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 derive the moment estimator of the model and the corresponding asymptotic covariance matrix. The results cover the moment estimation of 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. Using this approach it is also possible to derive the asymptotic bias of the estimator with wrong a priori identifying information. The small sample behavior of the two estimators and their sensitivities to misspecified a priori identifying information are studied through Monte Carlo simulations.