Foerster, Andrew Rubio-Ramírez, Juan Waggoner, Daniel F. Zha, Tao
Year of Publication:
Working Paper, Federal Reserve Bank of Atlanta 2013-1
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 finding 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.
Markov-switching parameters partition higher order approximations no certainty equivalence quadratic system Grobner bases