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, 2018. "Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 463-492, March.
    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. Brian D. Wright & Jeffrey C. Williams, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(1), pages 169-192.
    7. John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A generalized endogenous grid method for discrete-continuous choice," 2012 Meeting Papers 1162, Society for Economic Dynamics.
    8. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-255, March-Apr.
    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. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    11. 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.
    12. 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.
    13. 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(4), pages 352-352.
    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. 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. Ayse Kabukcuoglu & Enrique Martínez García, 2016. "The market resources method for solving dynamic optimization problems," Globalization Institute Working Papers 274, Federal Reserve Bank of Dallas.
    2. Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
    3. 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.
    4. Alexander Ludwig & Matthias Schön, 2018. "Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 463-492, March.
    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.
    6. 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.
    7. Ayşe Kabukçuoğlu & Enrique Martínez-García, 2021. "A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 435-460, August.
    8. Karsten O. Chipeniuk, 2020. "Optimal Grid Selection for the Numerical Solution of Dynamic Stochastic Optimization Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 883-928, December.
    9. Jeppe Druedahl, 2021. "A Guide on Solving Non-convex Consumption-Saving Models," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 747-775, October.

    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. Alexander Ludwig & Matthias Schön, 2018. "Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 463-492, March.
    2. Jeppe Druedahl, 2021. "A Guide on Solving Non-convex Consumption-Saving Models," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 747-775, October.
    3. 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.
    4. repec:mea:meawpa:13274 is not listed on IDEAS
    5. Matthew N. White, 2014. "Endogenous Gridpoints in Multiple Dimensions: Interpolation on Non-Linear Grids," Working Papers 14-17, University of Delaware, Department of Economics.
    6. Robert Kirkby Author-Email: robertkirkby@gmail.com|, 2017. "Convergence of Discretized Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 117-153, January.
    7. Ayşe Kabukçuoğlu & Enrique Martínez-García, 2021. "A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 435-460, August.
    8. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    9. Ayse Kabukcuoglu & Enrique Martínez-García, 2016. "The Market Resources Method for Solving Dynamic Optimization Problems," Koç University-TUSIAD Economic Research Forum Working Papers 1607, Koc University-TUSIAD Economic Research Forum.
    10. 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.
    11. 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.
    12. Fedor Iskhakov & Thomas Høgholm Jørgensen & John Rust & Bertel Schjerning, 2015. "Estimating Discrete-Continuous Choice Models: The Endogenous Grid Method with Taste Shocks," Discussion Papers 15-19, University of Copenhagen. Department of Economics.
    13. Guerra Vallejos, Ernesto & Bobenrieth Hochfarber, Eugenio & Bobenrieth Hochfarber, Juan & Wright, Brian D., 2021. "Solving dynamic stochastic models with multiple occasionally binding constraints," Economic Modelling, Elsevier, vol. 105(C).
    14. 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.
    15. Youngsoo Jang, 2016. "Income Inequality, Medical Conditions, and Household Bankruptcy," Proceedings of Economics and Finance Conferences 4206835, International Institute of Social and Economic Sciences.
    16. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    17. Jang, Youngsoo & Lee, Soyoung, 2019. "A Generalized Endogenous Grid Method for Models with the Option to Default," MPRA Paper 95721, University Library of Munich, Germany.
    18. Karsten O. Chipeniuk, 2020. "Optimal Grid Selection for the Numerical Solution of Dynamic Stochastic Optimization Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 883-928, December.
    19. Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
    20. Takeshi Fukasawa, 2024. "Simple method for efficiently solving dynamic models with continuous actions using policy gradient," Papers 2407.04227, arXiv.org.
    21. Brumm, Johannes & Grill, Michael, 2014. "Computing equilibria in dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 142-160.

    More about this item

    Keywords

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

    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.

    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: Saul Hoffman (email available below). General contact details of provider: https://edirc.repec.org/data/deudeus.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.