Fixed effects estimated from network data are central to many economic applications that aim to capture unobserved heterogeneity. However, most existing methods assume conditional independence of network observations, an assumption whose plausibility is often application-dependent. This paper studies fixed-effect regressions on network data under a conditional dependence structure in which errors arise from both node- and edge-level shocks that are not fully captured by the fixed effects. We show that the least-squares estimator of the fixed effects can be inconsistent due to a persistent noise term induced by the dependence structure. Leveraging information from the regression residuals, we propose new inference methods for fixed effects that explicitly account for dependence. We also introduce a bias-correction procedure for estimating the sample variance of the fixed effects under dependence. An empirical application using worker–firm matched data demonstrates the practical relevance of our methods and highlights the substantial impact of dependence on inference and variance estimation.

Ordinary least squares (OLS) estimators are widely used in network experiments to estimate spillover effects. We study the causal interpretation of, and inference for the OLS estimator under both design-based uncertainty from random treatment assignment and sampling-based uncertainty in network links. We show that correlations among regressors that capture the exposure to neighbors' treatments can induce contamination bias, preventing OLS from aggregating heterogeneous spillover effects for a clear causal interpretation. We derive the OLS estimator's asymptotic distribution and propose a network-robust variance estimator. Simulations and an empirical application demonstrate that contamination bias can be substantial, leading to inflated spillover estimates.

This paper addresses the sample selection problem in panel dyadic regression analysis. Dyadic data often include many zeros in the main outcomes due to the underlying network formation process. This not only contaminates popular estimators used in practice but also complicates the inference due to the dyadic dependence structure. We extend Kyriazidou (1997)’s approach to dyadic data and characterize the asymptotic distribution of our proposed estimator. The convergence rates are \(n\) or \(\sqrt{n^{2}h_n}\), depending on the degeneracy of the Hájek projection part of the estimator, where \(n\) is the number of nodes and \(h_n\) is a bandwidth. We propose a bias-corrected confidence interval and a variance estimator that adapts to the degeneracy. A Monte Carlo simulation shows the good finite-sample performance of our estimator and highlights the importance of bias correction in both asymptotic regimes when the fraction of zeros in outcomes varies. We illustrate our procedure using data from the paper by Moretti and Wilson (2017) on migration.