Estimation of Educational Borrowing Constraints Using Returns to ...

educational borrowing constraints 155
reject the hypothesis that OLS estimates and instrumental variable estimates
are the same.
Columns 4–6 exhibit estimates of the same specifications except that
test scores and family income are excluded. The OLS and instrumental
variable point estimates of the schooling coefficient are both higher,
but the instrumental variable estimate remains larger than its OLS counterpart.
Other specifications not reported here, including a more standard
one with AFQT score instead of the set of four test scores, all yield
similar patterns. These results are also similar to those of Arkes (1998),
who uses state unemployment rates in a similar design and finds instrumental
variable estimates higher than OLS estimates.
A potential problem with this specification is that it does not account
for influences of economic downturns on schooling choices that operate
through family income or through the decision to work while in college.
Borrowing-constrained families may find raising funds for college more
difficult during recessions. This possibility can reverse the direction of
labor market effects: schooling may increase during booms for children
whose parents are borrowing-constrained. Thus the influence of local
labor market conditions on schooling attendance is no longer monotonic.
Intuitively, the income and substitution effects of changes in local
labor market conditions go in opposite directions for borrowing-constrained
families, and it is not clear which effect dominates. However,
if families are not borrowing-constrained, there is no income effect on
schooling (as in a standard human capital model). Thus it is possible
that borrowing-constrained families send their children to college at
higher rates during a boom, whereas non-borrowing-constrained families
send their children at higher rates during a bust when forgone
earnings are low.
The negative association between county earnings and schooling reported
in table 2 supports the dominance of forgone earnings on schooling
decisions. However, this makes the instrumental variable results in
table 3 even more surprising. If children of borrowing-constrained families
have higher marginal returns to schooling and decrease schooling
during recessions, the discount rate bias should be negative. Our empirical
findings are counterintuitive if credit constraints are important.
The mechanics of this argument are formalized in section A of our
technical appendix (available at http://www.econ.northwestern.edu/
faculty/taber).
The case in which students work while in school is analogous. Students
who are borrowing-constrained would presumably be more likely to work
in college. Thus the effect of local labor market conditions would likely
have a larger effect on individuals who are not borrowing-constrained
since they depend less on opportunities to work during college in order