Efficient semiparametric estimation of network treatment effects under partial interference

Although many estimators for network treatment effects have been proposed, their optimality properties, in terms of semiparametric efficiency, have yet to be resolved. We present a simple yet flexible asymptotic framework for deriving the efficient influence function and the semiparametric efficiency lower bound for a family of network causal effects under partial interference. An important corollary of our results is that one existing estimator, that proposed by Liu et al. (2019), is locally efficient. We also present other estimators that are efficient and discuss results on adaptive estimation. We illustrate application of the efficient estimators in a study of the direct and spillover effects of conditional cash transfer programmes in Colombia.