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

  • Andrew Binning

    ()

    (Norges Bank (Central Bank of Norway))

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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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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  1. Ondrej Kamenik, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Working Papers 2005/10, Czech National Bank, Research Department.
  2. RUGE-MURCIA, Francisco J., 2010. "Estimating Nonlinear DSGE Models by the Simulated Method of Moments," Cahiers de recherche 19-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Galí, Jordi & Monacelli, Tommaso, 2005. "Optimal Monetary and Fiscal Policy in a Currency Union," CEPR Discussion Papers 5374, C.E.P.R. Discussion Papers.
  4. Paul Gomme & Paul Klein, 2009. "Second-order approximation of dynamic models without the use of tensors," Working Papers 09004, Concordia University, Department of Economics, revised 28 Apr 2010.
  5. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
  6. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," CEPR Discussion Papers 2963, C.E.P.R. Discussion Papers.
  7. anonymous, 2009. "Monetary policy report to the Congress," Web Site 46, Board of Governors of the Federal Reserve System (U.S.).
  8. Andrew Binning, 2013. "Third-order approximation of dynamic models without the use of tensors," Working Paper 2013/13, Norges Bank.
  9. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
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