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Inequality Constraints in Recursive Economies

  • Pontus Rendahl

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

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Date of creation: 2006
Date of revision:
Handle: RePEc:eui:euiwps:eco2006/6
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  1. 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.
  2. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
  3. Deaton, A., 1989. "Saving And Liquidity Constraints," Papers 153, Princeton, Woodrow Wilson School - Public and International Affairs.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  9. Ellen R. McGrattan, 1993. "Solving the stochastic growth model with a finite element method," Staff Report 164, Federal Reserve Bank of Minneapolis.
  10. Krusell, Per & Smith, Anthony A., 1997. "Income And Wealth Heterogeneity, Portfolio Choice, And Equilibrium Asset Returns," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 387-422, June.
  11. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  12. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
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