The Efficiency of Some Alternative Ridge Estimators for Seemingly Unrelated Regressions

Parametric Seemingly Unrelated Regression (SUR) models are used for multivariate regression analysis. However, statistical literature has revealed that, multicollinearity often affects the efficiency of SUR estimators. One of the popular methods for coping with Multicollinearity problem is ridge regression estimation. In this study, some alternative ridge estimators for SUR parameters are proposed when the explanatory variables are affected by multicollinearity. The efficiency of the proposed estimators is evaluated and compared through simulation study, in terms of the Trace Mean Squared Error (TMSE) and the Proportion of Replications, (PR) criterion, under a variety of data conditions. The empirical results indicated that, under certain conditions, the performance of the multivariate regression estimators based on some SUR ridge parameters are superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high, the unbiased SUR estimator produces a smaller TMSEs.