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Envelope Condition Method with an Application to Default Risk Models

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Listed:
  • Viktor Tsyrennikov

    (IMF)

  • Serguei Maliar

    (Santa Clara University)

  • Lilia Maliar

    (Stanford University)

  • Cristina Arellano

    (Federal Reserve Bank of Minneapolis)

Abstract

We develop an envelope condition method (ECM) for dynamic programming problems -- a tractable alternative to expensive conventional value function iteration. ECM has two novel features: First, to reduce the cost, ECM replaces expensive backward iteration on Bellman equation with relatively cheap forward iteration on an envelope condition. Second, to increase the accuracy of solutions, ECM solves for derivatives of a value function jointly with a value function itself. We complement ECM with other computational techniques that are suitable for high-dimensional problems, such as simulation-based grids, monomial integration rules and derivative-free solvers. The resulting value-iterative ECM method can accurately solve models with at least up to 20 state variables and can successfully compete in accuracy and speed with state-of-the-art Euler equation methods. We also use ECM to solve a challenging default risk model with a kink in value and policy functions, and we find it to be fast, accurate and reliable.

Suggested Citation

  • Viktor Tsyrennikov & Serguei Maliar & Lilia Maliar & Cristina Arellano, 2015. "Envelope Condition Method with an Application to Default Risk Models," 2015 Meeting Papers 1239, Society for Economic Dynamics.
  • Handle: RePEc:red:sed015:1239
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    Cited by:

    1. Chase Coleman & Spencer Lyon & Lilia Maliar & Serguei Maliar, 2021. "Matlab, Python, Julia: What to Choose in Economics?," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1263-1288, December.
    2. Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
    3. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    4. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    5. Willi Semmler & Christian R. Proaño, 2015. "Escape Routes from Sovereign Default Risk in the Euro Area," International Symposia in Economic Theory and Econometrics, in: William A. Barnett & Fredj Jawadi (ed.), Monetary Policy in the Context of the Financial Crisis: New Challenges and Lessons, volume 24, pages 163-193, Emerald Publishing Ltd.
    6. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    7. 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.
    8. 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.
    9. Damián Pierri & Julián Martínez, 2020. "Accuracy in Recursive Minimal State Space Methods," Working Papers 147, Universidad de San Andres, Departamento de Economia, revised Aug 2020.
    10. Coleman, Chase & Lyon, Spencer & Maliar, Lilia & Maliar, Serguei, 2018. "Matlab, Python, Julia: What to Choose in Economics?," CEPR Discussion Papers 13210, C.E.P.R. Discussion Papers.
    11. Maliar, Lilia & Maliar, Serguei & Winant, Pablo, 2021. "Deep learning for solving dynamic economic models," Journal of Monetary Economics, Elsevier, vol. 122(C), pages 76-101.

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    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • 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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