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

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Author Info
Wilfredo Leiva Maldonado () (Universidade Federal Fluminense)
Benar Fux Svaiter () (Instituto de Matematica Pura e Aplicada)

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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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Publisher Info
Article provided by Economics Bulletin in its journal Economics Bulletin.

Volume (Year): 3 (2001)
Issue (Month): ()
Pages: 1-8
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Handle: RePEc:ebl:ecbull:eb-01c60003

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Related research
Keywords: Stochastic dynamic programing problem; estimation of the policy function;

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Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming

References listed on IDEAS
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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. [Downloadable!]
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  2. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December. [Downloadable!] (restricted)
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  3. 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.
  4. 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.
  5. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July. [Downloadable!] (restricted)
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  6. 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.
  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. 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.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance. [Downloadable!]
  2. Humberto Moreira & Wilfredo Maldonado, 2003. "A contractive method for computing the stationary solution of the Euler equation," Economics Bulletin, Economics Bulletin, vol. 3(1), pages 1-14. [Downloadable!]
    Other versions:
  3. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer, vol. 31(2), pages 141-160, March. [Downloadable!] (restricted)
    Other versions:
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