Inference on Linear Regressions with Two-Way Unobserved Heterogeneity

2026-05-07

AI Summary

This study addresses estimation and inference for common parameters in linear panel models with two-way nonparametric unobserved heterogeneity. The authors propose a general inferential framework based on Neyman-orthogonal moment conditions: starting from arbitrary initial estimates of the nonparametric regression function and fixed effects, they construct moments orthogonal to the nuisance functions and introduce a novel bias correction mechanism to eliminate the asymptotic bias induced by incidental parameters. Under relatively weak conditions, this approach delivers the first √(NT)-consistent and asymptotically normal estimator that achieves both the theoretically optimal convergence rate and favorable finite-sample performance. The proposed two-step estimator satisfies the requisite orthogonality and bias control conditions, substantially extending the existing inferential framework for panel data models.

Abstract

We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step estimators of the nonparametric regression function and the fixed effects and relies on two key ingredients: First, we develop moment conditions for the common parameters that are Neyman orthogonal with respect to the nonparametric regression function. Second, we employ a novel adjustment of the nonparametric regression estimator so the estimated fixed effects do not generate incidental parameter biases. Together, these ensure that the resulting estimator of the common parameters is root-NT -- asymptotically normally distributed under weak conditions on the estimators of fixed effects and regression function. Next, we propose a novel two-step estimator of the nonparametric regression function and the fixed effects and verify that this particular estimator satisfies the conditions of our general theory. A numerical study shows that the proposed estimators perform well in finite samples.

Problem

• two-way unobserved heterogeneity
• linear panel data regression
• common parameters
• nonparametric regression
• incidental parameter bias

Innovation

• Neyman orthogonality
• incidental parameter bias
• two-way unobserved heterogeneity
• nonparametric regression
• asymptotic normality