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

Author

Listed:
  • Andrew Binning

    (Norges Bank (Central Bank of Norway))

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.

Suggested Citation

  • Andrew Binning, 2013. "Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution," Working Paper 2013/18, Norges Bank.
    • Handle: RePEc:bno:worpap:2013_18
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    File URL: https://www.norges-bank.no/en/news-events/news-publications/Papers/Working-Papers/2013/WP-201318/
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    References listed on IDEAS

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    1. 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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    3. OndŘej KamenÍk, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 167-187, February.
    4. Andrew Binning, 2013. "Third-order approximation of dynamic models without the use of tensors," Working Paper 2013/13, Norges Bank.
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    7. RUGE-MURCIA, Francisco J., 2010. "Estimating Nonlinear DSGE Models by the Simulated Method of Moments," Cahiers de recherche 2010-10, Universite de Montreal, Departement de sciences economiques.
    8. 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.
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    Cited by:

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    2. Martin M. Andreasen & Giovanni Caggiano & Efrem Castelnuovo & Giovanni Pellegrino, 2021. "Why Does Risk Matter More in Recessions than in Expansions?," Monash Economics Working Papers 2021-11, Monash University, Department of Economics.
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    4. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    5. Martin M. Andreasen & Anders Kronborg, 2017. "The Extended Perturbation Method: New Insights on the New Keynesian Model," CREATES Research Papers 2017-14, Department of Economics and Business Economics, Aarhus University.
    6. Martin M. Andreasen, 2019. "Explaining Bond Return Predictability in an Estimated New Keynesian Model," CREATES Research Papers 2019-11, Department of Economics and Business Economics, Aarhus University.
    7. Martin M. Andreasen & Giovanni Caggiano & Efrem Castelnuovo & Giovanni Pellegrino, 2021. "Why Does Risk Matter More in Recessions than in Expansions?," "Marco Fanno" Working Papers 0275, Dipartimento di Scienze Economiche "Marco Fanno".
    8. Martin M. Andreasen & Kasper Jørgensen, 2016. "Explaining Asset Prices with Low Risk Aversion and Low Intertemporal Substitution," CREATES Research Papers 2016-16, Department of Economics and Business Economics, Aarhus University.

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