Group-Average Observables as Controls for Sorting on Unobservables When Estimating Group Treatment Effects: the Case of School and Neighborhood Effects

We consider the classic problem of estimating group treatment effects when individuals sort based on observed and unobserved characteristics that affect the outcome. 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 most conservative estimates indicate that a 90th versus 10th percentile school system increases the high school graduation probability by between 0.047 and 0.085 and increases the college enrollment probability by between 0.11 and 0.13. We also find large effects on adult earnings. We discuss a number of other applications of our methodology, including measurement of teacher value-added.