Fixed Effects as Generated Regressors

2026-02-09

AI Summary

This study addresses the first-order bias arising from fixed-effect estimation in nonlinear panel models, particularly when panel residuals are endogenous with respect to the moment conditions. To tackle this issue, the paper proposes an orthogonal moment estimation framework that constructs moment conditions locally orthogonal to the individual fixed effects, thereby eliminating the first-order bias without relying on conventional exogeneity assumptions. The approach integrates machine learning and empirical Bayes techniques to efficiently estimate nuisance parameters. Both theoretical analysis and simulation studies demonstrate that the proposed method substantially reduces estimation bias under endogeneity. An empirical application to a site selection experiment further confirms its robustness and practical utility.

Technology Category

• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Many economic models feature moment conditions that involve latent variables. When the latent variables are individual fixed effects in an auxiliary panel data regression, we construct orthogonal moments that eliminate first-order bias induced by estimating the fixed effects. Machine Learning methods and Empirical Bayes methods can be used to improve the estimate of the nuisance parameters in the orthogonal moments. We establish a central limit theorem based on the orthogonal moments without relying on exogeneity assumptions between panel data residuals and the cross-sectional moment functions. In a simulation study where the exogeneity assumption is violated, the estimator based on orthogonal moments has smaller bias compared with other estimators relying on that assumption. An empirical application on experimental site selection demonstrates how the method can be used for nonlinear moment conditions.

Problem

• fixed effects
• latent variables
• moment conditions
• panel data
• exogeneity

Innovation

• orthogonal moments
• fixed effects
• machine learning
• empirical Bayes
• nonlinear moment conditions