Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution
AbstractIn 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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Bibliographic InfoPaper provided by Norges Bank in its series Working Paper with number 2013/18.
Length: 49 pages
Date of creation: 05 Aug 2013
Date of revision:
Solving dynamic models; Second-order approximation; Third-order appeoximation; Second-order matrix chain rule; Third-order matrix chain rule; Generalised Sylvester equations;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-08-16 (All new papers)
- NEP-CBA-2013-08-16 (Central Banking)
- NEP-CMP-2013-08-16 (Computational Economics)
- NEP-DGE-2013-08-16 (Dynamic General Equilibrium)
- NEP-ECM-2013-08-16 (Econometrics)
- NEP-SPO-2013-08-16 (Sports & Economics)
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