Robust Priors in Nonlinear Panel Models with Individual and Time Effects

2026-04-04

AI Summary

This study addresses the challenge of bias in parameter estimation arising from individual and time fixed effects in high-dimensional nonlinear panel models, where conventional integration methods fail. The authors propose a likelihood-based bias correction approach that innovatively exploits the sparse higher-order derivative structure implicitly induced by additive fixed effects. By integrating this insight with a target-centered full-exponential Laplace–cumulant expansion, they construct a tractable high-dimensional integral approximation whose remainder term is asymptotically negligible. This framework yields a closed-form expression for bias-corrected average partial effects and accommodates binary, ordered, and multinomial response models. It also supports robust Bayesian priors and large-N,T asymptotic analysis. Monte Carlo simulations and empirical results demonstrate that the method substantially reduces estimation bias while preserving strong inferential performance.

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.

Problem

• nonlinear panel models
• individual and time effects
• bias reduction
• integrated likelihood
• high-dimensional integration

Innovation

• bias reduction
• nonlinear panel models
• Laplace–cumulant expansion
• robust priors
• two-way fixed effects