  This paper studies a semiparametric quantile regression model with endogenous
variables and random right censoring. The endogeneity issue is solved using
instrumental variables. It is assumed that the structural quantile of the
logarithm of the outcome variable is linear in the covariates and censoring is
independent. The regressors and instruments can be either continuous or
discrete. The specification generates a continuum of equations of which the
quantile regression coefficients are a solution. Identification is obtained
when this system of equations has a unique solution. Our estimation procedure
solves an empirical analogue of the system of equations. We derive conditions
under which the estimator is asymptotically normal and prove the validity of a
bootstrap procedure for inference. The finite sample performance of the
approach is evaluated through numerical simulations. An application to the
national Job Training Partnership Act study illustrates the method.
