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

TL;DR

This paper introduces FETWFE, a machine learning-based estimator for difference-in-differences with staggered adoptions, addressing bias and efficiency issues in existing methods through data-driven restriction selection.

Contribution

It proposes a novel fused extended two-way fixed effects estimator that automatically selects restrictions, improving efficiency and bias correction in difference-in-differences analysis.

Findings

FETWFE identifies correct restrictions with high probability under sparsity.

The estimator is consistent, asymptotically normal, and has the oracle property.

Demonstrated effectiveness through simulations and empirical application.

Abstract

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 (for example, subsequent treatment effects within a cohort) 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, which improves efficiency. We also prove the consistency, oracle property, and asymptotic normality of FETWFE for several classes of heterogeneous marginal treatment effect estimators under either conditional or marginal parallel trends, and we prove the same results for conditional average treatment effects under conditional parallel trends. We provide an R package implementing fused extended two-way fixed effects, and we demonstrate FETWFE in simulation studies and an empirical application.