Quantile selection in the gender pay gap
We propose a new approach to estimate selection-corrected quantiles of the gender wage gap. Our method employs instrumental variables that explain variation in the latent variable but, conditional on the latent process, do not directly affect selection. We provide semiparametric identification of the quantile parameters without imposing parametric restrictions on the selection probability, derive the asymptotic distribution of the proposed estimator based on constrained selection probability weighting, and demonstrate how the approach applies to the Roy model of labor supply.