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

65 Pages Posted: 12 Aug 2000 Last revised: 13 Jan 2005

See all articles by Joseph G. Altonji

Joseph G. Altonji

Yale University - Economic Growth Center; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

Todd E. Elder

Michigan State University

Christopher Taber

National Bureau of Economic Research (NBER); University of Wisconsin - Madison

Multiple version iconThere are 2 versions of this paper

Date Written: August 2000

Abstract

We develop estimation methods that use the amount of selection on the observables in a model as a guide to the amount of selection on the unobservables. We show that if the observed variables are a random subset of a large number of factors that influence the endogenous variable and the outcome of interest, then the relationship between the index of observables that determines the endogenous variable and the index that determines the outcome will be the same as the relationship between the indices of unobservables that determine the two variables. In some circumstances this fact may be used to identify the effect of the endogenous variable. 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 the endogenous variable 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, college attendance. We do not find much evidence for an effect on test scores.

Suggested Citation

Altonji, Joseph G. and Elder, Todd E. and Taber, Christopher R., Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools (August 2000). NBER Working Paper No. w7831, Available at SSRN: https://ssrn.com/abstract=238477

Joseph G. Altonji (Contact Author)

Yale University - Economic Growth Center ( email )

Box 208269
New Haven, CT 06520-8269
United States

National Bureau of Economic Research (NBER)

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Yale University - Cowles Foundation

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New Haven, CT 06520-8281
United States

Todd E. Elder

Michigan State University ( email )

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Department of Economics
East Lansing, MI 48824
United States
517-355-0353 (Phone)

Christopher R. Taber

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

University of Wisconsin - Madison ( email )

716 Langdon Street
Madison, WI 53706-1481
United States

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