Estimation of a Structural Break Point in Linear Regression Models

TL;DR

This paper introduces a new estimator for identifying the timing of a single structural break in linear regression models, especially effective when the break magnitude is small, outperforming traditional least-squares methods.

Contribution

It proposes a modified objective function-based estimator that is consistent, unimodal in finite samples, and better at detecting small break magnitudes compared to existing methods.

Findings

The new estimator outperforms least-squares in simulations.

It is consistent and has a unimodal distribution under small breaks.

Applied to economic data, it effectively identifies break points.

Abstract

This study 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 the ends of the finite sample period, regardless of the true break location. To solve this problem, I suggest an alternative estimator based on a modification of the least-squares objective function. 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 small break magnitudes. A limit distribution is provided under an in-fill asymptotic framework. Monte Carlo simulation results suggest that the new estimator outperforms the least-squares estimator. I apply the method to estimate the break date in U.S. real GDP growth and U.S. and UK stock return prediction models.