Estimation of a Structural Break Point in Linear Regression Models

Abstract

This paper proposes a point estimator of the break location for a one-time structural break in linear regression models. If the break magnitude is small, the least-squares estimator of the break date has two modes at ends of the finite sample period, regardless of the true break location. I suggest a modification of the least-squares objective function to solve this problem. The modified objective function incorporates estimation uncertainty that varies across potential break dates. The new break point estimator is consistent and has a unimodal finite sample distribution under a small break magnitude. A limit distribution is provided under a in-fill asymptotic framework which verifies that the new estimator outperforms the least-squares estimator.