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Almost Sure Convergence to Zero in Stochastic Growth Models

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Author Info
Takashi Kamihigashi (Research Institute for Economics and Business Administration, Kobe University)
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.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp140.pdf
File Format: application/pdf
File Function: First version, 2003
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Publisher Info
Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 140.

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Length: 11 pages
Date of creation: Sep 2003
Date of revision:
Handle: RePEc:kob:dpaper:140

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Related research
Keywords: Stochastic growth; Inada condition; convergence to zero.;

References listed on IDEAS
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.:

  1. Levhari, David & Srinivasan, T N, 1969. "Optimal Savings under Uncertainty," Review of Economic Studies, Blackwell Publishing, vol. 36(106), pages 153-63, April. [Downloadable!] (restricted)
  2. de Hek, Paul & Roy, Santanu, 2001. "On Sustained Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 801-13, August.
  3. Kelly, Morgan, 1992. "On endogenous growth with productivity shocks," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 47-56, October. [Downloadable!] (restricted)
  4. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September. [Downloadable!] (restricted)
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  5. Wang Yong, 1993. "Stationary Equilibria in an Overlapping Generations Economy with Stochastic Production," Journal of Economic Theory, Elsevier, vol. 61(2), pages 423-435, December. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Edmond S. Phelps, 1961. "The Accumulation of Risky Capital: A Discrete-Time Sequential Utility Analysis," Cowles Foundation Discussion Papers 109, Cowles Foundation, Yale University. [Downloadable!]
  8. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Olson, Lars & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics. [Downloadable!]
  2. 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. [Downloadable!]
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