "Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks," Discussion Paper Series 176, Research Institute for Economics & Business Administration, Kobe University.
  3. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
  4. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
  5. 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.
  6. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  7. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
  8. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  9. Mirman, Leonard J, 1972. "On the Existence of Steady State Measures for One Sector Growth Models with Uncertain Technology," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 271-86, June.
  10. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
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Cited by:
  1. 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.
  2. Yiyong Cai & Takashi Kamihigashi & John Stachurski, 2012. "Stochastic Optimal Growth with Risky Labor Supply," Discussion Paper Series DP2012-24, Research Institute for Economics & Business Administration, Kobe University.
  3. Gong, Liutang & Zhao, Xiaojun & Yang, Yunhong & Hengfu, Zou, 2010. "Stochastic growth with social-status concern: The existence of a unique stable distribution," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 505-518, July.
  4. Takashi Kamihigashi & John Stachurski, 2013. "Stochastic Stability in Monotone Economies," Discussion Paper Series DP2013-02, Research Institute for Economics & Business Administration, Kobe University.
  5. Halkos, George, 2009. "A Differential game approach in the case of a polluting oligopoly," MPRA Paper 23742, University Library of Munich, Germany.
  6. Liutang Gong & Xiaojun Zhao & Heng-fu Zou, 2010. "Stochastic Growth with the Social-Status Concern: The Existence of a Unique Stable Distribution," CEMA Working Papers 408, China Economics and Management Academy, Central University of Finance and 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. Takashi Kamihigashi & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Discussion Paper Series DP2014-02, Research Institute for Economics & Business Administration, Kobe University.
  9. Takashi Kamihigashi, 2006. "Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks," Discussion Paper Series 189, Research Institute for Economics & Business Administration, Kobe University.
  10. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer, vol. 54(3), pages 623-674, November.
  11. Takashi Kamihigashiw & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Working Papers 2014-402, Department of Research, Ipag Business School.
  12. 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.

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