IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_4837.html
   My bibliography  Save this paper

On the Applicability of Global Approximation Methods for Models with Jump Discontinuities in Policy Functions

Author

Listed:
  • Christoph Görtz
  • Afrasiab Mirza

Abstract

We show that the standard Value Function Iteration (VFI) algorithm has difficulties approximating models with jump discontinuities in policy functions. We find that VFI fails to accurately identify the location and size of jump discontinuities while other methods - such as the Endogenous Grid Method (EGM) and a Finite Element Method (FEM) - are much better at approximating this class of models. We illustrate differences across methods using a standard plant-level investment model with both variable and fixed capital adjustment costs. We find that the policy functions generated by VFI are quite different from those generated by EGM and FEM. Importantly, these differences are economically significant: for our baseline parameterization VFI generates investment spikes that are 5-8% larger in comparison to the other two methods. The choice between EGM and FEM depends on the context. While EGM is faster than FEM, it is much more difficult to implement. For larger models, the modifications necessary to apply EGM can lead to high code complexity. On the other hand, FEM can accommodate larger models with minimal implementation differences and its high scalability can reduce computation time significantly.

Suggested Citation

  • Christoph Görtz & Afrasiab Mirza, 2014. "On the Applicability of Global Approximation Methods for Models with Jump Discontinuities in Policy Functions," CESifo Working Paper Series 4837, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_4837
    as

    Download full text from publisher

    File URL: http://www.cesifo-group.de/DocDL/cesifo1_wp4837.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Whited, Toni M., 2006. "External finance constraints and the intertemporal pattern of intermittent investment," Journal of Financial Economics, Elsevier, vol. 81(3), pages 467-502, September.
    2. McGrattan, Ellen R., 1996. "Solving the stochastic growth model with a finite element method," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 19-42.
    3. Giulio Fella, 2014. "A generalized endogenous grid method for non-smooth and non-concave problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 329-344, April.
    4. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    5. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    6. Jose Luengo-Prado, Maria, 2006. "Durables, nondurables, down payments and consumption excesses," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1509-1539, October.
    7. Aubhik Khan & B. Ravikumar, 2002. "Costly Technology Adoption and Capital Accumulation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 5(2), pages 489-502, April.
    8. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    9. Aubhik Khan & Julia K. Thomas, 2008. "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics," Econometrica, Econometric Society, vol. 76(2), pages 395-436, March.
    10. Christopher A. Hennessy & Toni M. Whited, 2005. "Debt Dynamics," Journal of Finance, American Finance Association, vol. 60(3), pages 1129-1165, June.
    11. John Haltiwanger & Russell Cooper & Laura Power, 1999. "Machine Replacement and the Business Cycle: Lumps and Bumps," American Economic Review, American Economic Association, vol. 89(4), pages 921-946, September.
    12. Patrick Bajari & Phoebe Chan & Dirk Krueger & Daniel Miller, 2013. "A Dynamic Model Of Housing Demand: Estimation And Policy Implications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 409-442, May.
    13. Manuel S. Santos & Adrian Peralta-Alva, 2012. "Analysis of Numerical Errors," Working Papers 2012-6, University of Miami, Department of Economics.
    14. Øivind Anti Nilsen & Fabio Schiantarelli, 2003. "Zeros and Lumps in Investment: Empirical Evidence on Irreversibilities and Nonconvexities," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1021-1037, November.
    15. Russell W. Cooper & John C. Haltiwanger, 2006. "On the Nature of Capital Adjustment Costs," Review of Economic Studies, Oxford University Press, vol. 73(3), pages 611-633.
    16. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
    17. Laura Power, 1998. "The Missing Link: Technology, Investment, And Productivity," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 300-313, May.
    18. 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.
    19. Bayer, Christian, 2006. "Investment dynamics with fixed capital adjustment cost and capital market imperfections," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1909-1947, November.
    20. Barillas, Francisco & Fernandez-Villaverde, Jesus, 2007. "A generalization of the endogenous grid method," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2698-2712, August.
    21. Mark E. Doms & Timothy Dunne, 1998. "Capital Adjustment Patterns in Manufacturing Plants," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(2), pages 409-429, April.
    22. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
    23. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    24. Joao F. Gomes, 2001. "Financing Investment," American Economic Review, American Economic Association, vol. 91(5), pages 1263-1285, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    dynamic equilibrium economies; non-convex capital adjustment costs; computational methods; nonlinear solution methods;

    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:ces:ceswps:_4837. 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: (Klaus Wohlrabe). General contact details of provider: http://edirc.repec.org/data/cesifde.html .

    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.