Causal Interpretation of Linear Social Interaction Models with Endogenous Networks

TL;DR

This paper explores how to accurately estimate direct and spillover effects in social networks with endogenous formation, proposing an instrumental variable approach to address bias and negative weights in spillover effect estimation.

Contribution

It introduces an IV-based method using potential peer treatment to obtain valid causal estimates of spillover effects in endogenous social networks.

Findings

Linear regression estimates are valid for direct treatment effects.

Ignoring network endogeneity causes bias in spillover effect estimates.

Proposed IV approach yields interpretable local average treatment effects.

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.