  We consider a causal inference model in which individuals interact in a
social network and they may not comply with the assigned treatments. In
particular, we suppose that the form of network interference is unknown to
researchers. To estimate meaningful causal parameters in this situation, we
introduce a new concept of exposure mapping, which summarizes potentially
complicated spillover effects into a fixed dimensional statistic of
instrumental variables. We investigate identification conditions for the
intention-to-treat effects and the average treatment effects for compliers,
while explicitly considering the possibility of misspecification of exposure
mapping. Based on our identification results, we develop nonparametric
estimation procedures via inverse probability weighting. Their asymptotic
properties, including consistency and asymptotic normality, are investigated
using an approximate neighborhood interference framework. For an empirical
illustration, we apply our method to experimental data on the anti-conflict
intervention school program. The proposed methods are readily available with
the companion R package latenetwork.
