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Inequality Constraints in Recursive Economies

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  • Rendahl Pontus

    (European University Institute)

Abstract

Dynamic models with inequality constraints pose a challenging prob- lem for two major reasons: Dynamic Programming techniques often necessitate a non established differentiability of the value function, while Euler equation based techniques have problematic or unknown convergence properties. This paper aims to resolve these two concerns: An envelope theorem is presented that establishes the differentiability of any element in the convergent sequence of approximate value functions when inequality constraints may bind. As a corollary, convergence of an iterative procedure on the Euler equation, usually referred to as time iteration, is ascertained. This procedure turns out to be very convenient from a computational perspective; dynamic economic problems with inequality constraints can be solved reliably and extremely effciently by exploiting the theoretical insights provided by the paper

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 174.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:174

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Keywords: Inequality constraints; Envelope theorem; Recursive methods; Time iteration;

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  1. Christopher Carroll, 2005. "The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems," Economics Working Paper Archive 520, The Johns Hopkins University,Department of Economics.
  2. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
  3. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.
  4. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  5. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  6. Patrick J. Kehoe & Fabrizio Perri, 2000. "International business cycles with endogenous incomplete markets," Staff Report 265, Federal Reserve Bank of Minneapolis.
  7. 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.
  8. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns," GSIA Working Papers 1997-45, Carnegie Mellon University, Tepper School of Business.
  9. Deaton, A., 1989. "Saving And Liquidity Constraints," Papers 153, Princeton, Woodrow Wilson School - Public and International Affairs.
  10. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  11. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
  12. Ellen R. McGrattan, 1993. "Solving the stochastic growth model with a finite element method," Staff Report 164, Federal Reserve Bank of Minneapolis.
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Cited by:
  1. Emilio Espino & Thomas Hintermaier, 2009. "Asset trading volume in a production economy," Economic Theory, Springer, vol. 39(2), pages 231-258, May.
  2. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
  3. Michael Grill & Johannes Brumm, 2010. "Computing Equilibria in Dynamic Models with Occasionally Binding Constraints," 2010 Meeting Papers 695, Society for Economic Dynamics.

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