Estimation of Stochastic Block Networks from Panel Data
Abstract
Network spillovers shape many economic outcomes, yet the underlying interaction network is often unobserved in the administrative and survey panels most commonly used in empirical work. This paper develops an econometric framework to estimate a stochastic block model (SBM) representation of a latent interaction network using only panel data on outcomes and covariates. We embed an SBM restriction into a canonical linear social-interactions (spatial autoregressive) panel model and show that the community structure (block memberships), block-to-block link intensities, and spillover parameters are jointly identified from reduced-form panel variation under mild rank and stability conditions. Exploiting the implied low-dimensional structure, we propose a computationally tractable estimator that (i) recovers an empirical “influence” object from the panel via regularized moment-based methods and (ii) uses spectral clustering and blockwise refinement to estimate community assignments and block connection parameters, with data-driven selection of the number of blocks. We establish consistency and provide asymptotic characterizations for both spillover parameters and community recovery under large-N, short-T asymptotics. Monte Carlo evidence shows that imposing stochastic block structure can substantially improve the precision and stability of recovered interaction patterns and spillover estimates relative to unrestricted link-by-link recovery. An empirical illustration demonstrates that the approach delivers economically interpretable communities and a parsimonious map of interactions when network data are unavailable.