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Almost Sure Convergence to Zero in Stochastic Growth Models

  • Takashi Kamihigashi

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

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 Function: First version, 2003
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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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  1. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  2. 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.
  3. 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.
  4. Kelly, Morgan, 1992. "On endogenous growth with productivity shocks," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 47-56, October.
  5. Edmond S. Phelps, 1961. "The Accumulation of Risky Capital: A Discrete-Time Sequential Utility Analysis," Cowles Foundation Discussion Papers 109, Cowles Foundation for Research in Economics, Yale University.
  6. Danthine, Jean-Pierre & Donaldson, John B, 1981. "Certainty Planning in an Uncertain World: A Reconsideration," Review of Economic Studies, Wiley Blackwell, vol. 48(3), pages 507-10, July.
  7. 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.
  8. Levhari, David & Srinivasan, T N, 1969. "Optimal Savings under Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 36(106), pages 153-63, April.
  9. 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.
  10. Boylan, Edward S., 1979. "On the avoidance of extinction in one-sector growth models," Journal of Economic Theory, Elsevier, vol. 20(2), pages 276-279, April.
  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. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
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