Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2023, Volume 91, Issue 2

Network Cluster-Robust Inference
p. 641-667

Michael P. Leung

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster‐robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network‐dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster‐robust methods control size better than HAC estimators. However, for important classes of networks lacking low‐conductance clusters, the former can exhibit substantial size distortion. To determine the number of low‐conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low‐conductance clusters and spectral clustering to construct them.

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Supplemental Material

Supplement to "Network Cluster-Robust Inference"

Michael P. Leung

Data and Programs