Inference on panel data models with a generalized factor structure

TL;DR

This paper develops methods for inference in panel data models with a generalized factor structure, allowing for flexible unobserved heterogeneity modeling, and provides consistent estimators, tests, and bootstrap inference.

Contribution

It introduces a nonparametric approach to identify and estimate panel data models with complex factor structures, including tests for model specification.

Findings

Consistent estimators at optimal convergence rates

A valid specification test based on conditional moment methods

Good finite sample performance demonstrated through simulations

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.