Estimation of Educational Borrowing Constraints Using Returns to ...

educational borrowing constraints 149
reveal that the probability of living at home while in college is about
55 percent for students with a college in their county of residence at
age 17 and 34 percent for others.
The second cost of college is the opportunity cost, denoted in the
term W 0 of equation (7). The prevailing wage rate in the county in
which a person lived at age 17 (the variable local earnings at age 17 in
table 1) is a candidate instrument since it should be correlated with
W 0 but uncorrelated with unobserved ability. The major concern in using
this variable as an instrument is that labor market variables at age 17
are almost certainly correlated with local labor market variables later in
life and hence correlated with current-period wages. To address this
concern, we include directly in the wage regression a time-varying measure
of local average earnings in the current county of residence. This
variable is called current local earnings in table 1 and is denoted by
l it in equation (17). The crucial assumption justifying the instrument is
that, conditional on l it , local labor market conditions at age 17 are
unrelated to the error term u it in (17).
Including l it directly in the wage function (17) leads to a new concern.
Migration is potentially endogenous and related to schooling outcomes.
For instance, college graduates may move more readily to better local
labor markets. Since l it is measured in the county in which a person
resides at time t, it may be endogenous to schooling choice. Consistent
estimation of the coefficient b1 associated with lit
in equation (17) re-
quires an additional instrument correlated with l it but not itself endog-
enous. The natural choice in this case is the prevailing wage rate at time
t measured in the county in which person i lived at age 17. Since many
individuals do not stray far from their county of residence at age 17,
this instrument correlates strongly with prevailing earnings in the current
county of residence. In addition, since its value is determined by
the county in which a student lived at age 17, it does not depend on
residential location decisions made after schooling completion.
A last concern, often mentioned in the returns to schooling literature,
is endogeneity of experience. Our experience variable is a measure of
potential experience and is equal to age minus schooling minus six. If
schooling is endogenous and potential experience depends directly on
schooling, potential experience would be endogenous as well. To account
for this problem, we follow the literature by instrumenting for
experience and experience squared using age and age squared in some
specifications below.
2. Complications Concerning Random Effects
The second complication in our analysis arises because we allow returns
to schooling, , to vary across individuals. If returns were constant and
g i