Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments

Many estimators of the average treatment effect, including difference-in-means, may be biased when clusters of units are allocated to treatment. This bias may remain even when the number of units grows asymptotically large. In this paper, we propose simple, unbiased and scale-invariant design-based estimators of the average treatment effect, along with associated variance estimators. We then analyze a cluster-randomized field experiment on voter mobilization in the United States, demonstrating that the proposed estimators have precision that is comparable (if not superior) to that of existing biased estimators of the average treatment effect. Our results have methodological implications for both experimental and observational research reliant on the Neyman-Rubin Causal Model of potential outcomes