Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

TLDR

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. The authors aim to develop an estimator that addresses the bias introduced by negative weights in such regressions. They propose a new estimator that corrects for these negative weights, thereby providing unbiased treatment effect estimates. They demonstrate that the standard fixed‑effects estimator yields weighted sums of ATEs with potentially negative weights, which can produce misleading signs, and that their new estimator differs significantly from the standard one in two empirical applications. JEL codes: C21, C23, D72, J31, J51, L82.

Abstract

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate 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 coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator. (JEL C21, C23, D72, J31, J51, L82)