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

Andrew Binning

No 2013/18, Working Paper from Norges Bank

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.

Keywords: Solving dynamic models; Second-order approximation; Third-order appeoximation; Second-order matrix chain rule; Third-order matrix chain rule; Generalised Sylvester equations (search for similar items in EconPapers)
Pages: 49 pages
Date: 2013-08-05
New Economics Papers: this item is included in nep-cba, nep-cmp, nep-dge, nep-ecm and nep-spo
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:bno:worpap:2013_18

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