IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v34y2010i3p388-403.html
   My bibliography  Save this article

A new algorithm for solving dynamic stochastic macroeconomic models

Author

Listed:
  • Dorofeenko, Victor
  • Lee, Gabriel S.
  • Salyer, Kevin D.

Abstract

This paper introduces a new algorithm, the recursive upwind Gauss-Seidel method, and applies it to solve a standard stochastic growth model in which the technology shocks exhibit heteroskedasticity. This method exploits the fact that the equations defining equilibrium can be viewed as a set of algebraic equations in the neighborhood of the steady-state. In a non-stochastic setting, the algorithm, in essence, continually extends a local solution to a globally accurate solution. When stochastic elements are introduced, it then uses a recursive scheme in order to determine the global solution. This method is compared to projection, perturbation, and linearization approaches and is shown to be fast and globally accurate. We also demonstrate that linearization methods perform poorly in an environment of heteroskedasticity even though the unconditional variance of technology shocks is relatively small and similar to that typically used in RBC analysis.

Suggested Citation

  • Dorofeenko, Victor & Lee, Gabriel S. & Salyer, Kevin D., 2010. "A new algorithm for solving dynamic stochastic macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 388-403, March.
  • Handle: RePEc:eee:dyncon:v:34:y:2010:i:3:p:388-403
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(09)00178-X
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    4. 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.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    6. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    7. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, Oxford University Press, vol. 121(3), pages 823-866.
    8. 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.
    9. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    10. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    11. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    12. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    13. 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, vol. 13(3), pages 449-470, July.
    14. Salyer, Kevin D., 2007. "Macroeconomic priorities and crash states," Economics Letters, Elsevier, vol. 94(1), pages 64-70, January.
    15. 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.
    16. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    17. 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.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, Department of Economics and Business Economics, Aarhus University.
    3. Rodolphe Buda, 2013. "SIMUL 3.2: An Econometric Tool for Multidimensional Modelling," Computational Economics, Springer;Society for Computational Economics, vol. 41(4), pages 517-524, April.
    4. Ikefuji, M. & Laeven, R.J.A. & Magnus, J.R. & Muris, C.H.M., 2010. "Scrap Value Functions in Dynamic Decision Problems," Discussion Paper 2010-77, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    Numerical methods Gauss Seidel method Projection methods Real business cycles Crash state;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:34:y:2010:i:3:p:388-403. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jedc .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.