The Equity Estimator for Marketing Research

We introduce a new biased estimator called the Equity estimator to estimate parameters of linear models in the presence of multicollinearity. We then employ a comprehensive simulation methodology to evaluate OLS, the Equity estimator, and a particular form of the Ridge estimator which has received some attention in the statistical literature. We show that both Equity and Ridge perform significantly better than OLS on a variety of performance measures over most of the parameter space. The Equity estimator does much better than the Ridge estimator on the squared error criterion. On other criteria, the Equity estimator performs marginally better than Ridge. In particular, Equity does well when the degree of multicollinearity among the explanatory variables is high and/or the R2 of OLS for the sample is less than 0.7, conditions frequently encountered in marketing research. We discuss how the results of this study can be used by marketing researchers in choosing an appropriate estimator for their particular application.