MSE superiority of the unrestricted Stein-rule estimator in a regression model with a possible structural break

Abstract

This paper investigates the estimation of a linear regression model with a possible structural break at a known point. We analytically derive the exact formulae of the MSE for the restricted SR and PSR estimators, which shrinks the OLS estimator toward the restriction of no structural break. We compare the MSE performance of restricted/unrestricted SR, PSR, and least squared estimators. We analytically show that the unrestricted SR estimator can have a smaller MSE than the restricted SR estimator even when the restriction is correct. Further, our numerical results show that the unrestricted PSR estimator has the best MSE performance over a wide region of parameter space. These results indicate that the use of the unrestricted PSR estimator is recommended even when a structural break may not exist, although the unrestricted PSR estimator does not take the possibility of no structural break into consideration.

Keywords:

• Stein-rule estimator
• structural break
• MSE performance

Acknowledgments

The authors thank the editor and two anonymous referees for their extensively valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Humanities and Social Science Fund of Ministry of Education of China [Grant Number 23YJC790162], JSPS KAKENHI [Grant Number 18K01546, 23K01336].