Factor-Augmented Panel Regressions and Variance-Weighted Treatment Effects

TL;DR

This paper demonstrates that two-way panel estimators with latent factors consistently estimate a variance-weighted average of treatment effects under nonparametric assumptions, extending prior results to more general settings.

Contribution

It shows that principal components and interactive fixed effects estimators converge to the same interpretable estimand in nonparametric panel models with latent factors.

Findings

Both estimators estimate the same variance-weighted average treatment effect.

The estimators require the number of factors to grow with sample size.

Results apply to the single regressor case under nonparametric assumptions.

Abstract

We revisit panel regressions with unobserved heterogeneity through the lens of variance-weighted average treatment effects. Building on established results for cross-sectional OLS and one-way fixed effects panels, we show that two-way panel estimators with latent factors, specifically the principal components estimator of Greenaway-McGrevy, Han and Sul (2012) and the interactive fixed effects estimator of Bai (2009), also converge to interpretable estimands under fully nonparametric assumptions. Both estimators consistently estimate the same variance-weighted average of unit-time-specific treatment effects, where the weights are proportional to the conditional variance of the regressor given the unobserved heterogeneity. The result requires the number of estimated factors to grow with the sample size and applies to the single regressor case. We discuss the challenges that arise when extending to multiple regressors and to inference.