Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity

Powellʹs (1984, Journal of Econometrics 25, 303–325) censored least absolute deviations (CLAD) estimator for the censored linear regression model has been regarded as a desirable alternative to maximum likelihood estimation methods due to its robustness to conditional heteroskedasticity and distributional misspecification of the error term. However, the CLAD estimation procedure has failed in certain empirical applications due to the restrictive nature of the ‘full rank’ condition it requires. This condition can be especially problematic when the data are heavily censored. In this paper we introduce estimation procedures for heteroskedastic censored linear regression models with a much weaker identification restriction than that required for the LCAD, and which are flexible enough to allow for various degrees of censoring. The new estimators are shown to have desirable asymptotic properties and perform well in small-scale simulation studies, and can thus be considered as viable alternatives for estimating censored regression models, especially for applications in which the CLAD fails.