Norges Bank

Working Paper

Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution

Author:
Andrew Binning
Series:
Working Paper
Number:
18/2013

Abstract
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.

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ISSN 1502-8190 (online)

Published 5 August 2013 10:45
Published 5 August 2013 10:45