A Note on Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects
No 22-1362, TSE Working Papers from Toulouse School of Economics (TSE)
I use a generalized decomposition of the Two-Way Fixed Effects (TWFE) estimator to show that it is a weighted sum of five different types of two-by-two comparisons, with positive weights. I impose the same assumptions as de Chaisemartin and d’Haultfoeuille (2020a) for their heterogeneity-robust estimator to be unbiased. I find that these restrictions are sufficient for each comparison to estimate without bias the Average Treatment Effect (ATE) of the group switching treatment status. Thus, the TWFE estimator weighs each ATE positively, even with heterogeneous treatment effects. I exploit all available comparisons to build unbiased estimators of the ATT and ATE.
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