Fused Extended Two-Way Fixed Effects for Difference-in-Differences with Staggered Adoptions

To address the bias of the canonical two-way fixed effects estimator for difference-in-differences under staggered adoptions, Wooldridge (2021) proposed the extended two-way fixed effects estimator, which adds many parameters. However, this reduces efficiency. Restricting some of these parameters to be equal helps, but ad hoc restrictions may reintroduce bias. We propose a machine learning estimator with a single tuning parameter, fused extended two-way fixed effects (FETWFE), that enables automatic data-driven selection of these restrictions. We prove that under an appropriate sparsity assumption FETWFE identifies the correct restrictions with probability tending to one. We also prove the consistency, asymptotic normality, and oracle efficiency of FETWFE for two classes of heterogeneous marginal treatment effect estimators under either conditional or marginal parallel trends, and we prove consistency for two classes of conditional average treatment effects under conditional parallel trends. We demonstrate FETWFE in simulation studies and an empirical application.