# Fixed-Effect Regressions on Network Data

arXiv: https://arxiv.org/abs/1608.01532 · HTML: https://mlsanity.com/paper/1608.01532/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2016.

## Built on by (most cited first, 2 of 2)

- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Entry-Specific Matrix Estimation under Arbitrary Sampling Patterns through the Lens of Network Flows](https://mlsanity.com/paper/2409.03980/) (2024)

## Abstract (arXiv)

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.