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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. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper, Federal Reserve Bank of Atlanta 2003-27, Federal Reserve Bank of Atlanta.
  2. Jinill Kim and Sunghyun Henry Kim, 2001. "Spurious Welfare Reversals in International Business Cycle Models," Computing in Economics and Finance 2001, Society for Computational Economics 3, Society for Computational Economics.
  3. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(8), pages 1179-1232, July.
  4. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  5. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2963, C.E.P.R. Discussion Papers.
  6. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, Econometric Society, vol. 77(3), pages 623-685, 05.
  7. Tesar, Linda L., 1995. "Evaluating the gains from international risksharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, Elsevier, vol. 42(1), pages 95-143, June.
  8. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1345-70, November.
  9. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  10. Danthine, Jean-Pierre & Donaldson, John B. & Mehra, Rajnish, 1989. "On some computational aspects of equilibrium business cycle theory," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 13(3), pages 449-470, July.
  11. Christiano, Lawrence J, 1990. "Linear-Quadratic Approximation and Value-Function Iteration: A Comparison," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(1), pages 99-113, January.
  12. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, Elsevier, 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. 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.
  14. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(6), pages 1025-1042, June.
  15. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 371-96, March.
  16. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  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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Cited by:
  1. Rodolphe Buda, 2013. "SIMUL 3.2: An Econometric Tool for Multidimensional Modelling," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 41(4), pages 517-524, April.
  2. Posch, Olaf & Trimborn, Timo, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Hannover Economic Papers (HEP), Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät dp-450, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  3. Olaf Posch & Timo Trimborn, 2011. "Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty," CESifo Working Paper Series 3431, CESifo Group Munich.

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