Linear Panel Regressions with Two-Way Unobserved Heterogeneity

TL;DR

This paper develops methods for linear panel regressions with unknown smooth two-way unobserved effects, extending standard fixed effect models to more flexible, nonparametric settings, and demonstrates their effectiveness through simulations and real data.

Contribution

It introduces two estimation approaches for models with unknown smooth two-way unobserved heterogeneity, broadening the applicability of fixed effect methods.

Findings

Both estimators achieve asymptotic convergence.

Monte Carlo simulations validate the estimators' performance.

Empirical application to UK house prices illustrates practical usefulness.

Abstract

We study linear panel regression models in which the unobserved error term is an unknown smooth function of two-way unobserved fixed effects. In standard additive or interactive fixed effect models the individual specific and time specific effects are assumed to enter with a known functional form (additive or multiplicative). In this paper, we allow for this functional form to be more general and unknown. We discuss two different estimation approaches that allow consistent estimation of the regression parameters in this setting as the number of individuals and the number of time periods grow to infinity. The first approach uses the interactive fixed effect estimator in Bai (2009), which is still applicable here, as long as the number of factors in the estimation grows asymptotically. The second approach first discretizes the two-way unobserved heterogeneity (similar to what Bonhomme, Lamadon and Manresa 2021 are doing for one-way heterogeneity) and then estimates a simple linear fixed effect model with additive two-way grouped fixed effects. For both estimation methods we obtain asymptotic convergence results, perform Monte Carlo simulations, and employ the estimators in an empirical application to UK house price data.