In this paper, we measure the effect of Catholic high school attendance on educational attainment and test scores. Because we do not have a good instrumental variable for Catholic school attendance, we develop new estimation methods based on the idea that the amount of selection on the observed...

We develop estimation methods that use the amount of selection on the observables in a model as a guide to the amount of selection on the unobservables. We show that if the observed variables are a random subset of a large number of factors that influence the endogenous variable and the outcome...