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A foundation for the solution of consumption-saving behavior with a borrowing constraint and unbounded marginal utility

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  • Bobenrieth H., Eugenio S.A.
  • Bobenrieth H., Juan R.A.
  • Wright, Brian D.

Abstract

Models of precautionary saving or storage include cases where the marginal value of accumulated balances is unbounded, with an invariant distribution with infinite mean. Based on a uniform continuity argument, we show that a model of saving with bounded marginal value can be used to approximate the unbounded marginal value function, and the quantiles of its invariant distribution, arbitrarily accurately. These results offer a foundation for a strategy for numerical solution of marginal values in cases where they are unbounded, and for derivation of the quantiles of their invariant distributions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 3 (March)
Pages: 695-708

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:695-708

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  1. Eugenio S. A. Bobenrieth H. & Juan R. A. Bobenrieth H. & Brian D. Wright, 2002. "A Commodity Price Process with a Unique Continuous Invariant Distribution Having Infinite Mean," Econometrica, Econometric Society, vol. 70(3), pages 1213-1219, May.
  2. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
  3. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
  4. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-48, September.
  5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  6. Cuong Le Van & John Stachurski, 2007. "Parametric continuity of stationary distributions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101157, HAL.
  7. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper 9711, Federal Reserve Bank of Cleveland.
  8. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  9. Eugenio Bobenrieth & Juan Bobenrieth & Brian Wright, 2008. "Strict concavity of the value function for a family of dynamic accumulation models," Working Papers 02-2008, Departamento de Economía, Universidad de Concepción.
  10. Robert E. Lucas Jr., 2003. "Macroeconomic Priorities," American Economic Review, American Economic Association, vol. 93(1), pages 1-14, March.
  11. Leonard J Mirman & Olivier F. Morand & Kevin L. Reffett, 2004. "A Qualitative Approach to Markovian Equilibrium in Infinite Horizon Economies with Capital," Levine's Bibliography 122247000000000224, UCLA Department of Economics.
  12. Wright, Brian D & Williams, Jeffrey C, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, MIT Press, vol. 99(1), pages 169-92, February.
  13. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  14. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  15. repec:ags:afjare:141665 is not listed on IDEAS
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Cited by:
  1. Wright, Brian, 2009. "International grain reserves and other instruments to address volatility in grain markets," Policy Research Working Paper Series 5028, The World Bank.

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