Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution
- Andrew Binning
- Working Paper
In this paper I derive the matrix chain rules for solving a second and a third-order approximation to a DSGE model that allow the use of a recursive Sylvester equation solution method. In particular I use the solution algorithms of Kamenik (2005) and Martin & Van Loan (2006) to solve the generalised Sylvester equations. Because I use matrix algebra instead of tensor notation to find the system of equations, I am able to provide standalone Matlab routines that make it feasible to solve a medium scale DSGE model in a competitive time. I also provide Fortran code and Matlab/Fortran mex files for my method.
Norges Bank’s working papers present research projects and reports that are generally not in their final form. Other analyses by Norges Bank’s economists are also included in the series. The views and conclusions in these documents are those of the authors.
ISSN 1502-8190 (online)