Estimation of a local-aggregate network model with sampled networks

This work considers the estimation of a network model with sampled networks. Chandrasekhar and Lewis (2011) show that the estimation with sampled networks could be biased due to measurement error induced by sampling and propose a bias correction by restricting the estimation to sampled nodes to avoid measurement error in the regressors. However, measurement error may still exist in the instruments and thus induce the weak instrument problem when the sampling rate is low. For a local-aggregate model, we show that the instrument based on the outdegrees of sampled nodes is free of measurement error and thus remains informative even if the sampling rate is low. Simulation studies suggest that the 2SLS estimator with the proposed instrument works well when the sampling rate is low and the other instruments are weak.