Working Paper: NBER ID: w30564
Authors: Clément de Chaisemartin; Xavier Dhaultfoeuille
Abstract: We study two-way-fixed-effects regressions (TWFE) with several treatment variables. Under a parallel trends assumption, we show that the coefficient on each treatment identifies a weighted sum of that treatment’s effect, with possibly negative weights, plus a weighted sum of the effects of the other treatments. Thus, those estimators are not robust to heterogeneous effects and may be contaminated by other treatments’ effects. We further show that omitting a treatment from the regression can actually reduce the estimator’s bias, unlike what would happen under constant treatment effects. We propose an alternative difference-in-differences estimator, robust to heterogeneous effects and immune to the contamination problem. In the application we consider, the TWFE regression identifies a highly non-convex combination of effects, with large contamination weights, and one of its coefficients significantly differs from our heterogeneity-robust estimator.
Keywords: Differences-in-differences; Two-way fixed effects regressions; Multiple treatments; Heterogeneous treatment effects
JEL Codes: C21; C23
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Treatment variables (C90) | Outcome variables (C29) |
| Omitting a treatment (C22) | Enhanced estimator's accuracy (C51) |
| Multiple treatments (C32) | Contamination of treatment effects (C22) |
| Omitting a treatment (C22) | Reduces bias (C83) |
| Coefficients on treatments (C29) | Influenced by effects of other treatments (C22) |
| Coefficients in TWFE regression (C29) | Not robust to heterogeneous effects (C21) |
| TWFE regression (C29) | Coefficients significantly different from robust estimator (C20) |