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Discounting long run average growth in stochastic dynamic programs

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  • Duran, Jorge

Abstract

Finding solutions to the Bellman equation relies on restrictive boundedness assumptions. The literature on endogenous growth or business cycle models with unbounded random shocks provide with numerous examples of recursive programs in which returns are not bounded along feasible paths. In this paper we develop a method of proof that allows to account for models of this type. In applications our assumptions only imply that long run average (expected) growth is sufficiently discounted, in sharp contrast with classical assumptons either absolutely bounding growth or bounding each period (instead of long run) maximum (instead of average) growth. We discuss our work in relation to the literature and provide several examples.

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Bibliographic Info

Paper provided by CEPREMAP in its series CEPREMAP Working Papers (Couverture Orange) with number 0101.

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Length: 26 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:cpm:cepmap:0101

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  1. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 185-200, January.
  2. DUTTA, Jayasri & MICHEL, Philippe, 1995. "The Distribution of Wealth with Imperfect Altruism," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1995058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(2), pages 326-345, April.
  4. Javier Díaz-Giménez & Vincenzo Quadrini & José-Víctor Ríos-Rull, 1997. "Dimensions of inequality: facts on the U.S. distributions of earnings, income, and wealth," Quarterly Review, Federal Reserve Bank of Minneapolis, Federal Reserve Bank of Minneapolis, issue Spr, pages 3-21.
  5. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Growth with Many Consumers," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 518, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27.
  7. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 82(1), pages 167-189, September.
  8. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 25(4), pages 391-442.
  9. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 843-67, June.
  10. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 98(5), pages 1008-38, October.
  11. Streufert, Peter A., 1996. "Biconvergent stochastic dynamic programming, asymptotic impatience, and 'average' growth," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 20(1-3), pages 385-413.
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Cited by:
  1. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 43(3-4), pages 477-500, April.
  2. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer, Springer, vol. 46(3), pages 455-474, April.
  3. LE VAN, Cuong & VAILAKIS, Yiannis, 2002. "Recursive utility and optimal growth with bounded or unbounded returns," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2002055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Francisco Xavier Lores, 2001. "Cyclical Behaviour Of Consumption Of Non-Durable Goods: Spain Versus U.S.A," Economics Working Papers, Universidad Carlos III, Departamento de Economía we014710, Universidad Carlos III, Departamento de Economía.

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