Likelihood-ratio-based confidence sets for the timing of structural breaks

We propose the use of likelihood-ratio-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 confidence set constructed by inverting the likelihood ratio test. Notably, the likelihood-ratio-based confidence sets are more precise than other confidence sets considered in the literature. Monte Carlo analysis confirms their greater precision in finite 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 gross domestic product 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 co-integration between output and consumption into account, confidence 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.