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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 considers the resource constraint commonly used in stochastic one-sector growth models. Shocks are not required to be i.i.d. It is shown that any feasible path converges to zero exponentially fast almost surely under a certain condition. In the case of multiplicative shocks, the condition means that the shocks are sufficiently volatile. Convergence is faster the larger their volatility is, and the smaller the maximum average product of capital is.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp170.pdf
File Function: Revised version, 2005
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 170.

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Length: 10 pages
Date of creation: Sep 2003
Date of revision: May 2005
Handle: RePEc:kob:dpaper:170

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Keywords: Stochastic growth; Inada condition; Convergence to zero; Extinction;

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References

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  1. 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.
  2. 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.
  3. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
  4. 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.
  5. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
  6. Kelly, Morgan, 1992. "On endogenous growth with productivity shocks," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 47-56, October.
  7. 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.
  8. 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.
  9. Levhari, David & Srinivasan, T N, 1969. "Optimal Savings under Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 36(106), pages 153-63, April.
  10. 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.
  11. 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.
  12. 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.
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Citations

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Cited by:
  1. Takashi Kamihigashi, 2007. "The Spirit of Capitalism, Stock Market Bubbles, and Output Fluctuations," Discussion Paper Series 205, Research Institute for Economics & Business Administration, Kobe University, revised Oct 2007.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, 03.
  7. 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.
  8. Mitra, Tapan & Roy, Santanu, 2010. "Sustained Positive Consumption in a Model of Stochastic Growth: The Role of Risk Aversion," Working Papers 10-03, Cornell University, Center for Analytic Economics.
  9. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.

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