Estimation in truncated samples when there is heteroscedasticity

Abstract

If the population parameters of a regression function are estimated from a truncated sample by maximum likelihood under the incorrect assumption of a population homoscedastic disturbance term, the estimators are not consistent for the population parameters, and the size of the asymptotic bias may be substantial. The inconsistency is proved in the first part of the paper for a simple model. In the second part, the asymptotic bias is calculated for a number of combinations of parameters, and it is found that the bias is considerable even when the heteroscedasticity is in the range to be expected in empirical work. It is concluded that heteroscedasticity may be a serious empirical problem in truncated-sample models.