Finite sample properties of an HPT estimator when each individual regression coefficient is estimated in a misspecified linear regression model

ABSTRACT

In this paper, assuming that there exist omitted variables in the specified model, we analytically derive the exact formula for the mean squared error (MSE) of a heterogeneous pre-test (HPT) estimator whose components are the ordinary least squares (OLS) and feasible ridge regression (FRR) estimators. Since we cannot examine the MSE performance analytically, we execute numerical evaluations to investigate small sample properties of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Our numerical results show that (1) the HPT estimator is more efficient when the model misspecification is severe; (2) the HPT estimator with the optimal critical value obtained under the correctly specified model can be safely used even when there exist omitted variables in the specified model.

Keywords:

• Feasible ridge regression estimator
• Heterogeneous preliminary test estimator
• MSE performance
• Omitted variables
• Optimal critical value

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05
• 62J07

Acknowledgments

I would like to thank Kazuhiro Ohtani for his guidance and suggestions. I would also like to thank Akio Namba and an anonymous referee for their valuable comments which greatly improved the present version of the article.

Notes

¹The SR, PSR, and AMMSE estimator are proposed by Stein (1956), Baranchik (1970), and Ohtani (1996), respectively.

²The MMSE estimator is proposed by Farebrother (1975).