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Comparing accuracy of second-order approximation and dynamic programming

Author

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  • Stephanie Becker
  • Lars Grüne
  • Willi Semmler
Abstract
The accuracy of the solution of dynamic general equilibrium models has become a major issue. Recent papers, in which second-order approximations have been substituted for first-order, indicate that this change may yield a significant improvement in accuracy. Second order approximations have been used with considerable success when solving for the decision variables in both small and large-scale models. Additionally, the issue of accuracy is relevant for the approximate solution of value functions. In numerous dynamic decision problems, welfare is usually computed via this same approximation procedure. However, Kim and Kim (Journal of International Economics, 60, 471–500, 2003) have found a reversal of welfare ordering when they moved from first- to second-order approximations. Other researchers, studying the impact of monetary and fiscal policy on welfare, have faced similar challenges with respect to the accuracy of approximations of the value function. Employing a base-line stochastic growth model, this paper compares the accuracy of second-order approximations and dynamic programming solutions for both the decision variable and the value function as well. We find that, in a neighborhood of the equilibrium, the second-order approximation method performs satisfactorily; however, on larger regions, dynamic programming performs significantly better with respect to both the decision variable and the value function. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Stephanie Becker & Lars Grüne & Willi Semmler, 2007. "Comparing accuracy of second-order approximation and dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 30(1), pages 65-91, August.
    • Handle: RePEc:kap:compec:v:30:y:2007:i:1:p:65-91
    DOI: 10.1007/s10614-007-9087-1
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    Citations

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    Cited by:

    1. Atolia, Manoj & Chatterjee, Santanu & Turnovsky, Stephen J., 2010. "How misleading is linearization? Evaluating the dynamics of the neoclassical growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1550-1571, September.
    2. Grüne, Lars & Semmler, Willi, 2008. "Asset pricing with loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3253-3274, October.
    3. Alfred Greiner & Willi Semmler & Tobias Mette, 2012. "An Economic Model of Oil Exploration and Extraction," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 387-399, December.
    4. Pu Chen & Willi Semmler, 2018. "Short and Long Effects of Productivity on Unemployment," Open Economies Review, Springer, vol. 29(4), pages 853-878, September.
    5. Mittnik, Stefan & Semmler, Willi, 2012. "Regime dependence of the fiscal multiplier," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 502-522.
    6. Parra-Alvarez, Juan Carlos, 2018. "A Comparison Of Numerical Methods For The Solution Of Continuous-Time Dsge Models," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1555-1583, September.
    7. Ernst, Ekkehard & Semmler, Willi, 2010. "Global dynamics in a model with search and matching in labor and capital markets," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1651-1679, September.

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    More about this item

    Keywords

    Dynamic general equilibrium model; Approximation methods; Second-order approximation; Dynamic programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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