Normal Approximation in Large Network Models

69 Pages Posted: 3 Jun 2019 Last revised: 1 Mar 2021

See all articles by Michael P. Leung

Michael P. Leung

University of Southern California - Department of Economics

Hyungsik Roger Moon

University of Southern California - Department of Economics; USC Dornsife Institute for New Economic Thinking

Date Written: April 24, 2019

Abstract

We develop a methodology for proving central limit theorems in network 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 tends to infinity. In the presence of strategic interactions, network moments are generally complex functions of 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. We establish a CLT for a network moments satisfying stabilization and provide 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.

Keywords: social networks, strategic interactions, weak dependence, network formation

JEL Classification: C31, C57, D85

Suggested Citation

Leung, Michael and Moon, Hyungsik Roger, Normal Approximation in Large Network Models (April 24, 2019). Available at SSRN: https://ssrn.com/abstract=3377709 or http://dx.doi.org/10.2139/ssrn.3377709

Michael Leung (Contact Author)

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave.
Kaprielian (KAP) Hall, 310A
Los Angeles, CA 90089
United States

Hyungsik Roger Moon

University of Southern California - Department of Economics ( email )

KAP 300
Los Angeles, CA 90089-0253
United States
213-740-2108 (Phone)
213-740-8543 (Fax)

USC Dornsife Institute for New Economic Thinking ( email )

3620 S. Vermont Avenue, KAP 364F
Los Angeles, CA 90089-0253
United States

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