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Almost sure convergence to zero in stochastic growth models

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  • Takashi Kamihigashi

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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://hdl.handle.net/10.1007/s00199-005-0006-1
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 29 (2006)
Issue (Month): 1 (September)
Pages: 231-237

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Handle: RePEc:spr:joecth:v:29:y:2006:i:1:p:231-237

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Related research

Keywords: Stochastic growth; Inada condition; Convergence to zero; Extinction; C61; C62; E30; O41;

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References

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  1. 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.
  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. 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. Levhari, David & Srinivasan, T N, 1969. "Optimal Savings under Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 36(106), pages 153-63, April.
  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. 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.
  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. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
  9. 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.
  10. Kelly, Morgan, 1992. "On endogenous growth with productivity shocks," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 47-56, October.
  11. 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.
  12. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, 03.
  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. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.
  7. 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.
  8. 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.
  9. 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.

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