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A New Algorithm for Solving Dynamic Stochastic Macroeconomic Models

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  • Kevin Salyer
  • Victor Dorofeenko
  • Gabriel Lee

    (Department of Economics, University of California Davis)

Abstract

We introduce a new algorithm that can be used to solve stochastic dynamic general equilibrium models. This approach exploits the fact that the equations defining equilibrium can be viewed as a set of differential algebraic equations in the neighborhood of the steady-state. Then a modified recursive upwind Gauss Seidel method can be used to determine the global solution. This method, within the context of a standard real business cycle model, is compared to projection, perturbation, and linearization approaches and demonstrated to be fast and globally accurate. This comparison is done within a discrete state setting with heteroskedasticity in the technology shocks. It is shown that linearization methods perform poorly in this environment even though the unconditional variance of shocks is relatively small.

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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 62.

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Length: 26
Date of creation: 29 Nov 2005
Date of revision:
Handle: RePEc:cda:wpaper:06-2

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Related research

Keywords: numerical methods; projection methods; real business cycles;

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References

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  1. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  2. 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.
  3. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  4. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  5. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  6. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for Solving Dynamic Models with Occasionally Binding Constraints," NBER Technical Working Papers 0218, National Bureau of Economic Research, Inc.
  7. Jean-Pierre DANTHINE & John B. DONALDSON & Rajnish MEHRA, 1988. "On some computational Aspects of Equilibrium Business Cycle Theory," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 8810, Université de Lausanne, Faculté des HEC, DEEP.
  8. 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.
  9. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  11. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
  12. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585 Elsevier.
  13. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  14. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
  15. Christiano, Lawrence J, 1990. "Linear-Quadratic Approximation and Value-Function Iteration: A Comparison," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 99-113, January.
  16. Tesar, Linda L., 1995. "Evaluating the gains from international risksharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 42(1), pages 95-143, June.
  17. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
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Citations

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Cited by:
  1. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
  2. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, School of Economics and Management, University of Aarhus.
  3. Rodolphe Buda, 2013. "SIMUL 3.2: An Econometric Tool for Multidimensional Modelling," Computational Economics, Society for Computational Economics, vol. 41(4), pages 517-524, April.

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