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Almost Sure Convergence to Zero in Stochastic Growth Models

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

This paper shows that in stochastic one-sector growth models, if the production function does not satisfy the Inada condition at zero, any feasible path converges to zero with probability one provided that the shocks are sufficiently volatile. This result seems significant since, as we argue, the Inada condition at zero is difficult to justify on economic grounds. Our convergence result is extended to the case of a nonconcave production function. The generalized result applies to a wide range of stochastic growth models, including stochastic endogenous growth models, overlapping generations models, and models with nonconcave production functions.

Suggested Citation

  • Takashi Kamihigashi, 2003. "Almost Sure Convergence to Zero in Stochastic Growth Models," Discussion Paper Series 140, Research Institute for Economics & Business Administration, Kobe University.
  • Handle: RePEc:kob:dpaper:140
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    File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp140.pdf
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    References listed on IDEAS

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    7. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    8. Larry E. Jones & Rodolfo E. Manuelli & Henry E. Siu & Ennio Stacchetti, 2005. "Fluctuations in Convex Models of Endogenous Growth I: Growth Effects," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(4), pages 780-804, October.
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    Citations

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    Cited by:

    1. Raouf Boucekkine & Patrick Pintus & Benteng Zou, 2015. "Stochastic Stability of Endogenous Growth: Theory and Applications," AMSE Working Papers 1532, Aix-Marseille School of Economics, Marseille, France.
    2. Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, March.
    3. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
    4. 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.
    5. Nævdal, Eric, 2015. "Catastrophes and Expected Marginal Utility – How The Value Of The Last Fish In A Lake Is Infinity And Why We Shouldn't Care (Much)," Memorandum 08/2015, Oslo University, Department of Economics.
    6. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
    7. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    8. Takashi Kamihigashi, 2008. "The spirit of capitalism, stock market bubbles and output fluctuations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 3-28.
    9. Tapan Mitra & Gerhard Sorger, 2014. "Extinction in common property resource models: an analytically tractable example," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 41-57, September.
    10. Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2137-2147, July.
    11. repec:eee:ecolet:v:166:y:2018:i:c:p:18-24 is not listed on IDEAS
    12. Nævdal, Eric, 2016. "Catastrophes and ex post shadow prices—How the value of the last fish in a lake is infinity and why we should not care (much)," Journal of Economic Behavior & Organization, Elsevier, vol. 132(PB), pages 153-160.
    13. Kazuo Nishimura & Ryszard Rudnicki & John Stachurski, 2004. "Stochastic Growth With Nonconvexities:The Optimal Case," Department of Economics - Working Papers Series 897, The University of Melbourne.
    14. Mitra, Tapan & Roy, Santanu, 2012. "Sustained positive consumption in a model of stochastic growth: The role of risk aversion," Journal of Economic Theory, Elsevier, vol. 147(2), pages 850-880.
    15. Mitra, Tapan & Roy, Santanu, 2007. "On the possibility of extinction in a class of Markov processes in economics," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 842-854, September.
    16. Boucekkine, Raouf & Pintus, Patrick A. & Zou, Benteng, 2018. "Mean growth and stochastic stability in endogenous growth models," Economics Letters, Elsevier, vol. 166(C), pages 18-24.
    17. Kam, Timothy & Lee, Junsang, 2014. "On stationary recursive equilibria and nondegenerate state spaces: The Huggett model," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 156-159.
    18. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.

    More about this item

    Keywords

    Stochastic growth; Inada condition; Convergence to zero;

    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
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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