  We investigate large-sample properties of treatment effect estimators under
unknown interference in randomized experiments. The inferential target is a
generalization of the average treatment effect estimand that marginalizes over
potential spillover effects. We show that estimators commonly used to estimate
treatment effects under no interference are consistent for the generalized
estimand for several common experimental designs under limited but otherwise
arbitrary and unknown interference. The rates of convergence depend on the rate
at which the amount of interference grows and the degree to which it aligns
with dependencies in treatment assignment. Importantly for practitioners, the
results imply that if one erroneously assumes that units do not interfere in a
setting with limited, or even moderate, interference, standard estimators are
nevertheless likely to be close to an average treatment effect if the sample is
sufficiently large. Conventional confidence statements may, however, not be
accurate.
