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Comparing Accuracy of Second Order Approximation and Dynamic Programming

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  • Willi Semmler

    ()
    (Economics New School University and CEM Bielefeld)

  • Stephanie Becker

    (University of Bayreuth)

  • Lars Gruene

    (University of Bayreuth)

Abstract

The accuracy of the solution of dynamic general equilibrium models has become a major issue. Recent papers, substituting second order for first order approximations, have shown to obtain significant differences in accuracy. Second order approximations have had some considerable success in solving the policy function of small as well as large scale models. Yet, the issue of accuracy is also relevant for the approximate solution of the value function. In numerous dynamic decision problems welfare needs to be computed through the approximation of the value function. Kim and Kim (2003), for example, find a reversal of welfare ordering by moving from first to second order approximations. Studies of the impact of monetary and fiscal policy on welfare have also to deal with the accuracy of the value function. Employing the base line stochastic growth model this paper compares the accuracy of the second order approximation and dynamic programming solution for both the policy as well as the value functions. We find that dynamic programming performs better with respect to both.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 469.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:469

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  1. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report 171, Federal Reserve Bank of Minneapolis.
  2. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  3. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, Spring.
  4. Benigno, Pierpaolo & Woodford, Michael, 2006. "Linear-Quadratic Approximation of Optimal Policy Problems," CEPR Discussion Papers 5964, C.E.P.R. Discussion Papers.
  5. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
  6. Jinill Kim & Sunghyun Henry Kim, 1999. "Spurious Welfare Reversals in International Business Cycle Models," Virginia Economics Online Papers 319, University of Virginia, Department of Economics.
  7. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  8. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Optimal Fiscal and Monetary Policy Under Sticky Prices," NBER Working Papers 9220, National Bureau of Economic Research, Inc.
  9. Pierpaolo Benigno & Michael Woodford, 2004. "Optimal taxation in an RBC model: A linear-quadratic approach," Discussion Papers 0405-16, Columbia University, Department of Economics.
  10. Collard, Fabrice & Juillard, Michel, 1999. "Accuracy of stochastic perturbuation methods: the case of asset pricing models," CEPREMAP Working Papers (Couverture Orange) 9922, CEPREMAP.
  11. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
  12. Gong, Gang & Semmler, Willi, 2006. "Stochastic Dynamic Macroeconomics: Theory and Empirical Evidence," OUP Catalogue, Oxford University Press, number 9780195301625, Octomber.
  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.
  14. 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.
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Cited by:
  1. 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.
  2. 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.
  3. Grüne, Lars & Semmler, Willi, 2008. "Asset pricing with loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3253-3274, October.
  4. 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.
  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. 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.

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