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Stochastic growth with social-status concern: The existence of a unique stable distribution

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  • Gong, Liutang
  • Zhao, Xiaojun
  • Yang, Yunhong
  • Hengfu, Zou

Abstract

This paper extends Kurz's (1968) growth model to a stochastic growth framework with social-status concern and unbounded production shocks. Using the stochastic monotonicity of a stochastic dynamic system and the methods adopted in Zhang (2007), the existence, uniqueness, and stability of invariant distribution are investigated. Different from the existence of multiple steady states under certainty, it is shown here that there exists a unique stable invariant distribution under uncertainty.

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Bibliographic Info

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

Volume (Year): 46 (2010)
Issue (Month): 4 (July)
Pages: 505-518

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Handle: RePEc:eee:mateco:v:46:y:2010:i:4:p:505-518

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Stochastic growth Social-status concern Multiple equilibria Invariant distribution;

References

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  1. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-42, March.
  2. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
  3. Heng-fu Zou, 1995. "The spirit of capitalism and savings behavior," CEMA Working Papers 79, China Economics and Management Academy, Central University of Finance and Economics.
  4. Fershtman, Chaim & Murphy, Kevin M & Weiss, Yoram, 1996. "Social Status, Education, and Growth," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 108-32, February.
  5. 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.
  6. Harold L. Cole & George J. Mailath & Andrew Postlewaite, . ""Incorporating Concern for Relative Wealth into Economic Models''," CARESS Working Papres 95-14, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  7. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
  8. 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.
  9. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  10. Chaim Fershtman & Yoram Weiss, 1991. "Social Status, Culture and Economic Performance," Discussion Papers 1007, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
  12. Gong, Liutang & Zou, Heng-fu, 2002. "Direct preferences for wealth, the risk premium puzzle, growth, and policy effectiveness," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 247-270, February.
  13. Ricard Torres, 1990. "Stochastic Dominance," Discussion Papers 905, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Gurdip S. Bakshi & Zhiwu Chen, 1996. "The Spirit of Capitalism and Stock-Market Prices," CEMA Working Papers 511, China Economics and Management Academy, Central University of Finance and Economics.
  15. Heng-fu Zou, 1995. "'The spirit of capitalism' and long-run growth," CEMA Working Papers 94, China Economics and Management Academy, Central University of Finance and Economics.
  16. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
  17. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
  18. Cole, Harold L & Mailath, George J & Postlewaite, Andrew, 1992. "Social Norms, Savings Behavior, and Growth," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1092-1125, December.
  19. 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.
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Cited by:
  1. 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.
  2. 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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