Network Cluster-Robust Inference

36 Pages Posted: 25 Mar 2021

See all articles by Michael P. Leung

Michael P. Leung

University of Southern California - Department of Economics

Date Written: January 9, 2021


Network data commonly consists of observations on a single large network. Accordingly, researchers often partition the network into clusters in order to apply cluster-robust inference methods. All existing such methods require clusters to be asymptotically independent. We show that for this requirement to hold, under certain conditions, it is necessary and sufficient for clusters to have small "conductance," which is the ratio of edge boundary size to volume. This yields a quantitative measure of cluster quality. Unfortunately, there are important classes of networks for which small-conductance clusters appear not to exist. Our simulation results show that for such networks, cluster-robust methods can exhibit substantial size distortion. Based on well-known results in spectral graph theory, we suggest using the eigenvalues of the graph Laplacian to determine the existence and number of small-conductance clusters. We also discuss the use of spectral clustering for constructing clusters in practice.

Keywords: Social Networks, Clustered Standard Errors, Graph Laplacian, Spectral Clustering

JEL Classification: C11, C21, C38

Suggested Citation

Leung, Michael, Network Cluster-Robust Inference (January 9, 2021). Available at SSRN: or

Michael Leung (Contact Author)

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave.
Kaprielian (KAP) Hall, 310A
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