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Linearization about the Current State: A Computational Method for Approximating Nonlinear Policy Functions during Simulation

Author

Listed:
  • Richard W. Evans

    (Department of Economics, Brigham Young University)

  • Kerk L. Phillips

    (Department of Economics, Brigham Young University)

Abstract

This paper presents an adjustment to commonly used approximation methods for dynamic stochastic general equilibrium (DSGE) models. Policy functions approximated around the steady state will be inaccurate away from the steady state. In some cases, this does not lead to substantial inaccuracies. In other cases, however, the model may not have a well-defined steady state, or the nature of the steady state may be at odds with its off-steady-state dynamics. We show how to simulate a DSGE model by approximating about the current state. Our method introduces an approximation error, but minimizes the error associated with a finite-order Taylor-series expansion of the model’s characterizing equations. This method is easily implemented using available simulation software and has the advantage of mimicking highly non-linear behavior. We illustrate this with a variety of simple models. We compare our technique with other simulation techniques and show that the approximation errors are approximately the same for stable, well-defined models. We also illustrate how this method can solve and simulate models that are not tractable with standard approximation methods.

Suggested Citation

  • Richard W. Evans & Kerk L. Phillips, 2015. "Linearization about the Current State: A Computational Method for Approximating Nonlinear Policy Functions during Simulation," BYU Macroeconomics and Computational Laboratory Working Paper Series 2015-02, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
  • Handle: RePEc:byu:byumcl:201502
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    File URL: https://drive.google.com/file/d/0B6KGaihAO5TJZGJLemE1V1d5bFE/view
    File Function: First version, 2015
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Linearization about the Current State: A Computational Method for Approximating Nonlinear Policy Functions during Simulation
      by Christian Zimmermann in NEP-DGE blog on 2015-09-30 23:56:23

    Citations

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    Cited by:

    1. Phillips, Kerk L., 2010. "A Dynamic General Equilibrium Analysis of Japanese & Korean Immigration," MPRA Paper 23501, University Library of Munich, Germany.
    2. Sergei Seleznev, 2016. "Solving DSGE models with stochastic trends," Bank of Russia Working Paper Series wps15, Bank of Russia.

    More about this item

    Keywords

    ynamic stochastic general equilibrium; linearization methods; numerical simulation; computational techniques; simulation modeling; unstable models; unbalanced growth;

    JEL classification:

    • 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
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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