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Stochastic Growth with the Social-Status Concern: The Existence of a Unique Stable Distribution


  • Liutang Gong

    (Guanghua School of Management, Peking University)

  • Xiaojun Zhao

    (Guanghua School of Management, Peking University)

  • Heng-fu Zou

    (China Economics and Management Academy, CUFE)


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

Suggested Citation

  • 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.
  • Handle: RePEc:cuf:wpaper:408

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    References listed on IDEAS

    1. Zou, Heng-fu, 1994. "'The spirit of capitalism' and long-run growth," European Journal of Political Economy, Elsevier, vol. 10(2), pages 279-293, July.
    2. 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.
    3. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    4. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    5. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    6. 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 108-132, February.
    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. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    9. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    10. Fershtman, Chaim & Weiss, Yoram, 1993. "Social Status, Culture and Economic Performance," Economic Journal, Royal Economic Society, vol. 103(419), pages 946-959, July.
    11. 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.
    12. 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.
    13. Heng-fu Zou, 1995. "The spirit of capitalism and savings behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 28(1), pages 131-143, September.
    14. 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. Wang, Haijun, 2016. "Precautionary saving demand and consumption dynamics with the spirit of capitalism and regime switching," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 48-65.
    2. 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.
    3. Stachurski, John & Kamihigashi, Takashi, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.

    More about this item


    Stochastic growth; the Spirit of capitalism; Stochastic dominance; Multiple equilibria;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models


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