Clustering and External Validity in Randomized Controlled Trials

The randomization inference literature studying randomized controlled trials (RCTs) assumes that units' potential outcomes are deterministic. This assumption is unlikely to hold, as stochastic shocks may take place during the experiment. In this paper, we consider the case of an RCT with individual-level treatment assignment, and we allow for individual-level and cluster-level (e.g. village-level) shocks. We show that one can draw inference on the ATE conditional on the realizations of the cluster-level shocks, using heteroskedasticity-robust standard errors, or on the ATE netted out of those shocks, using cluster-robust standard errors.