Estimation of Educational Borrowing Constraints Using Returns to ...

educational borrowing constraints 171
high school graduate ( S p 2), some college ( S p 4), and college graduate
or more ( S p 6). 34 During high school, students incur no direct
costs of schooling but must pay some direct costs to attend college and
to graduate from college.
We assume that n Si has a generalized extreme value (GEV) distribution,
so the model can be estimated as a nested logit. We use two levels of
nesting. The high school decisions are nested together, and college
decisions are nested. Observable components of the utilities take the
form
′ ′ ˜
m p a (X b X b ) a ,
0i 1 Wi W L0i L0 20
′ ′ ′
m 2i p a 1[2log(R i) XWibW XL2ib L2] a22 a32log (R i) XTib T2,
[( ) ( ) ]
4 3 t
1 1
′ ′ ˜
′
4i 1 Wi W L4i L4 Ci C 24
Ri
tp2 Ri
m p a log exp (X b X b ) X b a
′
a34 log (R i) XTib T4,
[( ) ( ) ]
6 5 t
1 1
′ ′ ˜
′
6i 1 Wi W L6i L6 Ci C 26
Ri
tp2 Ri
m p a log exp (X b X b ) X b a
′
a36 log (R i) XTib T6,
where the a jS are defined in equation (23).
Nesting yields the following schooling probabilities:
˜
exp (m 6i/r c)
Pr (S p 6FS 1 2, m 0i, …, m 6i) p ,
exp (m 6i/r c) exp (m 4i/r c)
Pr (S p 2FS 1 0, m 0i, …, m 6i) p
exp (m 2i/r h)
exp (m /r ) [exp (m /r ) exp (m /r )]
2i h 4i c 6i c
Pr (S p 0Fm 0i, …, m 6i) p
r c/rh
exp (m 0i)
r /r
exp (m ) {exp (m /r ) [exp (m /r ) exp (m /r )] }
0i 2i h 4i c 6i c
,
c h rh
where rh
and rc
are parameters for the nesting of high school graduates
and college attenders, respectively. 35 The model is estimated by maximum
likelihood, restricting r and r to lie between zero and one. Taber
h
34
Recipients of the general equivalency diploma who attend no college are counted as
dropouts (see Cameron and Heckman 1993).
35
The probability for S p 4 can be constructed from these three probabilities.
c
,