Two-stage estimation of limited dependent variable models with errors-in-variables

This paper deals with censored or truncated regression models where the explanatory variables are measured with additive errors. We propose a two-stage estimation procedure that combines the instrumental variable method and the minimum distance estimation. This approach produces consistent and asymptotically normally distributed estimators for model parameters. When the predictor and instrumental variables are normally distributed, we also propose a maximum likelihood based estimator and a two-stage moment estimator. Simulation studies show that all proposed estimators perform satisfactorily for relatively small samples and relatively high degree of censoring. In addition, the maximum likelihood based estimators are fairly robust against non-normal and /or heteroskedastic random errors in our simulations. The method can be generalized to panel data models. Copyright Royal Economic Society 2007