We consider the classic problem of estimating group treatment effects when individuals sort based on observed and unobserved characteristics. Using a standard choice model, we show that controlling for group averages of observed individual characteristics potentially absorbs all the across-group variation in unobservable individual characteristics. We use this insight to bound the treatment effect variance of school systems and associated neighborhoods for various outcomes. Across four datasets, our conservative estimates indicate that a 90th versus 10th percentile school system increases high school graduation and college enrollment probabilities by at least 0.047 and 0.11. Other applications include measurement of teacher value-added.