Conditional Parallel Trends
A covariate-adjusted version of Parallel-Trends: absent treatment, treated and control groups would have followed the same outcome trajectory conditional on observed covariates , even if their unconditional trends differ. Identification then requires reweighting or regression adjustment on (and Overlap in ). More plausible than unconditional parallel trends when observed covariates drive differential dynamics — though not logically weaker, since trends must now be parallel within every covariate stratum — and it still rests on having the right covariates.
Relied on by
DiD with covariates (semiparametric, doubly robust, and multi-period estimators).