Negative Weighting

The pathology of two-way fixed-effects (TWFE) DiD under staggered timing and Treatment-Effect-Heterogeneity: the TWFE coefficient is a weighted average of many 2×2 comparisons, and some weights are negative. The culprit is “forbidden comparisons” that use already-treated units as controls for later-treated units, which subtracts the evolution of earlier cohorts’ effects. With negative weights the estimate can lie outside the range of all underlying effects — even carry the wrong sign. Motivates the heterogeneity-robust estimators that avoid such comparisons.

Relied on by

Diagnoses of TWFE DiD; the case for robust estimators.

Referenced by

• GoodmanBacon2021-DiDVariationInTiming
• SunAbraham2021-EventStudies
• DeChaisemartinDHaultfoeuille2023-TWFESurvey
• BakerLarckerWang2022-HowMuchTrustStaggeredDiD
• CallawaySantAnna2021-DiDMultiplePeriods
• CallawayGoodmanBaconSantAnna-ContinuousTreatment
• Wooldridge2021-TWFEMundlakDiD
• RothSantAnna2023-WhatsTrendingInDiD
• BakerEtAl2025-DiDPractitionerGuide
• BorusyakEtAl2024-RevisitingEventStudyDesigns (coins “forbidden comparisons” for the treated-vs-earlier-treated comparisons that produce negative long-run weights)