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

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

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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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. Cuong Le Van & John Stachurski, 2006. "Parametric Continuity of Stationary Distributions," KIER Working Papers 616, Kyoto University, Institute of Economic Research.
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  6. Lawrence J. Christiano & Jonas D.M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues 94-6, Federal Reserve Bank of Chicago.
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  8. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
  9. 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.
  10. Bobenrieth Eugenio S.A. & Bobenrieth Juan R.A. & Wright Brian D., 2012. "Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-11, April.
  11. 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.
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  13. John B. Taylor & Harald Uhlig, 1989. "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. Robert E. Lucas Jr., 2003. "Macroeconomic Priorities," American Economic Review, American Economic Association, vol. 93(1), pages 1-14, March.
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