IDEAS home Printed from https://ideas.repec.org/p/dlw/wpaper/15-03.html
   My bibliography  Save this paper

The Method of Endogenous Gridpoints in Theory and Practice

Author

Listed:
  • Matthew N. White

    () (Department of Economics, University of Delaware)

Abstract

The method of endogenous gridpoints (ENDG) significantly speeds up the solution to dynamic stochastic optimization problems with continuous state and control variables by avoiding repeated computations of expected outcomes while searching for optimal policy functions. While the method has been used in specific settings with one endogenous state dimension and one control, it has never been characterized for use in n-dimensional models. Using a general theoretical framework for dynamic stochastic optimization problems, I formalize the method of endogenous gridpoints and present conditions for the class of models that can be solved using ENDG. The framework is applied to several example models to show the breadth of problems for which endogenous gridpoints can be used. Further, I provide an interpolation technique for non-rectilinear grids that allows ENDG to be used in n-dimensional problems in an intuitive and computationally educient way. Relative to the traditional approach, the method of endogenous gridpoints with non-linear grid interpolation" solves a benchmark 2D model 7.0 to 7.8 times faster than the traditional solution method.

Suggested Citation

  • Matthew N. White, 2015. "The Method of Endogenous Gridpoints in Theory and Practice," Working Papers 15-03, University of Delaware, Department of Economics.
  • Handle: RePEc:dlw:wpaper:15-03
    as

    Download full text from publisher

    File URL: http://www.lerner.udel.edu/sites/default/files/ECON/PDFs/RePEc/dlw/WorkingPapers/2015/UDWP2015-03.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Giulio Fella, 2011. "A Generalized Endogenous Grid Method for Non-concave Problems," Working Papers 677, Queen Mary University of London, School of Economics and Finance.
    2. Iskhakov, Fedor, 2015. "Multidimensional endogenous gridpoint method: Solving triangular dynamic stochastic optimization problems without root-finding operations," Economics Letters, Elsevier, vol. 135(C), pages 72-76.
    3. Alexander Ludwig & Matthias Schön, 2013. "Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods," Working Paper Series in Economics 65, University of Cologne, Department of Economics, revised 11 Jun 2014.
    4. 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.
    5. Maliar, Lilia & Maliar, Serguei, 2013. "Envelope condition method versus endogenous grid method for solving dynamic programming problems," Economics Letters, Elsevier, vol. 120(2), pages 262-266.
    6. 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.
    7. Brian D. Wright & Jeffrey C. Williams, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, Oxford University Press, vol. 99(1), pages 169-192.
    8. John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A generalized endogenous grid method for discrete-continuous choice," 2012 Meeting Papers 1162, Society for Economic Dynamics.
    9. 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.
    10. 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.
    11. Yoram Ben-Porath, 1967. "The Production of Human Capital and the Life Cycle of Earnings," Journal of Political Economy, University of Chicago Press, vol. 75, pages 352-352.
    12. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    13. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    14. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    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. Druedahl, Jeppe & Jørgensen, Thomas Høgholm, 2017. "A general endogenous grid method for multi-dimensional models with non-convexities and constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 87-107.
    2. repec:kap:compec:v:51:y:2018:i:3:d:10.1007_s10614-016-9611-2 is not listed on IDEAS
    3. Kabukcuoglu, Ayse & Martinez-Garcia, Enrique, 2016. "The market resources method for solving dynamic optimization problems," Globalization and Monetary Policy Institute Working Paper 274, Federal Reserve Bank of Dallas.
    4. Iskhakov, Fedor, 2015. "Multidimensional endogenous gridpoint method: Solving triangular dynamic stochastic optimization problems without root-finding operations," Economics Letters, Elsevier, vol. 135(C), pages 72-76.
    5. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.

    More about this item

    Keywords

    Dynamic models; numerical solution; endogenous gridpoint method; non-linear grid interpolation; endogenous human capital; durable goods;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

    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:dlw:wpaper:15-03. 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: (Saul Hoffman). General contact details of provider: http://edirc.repec.org/data/deudeus.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.