A Comparison of Alternative Methods to Construct to Confidence Intervals for the Estimate of a Break Date in Linear Regression Models

This paper considers constructing conÖdence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the per- formance of various procedures in terms of exact coverage rates and lengths of the conÖdence intervals. These include the procedures of Bai (1997) based on the asymp- totic distribution under a shrinking shift framework, Elliott and M ̧ller (2007) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2013) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and M ̧lleriÌ s (2007) approach is by far the best one. However, this comes with a very high cost in terms of the length of the conÖdence intervals. When the errors are se- rially correlated and dealing with a change in intercept or a change in the coe¢ cient of a stationary regressor with a high signal to noise ratio, the length of the conÖdence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and M ̧lleriÌ s (2007) method.