Counterfactual quantile decompositions with selection correction taking into account Huber/Melly (2015): An application to the German gender wage gap

Albrecht et al. (2009) use the approach of Buchinsky (1998; 2001) to estimate selection corrected quantile regressions for the estimation of counterfactual wage distributions. Huber and Melly (2015) point to the fact that the Buchinsky approach requires a conditional independence assumption that may be violated in applications and suggest a test for this. This paper proposes to transform the original quantile regression model in order to ensure the conditional independence assumption to hold when it is rejected for the original model. Our empirical results on the gender wage gap for Germany suggest that unobserved selection may be underestimated if no transformation is applied.