A Weak Law for Moments of Pairwise Stable Networks

Abstract

This paper studies the dependence structure of sparse networks realized according to a strategic model of network formation with homophilous agents. We argue that equilibrium selection and chains of indirect dependence generated by strategic interactions are the main drivers of network dependence. Drawing on results in random-graph theory, we derive weak-dependence conditions under which a law of large numbers holds for a general class of network moments. A key condition restricts the strength of strategic interactions, which constitutes the network analog of conventional weak-dependence assumptions in time series and spatial econometrics that bound the magnitude of autoregressive parameters. We apply our result to estimating models of strategic network formation and treatment effects under network interference.

Keywords: social networks, network formation, multiple equilibria, objective method

JEL Classification: C31, C57, D85