Estimation of Educational Borrowing Constraints Using Returns to ...

educational borrowing constraints 157
direct costs will be higher than instrumental variable estimates using
opportunity costs. The results in these tables do not bear out that prediction.
We find no evidence for discount rate bias using this approach.
E. Validity of the Instruments
In general, without a maintained assumption that one of the instruments
is valid, it is impossible to test the validity of any of them. In addition,
since the causal effect of schooling is assumed to vary across individuals,
standard overidentification tests do not apply. Nevertheless, it is still
worthwhile to investigate concerns about correlation between instruments
and the omitted ability component of wage equation residuals.
Finding no relationship between observable measures of ability and the
instruments cannot prove the validity of the instruments since correlation
with unobserved ability components may remain. Nevertheless,
such a finding still lends credence to their use.
Column 1 of table 5 shows the estimated relationship between the
indicator variable for presence of a local college and a standard set of
regressors: local earnings at 17, mean local earnings over the working
life, racial-ethnic indicators, the set of four test scores, and four family
background variables. The pattern of estimates is not encouraging for
the use of the local college variable as an instrument: math score and
automotive core are significantly related to presence of a college in the
county. If local college were correlated with unobserved ability in the
same way as these observed measures, then instrumental variable schooling
estimates would be biased upward. 22 Nevertheless, this correlation
makes the instrumental variable results presented above even more surprising
since it implies that the instrumental variable estimates should
be lower than they actually are.
By contrast, the fact that test scores do not predict local earnings at
age 17 (col. 2) supports using local labor market variation as an instrument.
Column 2 also shows that the only variable other than mean local
earnings over the working life with any significance is family income.
Given that family income is measured when students were close to age
17, this result is not particularly astounding. 23
The discovery that test scores predict presence of a local college is
not necessarily a problem since test score variables are included in the
specifications. Table 6 displays results that are more favorable to the
legitimacy of using local college as an instrument. The table displays
22
Altonji, Elder, and Taber (2002) provide a model that formally justifies this type of
argument. We do not have enough control variables in this case to use the type of formal
analysis they suggest.
23
Along the same lines, one may question whether family income is a valid control. The
empirical results here are robust to inclusion of family income.