Identification and Estimation of Causal Peer Effects Using Double Negative Controls for Unmeasured Network Confounding

Abstract: Scientists have been interested in estimating causal peer effects to understand how people's behaviors are affected by their network peers. However, it is well known that identification and estimation of causal peer effects are challenging in observational studies for two reasons. The first is the identification challenge due to unmeasured network confounding, for example, homophily bias and contextual confounding. The second issue is network dependence of observations, which one must take into account for valid statistical inference. Negative control variables, also known as placebo variables, have been widely used in observational studies including peer effect analysis over networks, although they have been used primarily for bias detection. In this article, we establish a formal framework which leverages a pair of negative control outcome and exposure variables (double negative controls) to nonparametrically identify causal peer effects in the presence of unmeasured network confounding. We then propose a generalized method of moments estimator for causal peer effects, and establish its consistency and asymptotic normality under an assumption about $\psi$-network dependence. Finally, we provide a network heteroskedasticity and autocorrelation consistent variance estimator. Our methods are illustrated with an application to peer effects in education.