IDEAS home Printed from https://ideas.repec.org/p/hhs/cbsfin/2004_004.html
   My bibliography  Save this paper

Upper Bounds on Numerical Approximation Errors

Author

Listed:
  • Raahauge, Peter

    (Department of Finance, Copenhagen Business School)

Abstract

This paper suggests a method for determining rigorous upper bounds on approximation errors of numerical solutions to infinite horizon dynamic programming models. Bounds are provided for approximations of the value function and the policy function as well as the derivatives of the value function. The bounds apply to more general problems than existing bounding methods do. For instance, since strict concavity is not required, linear models and piecewise linear approximations can be dealt with. Despite the generality, the bounds perform well in comparison with existing methods even when applied to approximations of a standard(strictly concave)growth model.

Suggested Citation

  • Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
    • Handle: RePEc:hhs:cbsfin:2004_004
    as

    Download full text from publisher

    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7171
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    3. 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.
    4. 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.
    5. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    6. Bechmann, Ken L. & Raaballe, Johannes, 2000. "A Regulation of Bids for Dual Class Shares. Implication: Two Shares { One Price," Working Papers 2000-5, Copenhagen Business School, Department of Finance.
    7. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    8. 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)

    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. 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. Manuel S. Santos & Adrian Peralta-Alva, 2012. "Analysis of Numerical Errors," Working Papers 2012-6, University of Miami, Department of Economics.
    4. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    5. 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.
    6. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    7. 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.
    8. Stephanie Becker & Lars Grüne & Willi Semmler, 2007. "Comparing accuracy of second-order approximation and dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 30(1), pages 65-91, August.
    9. 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.
    10. José Cao-Alvira, 2010. "Finite Elements in the Presence of Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 355-370, April.
    11. Francisco (F.) Blasques & Marc Nientker, 2019. "Transformed Perturbation Solutions for Dynamic Stochastic General Equilibrium Models," Tinbergen Institute Discussion Papers 19-012/III, Tinbergen Institute, revised 09 Feb 2020.
    12. 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.
    13. 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.
    14. Bobenrieth H., Eugenio S.A. & Bobenrieth H., Juan R.A. & Wright, Brian D., 2008. "A foundation for the solution of consumption-saving behavior with a borrowing constraint and unbounded marginal utility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 695-708, March.
    15. 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.
    16. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2009. "Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models," NBER Working Papers 15296, National Bureau of Economic Research, Inc.
    17. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics.
    18. Duffy, John & McNelis, Paul D., 2001. "Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1273-1303, September.
    19. repec:ebl:ecbull:v:3:y:2003:i:1:p:1-14 is not listed on IDEAS
    20. Ueda, Atsuko, 2000. "A Growth Model of "Miracle" in Korea," Journal of Policy Modeling, Elsevier, vol. 22(1), pages 43-59, January.
    21. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.

    More about this item

    Keywords

    Numerical approximation errors; Bellman contractions; Error bounds;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:cbsfin:2004_004. 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: Lars Nondal (email available below). General contact details of provider: https://edirc.repec.org/data/cbschdk.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.