Design-Based Ratio Estimators for Clustered, Blocked RCTs

This article develops design-based ratio estimators for clustered, blocked RCTs using the building blocks of experiments. We consider finite population regression estimators, allowing for weights and covariates. We prove consistency and asymptotic normality results and discuss simple variance estimators that share features with cluster-robust standard error (CRSE) estimators. Simulations show that with few clusters, the design-based estimator yields nominal rejection rates, while the standard CRSE estimator over-rejects. The key reason is that the randomization mechanism yields separate degrees of freedom adjustments for the treatment and control variances, rather than a single adjustment as for the CRSE estimator.