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A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model

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Collard, Fabrice
Juillard, Michel

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Abstract

We propose to apply to the simulation of general nonlinear rational-expectation models a method where the expectation functions are approximated through a higher-order Taylor expansion. This method has been advocated by Judd (1998) and others for the simulation of stochastic optimal-control problems and we extend its application to more general cases. The coefficients for the first-order approximation of the expectation function are obtained using a generalized eigen value decomposition as it is usual for the simulation of linear rational-expectation models. Coefficients for higher-order terms in the Taylor expansion are then obtained by solving a succession of linear systems. In addition, we provide a method to reduce a bias in the computation of the stochastic equilibrium of such models. These procedures are made available in DYNARE, a MATLAB and GAUSS based simulation program. This method is then applied to the simulation of a macroeconomic model embodying a nonlinear Phillips curve. We show that in this case a quadratic approximation is sufficient, but different in important ways from the simulation of a linearized version of the model. Copyright 2001 by Kluwer Academic Publishers

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Article provided by Springer in its journal Computational Economics.

Volume (Year): 17 (2001)
Issue (Month): 2-3 (June)
Pages: 125-39
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Handle: RePEc:kap:compec:v:17:y:2001:i:2-3:p:125-39

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  3. Alain Gabler, 2007. "Sector-specific Markup Fluctuations and the Business Cycle," Economics Working Papers ECO2007/25, European University Institute. [Downloadable!]
  4. Dorofeenko, Victor & Lee, Gabriel S. & Salyer, Kevin D., 2002. "Time-Varying Uncertainty and the Credit Channel," Economics Series 118, Institute for Advanced Studies. [Downloadable!]
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