This paper examines the effectiveness of Catholic schools by analyzing the relationship between Catholic school attendance and various educational outcomes. The authors develop estimation methods that use the degree of selection on observable variables to infer the degree of selection on unobservable variables. They argue that if observed variables are a random subset of the factors influencing the endogenous variable and the outcome, the relationship between the indices of observables and unobservables will be the same. This allows for the identification of the effect of the endogenous variable. The authors use their methods to estimate the effect of attending a Catholic high school on outcomes such as high school graduation and college attendance. They find that Catholic high schools substantially increase the probability of graduating from high school and, more tentatively, college attendance. However, they do not find much evidence for an effect on test scores. The paper also discusses the challenges of distinguishing correlation from causation in empirical research, particularly in the context of Catholic school effectiveness. The authors highlight the difficulties in identifying the true effect of Catholic schools due to potential selection bias. They propose an informal way to assess selectivity bias by measuring the ratio of selection on unobservables to selection on observables. The authors use data from the National Educational Longitudinal Survey of 1988 (NELS:88) to analyze the Catholic school effect. They find that Catholic high school students are more likely to graduate from high school and attend college compared to public school students. However, the effects on test scores are less clear. The authors also note that the effects of Catholic schools may be influenced by unobservable factors, such as family background and parental characteristics. The paper concludes that Catholic high schools have a substantial positive effect on high school graduation rates and, more tentatively, on college attendance rates. The authors emphasize the importance of considering selection bias when analyzing the effectiveness of Catholic schools. They also highlight the need for further research on the use of observable variables as a guide to selection bias.This paper examines the effectiveness of Catholic schools by analyzing the relationship between Catholic school attendance and various educational outcomes. The authors develop estimation methods that use the degree of selection on observable variables to infer the degree of selection on unobservable variables. They argue that if observed variables are a random subset of the factors influencing the endogenous variable and the outcome, the relationship between the indices of observables and unobservables will be the same. This allows for the identification of the effect of the endogenous variable. The authors use their methods to estimate the effect of attending a Catholic high school on outcomes such as high school graduation and college attendance. They find that Catholic high schools substantially increase the probability of graduating from high school and, more tentatively, college attendance. However, they do not find much evidence for an effect on test scores. The paper also discusses the challenges of distinguishing correlation from causation in empirical research, particularly in the context of Catholic school effectiveness. The authors highlight the difficulties in identifying the true effect of Catholic schools due to potential selection bias. They propose an informal way to assess selectivity bias by measuring the ratio of selection on unobservables to selection on observables. The authors use data from the National Educational Longitudinal Survey of 1988 (NELS:88) to analyze the Catholic school effect. They find that Catholic high school students are more likely to graduate from high school and attend college compared to public school students. However, the effects on test scores are less clear. The authors also note that the effects of Catholic schools may be influenced by unobservable factors, such as family background and parental characteristics. The paper concludes that Catholic high schools have a substantial positive effect on high school graduation rates and, more tentatively, on college attendance rates. The authors emphasize the importance of considering selection bias when analyzing the effectiveness of Catholic schools. They also highlight the need for further research on the use of observable variables as a guide to selection bias.