This paper studies identification and inference in transformation models with endogenous censoring. Many kinds of duration models, such as the accelerated failure time model, proportional hazard model, and mixed proportional hazard model, can be viewed as transformation models. We allow the censoring of a duration outcome to be arbitrarily correlated with observed covariates and unobserved heterogeneity. We impose no parametric restrictions on either the transformation function or the distribution function of the unobserved heterogeneity. In this setting, we develop bounds on the regression parameters and the transformation function, which are characterized by conditional moment inequalities involving U-statistics. Subsequently, we provide inference methods for them by constructing an inference approach for conditional moment inequality models in which the sample analogs of moments are U-statistics. We apply the proposed inference methods to evaluate the effect of unemployment insurance on duration of joblessness using data from the Current Population Survey's Displaced Workers Supplements.
