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Scientists have been interested in estimating causal peer effects tounderstand how people's behaviors are affected by their network peers. However,it is well known that identification and estimation of causal peer effects arechallenging in observational studies for two reasons. The first is theidentification challenge due to unmeasured network confounding, for example,homophily bias and contextual confounding. The second issue is networkdependence of observations, which one must take into account for validstatistical inference. Negative control variables, also known as placebovariables, have been widely used in observational studies including peer effectanalysis over networks, although they have been used primarily for biasdetection. In this article, we establish a formal framework which leverages apair of negative control outcome and exposure variables (double negativecontrols) to nonparametrically identify causal peer effects in the presence ofunmeasured network confounding. We then propose a generalized method of momentsestimator for causal peer effects, and establish its consistency and asymptoticnormality under an assumption about $\psi$-network dependence. Finally, weprovide a network heteroskedasticity and autocorrelation consistent varianceestimator. Our methods are illustrated with an application to peer effects ineducation.

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