Fixed-Effect Regressions on Network Data

TL;DR

This paper analyzes how network structure impacts the estimation of fixed effects in linear regression models, providing conditions for consistent inference in both dense and sparse networks.

Contribution

It formalizes the relationship between network structure and fixed effect estimation accuracy, offering new conditions for consistency and valid inference in general networks.

Findings

Derived sufficient conditions for consistent fixed effect estimation.

Provided asymptotic inference methods for network data.

Numerical illustrations with teacher value-added and occupational dummy regressions.

Abstract

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.