Fast Algorithms for Quantile Regression with Selection

Abstract The estimation of Quantile Regression with Selection (QRS) requires the estimation of the entire quantile process several times to estimate the parameters that model self-selection. Moreover, closed-form expressions of the asymptotic variance are too cumbersome, making the bootstrap more convenient to perform inference. I propose streamlined algorithms for the QRS estimator that significantly reduce computation time through preprocessing techniques and quantile grid reduction for the estimation of the parameters. I show the optimization enhancements and how they can improve the precision of the estimates without sacrificing computational efficiency with some simulations.