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Normal Approximation in Large Network Models

Michael Leung and Hyungsik Roger Moon

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Abstract: We prove central limit theorems for models of network formation and network processes with homophilous agents. The results hold under large-network asymptotics, enabling inference in the typical setting where the sample consists of a small set of large networks. We first establish a general central limit theorem under high-level `stabilization' conditions that provide a useful formulation of weak dependence, particularly in models with strategic interactions. The result delivers a square root n rate of convergence and a closed-form expression for the asymptotic variance. Then using techniques in branching process theory, we derive primitive conditions for stabilization in the following applications: static and dynamic models of strategic network formation, network regressions, and treatment effects with network spillovers. Finally, we suggest some practical methods for inference.

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Date: 2019-04
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Handle: RePEc:arx:papers:1904.11060