Economics & Finance / Economic Theory / Econometrics

Difference-in-Differences with Variation in Treatment TimingThis paper, authored by Andrew

Difference-in-Differences with Variation in Treatment Timing

Andrew Goodman-Bacon

Difference-in-Differences with Variation in Treatment Timing This paper, authored by Andrew Goodman-Bacon, delves into the econometric logic of difference-in-differences (DD) when dealing with variations in treatment timing. The authors reveal, through the decomposition theorem, that two-way fixed effects (TWFE) estimators are essentially variance-weighted averages of all possible “2x2” DD estimators in the data. The study points out that this traditional linear model becomes biased when policy effects change over time because units treated earlier serve as control groups for later units, leading to mutual subtraction of treatment effects and negative weighting. Based on this finding, the paper proposes a novel balance test and provides diagnostic tools for analyzing how different model settings (such as incorporating unit-specific time trends or weights) alter estimation results. Finally, through a re-evaluation of a unilateral divorce law case, the study provides important theoretical guidance for practitioners on how to correctly interpret estimators and identify potential biases when facing staggered policy pilots.