Treatment-effect heterogeneity and interactive fixed effects: Can we control for too much?

TL;DR

This paper examines the limitations of the interactive fixed effects estimator in panel data with heterogeneous treatment effects, highlighting potential identification issues due to absorption of heterogeneity.

Contribution

It reveals that IFE can fail to estimate the average treatment effect when heterogeneity has a linear factor structure, due to a bad-control problem.

Findings

IFE may not recover the average treatment effect under certain heterogeneity structures.

Excluding treated units in post-treatment periods can avoid identification problems.

Multicollinearity can further impair identification when factors are time-invariant or loadings are unit-invariant.

Abstract

This paper studies the interactive fixed effects (IFE) estimator in a panel-data setting with heterogeneous treatment effects. We show that, if the treatment-effect heterogeneity admits a linear factor structure, the IFE estimator could fail to recover the average treatment effect on the treated units. The problem arises because the interactive fixed effects absorb the heterogeneity in the treatment effect, creating a \textit{bad-control} problem. With time-invariant factors or unit-invariant loadings in the treatment effect heterogeneity, identification may further break down due to multicollinearity. These problems are not present in alternative estimation methods that exclude treated units in post-treatment periods from the factor estimation.