[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/sce/scecf0/254.html
   My bibliography  Save this paper

Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems

Author

Listed:
  • Michael Reiter

    (Universitat Pompeu Fabra)

Abstract
The paper provides a method to measure the accuracy of numerical solutions to stochastic dynamic optimization problems. The theorems proven in the paper provide, first, a tight upper bound on the loss in the value function that comes from using the numerical solution rather than the exact solution. The loss is computed at a given point of the state space, using the Euler residuals along simulated paths of the model. Second, they allow to compute an unbiased estimate of the error in the policy function at such a point. However, estimating the error in the policy function requires a higher computational effort than obtaining the value function error. Both measures can be obtained without knowing the exact solution.The measures are applied to several variants of the neoclassical growth model, some of them highly nonlinear. It is shown that the method provides indeed tight estimates of the error, which are helpful to evaluate numerical solution techniques according to their accuracy.

Suggested Citation

  • Michael Reiter, 2000. "Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems," Computing in Economics and Finance 2000 254, Society for Computational Economics.
    • Handle: RePEc:sce:scecf0:254
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/cef00/papers/paper254.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    3. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    4. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    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. Den Haan, Wouter J., 2010. "Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 79-99, January.
    2. Den Haan, Wouter J., 2010. "Comparison of solutions to the incomplete markets model with aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 4-27, January.
    3. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    2. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
    3. Adrian Peralta-Alva & Manuel S. Santos, 2012. "Analysis of numerical errors," Working Papers 2012-062, Federal Reserve Bank of St. Louis.
    4. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    5. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2017. "Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models," Econometrica, Econometric Society, vol. 85, pages 991-1012, May.
    6. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    7. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    8. 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.
    9. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    10. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
    11. Felix Kubler & Karl Schmedders, 2003. "Approximate Versus Exact Equilibria," Discussion Papers 1382, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. 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.
    13. Peter Woehrmann & Willi Semmler & Martin Lettau, "undated". "Nonparametric Estimation of the Time-varying Sharpe Ratio in Dynamic Asset Pricing Models," IEW - Working Papers 225, Institute for Empirical Research in Economics - University of Zurich.
    14. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    15. Maldonado, Wilfredo L. & Svaiter, B.F., 2007. "Holder continuity of the policy function approximation in the value function approximation," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 629-639, June.
    16. Kubler, Felix & Scheidegger, Simon, 2023. "Uniformly self-justified equilibria," Journal of Economic Theory, Elsevier, vol. 212(C).
    17. repec:mea:meawpa:13274 is not listed on IDEAS
    18. Christoffel, Kai & Kilponen, Juha & Jaccard, Ivan, 2011. "Government bond risk premia and the cyclicality of fiscal policy," Working Paper Series 1411, European Central Bank.
    19. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    20. Chris Papageorgiou & Fidel Perez‐Sebastian, 2007. "Is the Asymptotic Speed of Convergence a Good Proxy for the Transitional Growth Path?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(1), pages 1-24, February.
    21. Alvarez-Cuadrado, Francisco, 2008. "Growth outside the stable path: Lessons from the European reconstruction," European Economic Review, Elsevier, vol. 52(3), pages 568-588, April.

    More about this item

    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:sce:scecf0:254. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/sceeeea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.