AMS Weekly Seminar | Keith Levin

Abstract: Linear-in-means models are often used to investigate peer effects in networks, but their application requires care, as they may be subject to the “reflection problem”, an identification failure caused by perfect collinearity. In many settings, well-known identification conditions guarantee that perfect collinearity is not an issue. However, these identifying conditions are not sufficient to guarantee that peer effects are estimable. Even when identifying conditions guarantee that peer effect terms are not collinear, peer effects can become increasingly collinear as sample size grows larger. We show that asymptotic collinearity occurs whenever nodal covariates are independent of the network and the minimum degree of the network is growing. Asymptotic collinearity can cause estimates of peer effects to be inconsistent or to converge at slower than expected rates. We also show that dependence between nodal covariates and network structure can alleviate collinearity issues in random dot product graphs. These results suggest that linear-in-means models are less reliable for studying peer influence than previously believed.