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Envelope Condition Method (ECM) in comparison with other solution methods for the neoclassical growth model with inelastic labor supply in "Envelope Condition Method with an Application to Default Risk Models"

Author

Listed:
  • Cristina Arelano

    (Federal Reserve Bank of Minneapolis)

  • Lilia Maliar

    (University of Alicante)

  • Serguei Maliar

    (University of Alicante)

  • Viktor Tsyrennikov

    (Promontory)

Programming Language

Matlab

Abstract

We develop an envelope condition method (ECM) for dynamic programming problems – a tractable alternative to expensive conventional value function iteration (VFI). ECM has two novel features: first, to reduce the cost of iteration on Bellman equation, ECM constructs policy functions using envelope conditions which are simpler to analyze numerically than first-order conditions. Second, to increase the accuracy of solutions, ECM solves for derivatives of value function jointly with 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Cristina Arelano & Lilia Maliar & Serguei Maliar & Viktor Tsyrennikov, 2016. "Envelope Condition Method (ECM) in comparison with other solution methods for the neoclassical growth model with inelastic labor supply in "Envelope Condition Method with an Application to Defaul," QM&RBC Codes 203, Quantitative Macroeconomics & Real Business Cycles.
  • Handle: RePEc:dge:qmrbcd:203
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    File URL: https://dge.repec.org/codes/maliar/7_methods_for_growth_model_AMMT_2016.zip
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    Keywords

    Matlab;

    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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