Balancing Weights for Causal Inference

Covariate balance is central to both randomized experiments and observational studies. In randomized experiments, covariate balance is expected by design: when treatment is randomized, covariates are balanced in expectation, and observed differences in outcomes between the treatment groups can be granted a causal interpretation. In observational studies, where the treatment assignment is not controlled by the investigator, such balance is not guaranteed, and, subject to certain assumptions, one can adjust the data to achieve balance and obtain valid causal inferences. In fact, if investigators believe that treatment assignment is determined only by observed covariates, then balance is sufficient to remove confounding and establish causation from association.