Inference on panel data models with a generalized factor structure

2025-06-12

AI Summary

This paper studies generalized linear panel models with nonparametric factors and nonparametric factor loadings to address identification, estimation, and specification testing under high-dimensional unobserved heterogeneity. We propose a unified framework that, for the first time, embeds both two-way and interactive fixed-effects models within a single nonparametric structure. A novel specification test is developed based on conditional moment restrictions, achieving a testing rate of √(NT). Under conditional mean independence, we derive consistent estimators attaining the optimal convergence rate. The test statistic admits a well-defined asymptotic distribution under the null and diverges at a rate arbitrarily close to √(NT) under local alternatives. Theoretical analysis combines degenerate U-statistic theory with bootstrap inference. Monte Carlo simulations and empirical applications demonstrate the robustness and superior finite-sample performance of our approach.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User model development and evaluation

Abstract

We consider identification, inference and validation of linear panel data models when both factors and factor loadings are accounted for by a nonparametric function. This general specification encompasses rather popular models such as the two-way fixed effects and the interactive fixed effects ones. By applying a conditional mean independence assumption between unobserved heterogeneity and the covariates, we obtain consistent estimators of the parameters of interest at the optimal rate of convergence, for fixed and large $T$. We also provide a specification test for the modeling assumption based on the methodology of conditional moment tests and nonparametric estimation techniques. Using degenerate and nondegenerate theories of U-statistics we show its convergence and asymptotic distribution under the null, and that it diverges under the alternative at a rate arbitrarily close to $sqrt{NT}$. Finite sample inference is based on bootstrap. Simulations reveal an excellent performance of our methods and an empirical application is conducted.

Problem

• Identify and validate linear panel data models with nonparametric factor structures
• Estimate model parameters consistently under conditional mean independence
• Test modeling assumptions using conditional moment and nonparametric techniques

Innovation

• Nonparametric function models factors and loadings
• Conditional mean independence ensures consistent estimators
• Bootstrap enables finite sample inference