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Perturbation Solution of Nonlinear Rational Expectations Models


  • Peter A. Zadrozny

    () (Bureau of Labor Statistics)

  • Baoline Chen

    () (Rutgers University)


The paper derives and illustrates a convenient implementation of a perturbation method for computing an approximate perfect foresight solution of a nonlinear rational-expectations model. The solution space is the set of finite Taylor-series approximations. In discussing this setting, Gaspar and Judd (1997) wrote the higher-order Taylor terms in an algebraically unstructured form. Choosing an algebraic structure for the Taylor terms imparts a related structure to the solution equations, which facilitates understanding and design of a computer program. This paper contributes by providing such a structure. By generalizing a "good definition" of matrix derivatives (Magnus and Neudecker, 1988) to higher-order arrays, the paper shows how to derive structured solution equations for any model and any order of Taylor approximation in terms of conventional linear algebraic operations on vectors and matrices. The computations involve three major steps: (i) solve a nonlinear vector equation to obtain the constant term of the solution; (ii) solve a matrix polynomial equation to obtain the linear term of the solution; (iii) solve K-2 systems of linear equations to obtain remaining higher-order terms of a K -term solution. The computations are illustrated with a reduction of Taylor's (1993) G7-country macroeconomic model. Step (ii) is implemented with an eigenvalue method for solving a matrix polynomial equation (Zadrozny, 1998).

Suggested Citation

  • Peter A. Zadrozny & Baoline Chen, 1999. "Perturbation Solution of Nonlinear Rational Expectations Models," Computing in Economics and Finance 1999 334, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:334

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    References listed on IDEAS

    1. repec:adr:anecst:y:1990:i:17:p:04 is not listed on IDEAS
    2. Michel Juillard & Douglas Laxton, 1996. "A Robust and Efficient Method for Solving Nonlinear Rational Expectations Models," IMF Working Papers 96/106, International Monetary Fund.
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    Cited by:

    1. Baoline Chen & Peter A. Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Springer;Society for Computational Economics, vol. 21(1_2), pages 45-64, February.
    2. Baoline Chen & Peter A. Zadrozny, 2005. "Multi-Step Perturbation Solution of Nonlinear Rational Expectations Models," Computing in Economics and Finance 2005 254, Society for Computational Economics.

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