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On the accuracy of the estimated policy function using the Bellman contraction method

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  • Wilfredo L. Maldonado
  • Benar F. Svaiter

Abstract

In this paper we show that the approximation error of the optimal policy function in the stochastic dynamic programing problem using the policies defined by the Bellman contraction method is lower than a constant (which depends on the modulus of strong concavity of the one-period return function) times the square root of the value function approximation error. Since the Bellman's method is a contraction it results that we can control the approximation error of the policy function. This method for estimating the approximation error is robust under small numerical errors in the computation of value and policy functions.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2002 with number 30.

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Date of creation: 01 Jul 2002
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Handle: RePEc:sce:scecf2:30

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Web page: http://www.cepremap.cnrs.fr/sce2002.html/
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Keywords: Dynamic Programming; Accuracy of the estimated policy function;

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  1. Albert Marcet & David A. Marshall, 1994. "Solving nonlinear rational expectations models by parameterized expectations: convergence to stationary solutions," Discussion Paper / Institute for Empirical Macroeconomics 91, Federal Reserve Bank of Minneapolis.
  2. Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
  3. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
  4. 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.
  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. Christiano, Lawrence J, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 23-26, January.
  7. Baxter, Marianne & Crucini, Mario J & Rouwenhorst, K Geert, 1990. "Solving the Stochastic Growth Model by a Discrete-State-Space, Euler-Equation Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 19-21, January.
  8. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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Cited by:
  1. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
  2. John Stachurski, 2006. "Continuous State Dynamic Programming Via Nonexpansive Approximation," KIER Working Papers 618, Kyoto University, Institute of Economic Research.
  3. repec:ebl:ecbull:v:3:y:2003:i:1:p:1-14 is not listed on IDEAS

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