About the Difference-in-Differences category

All discussion regarding diff in diff!

With DiD there’s no talk about how close or far the control observations should be. The only assumption is the parallel trends. Is there any literature around if we should consider matching observations for the control set and how that affects, if at all, the bias etc? I think having matching/similar observations in the treatment and control should yield better/unbiased results as there’s more certainty that matching observations will have parallel trends.