68 P. Glick, D.E. Sahn Economics of Education Review 19 2000 63–87
also be expected that certain changes in household struc- ture will affect girls’ schooling more strongly than boys’.
An increase assumed exogenous in the number of very young children, for example, may raise the demand for
the labor of girls in childcare in the home. Given the time constraint, this will reduce their schooling relative
to that of boys. By the same logic, additional older sib- lings or adult women may reduce the opportunity cost
of a girl’s time by providing substitutes for household work or through economies of scale in household pro-
duction, thereby raising the likelihood of enrollment or the average level of schooling among girls in the house-
hold.
17
In the empirical work, we do not attempt to esti- mate endogenous shadow prices of time for girls and
boys. Instead, the reduced-form schooling demand func- tions include family composition and other household
factors represented by H in Eq. 5 that are expected to influence, possibly differentially by gender, the value
of children’s time.
Would the collective household model with individual preferences generate any different expectations about the
impacts of the factors discussed above on girls’ and boys’ schooling? The model predicts that factors that
raise the bargaining power of the wife should increase allocations to goods she prefers. The mother’s education
stands out as one such factor for which the dataset pro- vides information. Women with more schooling are able
to earn more, improving their fallback position and if they are actually working the level of income under
their direct control. Thus, if women value the schooling of their children more than men do, maternal schooling
will have a stronger impact than paternal schooling on children’s education. Further, mothers may prefer to allo-
cate resources including for human capital to daughters while fathers prefer sons, as suggested by evidence for
work, in preparation for their future likely roles as homemakers. As a result of this initial specialization and investment, girl’s
home productivity will be higher than boys in later periods, hence their opportunity costs will be higher. This is akin to the
“efficient specialization” hypothesis of Becker 1981. Thus the gender difference in the price of time is a manifestation of lower
returns to schooling for girls, not parental preferences.
17
Note that this conflicts with a major implication of the quantity–quality model described in note 7: that child quantity
and quality average schooling should be inversely related. An inverse relationship exists because having more children raises
the cost of providing a given amount of education resources to each child, and conversely, a higher level of quality raises the
implicit price of child quantity. However, in a context where child work is important, so that the cost of schooling includes
the opportunity cost of foregone labor in the home or family farmenterprise, the relation of the number of children to aver-
age educational investment is less obvious. As noted in the text, increases in the number of children in particular age or sex
categories can lower the marginal value of an individual child’s time, encouraging school investments.
child height in the US, Ghana and Brazil presented in Thomas 1992. Then increases in mother’s schooling
would have a larger beneficial effect on daughters’ edu- cation than on sons’, and father’s schooling would favor
sons’ education. The former is particularly plausible because the mother’s bargaining power and her prefer-
ences for daughters’ schooling are both likely to rise with her own education.
Note, however, that these relationships of maternal and child schooling are also compatible with unified
household preferences. For example, a larger maternal education impact on girls’ education than boys’ may
reflect maternal preferences for schooling girls in a bar- gaining framework or that households in which the
mother has an education also have strong common pref- erences for girls’ schooling. The latter will arise through
marital sorting if men who choose educated wives also want educated daughters or if educated women choose
spouses who also have a preference for educating daughters, resulting in heterogeneity in preferences
between households rather than within them. The prob- lem, as stated above, is that the dataset does not provide
a measure of individual bargaining positions that would not also be a determinant of schooling under common
household preferences.
18
3. Empirical approaches
3.1. Years of schooling The first schooling outcome we investigate, years of
schooling or grade attainment, is an indicator of the cumulative investment in an individual’s education. We
use an ordered probit model to estimate the determinants of years of schooling. This approach allows us to incor-
porate several features of the data that simpler alterna- tives, such as ordinary least squares, cannot. For
example, OLS assumes a continuous distribution for the dependent variable, grade level. Grade attainment, how-
ever, represents the outcome of a series of ordered dis- crete choices—whether to go on to the next grade or
withdraw from school. Also, the distribution of years of schooling is usually not normal around the mean. Typi-
cally it is bimodal or even trimodal, with peaks rep-
18
Thomas 1992 uses as proxies for bargaining power the unearned income of each parent as well as a dichotomous vari-
able for whether the mother is more educated than the father, arguing that the latter indicator will be associated with greater
bargaining power of the mother relative to the father. This is plausible, but in terms of distinguishing common from individ-
ual preferences such an indicator may not help much: choosing a wife who is well educated or even better educated may reflect
the husband’s preference for educated women, hence for girl’s schooling.
69 P. Glick, D.E. Sahn Economics of Education Review 19 2000 63–87
Fig. 1. Males and females aged 10–18: distribution of years of schooling.
resenting completion of specific levels, e.g. secondary school. In our sample, as shown in Fig. 1, the distribution
of years of school is not punctuated by sharp spikes but nevertheless bears little resemblance to a normal distri-
bution. For girls especially many observations cluster at zero no schooling; for both boys and girls there are
sharp drops following 6th grade completed primary and 10th grade completed lower secondary.
A third feature of the data is sample censoring. For children who are still enrolled, the current grade level
does not necessarily represent their final grade attain- ment; all that is known is that they will ultimately have
completed at least their last grade. The data on schooling for these observations, in other words, are right-cen-
sored. Not taking this censoring into account—that is, considering the education of such individuals to be ident-
ical to those who have ended their schooling at that grade—will result in biased estimates of the effects of
the regressors on true potential grade attainment.
19
The ordered probit model treats grade attainment as the outcome of ordered discrete choices and does not
assume a normal distribution for the dependent variable. The model can also be extended to allow for right-cen-
soring of years of schooling. Although completed
19
The censoring problem can be eliminated by restricting the sample to cohorts old enough to have completed their schooling
by the time of the survey, but this restricts the focus to an older group in a context where the determinants of schooling may
have changed over time. In any case, as described in the next section, data on parental backgrounds as well as relevant house-
hold characteristics are unavailable for adults not still residing with their parents.
schooling for children who are still in school is not known, it is known that the final grade attained will be
at least as high as the last grade. This information is incorporated into the likelihood function of the model,
making it possible to calculate unbiased estimates of pro- jected completed schooling of an individual of given
characteristics.
20
A further consideration for the estimation is that the residual terms are unlikely to be independent, reflecting
the fact that more than one child from the same house- hold may appear in the estimating sample. Children in
the same household are likely to share unmeasured by the researcher traits that make them more or less able
to perform well in school, affecting their demand for schooling in a similar way. Alternatively, households
may be heterogeneous with respect to unobserved prefer- ences for education. In either case, the error terms for
children from the same household will be correlated through a common family-level component, and if
ignored this lack of independence may result in substan- tially underestimated standard errors. We allow for such
correlations in the model through a random effects or variance component structure for the residuals; that is,
the errors of the index functions for schooling in the ordered probit formulation are assumed to consist of a
common household heterogeneity component and an idiosyncratic individual error. The estimation procedure
used is that suggested by Butler and Moffit 1982 for the random effects binary probit model. Details of the
20
The first use of the ordered probit model for the analysis of cumulative schooling appears to be Lillard and King 1984.
70 P. Glick, D.E. Sahn Economics of Education Review 19 2000 63–87
likelihood function and estimation of the random effects ordered probit model with censoring are presented in
Appendix A. We estimate separate ordered probit models of years
of schooling for boys and girls aged 10–18. The reason for choosing age 10 as the lower end of the range is that
delayed primary enrollment appears to be common in Conakry, so that some children who are, say, 8 or 9 and
who have never been enrolled may yet enter. For these children it would clearly be inappropriate to assign a
value of zero for grade attainment. By including only children 10 and over, we can be reasonably sure that
those who have not yet enrolled will never enroll and can be assigned zero years of schooling. The choice of
age 18 as the upper end of the range is dictated in part by the desire to minimize selectivity problems caused by
older children being absent from the household, an issue we discuss in detail below.
3.2. Current enrollment status Next
we estimate
the determinants
of school
enrollment status at the time of the survey. For assessing the effects of factors that are time-varying, analyzing the
current enrollment decision has advantages over the analysis of cumulative schooling just outlined, since it
allows us to relate current school choices to contempor- aneous aspects of the household such as income and
household structure. The latter includes the presence of young siblings, whose arrival will likely alter the allo-
cation of time among schooling, household work, and other uses.
21
On the other hand, a disadvantage of the current enrollment approach is that unlike the ordered
probit model of grade attainment it implicitly assumes that the current enrollment decision is independent of the
choices made in previous years; that is, it ignores the cumulative nature of schooling decisions. This is gener-
ally not a very plausible assumption: with the exception of younger children just beginning their schooling, a
child is more likely to be in school today if he or she has been previously enrolled than if she has never attended
21
If parents determine both the number and spacing of chil- dren and future investments in their schooling at the start of
childbearing or marriage, events such as a recent birth are anticipated and reflected in the cumulative schooling of older
siblings. It would then suffice only to look at the ordered probit models of grade attainment but excluding sibling covariates
from the equation, since they would clearly be endogenous. However, this assumes a very high level of planning on the part
of parents as well as an absence of uncertainty, both of which are unlikely in a poorly educated population with limited access
to contraceptives. The issue of the endogeneity of children is considered further below.
school.
22
Current enrollment decisions are estimated using a binary probit, with the dependent variable taking
the value of 1 if the child is currently attending school and zero otherwise. As with the ordered probits, we
allow for intrahousehold correlations in the disturbances. The model we estimate is therefore the random effects
binary probit model of Butler and Moffit 1982.
3.3. Leaving school Our third approach is somewhat novel and focuses on
a transition in schooling status: leaving school in the past 5 years. The ordered probit model of grade attainment
implicitly also models the decision of when i.e. after how many years of school to withdraw. Here, however,
we focus on the school departure decision within a spe- cific historical period. Since this period is recent the last
5 years, our right-hand-side variables should fairly closely capture the circumstances relevant to the
decision. The survey does not actually record the time since leaving school, so we impute it from the data using
information on the ages of students currently in each grade. Years since leaving school is estimated as the
individual’s current age minus the sex-specific median age of students currently enrolled in the last grade that
the individual attended. Thus our dependent variable for withdrawing in the past 5 years, WITHDRAW, equals 1
if, for an individual who is no longer enrolled and who reports s years of schooling, age
i
2 median
s
, 5, where
age
i
is the child’s age and median
s
is the median age for grade s. It equals zero for individuals who are still
enrolled. Individuals no longer in school but who com- pleted upper secondary school during the period are also
assigned WITHDRAW 5 0, while those who were never enrolled are not included in the sample.
23
Inferring recent
22
This may reflect state dependence: attendance in period t makes attendance in t 1 1 more likely because among other
possible reasons the cumulative acquisition of skills is more efficient with continuous schooling than with off-and-on
enrollment. An alternative explanation involves individual or household heterogeneity: children with a propensity for learning
or who have parents with a preference for schooling will be more likely to be enrolled each year, regardless of the direct
effect of attendance in one year on attendance in the next. These concepts are discussed in the context of female labor force par-
ticipation in Heckman 1981.
23
Note that withdrawing from school is not the same as drop- ping out of school as that term is usually defined. Dropping out
usually refers to departures from school prior to completing a certain level, e.g. primary. Our definition is broader and focuses
on stopping one’s schooling in a specific period as a function of contemporaneous household factors or events. Thus a child
who completed primary school during the period and declined to continue to secondary is said to have left school though
secondary graduates who do not go to university are not counted as school leavers. We thank an anonymous reviewer for stress-
ing the importance of this distinction to us.
71 P. Glick, D.E. Sahn Economics of Education Review 19 2000 63–87
school exit decisions in this way allows in a limited way for a dynamic analysis of schooling transitions using
cross-section data. For example, a key demographic vari- able on the right-hand side is the number of siblings
under 5, i.e. the number of brothers and sisters born and surviving and remaining in the household during the last
5 years. The analysis thus shows how school status is affected by “fertility shocks”, that is, additions to the
family of young children treated as exogenous during the period.
The determinants of leaving school are estimated using random effects probit on the samples of boys and
girls aged 15–18 who, using the method just described, are inferred to have been enrolled at the start of the per-
iod. Note that because of the way the dependent variable is constructed, we are effectively analyzing behavior
since age 10 for children currently 15, since 11 for those now 16, and so on. Since leaving school earlier than age
10 is rare, restricting the sample to children 15 and older is appropriate.
24
4. Data and descriptive statistics
