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A general endogenous grid method for multi-dimensional models with non-convexities and constraints

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  • Druedahl, Jeppe
  • Jørgensen, Thomas Høgholm

Abstract

The endogenous grid method (EGM) significantly speeds up the solution of stochastic dynamic programming problems by simplifying or completely eliminating root-finding. We propose a general and parsimonious EGM extended to handle (1) multiple continuous states and choices, (2) multiple occasionally binding constraints, and (3) non-convexities such as discrete choices. Our method enjoys the speed gains of the original one-dimensional EGM, while avoiding expensive interpolation on multi-dimensional irregular endogenous grids. We explicitly define a broad class of models for which our solution method is applicable, and illustrate its speed and accuracy using a consumption–saving model with both liquid assets and illiquid pension assets and a discrete retirement choice.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:74:y:2017:i:c:p:87-107
    DOI: 10.1016/j.jedc.2016.11.005
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    2. 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.
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    9. 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.
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    Cited by:

    1. Alonso, Cristian, 2018. "Hard vs. soft financial constraints: Implications for the effects of a credit crunch," Journal of Macroeconomics, Elsevier, vol. 58(C), pages 198-223.
    2. Claudio Daminato & Mario Padula, 2020. "The Life-Cycle Effects of Pension Reforms: A Structural Approach," CSEF Working Papers 585, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    3. Fedor Iskhakov & Michael Keane, 2018. "Effects of Taxes and Safety Net Pensions on life-cycle Labor Supply, Savings and Human Capital: the Case of Australia," Discussion Papers 2018-09, School of Economics, The University of New South Wales.
    4. Druedahl, Jeppe & Martinello, Alessandro, 2016. "Long-Run Saving Dynamics: Evidence from Unexpected Inheritances," Working Papers 2016:7, Lund University, Department of Economics, revised 08 May 2018.
    5. Harrison, Richard & Waldron, Matt, 2021. "Optimal policy with occasionally binding constraints: piecewise linear solution methods," Bank of England working papers 911, Bank of England.
    6. Clausen, Andrew & Strub, Carlo, 2020. "Reverse Calculus and nested optimization," Journal of Economic Theory, Elsevier, vol. 187(C).
    7. Fedor Iskhakov & Michael Keane, 2018. "Effects of Taxes and Safety Net Pensions on life-cycle Labor Supply, Savings and Human Capital: the Case of Australia," Discussion Papers 2018-09, School of Economics, The University of New South Wales.
    8. Sumudu Kankanamge & Alexandre Gaillard, 2019. "Entrepreneurship, Inter-Generational Business Transmission and Aging," 2019 Meeting Papers 1503, Society for Economic Dynamics.
    9. 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.
    10. Markus Karlman & Karin Kinnerud & Kasper Kragh-Sorensen, 2021. "Costly reversals of bad policies: the case of the mortgage interest deduction," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 40, pages 85-107, April.
    11. 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

    Endogenous grid method; Post-decision states; Stochastic dynamic programming; Continuous and discrete choices; Occasionally binding constraints;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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