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.
(2005) Semiparametric difference-in-differences estimators, The review of economic studies 72(1), 1--19
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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.