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Federal Reserve Bank of Atlanta
FRB Atlanta Working Paper
Perturbation methods for Markov-switching DSGE models
Andrew T. Foerster
Juan F. Rubio-Ramirez
Daniel F. Waggoner
Tao Zha

Markov-switching DSGE (MSDSGE) modeling has become a growing body of literature on economic and policy issues related to structural shifts. This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of MSDSGE models. Our new method, called "the partition perturbation method," partitions the Markov-switching parameter space to keep a maximum number of time-varying parameters from perturbation. For this method to work in practice, we show how to reduce the potentially intractable problem of solving MSDSGE models to the manageable problem of solving a system of quadratic polynomial equations. We propose to use the theory of Gröbner bases for solving such a quadratic system. This approach allows us to first obtain all the solutions and then determine how many of them are stable. We illustrate the tractability of our methodology through two examples.

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Andrew T. Foerster & Juan F. Rubio-Ramirez & Daniel F. Waggoner & Tao Zha, Perturbation methods for Markov-switching DSGE models, Federal Reserve Bank of Atlanta, FRB Atlanta Working Paper 2014-16, 01 Aug 2014.
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Keywords: partition principle; naive perturbation; uncertainty; Taylor series; high-order expansion; time-varying coefficients; nonlinearity; Gröbner bases
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