Estimation of Educational Borrowing Constraints Using Returns to ...

educational borrowing constraints 151
Second, schooling is a choice among more than two options, so the
Imbens and Angrist (1994) results do not apply directly. Instead, instrumental
variable estimates will be a weighted average of returns for
marginal decision makers at each level of schooling. The weights in the
average will likely depend on the instrument used. We strongly expect
that if borrowing constraints are important, the coefficient on schooling
will be higher when direct costs are the instrument, but we have not
formally proved this result. A major advantage of the structural econometric
model developed below is that identification of borrowing constraints
is formally justified.
B. First-Stage Results
This subsection presents first-stage estimates to demonstrate that the
instruments have predictive power in the first stage and that their signs
are consistent with the model presented above. Because individuals appear
in our data only after leaving school, the variable measuring schooling
attainment is constant. This makes for difficult interpretation of a
first-stage panel regression of schooling on time-varying local labor market
variables and other characteristics. However, to convey the content
of the first-stage regressions, we construct the variable mean local earnings
over working life, which takes the mean value of l it over the years
in which the individual is included in the wage regressions. We regress
schooling on this variable, local earnings at age 17, an indicator for the
presence of a college in the county (local college), and a number of
other control variables.
The first row in column 1 of table 2 shows that local college has a
large and statistically significant effect, implying that individuals with a
college in their county complete almost one-half year more of school,
on average. The other covariates have estimates with signs and magnitudes
consistent with those reported in other work (see, e.g., Cameron
and Heckman 2001).
Column 2 reports estimates when local earnings at age 17 is included
in the regression instead of local college (row 2). The estimated coefficient
has the expected negative sign but is not statistically significant
at conventional levels. This variable apparently reflects both time-series
variation in county earnings due to business cycle effects and crosssectional
differences in average earnings and wealth across counties.
Adding mean local earnings over working life to control for levels of
wealth across counties allows us to sort out these two avenues of influence.
The third row of column 3 shows that the coefficient on the new
variable is significant and positive, indicating that students from wealthier
counties are more likely to attend college—perhaps as a result of
superior schools or peer effects. In addition, the coefficient on local