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Comparing accuracy of second-order approximation and dynamic programming

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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

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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 30 (2007)
Issue (Month): 1 (August)
Pages: 65-91

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Handle: RePEc:kap:compec:v:30:y:2007:i:1:p:65-91

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: Dynamic general equilibrium model; Approximation methods; Second-order approximation; Dynamic programming;

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  1. Pierpaolo Benigno & Michael Woodford, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," NBER Working Papers 12672, National Bureau of Economic Research, Inc.
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  3. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics.
  4. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
  5. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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  12. Gong, Gang & Semmler, Willi, 2006. "Stochastic Dynamic Macroeconomics: Theory and Empirical Evidence," OUP Catalogue, Oxford University Press, number 9780195301625.
  13. 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.
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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. Juan Carlos Parra-Alvarez, 2013. "A comparison of numerical methods for the solution of continuous-time DSGE models," CREATES Research Papers 2013-39, School of Economics and Management, University of Aarhus.
  3. Alfred Greiner & Willi Semmler & Tobias Mette, 2012. "An Economic Model of Oil Exploration and Extraction," Computational Economics, Society for Computational Economics, vol. 40(4), pages 387-399, December.
  4. Mittnik, Stefan & Semmler, Willi, 2012. "Regime dependence of the fiscal multiplier," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 502-522.
  5. 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.
  6. Grüne, Lars & Semmler, Willi, 2008. "Asset pricing with loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3253-3274, October.

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