A comparative analysis of two-way fixed effects estimators in staggered treatment designs

Two-way fixed effects (TWFE) is a flexible and widely used approach for estimating treatment effects, and several TWFE estimators have been proposed for staggered treatment designs. This paper focuses on the extended TWFE estimator, introduced by Borusyak et al. (2024) and Wooldridge (2021), and compares it with alternative TWFE estimators. The main contribution is the derivation of an equation that connects the extended TWFE estimator with the difference-in-differences estimator. This equivalence provides a transparent decomposition of the components of the extended TWFE estimand. The results show that the extended TWFE estimand consists of two distinct components: one that captures meaningful comparisons and a residual term. The paper outlines the assumptions required to identify treatment effects. In line with previous literature, the findings show that the extended TWFE estimator relies on a parallel trends assumption that extends across multiple periods. Additionally, illustrative examples compare the TWFE estimators under violations of the parallel trends assumption. The results suggest that no single estimator outperforms the others. The choice of the TWFE estimator depends on the parameter of interest and the characteristics of the empirical application.