Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they identify weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression estimand may for instance be negative while all the ATEs are positive. In two articles that have used those regressions, half of the weights are negative. We propose another estimator that solves this issue. In one of the articles we revisit, it is of a different sign than the linear regression estimator.