Perturbation Methods for Markov-Switching DSGE Models

39 Pages Posted: 4 Apr 2015

See all articles by Andrew T. Foerster

Andrew T. Foerster

Federal Reserve Banks - Federal Reserve Bank of San Francisco

Juan Francisco Rubio-Ramirez

Federal Reserve Bank of Atlanta - Research Department

Daniel F. Waggoner

Federal Reserve Bank of Atlanta

Tao A. Zha

Federal Reserve Bank of Atlanta; Emory University

Multiple version iconThere are 4 versions of this paper

Date Written: August 1, 2014

Abstract

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.

Keywords: partition principle, naive perturbation, uncertainty, Taylor series, high-order expansion, time-varying coefficients, nonlinearity, Gröbner bases

JEL Classification: C6, E3, G1

Suggested Citation

Foerster, Andrew T. and Rubio-Ramirez, Juan Francisco and Waggoner, Daniel F. and Zha, Tao A., Perturbation Methods for Markov-Switching DSGE Models (August 1, 2014). FRB Atlanta Working Paper No. 2014-16, Available at SSRN: https://ssrn.com/abstract=2580449 or http://dx.doi.org/10.2139/ssrn.2580449

Andrew T. Foerster

Federal Reserve Banks - Federal Reserve Bank of San Francisco ( email )

101 Market Street
San Francisco, CA 94105
United States

Juan Francisco Rubio-Ramirez

Federal Reserve Bank of Atlanta - Research Department ( email )

1000 Peachtree Street, NE
Atlanta, GA 30309-4470
United States
404-498-8057 (Phone)
404-498-8956 (Fax)

HOME PAGE: http://www.econ.umn.edu/~rubio

Daniel F. Waggoner (Contact Author)

Federal Reserve Bank of Atlanta ( email )

1000 Peachtree Street N.E.
Atlanta, GA 30309-4470
United States
404-521-8278 (Phone)

Tao A. Zha

Federal Reserve Bank of Atlanta ( email )

1000 Peachtree Street N.E.
Atlanta, GA 30309-4470
United States
404-521-8353 (Phone)
404-521-8956 (Fax)

Emory University ( email )

201 Dowman Drive
Atlanta, GA 30322
United States

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