A0350
Title: Peer effects in the linear-in-means model may be inestimable even when identified
Authors: Alex Hayes - Stanford Univeristy (United States) [presenting]
Keith Levin - University of Wisconsin (United States)
Abstract: Estimation in the linear-in-means model when a randomized treatment is applied to all nodes in a network, and the potential for an identifiability-estimability gap is shown. When treatment is assigned independently of the network structure, peer effects are identified but potentially inestimable due to an asymptotic collinearity issue. The estimation error is lower-bounded for ordinary least squares, and it is shown that these estimates may be inconsistent or fail to achieve nominal coverage rates whenever the harmonic mean degree of the network diverges with sample size. Simulations show that two-stage least squares and quasi-maximum likelihood estimators behave similarly. Results thus suggest caution when using the linear-in-means model to model spillovers in random experiments on dense networks. The behavior of the linear-in-means model is further investigated when covariates are endogenous and associated with network structure. It is shown that explicitly modeling homophily with random dot product graphs can prevent asymptotic collinearity and estimability issues, provided that there is sufficient degree heterogeneity in the network.
