In two-period difference-in-differences, under linear faithfulness, parallel trends is incompatible with pre-treatment outcomes causing treatment or with the two outcomes having distinct minimally sufficient confounding sets.
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Using causal diagrams to assess parallel trends in difference-in-differences studies
In two-period difference-in-differences, under linear faithfulness, parallel trends is incompatible with pre-treatment outcomes causing treatment or with the two outcomes having distinct minimally sufficient confounding sets.