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

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  • Andrew Binning

    ()
    (Norges Bank (Central Bank of Norway))

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    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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    File URL: http://www.norges-bank.no/en/Published/Papers/Working-Papers/2013/WP-201318/
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    Bibliographic Info

    Paper provided by Norges Bank in its series Working Paper with number 2013/18.

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    Length: 49 pages
    Date of creation: 05 Aug 2013
    Date of revision:
    Handle: RePEc:bno:worpap:2013_18

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    Related research

    Keywords: 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:

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