Abstract:This paper examines the identification and estimation of partially linear quantile regression models in the presence of sample selection. To address the selection bias arising in quantile regression, we model the joint distribution of the unobserved disturbances in the outcome and selection equations-using, for instance, a copula specification-to obtain consistent estimates. We set out the assumptions required for identification and, building on the generalized method of moments for quantile regression, develop estimation procedures for both the quantile parameters (or functions) and the copula parameters. We establish the consistency and asymptotic normality of the proposed estimators. For inference, we implement a nonparametric bootstrap to compute standard errors and construct test statistics to assess the validity of the nonlinear specification. Using a control function framework, we further clarify the relationship between the endogenous linear quantile selection model and our proposed specification. Monte Carlo simulations indicate that the estimators perform well in finite samples. Finally, we apply the methodology to estimate the returns to female education, demonstrating the model’s practical relevance.