• First difference;
  • Limiting distribution;
  • Linear process;
  • Pitman drift;
  • Trend shift

Summary  This paper analyses two break point estimators: one for a univariate slope-shift model under unit root errors, the other for its first difference (a mean shift model). The asymptotic theory is developed for the estimators under a specific Pitman drift, assuming the break magnitude is within a T−1/2 neighbourhood of zero. Compared to the existing asymptotics assuming a fixed break magnitude or a shrinking one converging at a slower rate than T1/2, the limiting distributions here closely resemble the finite sample distributions of the break point estimators, especially the tail behaviours. Though with a lower convergence rate, the break point estimator from level model concentrates more around the true break point when the break magnitude is small relative to the noise magnitude. With the new limiting distributions, thresholds are provided for empirical researchers to choose the break point estimator based on a mean squared error criterion.