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The Method of Endogenous Gridpoints in Theory and Practice

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  • 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
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    References listed on IDEAS

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    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.
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    Citations

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    Cited by:

    1. Ayse Kabukcuoglu & Enrique Martinez-Garcia, 2016. "The market resources method for solving dynamic optimization problems," Globalization Institute Working Papers 274, Federal Reserve Bank of Dallas.
    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. 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.
    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. 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.
    6. Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
    7. 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.
    8. 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.
    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.

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    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

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