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The Goodman-Bacon Decomposition
Staggered adoption as four weighted 2×2 DiDs, including the forbidden comparison with already-treated units.
Day 70: Staggered Adoption: the Goodman-Bacon Decompositionearly vs neverlate vs neverearly vs not-yet-treated latelate vs already-treated earlyTWFEATT
TWFE = Σ weight × 2×2
1.636
ATT (treated unit-periods)
2.227
weight on forbidden comparison
18.2%
bias
-0.591
Three groups: early adopters, late adopters and never-treated, with a common trend. The TWFE coefficient equals the weighted sum of four 2×2 DiDs (bar heights; bar widths are the weights). With effects that grow over time, the comparison that uses already-treated early adopters as controls is biased, and TWFE drifts away from the average effect on treated unit-periods.