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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, 2015. "Inequality Constraints and Euler Equation‐based Solution Methods," Economic Journal, Royal Economic Society, vol. 125(585), pages 1110-1135, June.
    • Handle: RePEc:wly:econjl:v:125:y:2015:i:585:p:1110-1135
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    File URL: http://hdl.handle.net/10.1111/ecoj.2015.125.issue-585
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    3. Ayse Kabukcuoglu & Enrique Martínez García, 2016. "The market resources method for solving dynamic optimization problems," Globalization Institute Working Papers 274, Federal Reserve Bank of Dallas.
    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. 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.
    6. 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.
    7. Jensen, Henrik & Ravn, Søren Hove & Santoro, Emiliano, 2019. "Kinks and Gains from Credit Cycles," CEPR Discussion Papers 13795, C.E.P.R. Discussion Papers.
    8. Rendahl, Pontus, 2022. "Continuous vs. discrete time: Some computational insights," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    9. 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.
    10. 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.
    11. Fagan, Gabriel & McNelis, Paul D., 2020. "Sudden stops in the Euro Area: Does monetary union matter?," Journal of International Money and Finance, Elsevier, vol. 108(C).
    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 43-91, January.
    13. 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.
    14. 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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    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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