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ON THE NUMERICAL ACCURACY OF FIRST-ORDER APPROXIMATE SOLUTIONS TO DSGE MODELS

Published online by Cambridge University Press:  11 October 2016

Christopher Heiberger ,
Torben Klarl  and
Alfred Maussner
Christopher Heiberger
Affiliation:
University of Augsburg
Torben Klarl
Affiliation:
University of Augsburg
Alfred Maussner*
Affiliation:
University of Augsburg
*
Address correspondence to: Alfred Maußner, Department of Economics, University of Augsburg, Universitätsstraße 16, 86159 Augsburg, Germany; e-mail: alfred.maussner@wiwi.uni-augsburg.de.
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Abstract

Many algorithms that provide approximate solutions for dynamic stochastic general equilibrium (DSGE) models employ the QZ factorization because it allows a flexible formulation of the model and exempts the researcher from identifying equations that give raise to infinite eigenvalues. We show, by means of an example, that the policy functions obtained by this approach may differ from both the solution of a properly reduced system and the solution obtained from solving the system of nonlinear equations that arises from applying the implicit function theorem to the model's equilibrium conditions. As a consequence, simulation results may depend on the specific algorithm used and on the numerical values of parameters that are theoretically irrelevant. The sources of this inaccuracy are ill-conditioned matrices as they emerge, e.g., in models with strong habits. Researchers should be aware of those strange effects, and we propose several ways to handle them.

Keywords

DSGE ModelsQZ FactorizationSystem ReductionAccuracy of Solutions
Type
Notes
Information
Macroeconomic Dynamics , Volume 21 , Issue 7 , October 2017 , pp. 1811 - 1826
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

This paper is a substantially revised and extended version of our former working paper entitled “System Reduction and the Accuracy of Solutions of DSGE Models: A Note.” We are grateful to two anonymous referees for their comments and suggestions. Of course, all remaining errors and shortcomings are ours. Alfred Maußner acknowledges financial support by the Deutsche Forschungsgemeinschaft within the priority program “Financial Market Imperfections and Macroeconomic Performance” under Grant MA 1110/3-1.

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