Fixed-effect regressions on network data

This paper studies inference on fixed effects in a linear regression model estimated from network data. We derive bounds on the variance of the fixed-effect estimator that uncover the importance of the smallest non-zero eigenvalue of the (normalized) Laplacian of the network and of the degree structure of the network. The eigenvalue is a measure of connectivity, with smaller values indicating less-connected networks. These bounds yield conditions for consistent estimation and convergence rates, and allow to evaluate the accuracy of first-order approximations to the variance of the fixed-effect estimator.