Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T21:02:47.425Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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

Information

Type
Notes
Information
Macroeconomic Dynamics , Volume 21 , Issue 7 , October 2017, pp. 1811 - 1826
Copyright
Copyright © Cambridge University Press 2016 

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.

References

REFERENCES

Aruoba, S. Boragan, Fernández-Villaverde, Jesús, and Rubio-Ramírez, Juan F. (2006) Comparing solution methods for dynamic equilibrium economies. Journal of Economic Dynamics and Control 30, 2477–2508.Google Scholar
Blanchard, Olivier J. and Kahn, Charles M. (1980) The solution of linear difference models under rational expectations. Econometrica 48, 1305–1311.Google Scholar
De Paoli, Bianca, Scott, Alasdair, and Weeken, Olaf (2010) Asset pricing implications of a New Keynesian model. Journal of Economic Dynamics and Control 34, 2056–2073.Google Scholar
Golub, Gene H. and Van Loan, Charles F. (1996) Matrix Computations, 3rd ed. Baltimore: Johns Hopkins University Press.Google Scholar
Hansen, Gary D. (1985) Indivisible labor and the business cycle. Journal of Monetary Economics 16, 309–327.CrossRefGoogle Scholar
Heer, Burkhard and Maußner, Alfred (2008) Computation of business cycle models: A comparison of numerical methods. Macroeconomic Dynamics 12, 641–663.CrossRefGoogle Scholar
Heer, Burkhard and Maußner, Alfred (2009) Computation of business-cycle models with the generalized Schur method. Indian Growth and Development Review 2, 173–182.CrossRefGoogle Scholar
Heer, Burkhard and Maußner, Alfred (2013) Asset returns, the business cycle, and the labor market. German Economic Review 14, 372–397.Google Scholar
Heiberger, Christopher, Klarl, Torben, and Maußner, Alfred (2015) On the uniqueness of solutions to rational expectations models. Economics Letters 128, 14–16.Google Scholar
Jermann, Urban J. (1998) Asset pricing in production economies. Journal of Monetary Economics 41, 257–275.CrossRefGoogle Scholar
Judd, Kenneth L. and Guu, Sy-Ming (1997) Asymptotic methods for aggregate growth models. Journal of Economic Dynamics and Control 21, 1025–1042.Google Scholar
King, Robert G. and Watson, Mark W. (1998) The solution of singular linear difference systems under rational expectations. International Economic Review 39, 1015–1026.Google Scholar
King, Robert G. and Watson, Mark W. (2002) System reduction and solution algorithms for singular linear difference systems under rational expectations. Computational Economics 20, 57–86.Google Scholar
Klein, Paul (2000) Using the generalized Schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control 24, 1405–1423.Google Scholar
Lemonnier, Damien and Van Dooren, Paul (2006) Balancing regular matrix pencils. SIAM Journal on Matrix Analysis and Applications 28 (1), 253–263.Google Scholar
Schmitt-Grohé, Stephanie and Uribe, Martin (2004) Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics and Control 28, 755–775.Google Scholar
Sims, Christopher A. (2002) Solving linear rational expectations models. Computational Economics 20, 1–20.CrossRefGoogle Scholar
Uhlig, Harald (1999) A toolkit for analysing nonlinear dynamic stochastic models easily. In Marimon, Ramon and Scott, Andrew (eds.), Computational Methods for the Study of Dynamic Economies. Oxford, UK: Oxford University Press.Google Scholar
Ward, Robert C. (1981) Balancing the generalized eigenvalue problem. SIAM Journal on Scientific and Statistical Computing 2 (2), 141–152.Google Scholar