A Structural Model of Homophily and Clustering in Social Networks

Abstract

I develop and estimate a structural model of network formation with heterogeneous players and latent community structure, whose equilibrium homophily and clustering levels match those usually observed in real-world social networks. Players belong to communities unobserved by the econometrician and have community-specific payoffs, allowing preferences to have a bias for similar people. Players meet sequentially and decide whether to form bilateral links, after receiving a random matching shock. The model converges to a hierarchical exponential family random graph. Using school friendship network data from Add Health, I estimate the posterior distribution of parameters and unobserved heterogeneity, detecting high levels of racial homophily and payoff heterogeneity across communities. The posterior predictions of sufficient statistics show that the model is able to replicate the homophily levels and the aggregate clustering of the observed network, in contrast with standard exponential family network models without community structure.