Using Selection on Observed Variables to Assess Bias from Unobservables When Evaluating Swan-Ganz Catheterization by Joseph G. Altonji, Todd E. Elder and Christopher R. Taber. Published in volume 98, issue 2, pages 345-50 of American Economic Review, May 2008

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 explanatory variables in a model provides a guide to the amount of selection on the unobservables. We also propose an informal way to assess selectivity bias based on measuring the ratio of selection on unobservables to selection on observables that would be required if one is to attribute the entire effect of Catholic school attendance to selection bias. We use our methods to estimate the effect of attending a Catholic high school on a variety of outcomes. Our main conclusion is that Catholic high schools substantially increase the probability of graduating from high school and, more tentatively, attending college. We find little evidence of an effect on test scores.

We use linked birth and education records from Florida to investigate how the identification of childhood disabilities varies by race and school racial composition. Using a series of decompositions, we find that black and Hispanic students are identified with disabilities at lower rates than are observationally similar white students. Black and Hispanic students are overidentified in schools with relatively small shares of minorities and substantially underidentified in schools with large minority shares. Our results are consistent with a heightened awareness among school officials of disabilities in students who are racially and ethnically distinct from the majority race in the school.