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Inequality Constraints in Recursive Economies

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  • Pontus Rendahl

Abstract

Dynamic models with inequality constraints pose a challenging problem 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 efficiently by exploiting the theoretical insights provided by the paper.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2006/6.

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Date of creation: 2006
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Handle: RePEc:eui:euiwps:eco2006/6

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

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  1. 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.
  2. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 106(5), pages 867-896, October.
  3. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1221-48, September.
  4. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(1), pages 27-29, January.
  5. Carroll, Christopher D., 2005. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," CFS Working Paper Series 2005/18, Center for Financial Studies (CFS).
  6. Patrick J. Kehoe & Fabrizio Perri, 2000. "International Business Cycles with Endogenous Incomplete Markets," NBER Working Papers 7870, National Bureau of Economic Research, Inc.
  7. Ellen R. McGrattan, 1993. "Solving the stochastic growth model with a finite element method," Staff Report, Federal Reserve Bank of Minneapolis 164, Federal Reserve Bank of Minneapolis.
  8. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 1997-45, Carnegie Mellon University, Tepper School of Business.
  9. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 727-32, May.
  10. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, Econometric Society, vol. 70(2), pages 583-601, March.
  11. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  12. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, Econometric Society, vol. 68(6), pages 1377-1402, November.
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Cited by:
  1. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 34(10), pages 2074-2088, October.
  2. Michael Grill & Johannes Brumm, 2010. "Computing Equilibria in Dynamic Models with Occasionally Binding Constraints," 2010 Meeting Papers 695, Society for Economic Dynamics.
  3. Thomas Hintermaier & Emilio Espino, 2005. "Asset Trading Volume in a Production Economy," 2005 Meeting Papers 363, Society for Economic Dynamics.

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