  This study investigates the causal interpretation of linear social
interaction models in the presence of endogeneity in network formation under a
heterogeneous treatment effects framework. We consider an experimental setting
in which individuals are randomly assigned to treatments while no interventions
are made for the network structure. We show that running a linear regression
ignoring network endogeneity is not problematic for estimating the average
direct treatment effect. However, it leads to sample selection bias and
negative-weights problem for the estimation of the average spillover effect. To
overcome these problems, we propose using potential peer treatment as an
instrumental variable (IV), which is automatically a valid IV for actual
spillover exposure. Using this IV, we examine two IV-based estimands and
demonstrate that they have a local average treatment-effect-type causal
interpretation for the spillover effect.
