Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools
提出基于观测变量选择程度推断未观测变量选择程度的新估计方法，用于评估天主教高中对教育成就和考试成绩的影响，发现其显著提高高中毕业率和大学入学率，但对考试成绩影响不大。
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.