Estimation of censored linear errors-in-variables models

This paper deals with a linear errors-in-variables model where the dependent variable is censored. A two-step procedure is proposed to estimate the model and the corresponding asymptotic covariance matrices are derived. The framework covers the usual (error-free) Tobit model as a special case. It is shown that, under normality and a certain identifying condition, this model can be uniquely reduced to an error-free censored regression model and, hence, the existing estimators for the Tobit model can be used to obtain estimators for this model. In particular, the maximum-likelihood estimator is derived in this way. The small-sample behavior of the two estimators and their sensitivities to misspecified identifying information are studied through Monte-Carlo simulations.