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.

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