Likelihood-Based Confidence Sets for the Timing of Structural Breaks

49 Pages Posted: 17 May 2013 Last revised: 22 May 2013

See all articles by Yunjong Eo

Yunjong Eo

The University of Sydney - School of Economics

James Morley

University of Sydney

Multiple version iconThere are 2 versions of this paper

Date Written: March 30, 2013


We propose the use of likelihood-based confidence sets for the timing of structural breaks in parameters from time series regression models. The confidence sets are valid for the broad setting of a system of multivariate linear regression equations under fairly general assumptions about the error and regressors and allowing for multiple breaks in mean and variance parameters. In our asymptotic analysis, we determine the critical values for a likelihood ratio test of a break date and the expected length of a likelihood-based confidence set constructed by inverting the likelihood ratio test. Notably, the likelihood-based confidence set is considerably shorter than for other methods employed in the literature. Monte Carlo analysis confirms better performance than other methods in terms of length and coverage accuracy in finite samples, including when the magnitude of breaks is small. An application to postwar U.S. real GDP and consumption leads to a much tighter 95% confidence set for the timing of the “Great Moderation” in the mid-1980s than previously found. Furthermore, when taking cointegration between output and consumption into account, confidence sets for structural break dates are even more precise and suggest a sudden “productivity growth slowdown” in the early 1970s and an additional large, abrupt decline in long-run growth in the mid-1990s.

Keywords: Inverted Likelihood Ratio Confidence Sets, Multiple Breaks, Great Moderation, Productivity Growth Slowdown

JEL Classification: C22, C32, E20

Suggested Citation

Eo, Yunjong and Morley, James, Likelihood-Based Confidence Sets for the Timing of Structural Breaks (March 30, 2013). UNSW Australian School of Business Research Paper No. 2013-12. Available at SSRN: or

Yunjong Eo

The University of Sydney - School of Economics ( email )

Social Sciences Building (A02)
Sydney, NSW 2006

James Morley (Contact Author)

University of Sydney ( email )

Rm 370 Merewether (H04)
Sydney, NSW 2006 2008

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