Solving Second and Third-Order Approximations to DSGE Models: A Recursive Sylvester Equation Solution - Andrew Binning (Norges Bank, 2013)
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.
hdl:11250/2496688
Keywords: 330; generalised Sylvester equations; solving dynamic models; second-order approximation; third-order approximation; second-order matrix chain rule; third-order matrix chain rule