On Some Heteroskedasticity-Robust Estimators of Variance-Covariance Matrix of the Least Squares Estimators

Chesher and Jewitt (1987) demonstrated that the Eicker (1963) and White (1980) consistent estimator of the variance-covariance matrix in heteroskedastic models could be severely biased if the design matrix is highly unbalanced. In this paper we, therefore, reconsider Rao's (1970) minimum norm quadratic unbiased estimator (MINQUE). We derive the analytical expressions for the mean squared errors (MSE) of the Eicker-White, one of MacKinnon and White's (1985) and MINQUE estimators, and perform a numerical comparison. Our analysis shows that although MINQUE is unbiased by construction, it has very large variance particularly for the highly unbalanced design matrices. Since the variance is the dominant factor in our MSE computation, MINQUE is not the preferred estimator in terms of MSE comparison. We also studied the finite sample behavior of the confidence interval of regression coefficients in terms of coverage probabilities based on different variance-covariance matrix estimators. Our results indicate that although MINQUE generally has the largest MSE, it performs relatively well in terms of coverage probabilities