Parental characteristics, supply of schools, and child school-enrolment in Pakistan.
Burney, Nadeem A. ; Irfan, Mohammad
In recent years, due to a virtual unanimity about the critical role
of human capital in economic development, increased efforts are being
made in the developing countries to eradicate illiteracy. Despite a
significant increase over time in the number of educational institutions
and the government's expenditure on education in Pakistan, the
performance of the education sector in terms of output has been at best
meagre. This non-correspondence between the growth in the educational
institutions and the resultant output implies that failure to enlist the
participation of the population in education can hardly be attributed
exclusively to an insufficiency of the schools. To the extent that child
schooling reflects parental capacity to invest in human capital
formation, there is a need to reckon with factors bearing parental
decision regarding child schooling.
This paper investigates family's decision regarding child
schooling through an assessment of the determinants of child
school-enrolment, using choice theoretic framework. The regression results are indicative of the influence of household status, both
economic and social, on the propensity to invest in child schooling. A
positive association between the household income, parental education,
and tenurial status as land*owner bear out the importance of these
factors in shaping the household's decision regarding investment in
human capital formation. The study also finds traces of the
quantity-quality trade-off in family's preferences regarding the
number of children, and it is found to be male-specific. The most
disturbing finding of the study appears to be the predominance of the
influence originating from parental education. It is this
inter-generational transfer of human capital which needs more attention
as it also implies that illiteracy, and hence poverty, of the parents
gets transmitted to the off-spring. The analysis also brings out the
fact that the labour market hiring practices serve as an important
feedback to the household's human capital formation behaviour.
I. INTRODUCTION
The strategic importance of Human Capital for socio-economic development of a nation hardly needs to be emphasized. The recognition
that human resource development should be accorded a paramount importance has been manifest in the educational policies of the
developing world. To a certain extent, the development efforts in
Pakistan also reflect such a concern. There has been a significant
increase over time both in the government's expenditure on
education and in the number of educational institutions over the modest
base inherited at the time of independence in 1947. In real terms,
between 1959-60 and 1984-85, the expenditure on education in Pakistan
increased at an average compound growth rate of 9.6 percent. (1) The
number of educational institutions increased from 11099 in 1947-48 to
100243 in 1988-89, i.e., a more than 9-fold increase. (2)
The performance of the education sector in terms of output,
however, appears to be meagre in comparison to the expansion in the
facilities. For instance, as compared to the more than 9-fold increase
in the number of schools, the increase in school enrolment between 1951
and 1981 was only 3.75 times. Currently, the literacy level in Pakistan
is one of the lowest in the world. According to the 1981 population
census, 26 percent of the total population of Pakistan is literate.
Given that the literacy rate in 1951 was only 13 percent, and that many
other countries were able to achieve much higher literacy levels in a
relatively shorter period, the improvement in Pakistan's literacy
rate can at best be termed as modest. Furthermore, the school enrolment
ratios are hardly enviable. In 1981, out of the total population in the
age cohort of 10-24 years, 17.6 percent was enrolled in the schools
compared to only 11.8 percent in 1961. Notwithstanding the policy intent
of universalization of primary education, only a fraction of the
population in the relevant age group is enrolled in the educational
institutions.
In addition to the overall low literacy rate and school enrolment
ratio, large differentials exist between the performance of the urban
and the rural sectors and by sex within each sector. The enrolment
ratios reported in Table 1 indicate that not only the enrolment ratio in
the rural sector has remained far below that in the urban sector, but
that the differential has increased over time. Furthermore, within each
sector, the female enrolment ratio has remained substantially lower as
compared to the male enrolment ratio. However, while in the urban
sector, the differential in the male-female enrolment ratios has
somewhat narrowed over time, it has widened in the rural sector. The
literacy rates by the urban-rural and the male-female classifications
reported in Appendix Table 1 further highlight the fact that the
literacy rates exhibit a similar pattern and have followed the same
trend as the enrolment ratios.
The non-correspondence between the growth in the educational
institutions and the resultant output implies that failure to enlist the
participation of the population in education can hardly be attributed
exclusively to an insufficiency of schools. The education system may
possibly be suffering from problems of inadequacy and inefficiency in
certain respects. As for the observed urban-rural and male-female
differentials in the literacy and school enrolment, one might be tempted
to attribute them to differentials in the availability/access to the
schools. But this would be a simple treatment of a complex situation.
Similarly, one cannot single out culture as the sole factor influencing
female enrolment. Enrolment differentials are also influenced by the
parental characteristics and socio-economic status of the household.
Mason (1988) and Irfan (1985) in their studies on the determinants of
child school enrolment, in Thailand and the rural areas of Pakistan,
respectively, have highlighted the importance of such factors. (3)
To the extent that child schooling reflects the parental capacity
to invest in human capital formation, there is a need to reckon with the
factors beating upon the parental decision regarding child schooling. It
is likely that factors operating on the demand side may have a role in
explaining low school enrolment and large urban-rural and male-female
differentials in school enrolment ratios. Identification of the factors
underlying the meagre performance of the education sector is imperative for policy formulation. This exercise aims to investigate the
family's decision regarding child schooling through an assessment
of the determinants of child school enrolment, using choice theoretic
framework. The study examines the impact of the household income,
household size, ownership of assets, parents' education, and other
socio-economic factors on the schooling of an individual child. In so
doing, an explanation is provided of the inter- and intra-family
differences in educational investment, by sector, sex, and age cohorts.
The rest of the paper is organized as follows: Section II presents
the specifications of a model of child schooling. Section III discusses
data sources. The estimation technique of the model is briefly discussed
in Section IV. Section V is devoted to a discussion of the results. The
final section provides the principal findings and policy
recommendations.
II. A MODEL OF CHILD SCHOOLING
The parents' decision to educate their children, or invest in
human capital formation, has often been analyzed in a Chicago-Columbia
framework, (4) where the demand for schooling is determined jointly with
the number of children. (5) Both the quantity and the quality of
children are assumed to enter the family's utility function. Under
this framework, parents in their utility maximizing decisions regarding
the family size, investment in child's quality, and their own
consumption, substitute between the quantity and the quality of
children, depending upon the relative shadow price of the quantity and
the quality of children. The interaction between the quantity and the
quality in the full resource constraint means that the shadow price of
the quantity depends on the quality, and vice versa. Various empirical exercises have lent support to this quantity-quality trade-off [See
Lindert (1977); Rosenzweig and Wolpin (1980) and DeTray (1978)]. In this
framework, the parents' education and socio-economic status are
considered to have a significant impact on child schooling. For example,
in many empirical studies, the mother's schooling is found to be
positively associated with child schooling. This association is
interpreted to reflect the productivity-enhancing impact of schooling in
the market and household activities. (6) Within the Chicago-Columbia
framework, much of the work on child schooling has been done in the
context of fertility behaviour. A few researchers, however, have also
attempted to analyze child schooling per se. The studies by King and
Lillard (1983); Mason (1988) and Waite, DeTray and Rindfuss (1983) are
some of the examples.
The determinants of child school-enrolment in Pakistan have been
examined by Irfan (1985). The study focussed only on the rural areas and
investigated the school enrolment of children in 10-14 years of age
group. Furthermore, rather than taking the individual child in the
family as the unit of observation, the study focussed on the number of
school-going children in the family as a proportion of total household
members. This amounts to examining inter-family differences in school
enrolment which is indirectly assuming that there are no differences in
school enrolment across children within each family.
Assuming that child school enrolment is determined by the
household's characteristics, the model of child schooling can be
described as:
SCH = f(x) ... ... ... ... (2.1)
where SCH = 1 if the child goes to school, and 0 otherwise.
The parents' decision to send their children to school is
influenced by a number of factors reflecting upon the parents'
capacity to educate their children, the cost of schooling, the benefits
from schooling, the social status of the parents, the societal norm,
etc. The vector 'x' thus usually includes household income,
household size, ownership of assets, parents' education,
father's employment status and occupation, availability of school,
etc. Household income captures the impact of resource constraint on
child schooling, i.e., the income effect. A priori, it is expected to be
positively associated with child schooling. (7) The coefficient of the
household size is expected to reveal whether there exists any trade-off
between the child schooling and the larger family size. (8) The
relationship between the ownership of assets and child-schooling cannot
be determined a priori. Asset ownership can have at least three
different types of effects: a pure wealth effect which is positive; an
opportunity cost effect which is negative; and a bequest effect which
can be either positive or negative. (9) The net effect of these on an
individual child' s schooling depends on the relative implicit
price of schooling among siblings and on the sibling order which
produces the bequest effect. [See also King and Lillard (1983)].
Parents' schooling reflects the taste and the capacity of
parents to supervise child schooling. As more educated parents are more
efficient per unit of time and other inputs in the training of children,
their educational attainments by reducing the cost of schooling the
child are expected to be positively associated with child schooling. The
coefficients of the parents' education also reflect upon the
inter-generational transmission of educational attainment.
In both the Chicago-Columbia and the Pennsylvanian frameworks,
other factors, besides the household's income, family size,
ownership of assets, and parents' education, are also likely to
affect the parent's decision to educate their children. In this
context, the household's socio-economic status is considered to
have an important influence. (10) For instance, for given income and
educational qualifications, households belonging to low status group
face a totally different set of opportunities. This is because labour
market hiring procedures discriminate against them. (11) A priori
ascertainment of the impact of the household's social
status--determined to a large extent by the employment/tenurial status
and occupation of the household head (father)--on child schooling,
whether positive or negative, cannot be made.
It is generally believed that the neighbourhood in which a
household lives has considerable influence on its expenditure pattern.
For instance, a household living in a relatively rich neighbourhood is
likely to be spending a relatively larger proportion of its income on
consumer durables compared to a household living in a poor
neighbourhood. (12) Such a phenomenon, referred to as the
'Demonstration Effect' or the 'Duesenberry Effect',
is also usually observed in the context of the family's decisions
to educate their children. Households belonging to areas with a
relatively more literate population generally exhibit a higher level of
human capital formation, perhaps due to the demonstration effect. Thus,
area literacy level reflecting the societal norms regarding literacy is
included in order to test the existence or otherwise of the
demonstration effect. The availability of a school in the area, which
accounts for the cost of a school, is likely to be positively related to
the child's school enrolment.
III. THE DATA
The analysis in this paper will be based on the household level
micro data from the Population, Labour Force and Migration (PLM) Survey
undertaken by the Pakistan Institute of Development Economics (PIDE) in
collaboration with the ILO and UNFPA in 1979. The survey, based on a
national sample, covered 10288 households and generated data on the
households' decision-making process concerning four different
aspects, viz., fertility, migration, labour force participation, and
income and expenditure. As in Pakistan and many other developing
countries extended or joint families are common particularly in the
rural areas, the parents' choice regarding the schooling of their
children is unlikely to be clearly established where the households are
headed by someone other than the parents. Thus, in order to focus
sharply on the parents' decision to educate their children, we
restrict our analysis to the nuclear family households. (13)
The PLM data on the educational attainment or school enrolment
pertains to the information on the level of education of each person in
the household. The current enrolment in schools, however, is available
only for the household members aged 10 years and above. This latter
information is obtained in response to the question on "reason for
not working". As the focus of our analysis is the schooling of
individual child in the family, the dependent variable, i.e., SCH, takes
the value "1" if the reason for the child's not working
is stated to be 'engaged in studies'. In all other cases, the
dependent variable takes the value '0'. As in Pakistan the
school enrolment in the urban and the rural sectors are different, which
can be partly attributed to the difference in their respective labour
markets, the analysis will be carried out separately for the urban and
the rural households. In addition, since the parents' propensity
and capacity to educate their children is expected to be influenced by
the age and the sex of the child- as the opportunity cost of schooling
increases with age and the returns to schooling are lower for females
because they have lower rates of labour force participation -, children
of each sex are categorized into four age groups: (i) 10-14 years old,
(ii) 10-16 years old, (iii) 17-20 years old, and (iv) 21-25 years old.
(14) An alternative to running separate regressions by sector, sex, and
age of the child would be to run a single regression with appropriate
dummies as independent variables which take an account of the above
factors. A sufficient number of observations in different age/sex
categories for each sector are available but since the introduction of
too many dummies in the regression complicates measuring properly the
interaction and cross-interaction among the different variables and
dummies, a separate regression for each category is estimated. The
current school enrolment of children in different age groups, by sector
and sex, as observed in the data, is given in Table 2. (15)
The evidence given in the table indicates that around 45 percent of
the children in the 10-14 years age group attend school. (16) In the
case of children in 17-20 years and 21-25 years age groups, these
numbers are around 18 percent and 5 percent, respectively. For each age
group, the differences in the school enrolment, across sectors and
within each sector across children of different sex, are interesting to
note. While 65 percent of the children in 10-14 years age group in the
urban sector attend school, the enrolment in the rural sector is only 31
percent. A similar pattern appears for the other age groups. Within each
sector, large differences exist between the school enrolment of male and
female children, with the male enrolment being higher.
Besides information on the household composition, the survey
contains data on household income, expenditure, and saving. The survey,
however, is deficient in data on asset Ownership. As no information on
asset ownership is available for the urban households, the impact of
wealth on child schooling cannot be examined. In the case of the rural
households, however, the households' land-holding will be used as a
proxy for the wealth. A particular rural household is termed as a
landless household if the usual occupation of the household-head is
reported to be agricultural labour without any land. The impact of the
parents' education on child schooling will be analyzed by defining
various dummies for different educational levels of both the fathers and
the mothers, separately. This is because while father's education
is more likely to have an indirect effect via income, mother's
education has more direct role in training. The impact of the
household's social status will be examined by taking into
consideration father's employment/tenurial status and occupation.
In addition, the impact of the household's labour force
participation behaviour on child schooling is also examined by
considering the proportion of household members reported to be engaged
in labour force activities. This is primarily for the reason that for
households registering a high labour force participation the opportunity
cost of sending children to schools is relatively high. As literacy
level of the urban area was not available in the data tape, the impact
of the societal norm in the context of literacy level will be examined
only for the rural households by using the village literacy rate. The
impact of the availability of a school will be analysed only for the
rural areas by defining different dummies for the presence of a school
in the village. The description of all the explanatory variables to be
used in the regressions for both the urban and the rural sectors,
together with their mean values, is given in Table 3.
IV. ESTIMATION TECHNIQUE
As the dependent variable in our model is binary in nature and
takes discrete values 0 and 1, the ordinary least-square (OLS) method is
inappropriate not only because of the problems associated with
heteroscedasticity but also because there is nothing to constrain the
dependent variable to the unit interval. (17) The most commonly used
methods to examine the behaviour of binary dependent variables by
regression analysis are: (i) the Linear Probability Model, (ii) the
Probit Model, and (iii) the Logit Model. These models differ from each
other in terms of the different cumulative distribution function assumed
in the regression relationship. (18)
As the conditional probability interpretation of the linear
probability model is not always fully satisfied, the non-linear
functional forms, e.g., the probit and the logit, are preferred.
However, a priori, on theoretical grounds it is difficult to determine
which of the two non-linear models is appropriate for any particular
problem. In the case of binary variables, however, because normal and
logistic distributions are very close to each other except at the tails,
the estimates obtained using the probit and the logit forms are likely
to be close unless the samples are large (19) The estimates, however,
are not directly comparable because the variance in the distributions is
assumed to be different. (20)
In the standard OLS regression the value of the coefficient
represents change in the dependent variable caused by a unit change in
the independent variables. In the case of the probit and the logit
estimates, the effects of a unit change in an explanatory variable on
the probability of success depend on the particular value of the vector
of explanatory variables. The change in the probabilities given by the
linear probability model, the probit model, and the logit model, with
respect to the ith explanatory variable, respectively, is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where f(x'[beta]) is the density of the standard normal
distribution function. As is evident, while in the case of linear
probability model the effects of changes in the independent variables on
the probability of success are constant, for the probit and the logit
models they depend on the particular values of the explanatory
variables.
As the current school enrolment of children in both the urban and
the rural sectors is found to vary by the age and the sex of the child,
in this paper we shall estimate separate regressions for each age group
by sector and sex. Because, a priori it is difficult to determine which
of the three functional forms--viz., linear probability, probit, and
logit--is more appropriate for our data, we shall estimate the model
using all three functional forms. For comparison, the estimates obtained
by using different forms will be adjusted, using the transformation
suggested by Amemiya (1981). Finally, the marginal effects of the
independent variables on the probability of attending school will be
examined.
V. RESULTS
In order to highlight the importance of the household's
socio-economic status and community variables in accounting for the
urban-rural and the male-female differentials in the school enrolment of
children in a developing country like Pakistan, the relationship (2.1)
was first estimated with household income, family size, and
parents' education as the only explanatory variables. The results
for each sector by the sex and the age group of the child, obtained by
using the linear probability model, the probit model, and the logit
model, are presented in Annexure Tables 2-5. (21) The estimates are
consistent, qualitatively, across the alternative forms of the model.
(22) The explanatory variables included in the regressions explain 5 to
32 percent of the variations in the dependent variable, depending upon
the sector, sex, and age group of the child.
As the linear probability and the probit and the logit formulations
assume different functional forms for the distribution, the coefficients
are not directly comparable. For comparison, the linear probability and
the logit estimates reported in Annexure Tables 2-5 were adjusted, using
the transformation suggested by Amemiya (1981). The transformed
coefficients are reported in Annexure Tables 6-9. In general, the linear
probability coefficients are the smallest and the logit coefficients are
the largest. The difference between the probit and the logit
coefficients, however, does not appear to be large. As the other
statistics, e.g., R-square and log of likelihood function, for the two
models are also close, they suggest that both the probit and the logit
functional forms are equally appropriate for our data. Since the OLS
method does not yield satisfactory results anyway, only the probit
estimates will be used to discuss the effects of different explanatory
variables on the school enrolment of children.
The estimates reported in the tables indicate that, in general, all
the variables have anticipated signs. The coefficients, however, are not
necessarily significant in all the cases. The coefficient of the
household income is positive and, except for urban males of up to 20
years of age and urban females of 21-25 years of age, is significant for
other groups. It must be noted that the cross-sectional association
between household income and child school-enrolment can hardly be
treated as a true relationship because the household income is not
adjusted for the contribution of the working child of the same age
group. The regression results, therefore, tend to under-estimate the
actual effect of income to an unknown extent. Mason (1988) used
household expenditure as a proxy for permanent income and found that in
Thailand the household's permanent income has a significant
positive effect on the school enrolment of children in 15-17 and 18-24
years age groups. Mason, in his study, does not take account of the
difference in school enrolment arising due to the household's
residence in the urban/rural areas. In addition, separate regressions
for males and females are not estimated. However, significant
differences in the school enrolment by sex are found to exist.
The sign of the coefficient of the household size points to the
non-existence o f the trade-off between the quantity and the quality of
children in Pakistan. (23) Not only is the sign of the coefficient, in
general, positive, but also it is insignificant except for urban
females. Blake (1981) has demonstrated the existence of the trade-off
between the quantity and the quality of child in the case of the U. S.
A. For Thailand, Mason (1988) has found that additional young household
members discourage enrolment by increasing the opportunity cost of the
time of the potential students. Older members, on the other hand,
encourage enrolment by decreasing the opportunity cost of the time of
the other household members.
The educational level of the parents is positively associated with
child schooling. The coefficients, however, are not significant for all
the groups. It is interesting to note that the higher the educational
level of the parents, the more likely are the older children to be
attending school, as reflected by the size and significance of the
coefficients of different educational levels of the parents for children
in different age groups. Mason (1988) and King and Lillard (1983)
obtained similar results for Thailand and the Philippines, respectively.
To examine the impact of the household's socio-economic status
and the community variables on the school enrolment of children in
Pakistan, the relationship (2.1) was estimated in the second stage with
additional explanatory variables: father's employment/tenurial
status, father's occupation, the household's land-holdings,
presence of school in the area, area literacy, and the household's
labour-force participation pattern. The estimates thus obtained,
assuming normal cumulative distribution function, are reported in
Annexure Tables 10 and 11. It is evident from the tables that the
inclusion of the additional variables not only considerably increased
the explanatory power of the regressions but also improved the
significance of the coefficients of household income, household size,
and parents' education. As expected, however, the magnitude of the
coefficients decreased slightly. We now discuss in detail the effects of
each explanatory variables on the school enrolment of children
separately.
(i) Household Income
It is to be noted that in the extended regressions the coefficient
of the household's income is positive and, except for urban females
in the 21-25 years age group, is significant in all the cases. This
suggests that, in general, households with higher income are more likely
to educate their children Irrespective of child's age and sex. The
results reported in Table 4 further suggest that the impact of household
income on the school enrolment of children is considerably different
between the urban and the rural sectors. Furthermore, within each
sector, the impact varies by the age and sex of the child. While the
impact on female school enrolment is higher as compared to male
enrolment in the urban sector, the reverse is true in the case of the
rural sector. This may owe to the peculiar structure of jobs in the
rural sector, or the prestige associated with being able to afford not
having female family members in the labour market.
(ii) Household Size
In the extended regressions, the evidence on the quantity-quality
trade-off, as simulated by the sign of the coefficient of household
size, interestingly emerges to be sex-specific. As provided in the
Annexure Tables 10 and 11, the trade-off is visible in the case of
males. In the case of females, one does not find such a trade-off in the
urban sector. Pending an in-depth investigation, this finding can be
explained in terms of the opportunity costs of schooling and the
socio-cultural factors. The limited work opportunities for females
within or outside the households and the enhancement in the capacity to
get a better educated husband through a higher level of schooling may
underlie these results. The estimates reported in Table 5 show that the
marginal effect of the increase in the household size on the probability
of attending school shows different patterns across different age groups
in the urban and the rural sectors. Whereas in the urban sector the
impact on the probability first rises and then falls for both males and
females, in the rural sector it declines for males but rises for
females.
(iii) Land-holdings
Among the rural households, the size of land-holdings is found to
be negatively associated with boys' schooling. This suggests that
for households with large landholdings, the opportunity cost of sending
boys to school tends to dominate the pure wealth effect. (24) This
result is in sharp contrast to the one obtained by King and Lillard
(1983) for the Philippines. They have shown that an increase in the
household's landholdings increases school enrolment at all the
levels. (25) Boys of 10-16 years of age of a landless household are
found to be less likely to be attending school. As landless households
are generally engaged as agricultural labour, they are also likely to be
low-income households, where children usually start working at a young
age rather than going to school. Our estimates fail to establish any
relationship between female schooling and land-ownership.
(iv) Parental Education
In/he extended regressions, except for some minor quantitative changes in the impact of parents' education on the school enrolment
of children, the overall pattern appears to be similar to that in the
simple regression. The estimates show that the educational level of
parents is positively associated with child schooling. The coefficients,
however, are not significant in all the cases. It is interesting to note
that the higher the educational level of the parents, the more likely
are the older children to be attending school. For instance, in the
urban sector, primary education of the parents appears inconsequential for boys' schooling. Girls, however, are found to stand a better
chance. On the other hand, if the educational level of the parents is
Matric and/or Higher, both boys and girls of all ages are likely to be
attending school. In the rural sector, however, where literacy norms are
relatively lower as compared to those in the urban sector, even primary
education of the parents is found to be positively associated with the
schooling of the children. These estimates, thus, show that as the
educational level of the parents increases, the chances of their
children's attending school also increase irrespective of the
child's age and sex. In other words, children of Higher-educated
parents are likely to be more educated, i.e., educational attainments
are transmitted intergenerationally. Table 6 gives the marginal effects
of the parents' educational level on the probability of their
children's attending school. Although there appears to be no clear
pattern across different age groups by sex, yet, in general, the
marginal effect of father's educational level appears to be larger
as compared with that of mother's corresponding level. This can
partly be a reflection of father's role in the household
decision-making process. As expected, the effect of higher education,
e.g., Matric and Higher, is found to be greater than that of Primary and
Middle.
(v) Father's Tenurial/Employment Status and Occupation
For the urban households, father's employment status as
employer and/or being self-employed is found to be negatively associated
with child schooling. The coefficient, however, is significant only for
females up to 16 years of age. This suggests that if a person is either
self-employed or is an employer, his children, particularly the girls,
are less likely to be attending school. This can be partly attributed to
the high opportunity cost of schooling perceived by households because
of the need for boys' work in the family-based enterprises. In the
case of girls, the financial security that a household may feel by
owning a business seems to reinforce the cultural-cure-traditional bias
against girls' education. It also works against the need to educate
the children so as to support the parents in old age. In the case of the
rural households, the tenurial status of father being the land-owner is
found to have a significant positive influence on child schooling. For
Thailand, Mason (1988) has found that the household being a farm-owner
has a negative influence on school enrolment.
In general, father's occupation is not found to have any
significant impact on child schooling. Except for the clerical and sales
and service category, and that also only for boys, the other
occupational categories do not appear to be associated with child
schooling in any significant manner. A priori, one would expect the
professionals and administrative workers to have a higher propensity to
invest in human capital formation. Surprisingly, however, the estimates
do not show such a pattern. Since the professionals and administrative
workers are likely to be relatively more educated and well-paid, it is
possible that the influence of this occupational category is partly
captured by the income and education variables. (26) It must also be
noted that the occupational categories at the two-digit level mask tremendous variation, wherein, for instance, the primary school teacher
is grouped together with an engineer under the category of
'professional'. Hence, the insignificance of the occupation
may be partly a reflection of the data limitation.
(vi) Household Labour Force Participation
Except for urban females, the household's labour force
participation behaviour is found to be negatively related to child
schooling. This suggests that, for whatever reason, if a majority of the
other family members are in the labour force, a child is less likely to
be attending school. This could be because of the fact that households
registering a higher labour force participation either enjoy better
prospects in the labour market or this is imposed by the needs. In
either case, the opportunity cost of sending children to school is
higher than that of the counterpart households registering a lower
labour force participation. Table 7 shows that the marginal effect of
the household's labour force participation behaviour declines
across children's successively higher age groups.
(vii) Community Variables
For the rural households, the literacy level in the village is
found to be positively associated with child schooling. This indicates
that the households in the villages with a relatively more literate
population exhibit a higher level of human capital formation, perhaps
reflecting the 'Demonstration or Duesenberry' effect. The
marginal effect for females, however, is found to be greater among
children of 10-14 years of age and smaller among children of 10-16 years
of age.
Since in the rural sector the age cohorts under analysis are
generally enrolled in Middle, Secondary, and College level classes, one
would expect a significant positive association between school enrolment
and the existence of Middle and High schools in the village. However,
the binary variable denoting the existence of a Middle school in the
village is significant only in the case of boys. (27) The presence of
Primary or High schools in the village hardly appears to matter. For
girls the presence of a school, whether Primary, Middle or High, appears
to be inconsequential. The non-significance of a 'school in the
village' can possibly be attributed to the correlation between some
of the explanatory variables, e.g., village literacy and the presence of
a school in the village. Exclusion of the 'village literacy'
variable from the regression, however, did not improve the significance
of the 'school in the village' variables.
VI. CONCLUDING REMARKS
In addition to the usual caveats regarding the response and
non-response errors entailed by the survey data, it needs to be pointed
out that the problems such as current enrolment being a censored observation and the issues of joint determination of school enrolment
and attainment are not addressed in the foregoing exercise. Given these
limitations, the regression results are indicative of the influence of
household status, both economic and social, on the propensity to invest
in child schooling. A positive association between household income,
parental education, and tenurial status as landowner bears out the
importance of these factors in shaping the household's decision
regarding the investment in human capital formation. The study also
finds the traces of the quantity and quality trade-off, which is
male-specific.
The most disturbing, though not unexpected, finding of the study
appears to be the predominance of the influence originating from
parental education. It is this intergenerational transfer of human
capital which needs more attention, as it also implies that the
illiteracy and, hence, the poverty of parents gets transmitted to the
off-spring. Although the literature is replete with rationalization in
terms of the efficiency of educated parents in the educational
investment of their children, there is reason to believe that this
phenomenon of the positive association between parental education and
child school-enrolment finds its support from hiring practices in the
labour market.
A negative association between father's landlessness and child
school-enrolment, after controlling other variables in the equation,
alludes to the operation of labour market discrimination. The need to
have an in-depth investigation of the labour market processes--and the
resultant variation in the rate of return to education across different
socio-economic groups--can hardly be over-emphasized in this context. It
is expected to yield policy-relevant insights pertaining to the capacity
of the individual to participate in the facilities engendered by the
system.
Our analysis brings out that labour market hiring practices serve
as an important feed-back to the household's human capital
formation behaviour. In addition, it provides an explanation of the
urban-rural enrolment differentials and the low literacy level. Because
the rural labour market cannot absorb the rural educated youth
productively, the returns to education are low in the rural sector. On
the other hand, the opportunity cost of sending the children to school
in the rural areas is higher than that in the urban areas. Finally, our
results provide an insight into the male-female differentials in the
school enrolment within a given sector.
Authors' Note: We would like to express our gratitude to
Professor Syed Nawab Haider Naqvi, Director, Pakistan Institute of
Development Economics, for his constant encouragement. The helpful
comments made by an anonymous referee of the journal, and by Ashfaque H.
Khan and A. R. Kemal on earlier drafts of the paper, are gratefully
acknowledged. We are also thankful to Masood Ishfaq Ahmed for his
valuable assistance in programming and preparing the data tapes. We
alone are responsible for any remaining errors.
Annex Table 1
Literacy Rates for the Urban and Rural Areas in Pakistan, by Sex
(Age 10 and Above)
Both Sexes
1951 1961 1972 1981
Overall 13.2 18.4 21.7 26.2
Urban N.A. 36.7 41.5 47.1
Rural N.A. 12.2 14.3 17.3
Male
1951 1961 1972 1981
Overall 17.0 26.9 30.2 35.1
Urban N.A. 46.8 49.9 55.3
Rural N.A. 19.8 22.6 26.2
Female
1951 1961 1972 1981
Overall 8.6 8.2 11.6 16.0
Urban N.A. 23.3 30.9 37.3
Rural N.A. 3.6 4.7 7.3
Source: Estimated from Population Census Reports 1951,
1961, 1972 and 1981.
Annex Table 2 Estimates of Male Child Schooling in Urban Pakistan,
by Age Groups
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
Constant 0.606 0.209 0.294
(12.071) (1.146) (0.946)
Household Monthly Income 0.00002 0.0001 0.0002
(1.197) (1.577) (1.665)
Household Size 0.0014 0.0007 -0.0007
(0.214) (0.029) (-0.016)
Fathers Education
(i) Primary 0.088 0.248 0.385
(1.446) (1.204) (1.107)
(ii) Middle 0.172 0.542 0.917
(4.186) (3.630) (3.495)
(iii) Matric 0.201 0.688 1.191
(5.610) (4.995) (4.733)
(iv) Higher/Others 0.218 0.949 1.847
(3.988) (3.261) (2.959)
Mothers Education
(i) Primary 0.058 0.140 0.371
(0.634) (0.425) (0.627)
(ii) Middle 0.107 0.414 0.748
(2.272) (2.161) (2.085)
(iii) Matric 0.147 0.977 1.974
(3.198) (3.633) (3.249)
(iv) Higher/Others -- -- --
Number of Observations 950 950 950
Number of Positive Observation -- 725 725
R-Square 0.100 0.108 0.109
Adjusted R-Square 0.092 -- --
F-Statistics 11.65 -- --
Log of Likelihood Function -- -462.33 -461.62
Convergence Achieved
After-iterations -- 5 6
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
Constant 0.519 -0.0203 -0.044
(11.322) (-0.135) (-0.176)
Household Monthly Income 0.00001 0.00008 0.0002
(0.984) (1.509) (1.569)
Household Size 0.006 0.014 0.0202
(0.951) (0.722) (0.609)
Fathers Education
(i) Primary 0.068 0.176 0.276
(1.225) (1.047) (1.007)
(ii) Middle 0.111 0.276 0.462
(2.928) (2.358) (2.373)
(iii) Matric 0.238 0.754 1.275
(7.254) (6.670) (6.330)
(iv) Higher/Others 0.257 0.974 1.825
(5.022) (4.338) (3.983)
Mothers Education
(i) Primary 0.047 0.109 0.231
(0.531) (0.392) (0.489)
(ii) Middle 0.104 0.337 0.563
(2.369) (2.211) (2.096)
(iii) Matric 0.151 0.713 1.318
(3.542) (3.962) (3.723)
(iv) Higher/Others 0.118 0.551 0.865
(1.030) (0.999) (0.804)
Number of Observations 1263 1263 1263
Number of Positive Observation -- 896 896
R-Square 0.108 0.112 0.112
Adjusted R-Square 0.101 -- --
F-Statistics 15.19 -- --
Log of Likelihood Function -- -680.24 680.24
Convergence Achieved
After-iterations -- 5 5
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
Constant 0.162 -0.986 -1.604
(2.531) (-4.839) (-4.688)
Household Monthly Income 0.00002 0.00008 0.0001
(1.371) (1.452) (1.417)
Household Size -0.0007 -0.002 -0.006
(-0.091) (-0.090) (-0.144)
Fathers Education
(i) Primary 0.133 0.417 0.695
(1.531) (1.600) (1.612)
(ii) Middle 0.109 0.346 0.580
(1.678) (1.746) (1.752)
(iii) Matric 0.247 0.701 1.163
(4.907) (4.612) (4.569)
(iv) Higher/Others 0.414 1.177 1.949
(5.241) (4.837) (4.748)
Mothers Education
(i) Primary 0.179 0.466 0.775
(1.167) (1.053) (1.061)
(ii) Middle 0.002 0.020 0.013
(0.027) (0.088) (0.036)
(iii) Matric 0.211 0.591 0.953
(3.419) (3.228) (3.135)
(iv) Higher/Others 0.205 0.577 0.978
(2.042) (1.855) (1.823)
Number of Observations 538 538 538
Number of Positive Observation -- 197 197
R-Square 0.188 0.186 0.186
Adjusted R-Square 0.172 -- --
F-Statistics 12.17 -- --
Log of Likelihood Function -- -301.37 -301.55
Convergence Achieved
After-iterations -- 3 4
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
Constant -0.061 -2.379 -4.262
(-0.000) (-0.000) (-0.000)
Household Monthly Income 0.00004 0.0001 0.0002
(2.330) (2.185) (2.086)
Household Size 0.009 0.062 0.111
(1.510) (1.971) (1.975)
Fathers Education
(i) Primary 0.022 0.292 0.621
(0.281) (0.661) (0.700)
(ii) Middle 0.0411 0.409 0.848
(0.778) (1.383) (1.434)
(iii) Matric 0.083 0.587 1.220
(1.891) (2.322) (2.412)
(iv) Higher/Others 0.207 0.995 1.890
(3.411) (3.333) (3.322)
Mothers Education
(i) Primary 0.125 0.548 1.002
(1.262) (1.275) (1.295)
(ii) Middle 0.162 0.635 1.133
(2.731) (2.534) (1.622)
(iii) Matric 0.008 0.051 0.129
(0.161) (0.210) (0.298)
(iv) Higher/Others 0.892 0.209 0.314
(0.101) (0.523) (0.431)
Number of Observations 392 392 392
Number of Positive Observation -- 54 54
R-Square 0.117 0.424 0.112
Adjusted R-Square 0.094 -- --
F-Statistics 5.03 -- --
Log of Likelihood Function -- -134.66 -135.1
Convergence Achieved
After-iterations -- 5 5
Note: Figures in the parenthesis are t-ratios.
Annex Table 3 Estimates of Female Child Schooling in Urban Pakistan,
by Age Groups
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
Constant 0.121 -1.250 -2.045
(2.128) (-6.298) (-6.087)
Household Monthly Income 0.00004 0.0004 0.0007
(2.981) (4.430) (4.406)
Household Size 0.015 0.031 0.042
(2.089) (1.221) (1.000)
Fathers Education
(i) Primary 0.315 0.807 1.315
(4.097) (3.403) (3.370)
(ii) Middle 0.160 0.374 0.595
(3.580) (2.668) (2.563)
(iii) Matric 0.339 0.900 1.454
(9.025) (7.250) (7.066)
(iv) Higher/Others 0.480 1.648 3.057
(8.065) (5.681) (4.940)
Mothers Education
(i) Primary 0.133 0.398 0.656
(1.145) (1.095) (1.104)
(ii) Middle 0.294 0.906 1.592
(5.934) (5.139) (5.028)
(iii) Matric 0.298 1.244 2.219
(6.150) (5.917) (5.554)
(iv) Higher/Others -- -- --
-- -- --
Number of Observations 881 881 881
Number of Positive Obser-
vations -- 458 458
R-Square 0.291 0.317 0.319
Adjusted R-Square 0.283 -- --
F-Statistic 39.62 -- --
Log of Likelihood Function -- -452.62 -451.19
Convergence Observed-
After-iterations -- 5 5
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
Constant 0.112 -1.199 -1.970
(-2.345) (-7.450) (-7.111)
Household Monthly Income 0.00003 0.0002 0.0003
(2.576) (3.406) (3.346)
Household Size 0.014 0.040 0.061
(2.387) (1.976) (1.777)
Fathers Education
(i) Primary 0.262 0.680 1.117
(4.147) (3.558) (3.544)
(ii) Middle 0.159 0.407 0.657
(4.112) (3.378) (3.292)
(iii) Matric 0.325 0.877 1.430
(10.041) (8.419) (8.241)
(iv) Higher/Others 0.458 1.519 2.708
(8.774) (6.997) (6.324)
Mothers Education
(i) Primary 0.170 0.478 0.773
(1.716) (1.569) (1.553)
(ii) Middle 0.323 0.987 1.672
(7.521) (6.625) (6.380)
(iii) Matric 0.318 1.155 1.992
(7.756) (7.200) (6.810)
(iv) Higher/Others 0.250 1.002 1.653
(2.411) (1.790) (1.489)
Number of Observations 1199 1199 1199
Number of Positive Obser-
vations -- 591 591
R-Square 0.291 0.304 0.305
Adjusted R-Square 0.286 -- --
F-Statistic 48.86 -- --
Log of Likelihood Function -- -627.25 -626.42
Convergence Observed-
After-iterations -- 5 5
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
Constant -0.090 -2.141 -3.755
(-1.643) (-8.133) (-7.600)
Household Monthly Income 0.00005 0.0002 0.0003
(3.656) (3.269) (3.211)
Household Size 0.017 0.074 0.136
(2.494) (2.532) (2.638)
Fathers Education
(i) Primary -0.048 -0.213 -0.554
(-0.492) (-0.427) (-0.514)
(ii) Middle 0.019 0.094 0.233
(0.341) (0.389) (0.529)
(iii) Matric 0.752 0.276 0.545
(1.570) (1.366) (1.514)
(iv) Higher/Others 0.301 0.973 1.683
(4.668) (4.037) (4.032)
Mothers Education
(i) Primary 0.067 0.316 0.554
(0.548) (0.647) (0.626)
(ii) Middle 0.154 0.563 0.992
(2.507) (2.441) (2.518)
(iii) Matric 0.259 0.878 1.518
(4.642) (4.254) (4.266)
(iv) Higher/Others 0.150 0.530 0.918
(1.513) (1.470) (1.538)
Number of Observations 439 439 439
Number of Positive Obser-
vations -- 102 102
R-Square 0.248 0.255 0.256
Adjusted R-Square 0.231 -- --
F-Statistic 14.123 -- --
Log of Likelihood Function -- -184.24 -184.32
Convergence Observed-
After-iterations -- 4 5
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
Constant -0.071 -3.216 -6.196
(-2.443) (-7.755) (-6.688)
Household Monthly Income 0.000008 0.00003 0.00005
(0.649) (0.311) (0.292)
Household Size 0.0121 0.118 0.217
(2.551) (2.752) (2.575)
Fathers Education
(i) Primary -- -- --
-- -- --
(ii) Middle 0.020 0.460 1.219
(0.511) (0.994) (1.185)
(iii) Matric 0.040 0.651 1.536
(1.393) (1.869) (1.872)
(iv) Higher/Others 0.052 0.662 1.504
(1.327) (1.693) (1.685)
Mothers Education
(i) Primary -- -- --
-- -- --
(ii) Middle 0.034 0.420 0.979
(0.868) (1.125) (1.311)
(iii) Matric 0.094 0.758 1.533
(2.781) (2.567) (2.596)
(iv) Higher/Others 0.120 0.993 1.921
(2.316) (2.495) (2.409)
Number of Observations 423 423 423
Number of Positive Obser-
vations -- 25 25
R-Square 0.088 0.844 0.083
Adjusted R-Square 0.071 -- --
F-Statistic 5.01 -- --
Log of Likelihood Function -- -76.43 -76.98
Convergence Observed-
After-iterations -- 6 7
Note: Figures in the parenthesis are t-ratios.
Annex Table 4 Estimates of Male Child Schooling in Rural Pakistan,
by Age Groups
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
Constant 0.362 -0.382 -0.627
(8.001) (3.06) (3.03)
Household Income 0.0001 0.0003 0.0005
(3.40) (3.75) (3.73)
Household Size -0.007 -0.028 -0.046
(1.07) (1.59) (1.57)
Fathers Education
(i) Primary 0.271 0.705 1.130
(4.38) (4.06) (3.96)
(ii) Middle 0.254 0.667 1.079
(6.08) (5.72) (5.64)
(iii) Matric & Above 0.334 0.941 1.527
(7.20) (6.81) (6.52)
Mother's Education
(i) Primary 0.285 0.777 1.304
(3.89) (3.65) (3.59)
(ii) Middle 0.323 0.915 1.519
(5.16) (4.83) (4.64)
(iii) Matric & Above 0.289 0.880 1.421
(3.35) (3.31) (3.18)
Number of Observation 1442 1442 1442
No. of Positive Observation -- 680 680
R-Square 0.112 0.116 0.116
Adjusted R-Square 0.107 -- --
F-Statistics 22.6 -- --
Log of Likelihood Funct. -958.59 -909.12 -909.13
Convergence Achieved
After-iterations -- 4 4
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
Constant 0.285 -0.585 -0.955
(7.52) (5.52) (5.40)
Household Incom e 0.000001 0.000002 0.000004
(3.39) (3.54) (3.51)
Household Size -0.0004 -0.007 -0.011
(0.07) (0.45) (0.45)
Fathers Education
(i) Primary 0.227 0.585 0.932
(4.24) (3.98) (3.93)
(ii) Middle 0.265 0.695 1.120
(7.22) (6.81) (6.71)
(iii) Matric & Above 0.372 1.025 1.664
(9.08) (8.44) (8.07)
Mother's Education
(i) Primary 0.213 0.559 0.943
(3.22) (3.05) (3.07)
(ii) Middle 0.325 0.888 1.470
(5.91) (5.53) (5.38)
(iii) Matric & Above 0.293 0.864 1.386
(3.95) (3.88) (3.76)
Number of Observation 1898 1898 1898
No. of Positive Observation -- 814 814
R-Square 0.112 0.114 0.114
Adjusted R-Square 0.108 -- --
F-Statistics 0.490 -- --
Log of Likelihood Funct. 1245.55 -1185.12 -1185.11
Convergence Achieved
After-iterations -- 3 4
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
Constant 0.029 -1.610 -2.808
(0.77) (7.62) (7.04)
Household Income 0.0001 0.0002 0.0004
(3.49) (2.50) (2.38)
Household Size -0.001 -0.004 -0.001
(0.23) (0.14) (0.02)
Fathers Education
(i) Primary 0.047 0.265 (4.87)
(0.67) (0.80) (0.81)
(ii) Middle 0.162 0.693 1.257
(3.53) (3.36) (3.50)
(iii) Matric & Above 0.186 0.743 1.325
(3.67) (3.41) (3.47)
Mother's Education
(i) Primary -0.073 -0.382 -0.637
(0.81) (0.70) (0.60)
(ii) Middle 0.102 0.447 0.844
(1.38) (1.30) (1.40)
(iii) Matric & Above 0.285 0.992 1.739
(4.22) (3.57) (3.64)
Number of Observation 612 612 612
No. of Positive Observation -- 78 78
R-Square 0.106 -- --
Adjusted R-Square 0.094 0.097 0.095
F-Statistics 8.90 -- --
Log of Likelihood Funct. -162.16 -207.81 -208.42
Convergence Achieved
After-iterations -- 4 5
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
Constant -- -- --
Household Income -- -- --
Household Size -- -- --
Fathers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric & Above -- -- --
Mother's Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric & Above -- -- --
Number of Observation -- -- --
No. of Positive Observation -- -- --
R-Square -- -- --
Adjusted R-Square -- -- --
F-Statistics -- -- --
Log of Likelihood Funct. -- -- --
Convergence Achieved
After-iterations -- -- --
Note: Figures in the parenthesis are t-ratios.
Annex Table 5 Estimates of Female Child Schooling in Rural Pakistan,
by Age Groups
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
Constant 0.020 -1.708 -2.947
(0.63) (10.15) (9.32)
Household Monthly Income 0.0000004 0.000002 0.000002
(2.62) (2.29) (2.07)
Household Size 0.004 0.024 0.045
(0.89) (1.03) (1.02)
Fathers Education
(i) Primary 0.098 0.441 0.825
(2.00) (1.92) (2.05)
(ii) Middle 0.070 0.353 0.666
(2.31) (2.40) (2.47)
(iii) Matric & Above 0.208 0.801 1.438
(5.77) (5.14) (5.38)
Mothers Education
(i) Primary 0.189 0.708 1.256
(3.34) (2.88) (3.06)
(ii) Middle 0.083 0.392 0.700
(1.42) (1.45) (1.44)
(iii) Matric & Above 0.097 0.456 0.763
(1.47) (1.55) (1.43)
Number of Observations 1224 1224 1224
No. of Positive Observations -- 143 143
R-Square 0.059 0.054 0.053
Adjusted R-Square 0.053 -- --
F-Statistics 9.59 -- --
Log of Likelihood Funct. -309.31 -411.72 -412.48
Convergence Achieved
After-iterations -- 4 5
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
Constant 0.021 -1.771 -3.081
(0.86) (11.83) (10.76)
Household Monthly Income 0.0003 0.0001 0.0002
(2.23) (2.03) (1.86)
Household Size 0.003 0.021 0.037
(0.85) (1.02) (0.93)
Fathers Education
(i) Primary 0.102 0.500 0.943
(2.54) (2.44) (2.58)
(ii) Middle 0.064 0.362 0.705
(2.64) (2.73) (2.84)
(iii) Matric & Above 0.173 0.761 1.403
(5.90) (5.37) (5.60)
Mothers Education
(i) Primary 0.150 0.632 1.151
(3.31) (2.88) (3.06)
(ii) Middle 0.119 0.570 1.053
(2.63) (2.54) (2.65)
(iii) Matric & Above 0.178 0.767 1.356
(3.47) (3.23) (3.24)
Number of Observations 1591 1591 1591
No. of Positive Observations -- 157 157
R-Square 0.055 0.049 0.049
Adjusted R-Square 0.051 -- --
F-Statistics 11.60 -- --
Log of Likelihood Funct. -287.25 -476.79 -477.78
Convergence Achieved
After-iterations -- 4 5
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
Constant -- -- --
-- -- --
Household Monthly Income -- -- --
-- -- --
Household Size -- -- --
-- -- --
Fathers Education
(i) Primary -- -- --
-- -- --
(ii) Middle -- -- --
-- -- --
(iii) Matric & Above -- -- --
-- -- --
Mothers Education
(i) Primary -- -- --
-- -- --
(ii) Middle -- -- --
-- -- --
(iii) Matric & Above -- -- --
-- -- --
Number of Observations -- -- --
No. of Positive Observations -- -- --
R-Square -- -- --
Adjusted R-Square -- -- --
F-Statistics -- -- --
Log of Likelihood Funct. -- -- --
Convergence Achieved
After-iterations -- -- --
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
Constant -- -- --
-- -- --
Household Monthly Income -- -- --
-- -- --
Household Size -- -- --
-- -- --
Fathers Education
(i) Primary -- -- --
-- -- --
(ii) Middle -- -- --
-- -- --
(iii) Matric & Above -- -- --
-- -- --
Mothers Education
(i) Primary -- -- --
-- -- --
(ii) Middle -- -- --
-- -- --
(iii) Matric & Above -- -- --
-- -- --
Number of Observations -- -- --
No. of Positive Observations -- -- --
R-Square -- -- --
Adjusted R-Square -- -- --
F-Statistics -- -- --
Log of Likelihood Funct. -- -- --
Convergence Achieved
After-iterations -- -- --
Note: Figures in the parenthesis are t-ratios.
Annex Table 6 Comparison of the Linear Probability (L P), the Probit
and the Logit Estimates (Urban Male)
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
1. Constant 0.265 0.209 0.184
2. Household Income 0.0001 0.0001 0.0001
3. Household Size 0.004 0.001 -0.0004
4. Fathers Education
(i) Primary 0.220 0.248 0.241
(ii) Middle 0.430 0.542 0.573
(iii) Matric & Higher 0.503 0.688 0.714
(iv) Higher 0.545 0.949 1.154
5. Mothers Education
(i) Primary 0.145 0.140 0.232
(ii) Middle 0.268 0.414 0.468
(iii) Matric 0.368 0.977 1.234
(iv) Higher 0.000 0.000 0.000
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
1. Constant 0.048 -0.020 -0.028
2. Household Income 0.0002 0.0001 0.0001
3. Household Size 0.015 0.014 0.013
4. Fathers Education
(i) Primary 0.170 0.176 0.173
(ii) Middle 0.278 0.276 0.289
(iii) Matric & Higher 0.595 0.754 0.797
(iv) Higher 0.643 0.974 1.141
5. Mothers Education
(i) Primary 0.118 0.109 0.144
(ii) Middle 0.260 0.337 0.352
(iii) Matric 0.378 0.713 0.824
(iv) Higher 0.295 0.551 0.541
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
1. Constant -0.845 -0.986 -1.003
2. Household Income 0.0001 0.0001 0.0001
3. Household Size -0.002 -0.002 -0.004
4. Fathers Education
(i) Primary 0.333 0.417 0.434
(ii) Middle 0.273 0.346 0.363
(iii) Matric & Higher 0.618 0.701 0.727
(iv) Higher 1.035 1.177 1.218
5. Mothers Education
(i) Primary 0.448 0.466 0.484
(ii) Middle 0.005 0.020 0.008
(iii) Matric 0.528 0.591 0.596
(iv) Higher 0.513 0.577 0.611
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
1. Constant -1.403 -2.379 -2.664
2. Household Income 0.0001 0.0001 0.000
3. Household Size 0.023 0.062 0.069
4. Fathers Education
(i) Primary 0.055 0.292 0.388
(ii) Middle 0.103 0.409 0.530
(iii) Matric & Higher 0.208 0.587 0.763
(iv) Higher 0.518 0.995 1.181
5. Mothers Education
(i) Primary 0.313 0.548 0.626
(ii) Middle 0.405 0.635 0.708
(iii) Matric 0.020 0.051 0.081
(iv) Higher 2.230 0.209 0.196
Annex Table 7 Comparison of the Linear Probability (LP), the Probit
and the Logit Estimates (Urban Female)
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
1. Constant -0.948 -1.250 -1.278
2. Household Income 0.0001 0.0004 0.0004
3. Household Size 0.038 0.031 0.026
4. Fathers Education
(i) Primary 0.788 0.807 0.822
(ii) Middle 0.400 0.374 0.372
(iii) Matric 0.848 0.900 0.909
(iv) Higher 1.200 1.648 1.911
5. Mothers Education
(i) Primary 0.333 0.398 0.410
(ii) Middle 0.735 0.906 0.995
(iii) Matric 0.745 1.244 1.387
(iv) Higher 0.000 -- --
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
1. Constant -0.970 -1.199 -1.231
2. Household Income 0.0001 0.0002 0.0002
3. Household Size 0.035 0.040 0.038
4. Fathers Education
(i) Primary 0.655 0.680 0.698
(ii) Middle 0.398 0.407 0.411
(iii) Matric 0.815 0.877 0.898
(iv) Higher 1.145 1.519 1.693
5. Mothers Education
(i) Primary 0.425 0.478 0.483
(ii) Middle 0.808 0.987 1.045
(iii) Matric 0.795 1.555 1.245
(iv) Higher 0.625 1.002 1.033
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
1. Constant -1.475 -2.141 -2.347
2. Household Income 0.0001 0.0002 0.0002
3. Household Size 0.043 0.074 0.085
4. Fathers Education
(i) Primary -0.120 -0.213 -0.346
(ii) Middle 0.048 0.094 0.146
(iii) Matric 1.880 0.276 0.341
(iv) Higher 0.753 0.973 1.052
5. Mothers Education
(i) Primary 0.168 0.316 0.346
(ii) Middle 0.385 0.563 0.620
(iii) Matric 0.648 0.878 0.949
(iv) Higher 0.375 0.530 0.574
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
1. Constant -1.428 -3.216 -3.873
2. Household Income 0.00002 0.00003 0.0000
3. Household Size 0.030 0.118 0.136
4. Fathers Education
(i) Primary 0.000 0.000 0.000
(ii) Middle 0.050 0.460 0.762
(iii) Matric 0.100 0.651 0.960
(iv) Higher 0.130 0.662 0.940
5. Mothers Education
(i) Primary 0.000 0.000 0.000
(ii) Middle 0.085 0.420 0.612
(iii) Matric 0.235 0.758 0.958
(iv) Higher 0.300 0.993 1.201
Annex Table 8 Comparison of the Linear Probability (LP), the Probit
and the Logit Estimates (Rural Male)
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
1. Constant -0.345 -0.382 -0.392
2. Household Income 0.0003 0.0003 0.0003
3. Household Size -0.018 -0.028 -0.029
4. Fathers Education
(i) Primary 0.678 0.705 0.706
(ii) Middle 0.635 0.667 0.674
(iii) Matric 0.835 0.941 0.954
5. Mothers Education
(i) Primary 0.713 0.777 0.815
(ii) Middle 0.808 0.915 0.949
(iii) Matric 0.723 0.880 0.888
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
1. Constant -0.538 -0.585 -0.597
2. Household Income 0.000003 0.000002 0.000003
3. Household Size -0.001 -0.007 -0.007
4. Fathers Education
(i) Primary 0.568 0.585 0.583
(ii) Middle 0.663 0.695 0.700
(iii) Matric 0.930 1.025 1.040
5. Mothers Education
(i) Primary 0.533 0.559 0.584
(ii) Middle 0.813 0.888 0.919
(iii) Matric 0.733 0.864 0.866
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
1. Constant -1.775 -1.610 -1.755
2. Household Income 0.0003 0.0002 0.0003
3. Household Size -0.003 -0.004 -0.001
4. Fathers Education
(i) Primary 0.118 0.265 0.265
(ii) Middle 0.405 0.693 0.786
(iii) Matric 0.465 0.743 0.828
5. Mothers Education
(i) Primary -0.183 -0.382 -0.398
(ii) Middle 0.255 0.447 0.528
(iii) Matric 0.713 0.992 1.087
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
1. Constant -- -- --
2. Household Income -- -- --
3. Household Size -- -- --
4. Fathers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric -- -- --
5. Mothers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric -- -- --
Annex Table 9 Comparison of the Linear Probability (LP), the Probit
and the Logit Estimates (Rural Female)
Age Group/Method 10-14 Years
Independent Variables LP Probit Logit
1. Constant -1.200 -1.708 -1.842
2. Household Income 0.000001 0.000002 0.000001
3. Household Size 0.010 0.024 0.028
4. Fathers Education
(i) Primary 0.245 0.441 0.516
(ii) Middle 0.175 0.353 0.416
(iii) Matric 0.520 0.801 0.899
(iv) Above -- -- --
5. Mothers Education
(i) Primary 0.473 0.708 0.785
(ii) Middle 0.208 0.392 0.438
(iii) Matric 0.243 0.456 0.477
(iv) Above -- -- --
Age Group/Method 10-16 Years
Independent Variables LP Probit Logit
1. Constant -1.198 -1.771 -1.926
2. Household Income 0.0001 0.0001 0.0001
3. Household Size 0.008 0.021 0.023
4. Fathers Education
(i) Primary 0.255 0.500 0.589
(ii) Middle 0.160 0.362 0.441
(iii) Matric 0.433 0.761 0.877
(iv) Above -- -- --
5. Mothers Education
(i) Primary 0.375 0.632 0.719
(ii) Middle 0.298 0.570 0.658
(iii) Matric 0.445 0.767 0.848
(iv) Above -- -- --
Age Group/Method 17-20 Years
Independent Variables LP Probit Logit
1. Constant -- -- --
2. Household Income -- -- --
3. Household Size -- -- --
4. Fathers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric -- -- --
(iv) Above -- -- --
5. Mothers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric -- -- --
(iv) Above -- -- --
Age Group/Method 21-25 Years
Independent Variables LP Probit Logit
1. Constant -- -- --
2. Household Income -- -- --
3. Household Size -- -- --
4. Fathers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric -- -- --
(iv) Above -- -- --
5. Mothers Education
(i) Primary -- -- --
(ii) Middle -- -- --
(iii) Matric -- -- --
(iv) Above -- -- --
Annex Table 10 Probit Estimates of Child Schooling in Urban Pakistan
by Age Group and Sex
Age Group/Sex 10-14 Years
Independent Variables Male Female
1. Constant 0.960 -0.171
(3.65) (-4.63)
2. Household Monthly Income 0.0002 0.0004
(2.76) (4.66)
3. Household Size -0.057 0.038
(-0.00) (1.46)
4. Fathers Education
(i) Primary 0.274 0.796
(1.29) (3.35)
(ii) Middle 0.450 0.389
(2.99) (2.73)
(iii) Matric 0.582 0.820
(3.96) (6.27)
(iv) Higher/Others 0.743 1.293
(2.36) (4.05)
5. Mother's Education
(i) Primary 0.254 0.357
(0.71) (0.98)
(ii) Middle 0.403 0.856
(2.01) (4.74)
(iii) Matric 0.89 1.156
(3.25) (5.42)
(iv) Higher/Others -- --
6. Father's Employment Status
(Employer-self-Employed/ -0.114 -0.363
Employer) (-1.04) (-3.30)
7. Fathers Occupation
(i) Professional & Administrative
Workers 0.036 0.347
(0.13) (1.25)
(ii) Clerical, Sales & Service
Workers 0.410 -0.081
(2.20) (-0.44)
(iii) Agriculture & Production
Workers 0.218 -0.138
(1.26) (-0.82)
8. Labour Force Participation Ratio -2.11 0.411
(-7.01) (1.26)
Number of Observations 950 881
Number of Positive Observations 725 458
R-Statistics 0.184 0.336
Log of Likelihood Function -434.36 -442.94
Convergence Achieved After
(No of Iterations) 5 5
Age Group/Sex 10-16 Years
Independent Variables Male Female
1. Constant 0.964 -1.037
(4.30) (-5.03)
2. Household Monthly Income 0.0002 0.0002
(2.98) (3.67)
3. Household Size -0.056 0.046
(-2.61) (2.22)
4. Fathers Education
(i) Primary 0.212 0.692
(1.21) (3.58)
(ii) Middle 0.218 0.421
(1.81) (3.45)
(iii) Matric 0.608 0.807
(4.97) (7.35)
(iv) Higher/Others 0.642 1.224
(2.61) (5.12)
5. Mother's Education
(i) Primary 0.244 0.430
(0.79) (1.40)
(ii) Middle 0.311 0.922
(1.93) (6.10)
(iii) Matric 0.639 1.059
(3.37) (6.50)
(iv) Higher/Others 0.423 0.876
(0.76) (1.56)
6. Father's Employment Status
(Employer-self-Employed/ -0.169 -0.307
Employer) (-1.83) (-3.28)
7. Fathers Occupation
(i) Professional & Administrative
Workers 0.299 0.178
(1.30) (0.80)
(ii) Clerical, Sales & Service
Workers 0.449 -0.087
(2.91) (-0.581)
(iii) Agriculture & Production
Workers 0.237 -0.203
(1.64) (-1.43)
8. Labour Force Participation Ratio -2.538 0.224
(-10.02) (0.85)
Number of Observations 1263 1199
Number of Positive Observations 896 591
R-Statistics 0.212 0.317
Log of Likelihood Function -621.78 -617.59
Convergence Achieved After
(No of Iterations) 5 5
Age Group/Sex 17-20 Years
Independent Variables Male Female
1. Constant -0.222 -1.925
(-0.76) (-5.56)
2. Household Monthly Income 0.0001 0.0002
(1.78) (3.11)
3. Household Size -0.052 0.071
(-1.93) (2.32)
4. Fathers Education
(i) Primary 0.427 -0.183
(1.61) (-0.37)
(ii) Middle 0.354 0.054
(1.75) (0.22)
(iii) Matric 0.613 0.232
(3.71) (1.10)
(iv) Higher/Others 1.017 0.787
(3.72) (2.78)
5. Mother's Education
(i) Primary 0.489 0.252
(1.11) (0.51)
(ii) Middle 0.024 0.530
(0.10) (2.25)
(iii) Matric 0.638 0.859
(3.28) (4.03)
(iv) Higher/Others 0.696 0.507
(2.09) (1.37)
6. Father's Employment Status
(Employer-self-Employed/ -0.211 -0.092
Employer) (-1.45) (-0.50)
7. Fathers Occupation
(i) Professional & Administrative
Workers 0.238 0.204
(0.87) (0.66)
(ii) Clerical, Sales & Service
Workers 0.379 -0.065
(1.80) (-0.26)
(iii) Agriculture & Production
Workers 0.319 -0.188
(1.55) (-0.75)
8. Labour Force Participation Ratio -1.885 -0.106
(-5.37) (-0.27)
Number of Observations 538 439
Number of Positive Observations 197 102
R-Statistics 0.234 0.261
Log of Likelihood Function -284.17 -182.96
Convergence Achieved After
(No of Iterations) 4 4
Age Group/Sex 21-25 Years
Independent Variables Male Female
1. Constant -1.643 -3.336
(-4.30) (-5.70)
2. Household Monthly Income 0.0002 -0.0001
(2.32) (-0.92)
3. Household Size 0.065 0.136
(1.98) (2.92)
4. Fathers Education
(i) Primary 0.326 --
(0.69)
(ii) Middle 0.507 0.479
(1.60) (0.95)
(iii) Matric 0.546 0.841
(1.96) (2.11)
(iv) Higher/Others 0.974 0.981
(2.64) (2.05)
5. Mother's Education
(i) Primary 0.712 --
(1.61)
(ii) Middle 0.682 0.348
(2.62) (0.87)
(iii) Matric -0.008 0.724
(-0.03) (2.30)
(iv) Higher/Others 0.178 0.923
(0.40) (2.08)
6. Father's Employment Status
(Employer-self-Employed/ 0.207 0.469
Employer) (0.89) (1.64)
7. Fathers Occupation
(i) Professional & Administrative
Workers -0.422 -0.265
(-1.09) (-0.62)
(ii) Clerical, Sales & Service
Workers -0.594 -0.538
(-2.00) (-1.36)
(iii) Agriculture & Production
Workers -0.813 -0.694
(-2.65) (-1.53)
8. Labour Force Participation Ratio -1.408 1.449
(-2.80) (2.61)
Number of Observations 392 423
Number of Positive Observations 54 25
R-Statistics 0.147 0.110
Log of Likelihood Function -127.09 -70.97
Convergence Achieved After
(No of Iterations) 5 6
Note: Figures in the parenthesis are t-ratios.
Annex Table 11
Probit Estimates of Child Schooling in Rural Pakistan by Age
Group and Sex
Age Group/Sex 10-14 Years 10-16 Years
Independent Variables Male Female Male Female
1. Constant 0.372 -1.352 0.177 -1.278
(2.16) (-5.85) (1.19) (-6.18)
2. Household Monthly 0.0004 0.0002 0.0003 0.0001
Income (4.46) (2.28) (4.21) (2.35)
3. Household Size -0.075 -0.003 -0.054 -0.014
(-3.89) (-0.12) (-0.32) (-0.64)
4. Household Land -0.006 0.002 -0.006 0.002
Holding (-2.03) (0.85) (-2.13) (0.56)
5. Landless -0.285 -- -0.278 --
(-2.09) (-2.24)
6. Father's Education
(i) Primary 0.645 0.326 0.514 0.419
(3.62) (1.36) (3.40) (1.98)
(ii) Middle 0.573 0.246 0.582 0.269
(4.73) (1.59) (5.49) (1.93)
(iii) Matric & Higher 0.754 0.625 0.844 0.609
(5.24) (3.79) (6.65) (4.11)
7. Mothers Education
(i) Primary 0.651 0.621 0.453 0.550
(2.91) (2.44) (2.36) (2.40)
(ii) Middle 0.791 0.232 0.744 0.444
(3.84) (0.81) (4.29) (1.86)
(iii) Matric & Higher 0.752 0.387 0.641 0.664
(2.70) (1.25) (2.79) (2.65)
8. Fathers Tenurial 0.245 0.275 0.230 0.244
Status (Owner/Tenant- (2.93) (2.34) (3.20) (2.27)
leaseholder)
9. Village Literacy 0.637 1.714 0.829 0.812
(2.53) (4.56) (3.50) (3.78)
10. School in Village
(i) Primary -0.023 -0.048 -0.025 -0.067
(-0.28) (-0.39) (-0.34) (-0.59)
(ii) Middle 0.210 0.164 0.150 0.204
(2.32) (1.34) (1.90) (1.83)
(iii) Higher 0.106 0.301 0.017 0.270
(0.69) (1.67) (0.14) (1.65)
11. Labour Force -1.850 -1.684 -1.778 -1.585
Participation Ratio (-9.70) (-5.43) (-10.93) (-5.87)
No. of Observations 1442 1224 1899 1591
No. of Positive 680 143 814 157
Observations
R-Squared 0.205 0.130 0.202 0.106
Log of Likelihood 836.24 -376.02 -1092.4 -443.03
Function
Convergence Achieved
After (No. of 4 5 4 5
Iterations)
Age Group/Sex 17-20 Years 21-25 Years
Independent Variables Male Female Male Female
1. Constant -1.556 -- -- --
(-5.00)
2. Household Monthly 0.0003 -- -- --
Income (3.28)
3. Household Size -0.012 -- -- --
(-0.39)
4. Household Land -0.022 -- -- --
Holding (-2.42)
5. Landless 0.210 -- -- --
(0.77)
6. Father's Education
(i) Primary 0.275 -- -- --
(0.80)
(ii) Middle 0.654 -- -- --
(3.07)
(iii) Matric & Higher 0.661 -- -- --
(2.85)
7. Mothers Education
(i) Primary -0.466 -- -- --
(-0.85)
(ii) Middle 0.352 -- -- --
(0.94)
(iii) Matric & Higher 0.948 -- -- --
(3.15)
8. Fathers Tenurial 0.328 -- -- --
Status (Owner/Tenant- (1.81)
leaseholder)
9. Village Literacy 0.231 -- -- --
(0.76)
10. School in Village
(i) Primary 0.025 -- -- --
(0.13)
(ii) Middle 0.409 -- -- --
(2.36)
(iii) Higher 0.050 -- -- --
(0.21)
11. Labour Force -0.705 -- -- --
Participation Ratio (-2.08)
No. of Observations 612 -- -- --
No. of Positive 78 -- -- --
Observations
R-Squared 0.157 -- -- --
Log of Likelihood -195.13 -- -- --
Function
Convergence Achieved
After (No. of 5 -- -- --
Iterations)
Note: Figures in the parenthesis are t-ratios.
REFERENCES
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(1) In nominal terms, the expenditure on education increased from
Rs 30.4 million in 1947-48 to Rs 21425 million in 1988-89. Around 70
percent of the expenditure on education has been non-development, and
the rest has been development. As a percentage of the GNP, however, the
expenditure on education has remained modest, e.g., in 1987-88 it was
only 2.4 percent compared to 0.9 percent in 1959-60.
(2) The sharpest increase came in the number of Colleges followed
by High Schools, Universities, Primary Schools, Professional Colleges,
and Middle Schools--in that order. The increase in the number of such
institutions for females, across almost all the categories, was
considerably higher than the national average increases.
(3) See also Waite, DeTray and Rindfuss (1983) on the importance of
the mother's background in influencing expectation about their
children's educational attainments.
(4) For details, the readers are referred to Becker and Lewis
(1973); Becker and Tomes (1976) and DeTray (1973).
(5) In most empirical studies, child schooling is also widely
interpreted to represent child quality. Becker and Tomes (1976),
however, have raised serious doubts about this interpretation. See Wolfe
and Behrman (1983) for an elaborate exposition of the issue. Other
factors, which affect child quality, are genetic endowment, investment
in child health and nutrition, parental time, etc.
(6) In the alternative 'Pennsylvanian' model, this is
interpreted to reflect an inter-generational effect rather than the
productivity effect of educated parents. This implies that the
parents' schooling in the Pennsylvanian model does not have as
large a productivity effect as in the Chicago-Columbia framework.
(7) In the strict Chicago-Columbia tradition, full permanent income
is considered to be positively associated with child schooling. Behrman
and Wolfe (1984), however, have argued that actual household income is a
better representative of permanent income if there are important fixed
effects. In most household studies, total household expenditures have
been used as a proxy for a permanent income. As the coefficients of
independent variables are not likely to differ significantly, whether
actual income or expenditure is used, we focus on the actual household
income only.
(8) As our analysis will be restricted to nuclear family
households, a larger family implies more children. If child schooling is
taken as a proxy of child quality, then the sign of the coefficient of
the household size would also indicate whether there is any trade-off
between the quantity and the quality of children.
(9) The impact of the increase in the quantity of the
household's assets on the parents' decision to educate their
children is taken as the 'pure wealth effect' of asset
ownership. By increasing the permanent (expected) income of the
household, the increase in the quantity of assets favourably influences
the parents' decision regarding their children's schooling.
The impact of the increase in the value of assets, on the other hand, is
taken as the 'opportunity cost effect' of asset ownership on
child schooling. An increase in the value of assets, by raising the
opportunity cost of the child's time as wall as the family's
wealth, adversely affects the school enrolment of the children. The
impact of a possible bequest by the parents on child schooling is taken
as the 'bequest effect' of asset ownership. Since one of the
objectives of investing in child schooling is insuring better earnings
in the future, parents with more wealth may invest less in the schooling
of their children, knowing that the children will inherit their wealth
and, hence, such investment is not income-increasing.
(10) Socio-economic status can also be taken as a measure of the
parents' background, which is given considerable importance in the
Pennsylvanian framework.
(11) Khan and Irfan (1985) have found that wage income of the
secondary earner is positively influenced by the parental status even
after controlling the human capital variables of the secondary earners.
(12) For a more systematic treatment of such a phenomenon, see
Duesenberry (1952).
(13) It may be pointed out that this does not, in any significant
way, affect the conclusions of this study because even in a joint family
system, the decision to educate a child is generally taken by the
parents rather than the household head. Among the households included in
the sample, 59 percent of the urban and 61 percent of the rural
households are reported to be nuclear families.
(14) Most of the children falling in the 10-16 years age group are
expected to be attending the middle (class VI-VIII) and secondary (class
IX and X) schools. A small fraction, however, may be enrolled in primary
classes. Children falling in the 17-20 years, and 21-25 years of age
group, respectively, are likely to be attending colleges and
universities. Separate regression for children in 10-14 years of age
group is estimated because this is one of the categories for which the
data on literacy and school enrolment are reported in the Population
Census Reports. As such, the separate estimates can be used for
comparison with the overall macro situation.
(15) See also Rosenzweig (1978); Birdsall (1980) and Harrison
(1980) for an analysis of age- and sex-specific school enrolment of
children.
(16) It must be mentioned that, as compared to Population Census
1981, the school attendance reported in the PLM Survey appears to be on
the high side. It is difficult to determine whether the PLM data reflect
an over-reporting or the Population Census underreports the school
enrolment. The discrepancy between the two sources merits further
investigation.
(17) [See Goldberger (1964), p. 249].
(18) If y is the binary dependent variable and x a vector of
explanatory variables, then each of these models implies that the
probability of success, in our case the probability of the child going
to school, can be written as:
E(y/x) = p(x) = F(x'[beta])
where F(.) is the cumulative distribution function and [beta] a
vector of the parameters to be estimated. The linear probability, the
probit and the logit models, respectively, assume that the cumulative
distribution function is linear, normal, and logistic, which can be
written as:
F(x '[beta]) = x '[beta] Linear
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
F(x '[beta]) = 1/(1 + exp (-x '[beta])) Logit
For a detailed discussion on each of these models, the reader is
referred to Kmenta (1986, ch. 11); Goldfeld and Quandt (1972, ch. 4) and
Maddala (1983, ch. 2). The Linear Probability Model has also been termed
as the Uniform Model by Goldfeld and Quandt.
(19) For more on this, see, for example, Kmenta (1986) and Maddala
(1983).
(20) Amemiya (1981) has suggested the following transformation to
make the coefficients comparable:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[beta].sub.p], [[beta].sub.L] and [[beta].sub.LP] are
probit, logit, and linear probability estimates, respectively.
(21) The linear probability model has been estimated using the OLS
method rather than the GLS, i.e., the correction for hetemscedasticity
has not been made. Goldfeld and Quandt (1972, oh. 4) have shown that for
the linear probability model there appears no appreciable difference
between the OLS and the GLS estimates.
(22) As very few positive observations for the dependent variable
were available in the case of the rural male in the 21-25 years age
group and the rural female in the 17-20 years and 21-25 years age
groups, the results corresponding to these groups are not being
reported.
(23) For a trade-off (between the quantity and the quality of the
children) to exist, the coefficient of the household-size should be
negative. This follows from the fact that, at a given household income,
an increase in household size implies a lower income per capita. If the
resource constraint is one of the major factors affecting child
schooling, then fewer per capita resources are likely to adversely
affect the chances of children attending school.
(24) It must be noted that household income is controlled in the
equation which captures the wealth effect due to land.
(25) The coefficient of the land value is found to be positive and
greater for females than for males.
(26) In most of the cases, with the regressions estimated without
the intercept term, the coefficient of father's occupation was
found to be significant. For boys up to 16 years of age, the coefficient
of each occupational category was positive and significant. In the case
of higher aged boys, however, the coefficients were negative and
significant. For girls, however, the coefficient of the clerical and
production workers was found to be negative and significant in all the
cases. The exclusion of income and parents' education did not alter
the results in any significant manner.
(27) The availability of a school in the village or the distance to
school has been used to measure the cost of attending school. For the
Philippines, King and Lillard (1983) have found that if the mean
distance to elementary school is decreased from 0.5 to 0.1 kilometer,
the enrolment in the elementary schools will increase by 2.5 percent
with favourable repercussions at the High levels. The effect on female
enrolment was found to be slightly greater than that on male enrolment.
Nadeem A. Burney and Mohammad Irfan are both Chief of Research in
the Pakistan Institute of Development Economics, Islamabad.
Table 1
School Enrolment Ratio of Population, 10-24 Years of
Age in Pakistan, by Sector and Sex
Sex/Years Both Sexes Male Female
Sectors 1961 1981 1961 1981 1961 1981
Overall 11.8 17.6 17.0 22.9 5.71 11.5
Urban 21.6 31.3 26.3 34.6 15.7 27.5
Rural 8.1 11.4 13.3 17.6 2.2 4.3
Source: Population Census 1961 and 1981.
Table 2
Current School Enrolment of Children in Different Age Groups,
by Sector and Sex
Age Group
Sectors/Sex
10-14 10 -16 17-20 21-25
Years Years Years Years
Overall 44.60 41.30 18.10 5.30
Urban
Both Sexes 64.60 60.40 30.60 9.70
Male 76.30 70.90 36.60 13.80
Female 52.00 49.30 23.20 5.90
Rural
Both Sexes 30.90 27.80 7.60 1.90
Male 37.20 42.90 12.80 3.60
Female 11.70 9.90 1.70 0.70
Source: PLM Survey, 1979.
Table 3
List of Independent Variables and their Mean Values
1. Household's Monthly Income (Y) Rs 1436.62
2. Household Size (HS) Nos. 7.33
3.
4.
5. Fathers Education (FE)
FE 1 = 1 if Father's education level Primary 0.05
= 0 otherwise.
FE 2 = 1 if Fathers education level Middle 0.13
= 0 otherwise.
FE 3 = 1 if Fathers education level Matric 0.26
= 0 otherwise.
FE 4 = 1 if Fathers education level Higher 0.11
= 0 otherwise.
6. Mother's Education (ME)
ME 1 = 1 if Mothers education level Primary 0.02
= 0 otherwise.
ME 2 = 1 if Mothers education level Middle 0.09
= 0 otherwise.
ME 3 = 1 if Mothers education level Matric 0.14
= 0 otherwise.
ME 4 = 1 if Mothers education level Higher 0.03
= 0 otherwise.
7. Father's Employment Status (FES)
FES = 1 if employer or self-employed 0.44
= 0 otherwise.
8. Fathers
FOP 1 = 1 if Professional or Administrative
Worker 0.10
= 0 otherwise.
FOP 2 = 1 if Clerical or Sale and Service
Worker 0.38
= 0 otherwise.
FOP 3 = 1 if Agriculture and Production
Worker 0.39
= 0 otherwise.
9.
10.
11. Labour Force Participation Ratio (LFPR) 0.26
LFPR = Household Member in Labour Force/
Household Size-1 if the child
goes to school
or is temporarily
out of the job
market
= Household Member in Labour Force-1/ if the child
Household Size-1 does not go to
school and is
looking for
a job
Rural
Household's Monthly Income (Y) Rs 932.31
Household Size (HS) Nos. 6.58
Household's Land Holding (HLH) Acres 7.91
Landlessness (L D L) 0.08
LDL = 1 if the father agriculture labour with no land
= 0 otherwise.
Fathers Education (FE)
FE1 = 1 if Father's education level Primary 0.04
= 0 otherwise.
FE2 = 1 if Fathers education level Middle 0.10
= 0 otherwise.
FE3 = 1 if Father's education level Matric 0.08
= 0 otherwise.
Mothers Education (ME)
ME1 = 1 if Mothers education level Primary 0.02
= 0 otherwise.
ME2 = 1 if Mother's education level Middle 0.03
= 0 otherwise.
ME3 = 1 if Mothers education level Matric 0.02
= 0 otherwise.
Father's Tenurial Status (FTS)
FTS = 1 if owner 0.33
= 0 otherwise (Tanant-Leaseholder)
Village Literary Level (VIL) 0.11
School in Village (SV)
SV1 = 1 if Primary School in village 0.76
= 0 otherwise.
SV2 = 1 if Middle School in village 0.23
0 otherwise.
SV3 = 1 if High School in village 0.08
= 0 otherwise.
Labour Force Participation Ratio (LFPR) 0.35
LFPR = Household Member in Labour Force/
Household Size-1 if the child
goes to school
or is temporarily
out of the job
market
= Household Member in Labour Force-1/ if the child
Household Size-1 does not go to
school and is
looking for
a job
Table 4
Change in the Probability of Child's Attending School for a
Rupee Change in the Household Income
Age Group
Sectors/Sex
10 -14 10 -16 17-20 21-25
Years Years Years Years
Urban
Male 0.00005 0.00005 0.00003 0.00003
Female 0.00012 0.00006 0.00005 0.00001
Rural
Male 0.00013 0.0001 0.00006 --
Female 0.00003 0.00002 -- --
Table 5
Change in the Probability of Child's Attending School for a
Unit Change in the Household Size
Age Group
Sectors/Sex
10-14 10-16 17-20 21-25
Years Years Years Years
Urban
Male -0.015 -0.016 -0.015 0.012
Female 0.011 0.013 0.016 0.012
Rural
Male -0.025 -0.018 -0.002 --
Female -0.0005 -0.002 -- --
Table 6
Change in the Probability of Child's Attending School for a Unit
Change in the Parent's Educational Level
Sector, Sex, and Age Urban Male
Parent's Education 10-14 10-16 17-20 21-25
Level Years Years Years Years
Father's Education
Primary 0.071 0.059 0.127 0.058
Middle 0.116 0.061 0.105 0.090
Matric 0.151 0.170 0.182 0.097
Higher 0.192 0.179 0.303 0.173
Mother's Education
Primary 0.066 0.068 0.145 0.126
Middle 0.104 0.087 0.007 0.121
Matric 0.230 0.178 0.190 -0.001
Higher -- 0.118 0.207 0.32
Sector, Sex, and Age Urban Female
Parent's Education 10-14 10-16 17-20 21-25
Level Years Years Years Years
Father's Education 0.227 0.202 -0.043 --
Primary 0.111 0.123 0.013 0.043
Middle 0.234 0.235 0.054 0.075
Matric 0.369 0.357 0.182 0.088
Higher
Mother's Education 0.102 0.125 0.058 --
Primary 0.244 0.269 0.123 0.031
Middle 0.330 0.309 0.199 0.065
Matric 0.255 0.118 0.083 --
Higher
Sector, Sex, and Age Rural Male
Parent's Education 10-14 10-16 17-20
Level Years Years Years
Father's Education
Primary 0.213 0.168 0.048
Middle 0.189 0.191 0.114
Matric 0.249 0.276 0.115
Higher -- -- --
Mother's Education
Primary 0.215 0.148 -0.081
Middle 0.261 0.244 0.061
Matric 0.248 0.210 0.165
Higher -- -- --
Sector, Sex, and Age Rural Female
Parent's Education 10-14 10-16
Level Years Years
Father's Education
Primary 0.055 0.063
Middle 0.041 0.040
Matric 0.105 0.092
Higher -- --
Mother's Education
Primary 0.104 0.083
Middle 0.039 0.067
Matric 0.065 0.100
Higher -- --
Table 7
Change in the Probability of Child's Attending School for a Unit
Change in the Household Labour Force Participation Ratio
Age Group
Sectors/Sex 10-14 10-16 17-20 21-25
Years Years Years Years
Urban
Male -0.546 -0.708 0.561 -0.250
Female 0.117 0.065 0.025 0.130
Rural
Male -0.611 -0.582 -0.123 --
Female -0.282 -0.239 -- --
