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Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks

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  • Kamihigashi, Takashi

Abstract

This paper studies a one-sector stochastic optimal growth model with i.i.d. productivity shocks in which utility is allowed to be bounded or unbounded, the shocks are allowed to be bounded or unbounded, and the production function is not required to satisfy the Inada conditions at zero and infinity. Our main results are threefold. First, we confirm the Euler equation as well as the existence of a continuous optimal policy function under a minimal set of assumptions. Second, we establish the existence of an invariant distribution under quite general assumptions. Third, we show that the output density converges to a unique invariant density independently of initial output under the assumption that the shock distribution has a density whose support is an interval, bounded or unbounded. In addition, we provide existence and stability results for general one-dimensional Markov processes.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 43 (2007)
Issue (Month): 3-4 (April)
Pages: 477-500

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Handle: RePEc:eee:mateco:v:43:y:2007:i:3-4:p:477-500

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Web page: http://www.elsevier.com/locate/jmateco

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References

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  1. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
  2. Takashi Kamihigashi & Santanu Roy, 2005. "A nonsmooth, nonconvex model of optimal growth," Discussion Paper Series 173, Research Institute for Economics & Business Administration, Kobe University.
  3. Jorge Durán, 2002. "Discounting Long Run Average Growth In Stochastic Dynamic Programs," Working Papers. Serie AD 2002-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer, vol. 23(1), pages 39-71, December.
  5. Takashi Kamihigashi, 2006. "Almost sure convergence to zero in stochastic growth models," Economic Theory, Springer, vol. 29(1), pages 231-237, September.
  6. Yuzhe Zhang, 2005. "Stochastic optimal growth with a non-compact state space," Working Papers 639, Federal Reserve Bank of Minneapolis.
  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. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
  9. Mitra, Tapan & Roy, Santanu, 2003. "Optimal Exploitation of Renewable Resources under Uncertainty and the Extinction of Species," Working Papers 03-10, Cornell University, Center for Analytic Economics.
  10. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.
  11. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  12. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
  13. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  14. 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.
  15. 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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Citations

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Cited by:
  1. Yiyong Cai & Takashi Kamihigashi & John Stachurski, 2012. "Stochastic Optimal Growth with Risky Labor Supply," Discussion Paper Series DP2012-24, Research Institute for Economics & Business Administration, Kobe University.
  2. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research.
  3. Takashi Kamihigashi & John Stachurski, 2011. "Stability of Stationary Distributions in Monotone Economies," ANU Working Papers in Economics and Econometrics 2011-561, Australian National University, College of Business and Economics, School of Economics.
  4. Stachurski, John & Kamihigashi, Takashi, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
  5. Gong, Liutang & Zhao, Xiaojun & Yang, Yunhong & Hengfu, Zou, 2010. "Stochastic growth with social-status concern: The existence of a unique stable distribution," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 505-518, July.
  6. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.
  7. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
  8. 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.
  9. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
  10. Liutang Gong & Xiaojun Zhao & Heng-fu Zou, 2010. "Stochastic Growth with the Social-Status Concern: The Existence of a Unique Stable Distribution," CEMA Working Papers 408, China Economics and Management Academy, Central University of Finance and Economics.
  11. R. Anton Braun & Huiyu Li & John Stachurski, 2011. "Generalized Look-Ahead Methods for Computing Stationary Densities," ANU Working Papers in Economics and Econometrics 2011-558, Australian National University, College of Business and Economics, School of Economics.

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