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Discounting long run average growth in stochastic dynamic programs

  • Duran, Jorge

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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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. Streufert, Peter A., 1996. "Biconvergent stochastic dynamic programming, asymptotic impatience, and 'average' growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 385-413.
  2. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
  3. Dutta, Jayasri & Michel, Philippe, 1998. "The Distribution of Wealth with Imperfect Altruism," Journal of Economic Theory, Elsevier, vol. 82(2), pages 379-404, October.
  4. 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, vol. 98(5), pages 1008-38, October.
  5. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June.
  6. 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, issue Spr, pages 3-21.
  7. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442.
  8. Ellen R. McGrattan, 1998. "A defense of AK growth models," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 13-27.
  9. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  10. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  11. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
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