Revisiting the propensity score's central role: Towards bridging balance and efficiency in the era of causal machine learning

TL;DR

This paper revisits the fundamental role of the propensity score in causal inference, especially in the context of machine learning and efficiency, proposing new tests for estimator balance and efficiency.

Contribution

It critically re-examines the propensity score's balancing property in relation to asymptotic efficiency and introduces a score test for estimator balance in modern causal inference methods.

Findings

Proposes a score test for evaluating estimator balance.

Clarifies the connection between balancing property and efficiency.

Re-examines the role of propensity scores in modern causal methods.

Abstract

About forty years ago, in a now--seminal contribution, Rosenbaum & 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 fronts in causal inference, notably including the re-weighting and matching paradigms. Focusing on the former and specifically on its intersection with machine learning and semiparametric efficiency theory, we re-examine the role of the propensity score in modern methodological developments. As Rosenbaum & 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 balance.