Identify the estimand of the Sun–Abraham saturated TWFE event-study regression in unbalanced panels

Ascertain the precise statistical estimand recovered by the Sun and Abraham (2021) saturated two-way fixed effects event-study regression when applied to unbalanced panel or repeated cross-section data, and characterize conditions under which it equals the group-time ATT(g,t) estimand based on never-treated comparisons.

Background

In balanced panels, the Sun–Abraham saturated event-paper regression using never-treated comparisons coincides with certain 2×2 difference-in-differences estimators for ATT(g,t). The authors explain that this equivalence breaks down with repeated cross-sections or unbalanced panels, raising questions about the interpretation of the regression coefficients in these settings.

Clarifying the estimand in unbalanced panels would provide guidance for practitioners on how to interpret event-paper coefficients, when they match ATT(g,t), and how deviations arise due to sampling and composition. This would also help align regression-based practice with the forward-engineered, building-block framework emphasized throughout the paper.