Abstract: This paper proposes an approach to estimate quantiles of the distribution of treatment effects under the identifying assumption that treatment assignment is based on observed characteristics. We use a matching approach to derive the distribution of treatment effects from differences in outcomes between matched treatment and control units. Our parameters of interest may be interpreted as generalized versions of the quantile treatment effect (QTE) and the quantile treatment effect on the treated (QTT), which can be identified without imposing a rank preservation assumption. We prove consistency and asymptotic normality of our estimators and show that replacing the variances with estimated variances does not affect the asymptotic distributions. We apply the approach to study the effects of a job training program on earnings. We find that while the average treatment effect on the treated is positive, about 40% of individuals in the treatment group have significantly lower earnings than comparable individuals in the control group.
Mathias Sinning is an Associate Professor at the Crawford School of Public Policy of the Australian National University (ANU).