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Recent articles using the same data and variants of the same estimation technique report conflicting estimates of the relative quality of education provided by public and Catholic schools. This article explains the reasons for the conflict. In so doing, the article clarifies the assumptions underlying the increasingly popular two-step methods for controlling selectivity bias and highlights the hazards of using these methods when the assumptions are not satisfied. The article also illustrates an alternative method for detecting the presence of selectivity bias.
Murnane et al. (Tue,) studied this question.