In the literature studying randomized controlled trials (RCTs), it is often
assumed that the potential outcomes of units participating in the experiment
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 to affect the
potential outcomes. We show that one can draw inference on two estimands: the
ATE conditional on the realizations of the cluster-level shocks, using
heteroskedasticity-robust standard errors; the ATE netted out of those shocks,
using cluster-robust standard errors. By clustering, researchers can test if
the treatment would still have had an effect, had the stochastic shocks that
occurred during the experiment been different. Then, the decision to cluster or
not depends on the level of external validity one would like to achieve