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Likelihood-Ratio-Based Confidence Sets for the Timing of Structural Breaks

55 Pages Posted: 11 Sep 2008 Last revised: 2 Mar 2016

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: February 20, 2014


We propose the use of likelihood-ratio-based con fidence sets for the timing of structural breaks in parameters from time series regression models. The con fidence 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 con fidence set constructed by inverting the likelihood ratio test. Notably, the likelihood-ratio-based con fidence sets are more precise than other con fidence sets considered in the literature. Monte Carlo analysis confi rms their greater precision in fi nite samples, including in terms of maintaining accurate coverage even when the sample size or magnitude of a break is small. An application to postwar U.S. real GDP and consumption leads to a shorter 95% confidence set for the timing of the "Great Moderation" in the mid-1980s than previously found in the literature. Furthermore, when taking cointegration between output and consumption into account, con fidence sets for structural break dates become even shorter and suggest a 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, System of Equations; Great Moderation, Productivity Growth Slowdown

JEL Classification: C22, C32, E20

Suggested Citation

Eo, Yunjong and Morley, James, Likelihood-Ratio-Based Confidence Sets for the Timing of Structural Breaks (February 20, 2014). Available at SSRN: or

Yunjong Eo (Contact Author)

The University of Sydney - School of Economics ( email )

Rm 370 Merewether (H04)
Merewether Bldg (H04)
Sydney, NSW 2006

James Morley

University of Sydney ( email )

Rm 370 Merewether (H04)
Sydney, NSW 2006 2008

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