Basically I have many treated units and I would like to estimate (by applying the Diff-in-Diff methodology) the effect of the treatment. In my particular case it's very likely to observe certain heterogeneity in the "effect of treatment" across units, and that's why I would like to estimate a regression using time invariant characteristics of the units as covariates.
I haven't been able to find any article/text-book where this particular method is applied which makes me doubt about its theoretical validity.
(of course that in order to make everything comparable I will include control variables, or instead pre-match similar units in order to have more reliable conclusions).
Any suggestion? Thanks in advance