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Accuracy estimates for a numerical approach to stochastic growth models

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  • Manuel S. Santos
  • Jesus Vigo

Abstract

In this paper we develop a discretized version of the dynamic programming algorithm and derive error bounds for the approximate value and policy functions. We show that under the proposed scheme the computed value function converges quadratically to the true value function and the computed policy function converges linearly, as the mesh size of the discretization converges to zero. Moreover, the constants involved in these orders of convergence can be computed in terms of primitive data of the model. We also discuss several aspects of the implementation of our methods, and present numerical results for some commonly studied macroeconomic models.

Suggested Citation

  • Manuel S. Santos & Jesus Vigo, 1995. "Accuracy estimates for a numerical approach to stochastic growth models," Discussion Paper / Institute for Empirical Macroeconomics 107, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmem:107
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    Cited by:

    1. Grüne, Lars & Semmler, Willi & Stieler, Marleen, 2015. "Using nonlinear model predictive control for dynamic decision problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 112-133.
    2. Grune, Lars & Semmler, Willi, 2004. "Using dynamic programming with adaptive grid scheme for optimal control problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2427-2456, December.
    3. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    4. Ihrig, Jane, 2000. "Multinationals' response to repatriation restrictions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(9), pages 1345-1379, August.

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    Keywords

    Economic development;

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