Set identification of the censored quantile regression model for short panels with fixed effects

This paper studies identification and estimation of a censored quantile regression model for short panel data with fixed effects. Using the redistribution-of-mass idea, we obtain bounds on the conditional distribution of differences of the model across periods, under conditional quantile restrictions together with a weak conditional independence assumption along the lines of Rosen (2012). The inversion of the distribution bounds characterizes the sharp identified set via a set of inequalities based on conditional quantile functions. Due to the presence of censoring, some of the inequalities defining the identified set hold trivially and have no identification power. Moreover, those trivial inequalities cause a difficulty in estimating the identified set. To deal with the issue, we propose a two-step estimation method, where the first step consists of excluding trivial inequalities and the second step performs minimization of a convex criterion function using the remaining inequalities. We establish asymptotic properties of the set estimator and also consider sufficient conditions under which point identification can be attained.