An optimization-based propensity score matching estimator

Abstract

This paper proposes a simple alternative for the treatment e ect estimators based on match- ing on the estimated propensity score. In this approach, both weights and the number of coun- terfactuals employed in realizing the potential outcomes used to determine the average treatment e ects are endogenously determined after minimizing a proper bound of the individual bias that the unit under analysis aggregates to the whole conditional bias of the estimation. We provide a new Stata routine, called blopmatchingps, that implements the method, and we carry out di erent numerical experiments to assess the performance of our estimator using nite samples. Finally, large sample properties, and a consistent estimator for the asymptotic variance of our proposal, are also given in this paper. Keywords: Propensity score, matching estimator, treatment e ect estimator, semiparametric methods, optimization.