Normal Approximation in Large Network Models

Abstract

We develop a methodology for proving central limit theorems in network models with strategic interactions and homophilous agents. We consider an asymptotic framework in which the size of the network tends to infinity, which is useful for inference in the typical setting in which the sample consists of a single large network. In the presence of strategic interactions, network moments are generally complex functions of network components, where a node's component consists of all alters to which it is directly or indirectly connected. We find that a modification of "exponential stabilization" conditions from the stochastic geometry literature provides a useful formulation of weak dependence for moments of this type. Our first contribution is to prove a CLT for a large class of network moments satisfying stabilization and a moment condition. Our second contribution is a methodology for deriving primitive sufficient conditions for stabilization using results in branching process theory. We apply the methodology to static and dynamic models of network formation and discuss how it can be used more broadly.