Treatment-effect heterogeneity and interactive fixed effects: Can we control for too much?
Murilo Cardoso, Bruno Ferman, Marcelo Fernandes
TLDR
Interactive fixed effects (IFE) can fail to estimate average treatment effects when heterogeneity has a linear factor structure, due to a "bad-control" problem.
Key contributions
- IFE estimators can fail to recover average treatment effects with heterogeneous treatment effects.
- This failure occurs because IFE absorbs treatment effect heterogeneity, creating a "bad-control" issue.
- Identification further breaks down with time-invariant factors or unit-invariant loadings due to multicollinearity.
- Alternative methods that exclude treated units from factor estimation avoid these problems.
Why it matters
This paper highlights a critical flaw in the widely used IFE estimator when treatment effects are heterogeneous, warning researchers against potential misestimation. It provides crucial insights into when and why IFE might fail, guiding practitioners towards more robust alternative methods.
Original 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.
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