Li, Mingliang; Poirier, Dale J; Tobias, Justin

Journal of Applied Econometrics Vol. 19 (2003): 203-225.

In this paper we describe methods for predicting
distributions of
outcome gains in the framework of a latent variable
selection model. We describe such procedures
for Student-t selection models and a finite
mixture of Gaussian selection models. Importantly,
our algorithms for fitting these models are
simple to implement in practice, and also
permit learning to take place about the
non-identified cross-regime correlation
parameter.

Using data from High School
and Beyond, we apply our methods to determine
the impact of dropping out of high school
on a math test score taken at the senior
year of high school. Our results show that
selection bias is an important feature of
this data, that our beliefs
about this non-identified correlation
are updated from the data, and that
generalized models of selectivity offer
an improvement over the ``textbook'' Gaussian
model. Further, our results indicate
that on average dropping out of high school
has a large negative impact on senior-year test
scores. However, for those individuals
who actually drop out of high school,
the act of dropping out of high school
does not have a significantly negative
impact on test scores. This suggests
that policies aimed at keeping students
in school may not be as beneficial as
first thought, since those individuals who
must be induced to stay in school are
not the ones who benefit
significantly (in terms of test scores)
from staying in school.