Robust Priors in Nonlinear Panel Models with Individual and Time Effects

Zizhong Yan, Zhengyu Zhang, Mingli Chen, Jingrong Li, Iván Fernández-Val

arXiv 4 Apr 2026 · Econometrics

arXiv:2604.03663 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We develop likelihood-based bias reduction for nonlinear panel models with additive individual and time effects. In two-way panels, integrated-likelihood corrections are attractive but challenging because the required integration is high dimensional and standard Laplace approximations may fail when the parameter dimension grows with the sample size. We propose a target-centered full-exponential Laplace--cumulant expansion that exploits the sparse higher-order derivative structure implied by additive effects, delivering a tractable approximation with a negligible remainder under large-$N,T$ asymptotics. The expansion motivates robust priors that yield bias reduction for both common parameters and fixed effects. We provide implementations for binary, ordered, and multinomial response models with two-way effects. For average partial effects, we show that the remaining first-order bias has a simple variance form and can be removed by a closed-form adjustment. Monte Carlo experiments and an empirical illustration show substantial bias reduction with accurate inference.

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