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Inequality Constraints and Euler Equation based Solution Methods

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  • Pontus Rendahl

Abstract

Solving dynamic models with inequality constraints poses a challenging problem for two major reasons: dynamic programming techniques are reliable but often slow, while Euler equation based methods are fast but have problematic or unknown convergence properties. This paper attempts to bridge this gap. I show that a common iterative procedure on the Euler equation { usually referred to as time iteration { delivers a sequence of approximate policy functions that converges to the true solution under a wide range of circumstances. These circumstances extend to an arbitrarily large, but nite, set of endogenous and exogenous state-variables as well as a very broad spectrum of occasionally binding constraints.

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  • Pontus Rendahl, 2013. "Inequality Constraints and Euler Equation based Solution Methods," Cambridge Working Papers in Economics 1320, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1320
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    2. Guerra Vallejos, Ernesto & Bobenrieth Hochfarber, Eugenio & Bobenrieth Hochfarber, Juan & Wright, Brian D., 2021. "Solving dynamic stochastic models with multiple occasionally binding constraints," Economic Modelling, Elsevier, vol. 105(C).
    3. Werner, Maximilian, 2023. "Occasionally binding liquidity constraints and macroeconomic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 150(C).
    4. 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.
    5. 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.
    6. Coeurdacier, Nicolas & Rey, Hélène & Winant, Pablo, 2020. "Financial integration and growth in a risky world," Journal of Monetary Economics, Elsevier, vol. 112(C), pages 1-21.
    7. Klaus Adam & Albert Marcet & Johannes Beutel, 2017. "Stock Price Booms and Expected Capital Gains," American Economic Review, American Economic Association, vol. 107(8), pages 2352-2408, August.
    8. Jensen, Henrik & Ravn, Søren Hove & Santoro, Emiliano, 2019. "Kinks and Gains from Credit Cycles," CEPR Discussion Papers 13795, C.E.P.R. Discussion Papers.
    9. Rendahl, Pontus, 2022. "Continuous vs. discrete time: Some computational insights," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    10. 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.
    11. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    12. Anagnostopoulos Alexis & Tang Xin, 2015. "Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(1), pages 1-49, January.
    13. Nicolas Coeurdacier & Hélène Rey & Pablo Winant, 2020. "Financial Integration and Growth in a Risky World," Post-Print hal-03799686, HAL.
    14. 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.
    15. Kabukçuoğlu, Ayşe, 2017. "The winners and losers of tax reform: An assessment under financial integration," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 90-122.

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    More about this item

    Keywords

    Inequality constraints; Envelope theorem; Time iteration;
    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
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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