Two-way Fixed Effects Regressions with Several Treatments

Abstract

We study regressions with period and group fixed effects and several treatment variables. Under a parallel trends assumption, the coefficient on each treatment identifies the sum of two terms. The first term is a weighted sum of the effect of that treatment in each group and period, with weights that may be negative and sum to one. The second term is a sum of the effects of the other treatments, with weights summing to zero. Accordingly, coefficients in those regressions are not robust to heterogeneous effects, and may be contaminated by the effect of other treatments. We propose alternative estimators.Comment: 25 pages. Compared to the previous version, we have added in particular Corollary 1, Section 4.2 on dynamic effects and an applicatio