Partial Identification and Inference in Censored Quantile Regression: A Sensitivity Analysis

In this paper we characterize the identified set and construct asymptotically valid and non-conservative confidence sets for the quantile regression coeffi cient in a linear quantile regression model, where the dependent variable is subject to possibly dependent censoring. The underlying censoring mechanism is characterized by an Archimedean copula for the dependent variable and the censoring variable. For a broad class of Archimedean copulas, we characterize an outer set of the corresponding identified set for the quantile regression coeffi cient via inequality constraints. For one-parameter ordered families of Archimedean copulas, we construct simple confidence sets by inverting asymptotically pivotal statistics related to kernel-based model specification testing. The methodology we develop in this paper allows practitioners to conduct sensitivity analysis of the robustness of conclusions on the quantile regression coeffi cient to the independent censoring mechanism. Bootstrap confidence sets are also constructed. Interpreting the dependent variable and the censoring variable in our censored quantile regression model as two competing risks, our methodology is useful in duration analysis with possibly dependent competing risks. We present an empirical application to the survival time after acute myocardial infarction.