Joseph G. Altonji, Todd E. Elder, and
Christopher R. Taber
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.
Joseph G. Altonji, Department
of Economics, Northwestern University
Todd E. Elder, Graduate student, Department
of Economics, Northwestern University
Christopher R. Taber, Department of Economics,
Northwestern University
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