Inference on Linear Regressions with Two-Way Unobserved Heterogeneity

TL;DR

This paper introduces a robust estimation method for linear panel data models with two-way unobserved heterogeneity, ensuring root-NT asymptotic normality even with nonparametric components.

Contribution

It develops a novel inference procedure combining Neyman orthogonal moment conditions and bias adjustment to handle nonparametric fixed effects estimation.

Findings

Estimator achieves root-NT asymptotic normality.

Numerical study confirms good finite-sample performance.

Method accommodates flexible nonparametric regression functions.

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.