🤖 AI Summary
This paper addresses inference failure of fixed-effects M-estimators in three-dimensional panel data (e.g., sender × receiver × time) and network data, arising from Nickell bias, incidental parameter bias, and degenerate limiting distributions. Unlike two-dimensional panels, we first systematically characterize the heterogeneous asymptotic behavior of fixed-effects estimators under three-way structures: asymptotic unbiasedness holds only in special settings, whereas most configurations suffer severe bias and nonstandard limiting distributions. To resolve this, we develop an explicit bias-correction formula based on high-dimensional fixed-effects bias decomposition—applicable to both linear and nonlinear models, weakly exogenous regressors, and multi-way additive unobserved effects (e.g., two-way, directed/undirected network, and bipartite structures). Our method substantially improves confidence interval coverage and test power, delivering the first unified, consistent, and feasible inferential framework for complex networked panel data.
📝 Abstract
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.