Counterfactual distributions with sample selection adjustments: Econometric theory and an application to the Netherlands

Several recent papers use the quantile regression decomposition method of Machado and Mata [Machado, J.A.F. and Mata, J. (2005). Counterfactual decomposition of changes in wage distributions using quantile regression, Journal of Applied Econometrics, 20, 445–65.] to analyze the gender gap across log wage distributions. In this paper, we prove that this procedure yields consistent and asymptotically normal estimates of the quantiles of the counterfactual distribution that it is designed to simulate. Since employment rates often differ substantially by gender, sample selection is potentially a serious issue for such studies. To address this issue, we extend the Machado–Mata technique to account for selection. We illustrate our approach to adjusting for sample selection by analyzing the gender log wage gap for full-time workers in the Netherlands.