Robust Estimators for Random Coefficient Regression Models

Random coefficient regression models have received considerable attention, especially from econometricians. Previous work has assumed that the coefficients have normal distributions. The variances of the coefficients have, in previous papers, been estimated by maximum likelihood or by least squares methodology applied to the squared residuals from a preliminary (unweighted) fit. Maximum likelihood estimation poses difficult numerical problems. Least squares estimation of the variances is inefficient because the squared residuals have a distribution with a heavy right tail. In this paper we propose several robust estimators for random coefficients models. We compare them by Monte Carlo with estimators based on least squares applied to the squared residuals. The robust estimators are best overall, even at the normal model. Among the different robust estimators, none stands out as best. All are rather satisfactory and can be tentatively recommended for routine use.