Causal Interpretation of Linear Social Interaction Models with Endogenous Networks

Abstract

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.