Quantile structural treatment effects: application to smoking wage penalty and its determinants

We propose a new treatment effect parameter called the quantile structural treatment effect (QSTE) to distinguish between observed and unobserved treatment heterogeneity in the semiparametric additive potential outcome framework. The QSTE is defined as the quantile treatment effect if the observed covariates were exogenously set to a fixed value while keeping unobserved heterogeneity unchanged. We show the QSTE is identified under unconfoundedness and propose a semiparametric inverse probability weighted-type estimator that converges weakly to a Gaussian process. A multiplier bootstrap procedure is also carried out to construct uniform confidence bands. Using data from the Panel Study of Income Dynamics and focusing on the female group for the plausibility of the unconfoundedness assumption, we examine observed and unobserved determinants of the adverse effects of smoking on wages known as the smoking wage penalty. Our findings suggest that different levels of observable human capital may partly explain the smoking heterogeneity on wages. However, no evidence is found to support unobservable explanations such as discrimination against smokers, especially in the upper tail of the unobserved heterogeneity distribution.