(Debiased) Inference for Fixed Effects Estimators with Three-Dimensional Panel and Network Data

Inference for fixed effects estimators of linear and nonlinear panel models is often unreliable due to Nickell- and/or incidental parameter biases. This article develops new inferential theory for (non)linear fixed effects M-estimators with data featuring a three-dimensional panel structure, such as sender x receiver x time. Our theory accommodates bipartite, directed, and undirected network panel data, integrates distinct specifications for additively separable unobserved effects with different layers of variation, and allows for weakly exogenous regressors. Our analysis reveals that the asymptotic properties of fixed effects estimators with three-dimensional panel data can deviate substantially from those with two-dimensional panel data. While for some specifications the estimator turns out to be asymptotically unbiased, in other specifications, it suffers from a particularly severe inference problem, characterized by a degenerate asymptotic distribution and complex bias structures. We address this atypical inference problem, by deriving explicit expressions to debias the fixed effects estimators.