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

Author

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  • Wilfredo Leiva Maldonado

    () (Universidade Federal Fluminense)

  • Benar Fux Svaiter

    () (Instituto de Matematica Pura e Aplicada)

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.

Suggested Citation

  • Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
  • Handle: RePEc:ebl:ecbull:eb-01c60003
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    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," Working Paper Series, Macroeconomic Issues 94-20, Federal Reserve Bank of Chicago.
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    3. 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.
    4. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    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. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    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. 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.
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    Cited by:

    1. Maldonado, Wilfredo L. & Svaiter, B.F., 2007. "Holder continuity of the policy function approximation in the value function approximation," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 629-639, June.
    2. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    3. Maldonado, Wilfredo L. & Moreira, Humberto Luiz Ataíde, 2006. "Solving Euler Equations: Classical Methods and the C^1 Contraction Mapping Method Revisited," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 60(2), November.
    4. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
    5. repec:ebl:ecbull:v:3:y:2003:i:1:p:1-14 is not listed on IDEAS

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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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