Estimation of a Structural Break Point in Linear Regression Models

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. and U.K. stock return prediction models.

Keywords:

• Change point
• Parameter instability
• Structural change

Supplementary Materials

Appendices: Appendix A provides an explanation of the Bayesian framework in Section 2, suggestions on other weight functions and the derivation that the estimator in (3) is a special case of (5). Appendix B includes all proofs of Sections 3 and 4. Additional tables and figures are in Appendix C. (pdf file)

Acknowledgments

I am very grateful for helpful comments and suggestions from Graham Elliott, James Hamilton, Brendan Beare, Kaspar Wuthrich, Yixiao Sun, Juwon Seo, Jungmo Yoon, and all seminar participants in UC San Diego Department of Economics and Peking University HSBC Business School. All remaining errors are my own.

Disclosure Statement

The author report there are no competing interests to declare.