34 E. Funkhouser Economics of Education Review 14 1999 31–50
Fig. 1. Continued.
rate in September 1982, and significant adjustment in the external sector.
Basic patterns in wages and enrollments during the 1980s are shown in Fig. 2. The pattern in real wages of
workers affiliated with the social insurance system and the mean wages reported in the annual household survey
are shown in Fig. 2A. The long-run increasing trend in real wages was broken by a large drop in real wages
between 1980 and 1983 during the period of economic crisis. The real minimum wage, an alternative measure of
the opportunity wage of teenagers, also fell substantially during this period Fig. 2B.
In the next two graphs of Fig. 2, I report changes in school enrollments using school enrollment data from
the educational system Ministerio de Educacion Pub- lica, 1969, 1991 and from tabulations for attendance
from the National Household Survey conducted in July of each year from 1976 to 1992. During the period of
the drop in real wages, school enrollments in grades 7– 12 fell in absolute numbers Fig. 2C and the proportion
of children in the annual household survey aged 12–17 reporting school attendance also fell Fig. 2D. These
aggregate data do show a correlation between wages and school enrollments. I now turn to explaining these pat-
terns.
2. Model
In this section, I provide a theoretical framework for the empirical estimation with data from repeated cross-
sections. The basic intuition of the model is that house- holds trade off future economic returns to schooling and
utility increases from higher quality of children versus
35 E. Funkhouser Economics of Education Review 14 1999 31–50
Fig. 1. Continued.
lower current income and any utility changes from time spent in school.
5
Consider a household that lives for two periods. In the household are adults and children who become adults
after the first period. During the first period, children may enter school, enter the workforce, or consume leis-
ure while adults may not go to school. During the second period, all members of the household engage in market
labor or consume leisure.
The household maximizes a utility function subject to a budget constraint, a time constraint for each member,
a production function for child quality that includes years of schooling as an argument, and a market wage determi-
5
More general models that incorporate family fixed effects including permanent income such as that of Foster 1995
require longitudinal data.
nation relation. Assuming a separable utility function over time, the household problem is then:
Max
C,T,L
Σ 1 1 d
− t
UC
t
,Q
j
,L
1t
,…,L
it
,…,L
nt
, 1
T
1t
,…,T
jt
,…,T
kt
;X
ft
,f
ct
in which C
t
is consumption in the household at time t, Q
j
is quality of the child, L
it
is leisure family time of each of the n household members, T
jt
is time spent in school for each of the k children equal to zero in the
second period, X
ft
is observable family characteristics at time t, and f
c
is community effects at time t. Maximization of Eq. 1 is subject to four constraints.
First, the budget constraint can be written:
O
t
1 1 r
− t
P
ct
1
O
k
P
st
E
jt
2 Σ
O
ti
1 1 r
− t
w
it
H
it
1a
36 E. Funkhouser Economics of Education Review 14 1999 31–50
Fig. 2. A Real wage in social insurance and HH data, 1979 5 100. B Real minimum wage, January 1979 5 100.
2 Y 5 0 where r is the market rate of interest, P
c
is the price of the consumption good, P
st
is the price of schooling, E
jt
is an indicator function for the enrollment of child j, w
it
is the wage rate and H
it
are the labor market hours of individual i in the household, and Y is initial non-labor
income of the household. With borrowing and lending, the present discounted
value of consumption over the lifetime of the house- hold — including consumption of schooling — is equal
to the present discounted value of lifetime income and current income should matter only to the extent that it
is a predictor of lifetime income. With borrowing and lending constraints, the budget constraint must hold per-
iod by period and current income during the time of the attendance decision is the only income that matters.
The second constraint is the time allocation restriction for each household member:
T 5 L
it
1 E
jt
T
it
1 H
it
1b where T is total time of individual i and T
it
is time in school of individual i. Time allocated to family time,
school, and labor market activities must be equal to total time available during each period.
The third constraint is the production function for child quality that includes previous schooling, current
time spent in school, potential time with other family members, observable individual characteristics, and
unobservable individual characteristics.
Q
j
5 QS
j
, T
sjt
E
jt
, Σ
L
i
V9
j
, d
j
1c where S
j
is number of previous school years of child j,
37 E. Funkhouser Economics of Education Review 14 1999 31–50
Fig. 2. C Secondary enrollments. D Percentage of teenagers aged 12–17 in school, hh Survey.
V9 is a vector of individual child factors affecting school quality, and d is unobservable quality of child j.
The last constraint is the wage determination function faced by each individual in the labor market. Own wages
depend on: w
it
5 a
wt
1 b
wt
V
it
1 r
st
S
it
1 b
u
u
c
1 u
it
1d where V
is a vector of observable characteristics, r
s
is the return to schooling, and u
c
is a vector of conditions in the local labor market.
6
The first order-condition for time spent in school states
6
The basic administrative district in Costa Rica is called a canton. The data for u
c
are calculated separately for urban and rural areas within each canton.
that the marginal benefit in child quality plus direct util- ity gained from an increase in time spent from school
is equal to the marginal cost in fees plus the marginal opportunity cost:
dU dQ
j
dq
j
ds
j
ds
j
dt
sj
1 du
dt
j
2 l{P
s
1 w
jt
2 1 2
1 i
− 1
r
s,t 1 1
} 5 0 The demand for time devoted to school, T
sj
can be written in reduced form as:
T
sj
5 T
j
P
c
, P
s
, w
L
, Y, r
s
, X
f
, N
f
V, f
c
, d
j
3 in which the vector V now includes V9 and V
and the vector f
c
includes u
c
. To simplify the problem in a non-
38 E. Funkhouser Economics of Education Review 14 1999 31–50
arbitrary fashion, within the household, time allocation decisions of adults are made prior to the time allocation
decision of children. With a sequential decision process in which adults make labor market decisions before teen-
agers make their time allocation decisions, teenagers condition their work and school decision on the actual
labor market outcomes of adults. In this case, pooling data across years and assuming that each teenager makes
the time allocation decision independently of other teen- agers in the household and the price of consumption
goods can be normalized to one, a first-order approxi- mation of Eq. 3 can be written:
T
sj
5 a 1 b
s
w ˆ
j
5
O
n i 5 j
b
wi
w
i
1 b
y
Y 1 b
r
r
j
4 1
O
k j
V
j
b
vj
1 X
f
b
x
1 f
c
1 f
t
1 e
j
in which the predicted wage, w
j
, is the opportunity cost of attending the next year of school for teenager j, f
t
is vector of year effects, and e
j
is an error that includes unobservable individual effects, d
j
, and any random effects. T
sj
is the indicator function for school attendance of child j:
E 5 1 if T
sj
5 E 5 0 if
T
sj
The estimation procedure involves four steps. First, mean wages within each canton and urban cell, con-
trolling for other factors, are calculated for each year from the sample of all workers to proxy for opportunities
in the local labor market. The second step is the calcu- lation of predicted wages for each teenager using Eq.
1d estimated separately by year. The predicted wages for individual j at time t estimated from the sample of
working teenagers is then applied to all teenagers aged 12–17 as a measure of P
s
. This equation is identified by the labor market opportunities variable. Third, the return
to the next year of education is calculated from the esti- mation of a wage equation for all workers in the same
year as the school attendance decision is made is used as a proxy for the future income differential resulting
from the investment in an additional year of education. The fourth step is the estimation of the reduced form
attendance equation, Eq. 4.
3. Data
