On the use of shrinkage estimators in filtering extraneous information

In this article we show how shrinkage estimators can be used to pool data from two different subjects, in order to estimate the coefficients of an econometric model specified for one of the two subjects. We propose a modified version of the classic James–Stein estimator and devise a new shrinkage estimator (that we label W2M) which overcomes the well known applicability limits of the James–Stein estimators. We show how Ullah et al. inequalities can be adapted in order to state when these estimators can dominate the (ordinary) least-squares estimator. The performances of the estimators are evaluated by Monte Carlo experiments. Ullah’s inequality turns out to be a valid tool for these kind of problems. Our specific James–Stein estimator behaves generally better than the classic James–Stein version. What comes out mostly, is the surprising good performance of W2M: W2M can actually overcome the application difficulties of James–Stein-like estimators and it generally behaves much better than the shrinkage estimators of the James–Stein class which are here considered.