Inference in Censored Models with Endogenous Regressors
This paper analyzes the linear regression model y = xb+e with a conditional median assumption Med( e | z)=0 where z is a vector of instruments. Added complication arises due to the censoring of the outcome y. We treat the censored model as a model with interval-observed outcome thus obtaining interval restrictions on conditional median regressions. This allows us to use the framework introduced by Manski and Tamer (2000) to analyze the information contained in these inequality restrictions. We first show identification of the parameter b in the absence of censoring and introduce a consistent estimator based on the minimum distance method. We then give conditions for global identification of b in the model above with censored y and endogenous x. We provide a consistent estimator that is based on a modified minimum distance method.
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