  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.
