Identification and Estimation of Treatment Effects from Network Data with Confounded Social Links

Abstract

In observational network data, the adoption of a treatment and the formation of social ties often depend on the same characteristics that affect outcomes. We propose a generalized propensity score for each unit's effective treatment, built from a model for treatment assignment and a dyadic model for network formation, which may include latent node heterogeneity. The score is marginalized over the network given covariates rather than conditioned on the realized network, and the estimand is a population effect: the average effect of an exposure level for a unit drawn from the population of units and networks. We relate this estimand to those of methods that condition on the realized network and show what marginalizing costs and buys. It requires network formation to be unconfounded given observed covariates, a stronger assumption than unconfoundedness of treatment given the network. In exchange, it defines effects at exposure levels that poorly connected units cannot reach, and at levels every unit can reach it gives an estimator whose asymptotic variance is no larger than the network-conditional one. We combine the score with an augmented inverse probability weighting estimator, prove asymptotic normality as the number of networks grows with bounded network size, discuss what carries over to a single large sparse network, and apply the method to the effect of a political communication technology on political participation in Uganda.