  This paper considers inference on fixed effects in a linear regression model
estimated from network data. An important special case of our setup is the
two-way regression model. This is a workhorse technique in the analysis of
matched data sets, such as employer-employee or student-teacher panel data. We
formalize how the structure of the network affects the accuracy with which the
fixed effects can be estimated. This allows us to derive sufficient conditions
on the network for consistent estimation and asymptotically-valid inference to
be possible. Estimation of moments is also considered. We allow for general
networks and our setup covers both the dense and sparse case. We provide
numerical results for the estimation of teacher value-added models and
regressions with occupational dummies.
