Covariate Distribution Balance via Propensity Scores

Abstract

This paper proposes new estimators for the propensity score that aim to maximize the covariate distribution balance among different treatment groups. Heuristically, our proposed procedure attempts to estimate a propensity score model by making the underlying covariate distribution of different treatment groups as close to each other as possible. Our estimators are data-driven, do not rely on tuning parameters such as bandwidths, admit an asymptotic linear representation, and can be used to estimate different treatment effect parameters under different identifying assumptions, including unconfoundedness and local treatment effects. We derive the asymptotic properties of inverse probability weighted estimators for the average, distributional, and quantile treatment effects based on the proposed propensity score estimator and illustrate their finite sample performance via Monte Carlo simulations and two empirical applications.

Keywords: Causal inference; Empirical process; Inverse probability weighting; Minimum distance; Quantile treatment effects; Treatment effect heterogeneity