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A General Endogenous Grid Method for Multi-Dimensional Models with Non-Convexities and Constraints

Author

Listed:
  • Jeppe Druedahl

    (Department of Economics, University of Copenhagen)

  • Thomas Høgholm Jørgensen

    (Department of Economics, University of Copenhagen)

Abstract

The endogenous grid method (EGM) significantly speeds up the solution of stochastic dynamic programming problems by simplifying or completely eliminating rootfinding. 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

  • Jeppe Druedahl & Thomas Høgholm Jørgensen, 2016. "A General Endogenous Grid Method for Multi-Dimensional Models with Non-Convexities and Constraints," Discussion Papers 16-09, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1609
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    2. Kasper Kragh Balke & Markus Karlman & Karin Kinnerud, 2024. "Winners and Losers from Property Taxation," Working Papers 04/2024, Centre for Household Finance and Macroeconomic Research (HOFIMAR), BI Norwegian Business School.
    3. Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
    4. 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.
    5. Keyvan Eslami & Thomas Phelan, 2025. "The Art of Temporal Approximation: An Investigation into Numerical Solutions to Discrete- and Continuous-Time Problems in Economics," Computational Economics, Springer;Society for Computational Economics, vol. 65(3), pages 1505-1547, March.
    6. Claudio Daminato & Mario Padula, 2024. "The Life-Cycle Effects of Pension Reforms: A Structural Approach," Journal of the European Economic Association, European Economic Association, vol. 22(1), pages 355-392.
    7. Iskhakov, Fedor & Keane, Michael, 2021. "Effects of taxes and safety net pensions on life-cycle labor supply, savings and human capital: The case of Australia," Journal of Econometrics, Elsevier, vol. 223(2), pages 401-432.
    8. Katrine M. Jakobsen & Thomas H. J�rgensen & Hamish Low, 2022. "Fertility and Family Labor Supply," CEBI working paper series 22-04, University of Copenhagen. Department of Economics. The Center for Economic Behavior and Inequality (CEBI).
    9. Richard Harrison & Matt Waldron, 2021. "Optimal policy with occasionally binding constraints: piecewise linear solution methods," Bank of England working papers 911, Bank of England.
    10. Clausen, Andrew & Strub, Carlo, 2020. "Reverse Calculus and nested optimization," Journal of Economic Theory, Elsevier, vol. 187(C).
    11. 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.
    12. Sumudu Kankanamge & Alexandre Gaillard, 2019. "Entrepreneurship, Inter-Generational Business Transmission and Aging," 2019 Meeting Papers 1503, Society for Economic Dynamics.
    13. 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.
    14. Marlon Azinovic-Yang & Jan v{Z}emliv{c}ka, 2025. "Deep Learning in the Sequence Space," Papers 2509.13623, arXiv.org.
    15. Karolos Arapakis, 2023. "A Method to Pre-compile Numerical Integrals When Solving Stochastic Dynamic Problems," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 593-610, February.
    16. Marlon Azinovic-Yang & Jan Zemlicka, 2025. "Deep Learning in the Sequence Space," CERGE-EI Working Papers wp802, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    17. 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.
    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. 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.
    20. Jeppe Druedahl & Alessandro Martinello, 2022. "Long-Run Saving Dynamics: Evidence from Unexpected Inheritances," The Review of Economics and Statistics, MIT Press, vol. 104(5), pages 1079-1095, December.
    21. Keyvan Eslami & Tom Phelan, 2023. "The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics," Working Papers 23-10, Federal Reserve Bank of Cleveland.

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    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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