Propensity Score and the Double Robust Estimator in the Tails

This study analyzes the performance of the double robust estimator to compute the treatment effect, not only at the mean but also in the tails in a Monte Carlo experiment. While previous research focused on shifting the regression component of the double robust estimator toward the tail, here we focus on the behavior of the propensity score away from the mean. Investigating the tails of the regression outcome allows for a closer look at the observations that are either highly or poorly responsive to treatment. Examining the tails of the propensity score distribution scrutinizes the observations with a higher or lower probability of being treated, which can be non-constant and even asymmetric. The goal is to assess the behavior of the double robust estimator when both components are computed away from the sample mean, in the tails of the treatment and control distributions. A case study on Italian education concludes the analysis. We find a positive double robust difference in higher education across regions, larger at the top location, due to the significant internal migration of qualified workers toward the northern regions. Women’s employment is higher for highly educated women, and gender has a significant impact: the analysis of the mismatch between probabilities and outcomes signals that women achieve higher education at rates exceeding their probabilities; they are more likely to exceed their predicted likelihood of attaining higher education.