John Bullock sends withal this from Joshua Angrist and Jorn-Steffen Pischke’s Mostly Harmless Econometrics—page 223, note 2:
They don’t seem to know well-nigh the idea of adjusting for the group-level midpoint of pre-treatment predictors (as in this 2006 paper with Joe Bafumi).
I like Angrist and Pischke’s typesetting a lot so am happy to be worldly-wise to help out by patching this little hole.
I’d moreover like to do some remoter wringer updating that paper with Bafumi using Bayesian analysis.