Estimation of Educational Borrowing Constraints Using Returns to ...

educational borrowing constraints 141
borrowing rate to be determined by the ability to collateralize loans
with personal or family assets during school. The specific form of borrowing
constraints is not essential to the results in this section. Since
our data do not have information on consumption or assets, we focus
on a simple type of borrowing constraint that is straightforward to estimate
in the structural econometric model described in Section VI.
Define R to be the borrowing rate during school and let R m denote
the market rate, which is normalized for convenience such that
1/R m p d. Students maximize utility subject to the lifetime budget
constraint
S1
() ()
tp0
t
S
t t S
tpS
1 1
tS
c d c ≤ I , (3)
R R
where S is total years of school and I S is the present value of income
net of direct schooling costs. The first-order conditions are
t/(1g)
ct p (dR) c 0, t ≤ S,
S/(1g)
ct p (dR) c 0, t 1 S.
Plugging these values into the budget constraint yields
S1
tg/(1g) t/(1g) Sg/(1g) t
S 0 0.
tp0
tpS
I p R d c (Rd) dc (4)
Finally, solving ct
in terms of IS
and inserting the value into the utility
function leaves us with the following expression for lifetime utility of a
person choosing S years of school:
[ ]
g S1 tg/(1g) t/(1g) Sg/(1g)
1g
t
S tp0 tpS
I R d (Rd) d
V p T(S). (5)
S
g
Equation (5) represents the indirect lifetime utility function conditional
on schooling choice S.
We next solve for the present value of income. To focus on borrowing
constraints, we abstract from earnings uncertainty by assuming that earnings
streams associated with all levels of S are known with certainty at
time 0. 13 Let w St be earnings at time t for an individual with S years of
schooling. Individuals have zero earnings while in school and pay direct
cost t at time S 1 to attend schooling level S. Abstracting from labor
S
13
Uncertainty in future returns to education introduces an option value to further
education. For instance, even if predicted returns to college completion were low, individuals
may still graduate from college in case realized returns outperform predicted
returns (see Taber 2001).