Working Paper: CEPR ID: DP9464
Authors: Andrew Foerster; Juan Francisco Rubio-Ramirez; Dan Waggoner; Tao Zha
Abstract: This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of definding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ascertain how many of them are stable. Our methodology is applied to three models to illustrate its feasibility and practicality.
Keywords: DSGE; Markov-switching; Perturbation
JEL Codes: E17; E37
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| partitioning the Markov-switching parameter space (C32) | defining a steady state consistent with the original economic model (E19) |
| solving a system of quadratic equations (C62) | finding approximations (C60) |
| Gröbner bases (C69) | reduction of the problem to solving a system of quadratic equations (C60) |
| mathematical tools employed (C65) | identification of stable approximations (C62) |
| nature of the approximations (C60) | behavior of agents in response to risk (D81) |