  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.
