Normal Approximation in Large Network Models

Michael P. Leung; Hyungsik Roger Moon

doi:10.1093/restud/rdag022

Normal Approximation in Large Network Models

Michael P. Leung¹; Hyungsik Roger Moon²

¹ Department of Economics, UC Santa Cruz · ² Department of Economics, University of Southern California, USA; and Yonsei University, South Korea

Review of Economic Studies 2026 open access

Abstract We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network size diverges. We argue that a modification of “stabilization” conditions from the literature on geometric graphs provides a useful high-level formulation of weak dependence which we utilize to establish an abstract central limit theorem. Using results in branching process theory, we derive interpretable primitive conditions for stabilization. The main conditions restrict the strength of strategic interactions and equilibrium selection mechanism. We discuss practical inference procedures justified by our results.

DOI: 10.1093/restud/rdag022
Language: en
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