Partial identification and inference in censored quantile regression

In this paper, we study partial identification and inference in a linear quantile regression, where the dependent variable is subject to possibly unknown dependent censoring characterized by an Archimedean copula. An outer set of the identified set for the regression coefficient is characterized via inequality constraints. For one-parameter ordered families of Archimedean copulas, we construct a simple confidence set by inverting an asymptotically pivotal statistic. A bootstrap confidence set is also constructed. Sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically.