Conditional Moment Restrictions in Censored and Truncated Regression Models

Censored and truncated regression models with unknown distribution are important in econometrics. This paper characterizes the class of all conditional moment restrictions that lead to root-n consistent estimators for these models. The semiparametric efficiency bound for each conditional moment restriction is derived. In the case of a nonzero bound it is shown how an estimator can be constructed, and that an appropriately weighted version can attain the efficiency bound. These estimators also work when the disturbance is independent of the regressors. The paper discusses selecting among several estimators in this case, as well as methods of combining them to improve efficiency