A modified confidence set for the structural break date in linear regression models

Elliott and Müller (EM) (2007) provide a method for constructing a confidence set for the structural break date by inverting a variant of the locally best test statistic. Previous studies have shown that the EM method produces a set with an accurate coverage ratio even for a small break; however, the set is often overly lengthy. This study proposes a simple modification to rehabilitate their method through the long-run variance estimation. Following the literature, we provide an asymptotic justification for the improvement of the modified method over the original method under a nonlocal asymptotic framework. A Monte Carlo simulation shows that the modified method achieves a shorter confidence set than the EM method, especially when the break is large or the HAC correction is conducted. The modified method may exhibit minor errors in the coverage rate when the break is small; however, the coverage is more stable than alternative methods when the break is large. We apply our method to a level shift in post-1980s Japanese inflation data.