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Perturbation Methods for Markov-Switching DSGE Models

Andrew Foerster, Juan Rubio-Ramírez, Daniel F. Waggoner, Tao Zha

NBER Working Paper No. 20390
Issued in August 2014
NBER Program(s):The Economic Fluctuations and Growth Program, The Monetary Economics Program

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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Document Object Identifier (DOI): 10.3386/w20390

Published: Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, 07. citation courtesy of

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