Generalizing Full Rank Conditions in Heteroscedastic Censored Regression Models

Powell's (1984) 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 heteroscedasticity and distributional misspecification of the error term. However, the CLAD estimation procedure has failed in certain empirical applications (e.g. Honore et.al. (1997) and Chay (1995)) due to the restrictive nature of the "full rank" condition it requires. This condition can be especially problematic when the data is heavily censored. In this paper we introduce estimation procedures for heteroscedastic censored linear regression models with a much weaker identification restriction than that required for the CLAD, 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 alternativ...