Robust Priors in Nonlinear Panel Models with Individual and Time Effects

TL;DR

This paper introduces a likelihood-based bias reduction method for nonlinear panel models with individual and time effects, using a novel Laplace-cumulant expansion to improve inference accuracy.

Contribution

It develops a new full-exponential Laplace expansion exploiting additive effects, enabling robust priors and bias reduction in complex two-way panel models.

Findings

Significant bias reduction demonstrated in Monte Carlo simulations.

Accurate inference achieved for binary, ordered, and multinomial response models.

Bias in average partial effects can be effectively removed with a simple adjustment.

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.