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An envelope method for solving continuous-time stochastic models with occasionally binding constraints

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  • White, Neil

Abstract

I introduce a finite-difference solution method based on the envelope condition in continuous-time stochastic dynamic programming problems. The envelope method is easier to code and, in the presence of occasionally binding constraints, faster and more stable than popular methods based on the Hamilton–Jacobi–Bellman equation. As an illustration, I solve a stochastic growth model with irreversible investment.

Suggested Citation

  • White, Neil, 2022. "An envelope method for solving continuous-time stochastic models with occasionally binding constraints," Economics Letters, Elsevier, vol. 214(C).
  • Handle: RePEc:eee:ecolet:v:214:y:2022:i:c:s0165176522000908
    DOI: 10.1016/j.econlet.2022.110434
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    References listed on IDEAS

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    1. McGrattan, Ellen R., 1996. "Solving the stochastic growth model with a finite element method," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 19-42.
    2. Maliar, Lilia & Maliar, Serguei, 2013. "Envelope condition method versus endogenous grid method for solving dynamic programming problems," Economics Letters, Elsevier, vol. 120(2), pages 262-266.
    3. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    4. 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.
    5. Greg Kaplan & Benjamin Moll & Giovanni L. Violante, 2018. "Monetary Policy According to HANK," American Economic Review, American Economic Association, vol. 108(3), pages 697-743, March.
    6. Nicolas Petrosky‐Nadeau & Lu Zhang, 2017. "Solving the Diamond–Mortensen–Pissarides model accurately," Quantitative Economics, Econometric Society, vol. 8(2), pages 611-650, July.
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    More about this item

    Keywords

    Numerical methods; Dynamic programming; Envelope condition; Occasionally binding constraints;
    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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