Revisiting the Propensity Score’s Central Role: Towards Bridging Balance and Efficiency in the Era of Causal Machine Learning

Abstract

About forty years ago, in a now–seminal contribution, Rosenbaum and Rubin (1983) introduced a critical characterization of the propensity score as a central quantity for drawing causal inferences in observational study settings. In the decades since, much progress has been made across several research frontiers in causal inference, notably including the re-weighting and matching paradigms. Focusing on the former and specifically on its inter-section with machine learning and semiparametric efficiency theory, we re-examine the role of the propensity score in modern methodological developments. As Rosenbaum and Rubin (1983)’s contribution spurred a focus on the balancing property of the propensity score, we re-examine the degree to which and how this property plays a role in the development of asymptotically efficient estimators of causal effects; moreover, we discuss a connection between the balancing property and efficient estimation in the form of score equations and propose a score test for evaluating whether an estimator achieves empirical balance.