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Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

Author

Listed:
  • Ludwig, Alexander
  • Schön, Matthias

    (Munich Center for the Economics of Aging (MEA))

Abstract
This paper investigates extensions of the method of endogenous gridpoints (ENDGM) introduced by Carroll (2006) to higher dimensions with more than one continuous endogenous state variable. We compare three di erent categories of algorithms: (i) the conventional method with exogenous grids (EXOGM), (ii) the pure method of endogenous gridpoints (ENDGM) and (iii) a hybrid method (HYBGM). ENDGM comes along with Delaunay interpolation on irregular grids. Comparison of methods is done by evaluating speed and accuracy. We nd that HYBGM and ENDGM both dominate EXOGM. In an in nite horizon model, ENDGM also always dominates HYBGM. In a nite horizon model, the choice between HYBGM and ENDGM depends on the number of gridpoints in each dimension. With less than 150 gridpoints in each dimension ENDGM is faster than HYBGM, and vice versa. For a standard choice of 25 to 50 gridpoints in each dimension, ENDGM is 1:4 to 1:7 times faster than HYBGM in the nite horizon version and 2:4 to 2:5 times faster in the in nite horizon version of the model.

Suggested Citation

  • Ludwig, Alexander & Schön, Matthias, 2014. "Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods," MEA discussion paper series 201309, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    • Handle: RePEc:mea:meawpa:201309
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    References listed on IDEAS

    as
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    Cited by:

    1. 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.
    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. Xu, Mengyi & Alonso-García, Jennifer & Sherris, Michael & Shao, Adam W., 2023. "Insuring longevity risk and long-term care: Bequest, housing and liquidity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 121-141.
    4. Enrique Mendoza & Sergio Villalvazo, 2020. "FiPIt: A Simple, Fast Global Method for Solving Models with Two Endogenous States & Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 81-102, July.
    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. repec:ulb:ulbeco:2013/340821 is not listed on IDEAS
    7. 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.
    8. 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.
    9. Huang, Tiancheng & Khemka, Gaurav & Chong, Wing Fung, 2024. "Monotonicity of savings function in Endogenous Gridpoint Method with stochastic portfolio returns," Economics Letters, Elsevier, vol. 239(C).

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    JEL classification:

    • 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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