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Envelope condition method versus endogenous grid method for solving dynamic programming problems

Author

Listed:
  • Lilia Maliar

    (Universidad de Alicante)

  • Serguei Maliar

    (Universidad de Alicante)

Abstract

We introduce an envelope condition method (ECM) for solving dynamic programming problems. The ECM method is simple to implement, dominates conventional value function iteration and is comparable in accuracy and cost to Carroll’s (2005) endogenous grid method. Codes are available.

Suggested Citation

  • Lilia Maliar & Serguei Maliar, 2013. "Envelope condition method versus endogenous grid method for solving dynamic programming problems," Working Papers. Serie AD 2013-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2013-07
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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2013-07.pdf
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    References listed on IDEAS

    as
    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    2. Maliar, Serguei & Maliar, Lilia & Judd, Kenneth, 2011. "Solving the multi-country real business cycle model using ergodic set methods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 207-228, February.
    3. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2011. "Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models," Quantitative Economics, Econometric Society, vol. 2(2), pages 173-210, July.
    4. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    5. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2012. "Merging simulation and projection approaches to solve high-dimensional problems," Working Papers. Serie AD 2012-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Barillas, Francisco & Fernandez-Villaverde, Jesus, 2007. "A generalization of the endogenous grid method," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2698-2712, August.
    7. Santos, Manuel S., 1999. "Numerical solution of dynamic economic models," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 5, pages 311-386, Elsevier.
    8. Villemot, Sébastien, 2012. "Accelerating the resolution of sovereign debt models using an endogenous grid method," Dynare Working Papers 17, CEPREMAP.
    9. Cai, Yongyang & Judd, Kenneth L., 2012. "Dynamic programming with shape-preserving rational spline Hermite interpolation," Economics Letters, Elsevier, vol. 117(1), pages 161-164.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. White, Matthew N., 2015. "The method of endogenous gridpoints in theory and practice," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 26-41.
    2. 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.
    3. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    4. 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.
    5. Alexander Ludwig & Matthias Schön, 2018. "Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 463-492, March.
    6. 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.
    7. 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.
    8. Sami Alpanda & Alexander Ueberfeldt, 2016. "Should Monetary Policy Lean Against Housing Market Booms?," Staff Working Papers 16-19, Bank of Canada.
    9. Nam Gang Lee, 2019. "Trend Growth Shocks and Asset Prices," Working Papers 2019-4, Economic Research Institute, Bank of Korea.
    10. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    11. Anastasios G Karantounias, 2018. "Optimal Fiscal Policy with Recursive Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2283-2317.
    12. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    13. Zuzana Mucka & Ludovit Odor, 2018. "Optimal sovereign debt: Case of Slovakia," Working Papers Working Paper No. 3/2018, Council for Budget Responsibility.
    14. Takeshi Fukasawa, 2024. "Simple method for efficiently solving dynamic models with continuous actions using policy gradient," Papers 2407.04227, arXiv.org.
    15. Robert Kirkby Author-Email: robertkirkby@gmail.com|, 2017. "Convergence of Discretized Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 117-153, January.
    16. 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.
    17. White, Neil, 2022. "An envelope method for solving continuous-time stochastic models with occasionally binding constraints," Economics Letters, Elsevier, vol. 214(C).
    18. 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.
    19. Benjamin Pugsley & Sebastian Dyrda, 2017. "Taxes, Regulations of Businesses and Evolution of Income Inequality in the US," 2017 Meeting Papers 1463, Society for Economic Dynamics.
    20. Robert Kirkby, 2016. "Value Function Iteration Toolkit: In Matlab, on the GPU," EcoMod2016 9122, EcoMod.
    21. Karmakar, Sudipto & Melolinna, Marko & Schnattinger, Philip, 2022. "What is productive investment? Insights from firm-level data for the United Kingdom," Bank of England working papers 992, Bank of England.
    22. Robert Kirkby, 2017. "A Toolkit for Value Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 1-15, January.

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    More about this item

    Keywords

    Numerical dynamic programming; Value function iteration; Endogenous grid; Envelope condition; Curse of dimensionality; Large scale;
    All these keywords.

    JEL classification:

    • 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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