Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools

TLDR

The study measures the impact of Catholic high school attendance on educational attainment and test scores, developing new estimation methods and an informal bias assessment due to the lack of a suitable instrumental variable. They develop estimation methods that use observed selection to infer unobserved selection, propose an informal bias assessment, and apply these methods to estimate Catholic school effects on various outcomes. Catholic high schools significantly raise high‑school graduation rates and, to a lesser extent, college attendance, but show little impact on test scores.

Abstract

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.