Sample empirical likelihood methods for causal inference

Causal inference plays a crucial role in understanding the true impact of interventions, medical treatments, policies, or actions, enabling informed decision making and providing insights into the underlying mechanisms that shape our world. In this article, we establish a framework for the estimation of and inference concerning average treatment effects using a two-sample empirical likelihood function. Two different approaches to incorporating propensity scores are developed. The first approach introduces propensity-score-calibrated constraints in addition to the standard model-calibration constraints; the second approach uses the propensity scores to form weighted versions of the model-calibration constraints. The resulting estimators from both approaches are doubly robust. The limiting distributions of the two-sample empirical likelihood ratio statistics are derived, facilitating the construction of confidence intervals and hypothesis tests for the average treatment effect. Bootstrap methods for constructing sample empirical likelihood ratio confidence intervals are also discussed for both approaches. The finite-sample performance of each method is investigated via simulation studies.