Abstract

In this paper, we investigate the LS estimator of a structural change point by using the in-fill asymptotic theory, which are recently used by Jiang, Wang, and Yu (2018, 2021), when the model with two structural changes is estimated as the model with only a one-time structural change. We show that the finite sample distribution of the estimator has four peaks, which is quite different from the classical long-span asymptotic distribution, which has only one peak. On the contrary, the in-fill asymptotic distribution of the estimator has four peaks and can approximate the finite sample distribution very well. We also show that the estimator is consistent in the in-fill asymptotics framework with a relatively large magnitude of the break. In the latter case, the finite sample distribution of the estimator has only one peak and is well approximated by both the in-fill and long-span asymptotic theory.