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Comments
CIC is a nice approach in many applications
Though it is less commonly used in empirical work than DID.
Need to estimate quantiles
Harder to include covariates (due to needing to estimate quantiles). I think (not 100% sure though) that it is not possible (at least not obvious) if one can do a doubly robust version of CIC.
Support conditions can have real bite in some applications
Not as much software support