Identification of panel data models with endogenous censoring

We study inference on parameters in linear panel data models when outcomes are censored. We allow the censoring to depend on both observable and unobservable variables in arbitrary ways. Generally, these models are set identified and the main contribution of this paper is to derive and characterize the identified sets under general conditions. Our main characterization theorems show that every parameter in the sharp set–and only those parameters–can generate the observed data under the maintained assumptions. In particular, we consider two separate sets of assumptions (2 models): the first uses stationarity on the unobserved disturbance terms. The second is a nonstationary model with a conditional independence restriction. Based on the characterizations of the identified sets, we provide an inference procedure that is shown to yield valid confidence sets based on inverting stochastic dominance tests. We also show how our results extend to empirically interesting dynamic versions of the model with both lagged observed outcomes, lagged indicators, and models with factor loads. In addition, we provide sufficient conditions for point identification in terms of support conditions. The paper then examines the size of the identified sets in particular designs, and a Monte Carlo exercise shows reasonable small sample performance of our procedures. We also apply our inference approach to two empirical illustrations that link endogenous censoring to treatment effects models.