Sample Selection in Quantile Regression: A Survey

Abstract

This chapter focuses on the question of correcting quantile regression estimates for nonrandom sample selection. It provides the empirical illustration in Huber and Melly, and estimate uncorrected and selection-corrected wage returns to experience and education based on data on female wages and employment status from the 1991 Current Population Survey. A central observation is that, in quantile models, even linear ones, quantile curves on the selected sample are generally not linear. However, a correction is available which involves rotating the check function of quantile regression by an amount that is observation-specific and depends on the strength of selection. A nonquantile regression based approach to selection correction is to parametrically specify both outcome and selection equations, thus providing non-Gaussian extensions to the Heckman model. The chapter deals with an alternative approach to Arellano and Bonhomme based on maximum likelihood. It provides the link between selection correction and censoring correction in quantile regression.