Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/101019
Authors: 
Foerster, Andrew
Rubio-Ramírez, Juan
Waggoner, Daniel F.
Zha, Tao
Year of Publication: 
2014
Series/Report no.: 
Working Paper, Federal Reserve Bank of Atlanta 2014-16
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.
Subjects: 
partition principle
naive perturbation
uncertainty
Taylor series
high-order expansion
time-varying coefficients
nonlinearity
Gröbner bases
JEL: 
C6
E3
G1
Document Type: 
Working Paper

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