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The method of endogenous gridpoints in theory and practice

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  • White, Matthew N.

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. I provide an interpolation technique for non-rectilinear grids that allow ENDG to be used in n-dimensional problems in an intuitive and computationally efficient way: the acceleration of ENDG with non-linear grid interpolation is nearly constant in the density of the grid. Further, ENDG has only been shown by example and has never been formally characterized. Using a theoretical framework for dynamic stochastic optimization problems, I formalize the method of endogenous gridpoints and present conditions for the class of models for which it can be used.

Suggested Citation

  • White, Matthew N., 2015. "The method of endogenous gridpoints in theory and practice," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 26-41.
  • Handle: RePEc:eee:dyncon:v:60:y:2015:i:c:p:26-41
    DOI: 10.1016/j.jedc.2015.08.001
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    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.
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    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. 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.
    9. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    10. 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.
    11. 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.
    12. 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.
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    14. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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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. 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. 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.
    5. 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.
    6. Ayse Kabukcuoglu & Enrique Martinez-Garcia, 2020. "A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints," Globalization Institute Working Papers 396, Federal Reserve Bank of Dallas.
    7. 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.

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    More about this item

    Keywords

    Dynamic models; Numeric solution; Endogenous gridpoint method; Non-linear grid interpolation; Endogenous human capital;
    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
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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