A test of the conditional independence assumption in sample selection models Martin Huber, Blaise Melly First draft: December 2006, Last changes: September 2012 Abstract: Identication in most sample selection models depends on the independence of the regressors and the error terms conditional on the selection probability. All quantile and mean functions are parallel in these models; this implies that quantile estimators cannot reveal anyper assumption non-existingheterogeneity. Quantile estimators are nevertheless useful for testing the conditional independence assumption because they are consistent under the null hypothesis. We propose tests of the Kolmogorov-Smirnov type based on the conditional quantile regression process. Monte Carlo simulations show that their size is satisfactory and their power su¢cient to detect deviations under realistic data generating processes. We apply our procedures to female wage data from the 2011 Current Population Survey and show that homogeneity is clearly rejected. Keywords: sample selection, quantile regression, independence, test JEL classication: C12, C13, C14, C21 This paper was previously circulated under the titles "Quantile regression in the presence of sample selection" and "Sample selection, heteroscedasticity, and quantile regression". We would like to thank the editor (Edward Vytlacil), four referees, Stefan Hoderlein, Frank Kleibergen, Michael Lechner, and seminar participants at Brown University, University of St. Gallen, the labor market seminar of the University of Zürich in Engelberg, the conference Inference and Tests in Econometrics in Marseille, and the COST A23 conference in Paris for very useful comments that helped improve the paper. Addresses for correspondence: Martin Huber, SEW, University of St. Gallen, Varnbüelstrasse 14, 9000 St. Gallen, Switzerland, martin.huber@unisg.ch; Blaise Melly, Brown University, Department of Economics, Providence, RI, USA, blaise_melly@brown.edu.