On the Use of Shrinkage Estimators in Filtering Extraneous Information

When estimating an econometric model, if the observations are scarce and, on the other side, there are several explanatory variables, we may obtain estimates with large standard errors. In such circumstances it becomes very important to get further information, in order to increase the precision of estimates. This can be done by enlarging the sample with observations taken from economic subjects which show a behaviour similar to the one we are directly interested in. However, if standard errors can be reduced by extraneous information, this operation may bias the estimates, due to possible differences between the coefficients of the subjects observed. In this article, in the framework of classic Econometrics, we show how shrinkage estimators can be used to introduce information from other samples, without biasing the estimates too much. Together with the classic James-Stein estimator, we shall specify a modified version of it, which seems to be more proper to problems similar to the one faced here; we shall then devise a new shrinkage estimator, which can overcome some applicability limits of the James-Stein estimator. The paper will also show how Ullah - Srivastava - Chandra (1983)'s inequalities can be adapted to the present problem, in order to state when the shrinkage estimators here considered dominate the "Ordinary least square" (OLS) estimator. The performances of the estimators here considered will be evaluated by Monte Carlo experiments, carried out under the hypothesis of normality.