Specification testing with grouped fixed effects

TL;DR

This paper introduces a Hausman test to assess the correctness of unobserved heterogeneity specifications in fixed-effects panel models, accommodating both linear and nonlinear cases with time-varying effects.

Contribution

It develops a novel Hausman test contrasting one-way and two-way grouped fixed-effects estimators, effective under minimal assumptions and capable of handling time-varying heterogeneity.

Findings

The test maintains good size and power in simulations.

It effectively detects misspecification of heterogeneity.

Application to empirical data demonstrates practical utility.

Abstract

We propose a Hausman test for the correct specification of unobserved heterogeneity in both linear and nonlinear fixed-effects panel data models. The null hypothesis is that heterogeneity is either time-invariant or, symmetrically, described by homogeneous time effects. We contrast the standard one-way fixed-effects estimator with the recently developed two-way grouped fixed-effects estimator, that is consistent in the presence of time-varying heterogeneity (or heterogeneous time effects) under minimal specification and distributional assumptions for the unobserved effects. The Hausman test compares jackknife corrected estimators, removing the leading term of the incidental parameters and approximation biases, and exploits bootstrap to obtain the variance of the vector of contrasts. We provide Monte Carlo evidence on the size and power properties of the test and illustrate its application in two empirical settings.