March 5, 2020 | Clément de Chaisemartin, Xavier D'Haultfœuille
This paper examines the properties of two-way fixed effects (FE) regressions when the constant effect assumption is violated, focusing on the estimation of treatment effects. The authors show that linear FE regressions estimate weighted sums of average treatment effects (ATEs) in each group and period, with weights that may be negative. This can lead to a coefficient that is negative while all ATEs are positive, which is misleading. They propose a new estimator, DID$_M$, that is valid even if the treatment effect is heterogeneous over time or across groups. DID$_M$ estimates the average treatment effect across all $(g,t)$ cells where the treatment changes from $t-1$ to $t$. The authors also provide a test to assess the robustness of the two-way FE coefficient to heterogeneous treatment effects. The paper includes empirical applications and discusses the implications for applied researchers using two-way FE regressions.This paper examines the properties of two-way fixed effects (FE) regressions when the constant effect assumption is violated, focusing on the estimation of treatment effects. The authors show that linear FE regressions estimate weighted sums of average treatment effects (ATEs) in each group and period, with weights that may be negative. This can lead to a coefficient that is negative while all ATEs are positive, which is misleading. They propose a new estimator, DID$_M$, that is valid even if the treatment effect is heterogeneous over time or across groups. DID$_M$ estimates the average treatment effect across all $(g,t)$ cells where the treatment changes from $t-1$ to $t$. The authors also provide a test to assess the robustness of the two-way FE coefficient to heterogeneous treatment effects. The paper includes empirical applications and discusses the implications for applied researchers using two-way FE regressions.