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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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Keywords: Dynamic Programming; Accuracy of the estimated policy function;

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  1. 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.
  2. 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.
  3. Albert Marcet & David A. Marshall, 1994. "Solving nonlinear rational expectations models by parameterized expectations: convergence to stationary solutions," Working Paper Series, Macroeconomic Issues 94-20, Federal Reserve Bank of Chicago.
  4. Wilbur John Coleman II, 1989. "Equilibrium in a production economy with an income tax," International Finance Discussion Papers 366, Board of Governors of the Federal Reserve System (U.S.).
  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. 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.
  7. 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.
  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. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Society for Computational Economics, vol. 31(2), pages 141-160, March.
  2. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
  3. repec:ebl:ecbull:v:3:y:2003:i:1:p:1-14 is not listed on IDEAS

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