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Difference-in-Differences when Parallel Trends Holds Conditional on Covariates
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We consider difference-in-differences identification and estimation strategies when the parallel trends assumption holds conditional on covariates, which can be time-varying, time-invariant, or both. We uncover several weaknesses of two-way fixed effects (TWFE) regressions in this context. The most important, which we call \textit{hidden linearity bias}, arises because transformations that eliminate unit fixed effects also transform the covariates, either implicitly changing the identification strategy or relying on correct model specification. We provide diagnostics for assessing a TWFE regression's susceptibility to hidden linearity bias and propose alternative estimation strategies that circumvent these issues.
Forward citations
Cited by 2 Pith papers
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Omitted variable bias sensitivity analysis with clustered treatment assignment
A correction for Cinelli-Hazlett sensitivity analysis in clustered designs: scale the outcome-confounding partial R² by the between-group residual variance share (η²) to avoid counting irrelevant within-group variation.
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Good Controls Gone Bad: Difference-in-Differences with Covariates
The paper introduces the common causal covariates (CCC) assumption and a saturated 'DID-INT' estimator that is unbiased when covariate effects vary by group and time, but the heterogeneity claim is not proven.
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