Network Cluster-Robust Inference

Since network data commonly consists of observations on a single large network, 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 prove that for this requirement to hold, under certain conditions, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume, which yields a measure of cluster quality. We show in simulations that, for important classes of networks lacking low-conductance clusters, cluster-robust methods can exhibit substantial size distortion, whereas for networks with such clusters, they outperform HAC estimators. To assess the existence of low-conductance clusters and construct them, we draw on results in spectral graph theory showing a close connection between conductance and the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to compute the number of low-conductance clusters and spectral clustering to compute the clusters. We illustrate our results and proposed methods in simulations and empirical applications.