Working Paper: NBER ID: w20390
Authors: Andrew Foerster; Juan Rubio-Ramirez; Daniel F. Waggoner; Tao Zha
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: Markov-switching; DSGE models; perturbation methods
JEL Codes: C6; E3; G1
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| partition perturbation method (C59) | improved accuracy in approximations (C60) |
| partition perturbation method (C59) | preservation of time-varying coefficients in high-order Taylor series expansions (C22) |
| preservation of time-varying coefficients in high-order Taylor series expansions (C22) | improved accuracy in approximations (C60) |
| partition perturbation method (C59) | reduction in complexity of solving Markov-switching models (C32) |
| reduction in complexity of solving Markov-switching models (C32) | managing a system of quadratic polynomial equations (C62) |
| partition perturbation method (C59) | unique stable solution (C62) |