SELECTION ON OBSERVED AND UNOBSERVED VARIABLES: ASSESSING THE EFFECTIVENESS OF CATHOLIC SCHOOLS

SELECTION ON OBSERVED AND UNOBSERVED VARIABLES: ASSESSING THE EFFECTIVENESS OF CATHOLIC SCHOOLS

August 2000 | Joseph G. Altonji, Todd E. Elder, Christopher R. Taber
This paper develops estimation methods to assess the effectiveness of Catholic schools by considering the selection on observed and unobserved variables. The authors propose a formal analysis to quantify the bias from selection on unobservables based on the relationship between the observables and unobservables. They show that if the observed variables are a random subset of a large number of factors influencing the endogenous variable and the outcome, the relationship between the indices of observables and unobservables will be the same. This allows for identifying the effect of the endogenous variable. The authors also propose an informal method to assess selectivity bias by measuring the ratio of selection on unobservables to selection on observables required to attribute the entire effect of the endogenous variable to selection bias. Using these methods, they estimate the effect of attending a Catholic high school on various outcomes, finding that Catholic high schools significantly increase the probability of graduating from high school and, tentatively, college attendance, but do not significantly affect test scores. The paper provides a detailed analysis of the data and regression models, highlighting the importance of controlling for observable and unobservable variables to reduce selection bias.This paper develops estimation methods to assess the effectiveness of Catholic schools by considering the selection on observed and unobserved variables. The authors propose a formal analysis to quantify the bias from selection on unobservables based on the relationship between the observables and unobservables. They show that if the observed variables are a random subset of a large number of factors influencing the endogenous variable and the outcome, the relationship between the indices of observables and unobservables will be the same. This allows for identifying the effect of the endogenous variable. The authors also propose an informal method to assess selectivity bias by measuring the ratio of selection on unobservables to selection on observables required to attribute the entire effect of the endogenous variable to selection bias. Using these methods, they estimate the effect of attending a Catholic high school on various outcomes, finding that Catholic high schools significantly increase the probability of graduating from high school and, tentatively, college attendance, but do not significantly affect test scores. The paper provides a detailed analysis of the data and regression models, highlighting the importance of controlling for observable and unobservable variables to reduce selection bias.
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