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Human capital formation within families: a study in the North Central Province of Sri Lanka
June/Dec 2010/2011Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
47
RESEARCH ARTICLE
Sri Lanka Journal of Social Sciences 2010/2011 33/34 (1 & 2)
Human capital formation within families: a study in the North
Central Province of Sri Lanka
D P S Chandrakumara
Department of Economics, Faculty of Humanities and Social Sciences, University of Sri Jayewardenepura, Nugegoda
Abstract: The aim of this paper is to uncover the role
of family in human capital formation through education,
so as to draw important policy implications for poverty
reduction. The study used both descriptive statistics
and Binary Logistic Analysis to examine the infl uence
of different family factors on the education level of
children. The study is based on primary data collected
from three villages of the North Central Province of Sri
Lanka. The study found that four family factors- namely,
family assets, presence of senior siblings, presence of
junior siblings and father’s age, had been signifi cant
in determining the children’s education level thereby
forming a family role model. The two factors, family
assets and presence of senior siblings, had a positive
relationship with children’s education level, while the
other two had an inverse relationship. Further, it was
found that gender, living area of the family were not
signifi cant factors to be included in the model. Finally,
the model developed by the study is useful in the public
policy decisions on human capital formation through
education, which uses the family as the bottom level
basis for reducing poverty.
Key words: Human capital, Education, Family factors,
Binary Logistic Model
INTRODUCTION
Background
In a society where children’s education from the
kindergarten to the collegiate level is mostly controlled by
parents and adults, the family plays a key role in human
capital formation. Parents and children collectively
involve in taking important decisions and allocate limited
family resources for education of children and other
purposes (Giannelli and Monfardini, 2000; Behrman,
Pollack and Taubman, 1995; Blundell, Dearden and
Sianesi, 1999). Thus, the demand for education of
children is basically dependent upon how far parents and
adult family members direct and motivate the children
for education using their limited resources.
A family is the fi rst and the most immediate socio-
economic environment to which a child is exposed. It is
an outstanding primary group, because it is in the family
that the child develops his/her knowledge and attitudes.
A family can basically exist in two forms, nuclear
family and extended family. A nuclear family ordinarily
consists of father, mother, one or more children, while
an extended family consists of near or distant relatives
and even servants (Behrman et al., 1995; Rao, 1990;
Horton and Hunt, 1980). The family may get more and
more children and become more complicated with the
passage of time, so that it may include elder and younger
children and male and female children etc. It also
undergoes continuous changes in knowledge, experience
and attitudes of parents and children. Thus, the family
background that a child faces during his/her education
process, changes from age to age and also from family
to family. Therefore, it seems that the family’s role in
human capital formation through education is a very
complicated process.
Human capital created in individuals due to education is
measured by the level of education that they have attained.
In that sense, the meaning of human capital formation is
the progression of individuals in their path of education
from kindergarten to the tertiary levels passing different
stages such as primary, junior secondary and senior
secondary. Human capital formation through education
chandrakumara62@gmail.com
D P S Chandrakumara
June/Dec 2010/2011 Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
48
which occurs at family level is important for an economy
in two main ways. First, it builds up the labour force
needed for a knowledge-based development and generates
social returns (Eicher, 1999; Mankiw, Romer and Weil,
1992; Lucas, 1988). Second, education increases the
stock of human capital, which in turn increases labour
productivity and wages and reduces poverty (Aakvik,
Salvanes and Vaage, 2005; Ranis, 2004; Tilak, 2002a,
2002b; Mingat and Tan, 1996; Weale, 1992; Sen, 1995,
1985; Schultz, 1961). Since labour is by far the most
important asset of the poor, provision of education to the
poor will tend to reduce poverty through increased labour
productivity (Rodriguez, 2002; Guneratne, 1985). Low-
education is one of the most serious causes of poverty.
In fact, there seems to be a vicious circle of poverty as
low education leads to poverty and poverty leads to low
education. The poor are not able to afford education,
even if it is freely provided by the government, because
of the high extra fi nancial and opportunity costs that they
face along with the need to sacrifi ce current consumption
(Mingat and Tan, 1996). In a situation where there are
no credit facilities available for students for education,
the importance of family members becomes still higher
(Roussel, 2000). Therefore, this paper attempts to
uncover the role of family in human capital formation
through education in the North Central Province of Sri
Lanka.
Importance of the Study
The study is theoretically and practically important due
to two main reasons:
First, the study builds a sound and productive empirical
basis on human capital formation at a family level and
provides policy implications related to education and
poverty reduction in Sri Lanka. It helps to understand
how the family units can be used, not only for producing
the necessary human capital requirements but also as a
strategy for reducing poverty at the family level.
Second, the study adds theoretical knowledge to research
on human capital formation within families. It tests the
validity of the model that family factors such as parents’
occupation, family assets together with sibling structure
determine the intra-family human capital formation. In a
society where economic activities are largely determined
at the family level, this study turns the attention of
economists to analyze the family in order to fi nd more
avenues to mobilize resources for development and
poverty reduction within the family itself.
The Problem
The human capital formation through education is
determined by both supply and demand for education
in any country. The supply of the education service is
mainly determined by government policy, quality and the
number of public and private schools. The demand side
of education is largely determined at the family level.
Even if education is freely provided by the government,
in the supplying of supplementary resources at the
bottom level, families have to play even more active
roles in enrolment of children to schools, choice of the
level of education, study-fi eld, motivation and guidance.
As such, the educational performance of a child is largely
dependent on the practices within the family to which
the child belongs. Therefore, the objective of the study is
to ascertain the role of family in creating human capital
within the family through the demand for children’s
education in different regional contexts of Sri Lanka.
Aim and Objectives
The aim of the study is to identify the role of family in the
determination of intra-family human capital formation
through education. Within this overall aim, the specifi c
objectives are as follows:
To identify and measure the effect of parents’ wealth
in the determination of human capital formation within
families.
To identify whether the education of elder siblings
generates externality effects on the education of younger
siblings.
To identify whether the existence of younger siblings
have an effect on the education of elder siblings.
Hypotheses
In order to achieve the objectives of the study, the
following hypotheses were drawn from the review of
literature and tested with empirical data.
Hypothesis-1•
Null hypothesis: The wealth level of family does not
have an infl uence on the education level of children of
the family.
Alternative hypothesis: The wealth level of family have
an infl uence on the education level of children of the
family.
Human capital formation within families: a study in the North Central Province of Sri Lanka
June/Dec 2010/2011Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
49
Rationale: Even in a situation where the government
provides free education, the benefi ts are not equally
distributed among children. Only the children with a
better economic background have the access to better
education services such as high quality schools and more
effective private tuition. Therefore, a positive relationship
between family wealth and the level of education of
children is expected.
Hypothesis-2•
Null hypothesis: Existence of elder siblings does not have
an infl uence on the education level of younger siblings.
Alternative hypothesis: Existence of elder siblings has
an infl uence on the education level of younger siblings.
Rationale: Elder siblings can either provide fi nancial
assistance or proper advice and guidance to younger
siblings based on their own experience, knowledge and
contacts. In addition, if the children are needed for work,
it is more likely that older children will work and the
younger will go to school. Therefore, existence of elder
siblings positively infl uences the education of younger
siblings.
Limitations
The study is subjected to a few limitations as follows:
First, the North Central Province (NCP) of Sri Lanka
was selected for the study as it was possible to cover the
cost of data collection under the SIDA/SAREC Research
Cooperation Project for this area.
Second, data collection was carried out in three areas in
one district of the North Central Province of Sri Lanka.
This district was considered as appropriate because it
is the district that consists of both rural and more urban
characteristics compared to the other districts in the same
province.
Third, the study was confi ned to the human capital
formation through formal education, even though there
may be a process of human capital formation through
informal education. Formal education is associated
with structured learning formats, purpose of obtaining
an educational qualifi cation, organized institutions,
methods or procedures, etc., while informal education is
the knowledge obtained by association, asking questions
from co-workers, being shown how to do something and
watching others etc. This was arranged in order to avoid
the possible complications of the study.
Finally, despite the differences in the stream of study
followed by different children – Arts, Commerce and
Science – all children who reached Advanced Level
were considered as the children who achieved the same
position in education.
METHODOLOGY
Specifi cation of the Model
In order to determine the relationship between family
characteristics and a child’s level of education, a set of
explanatory variables were initially identifi ed with the
help of the literature review. These variables could be
arranged to form the simplifi ed children’s education
function. Education of child ‘i’ in jth family was taken as
a production function,
Eij = f (GNRij, FAij, FPij, MAij, MPij, NJSij, NSSij, NOMij, ASIij, AREAij)
where,
Eij = Education level of ith child in jth family (Primary level-1, Lower
secondary level-2, Higher secondary level-3)-Categorical variable
GNRij= Gender (Male-1, Female-2)-Categorical variable
FAij = Father’s Age - Continuous variable
FPij = Father’s Profession (Categ-1, Categ-2, Categ-3, Categ-4,
Categ-5) - Categorical variable
Categ-1: No stable job
Categ-2: Agriculture, animal husbandry and minor self
employment
Categ-3: Minor workers in public and private sectors
Categ-4: Traders
Categ-5: Teachers and public and private executives
MAij = Mother’s Age - continuous variable
MPij = Mother’s Profession (Categ-1, Categ-2, Categ-3, Categ-4,
Categ-5) - Categorical variable
(Categories are same as in father’s profession)
NJSij = Number of Junior Siblings - Discrete variable
NSSij = Number of Senior Siblings - Discrete variable
NOMij= Number of Other Members in jth family of ith child
ASIij = Assets index of the ith child of jth family - Continuous variable
AREAij = Area of the ith child of jth family– Categorical Variable
A child’s siblings are separated into two groups in order
to capture the true interactions among siblings within a
family. For child ‘i’ in jth family, let the number of junior
sibings be denoted by NJSij. Similarly, NSSij denotes the
number of senior siblings.
The economic potential of a family is represented by an
asset index due to two main reasons. First, using ‘family
income’ for representing economic potential of a family
is diffi cult, as people generally do not provide accurate
information. Second, the current family income may
not measure the long-term economic status of a family
which is more relevant for the educational achievements.
Hence, instead of using ‘family income’ for representing
economic potential of a family, an ‘asset index’ (ASIij)
D P S Chandrakumara
June/Dec 2010/2011 Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
50
was constructed with the help of the statistical technique
‘Multiple Correspondent Analysis'.
As the dependent variable is dichotomous, the Binary
Logistic Model was used for the study. The structural
equation for the dependent variable can be presented in
the following form:
Where Y is the dependent variable, xi is the set of
explicative variables, β is the set of the parameters to
be estimated and ε is the error term. The relationship
between exploratory and dependent variables can be
introduced in the following form:
Therefore, for given values of exploratory variables:
Knowing the structural equation for the dependent
variable, transforming and re-arranging terms, the above
equation can be expressed in the following form:
Thus, in this model with a dependent binary variable, the
probabilities of the child to be successfully enrolled in
the Higher Secondary Level are estimated by using the
logistic distribution function.
Description and Construction of Variables
The Dependent Variable
The dependent variable (N=131) is a dichotomous
variable indicating whether or not a child reached the
higher secondary level. The value is 1 if the child did
not enter the advanced level. In a conceptual sense,
this category includes the children who never attended
school and the children who dropped out of school
before Advanced Level if they are in the age range of
18-21 years as at the time of the interview. However,
practically, there was no child who never attended school.
The variable takes the value of 2 if the child has either
Y ij
* = x ij β ij + ε ij
registered for an Advanced Level course or completed
the course despite its successfulness by the age range
of 18-21 years. Table 1 shows how the dichotomous
variable, level of schooling, has been distributed in the
three villages.
The Explanatory Variables
After reviewing the numerous studies completed as of
Shultz (1961) on human capital and Becker (1964) on
human capital formation within families, at the fi rst
step, eleven variables were included in the model. The
following is a list of all variables used in the estimated
function, as well as the rationale behind their inclusion.
Assets Index (ASI): In order to represent the economic
potential of the family, an ‘asset index’ was constructed.
This represents the resources possessed by the family
that can infl uence the child’s academic aspirations and
success.
Aiming the construction of an assets index, the researcher
included three sets of questions related to the economic
status of the family. First, families were asked about their
ownership of various assets, such as whether they own a
radio, a television set, a refrigerator, a bicycle, a motor-
cycle, a land vehicle, a motor car. Second, they were
asked about characteristics of their housing, namely the
number of square feets of their house per head, whether
the roof is permanent, whether the wall is permanent,
whether the fl oor is permanent. Third, in order to include
the basic human capital assets of the family, the level of
education of the father and mother was asked. Altogether,
the number of variables constructed through the questions
was 12 while the number of level categories was 29 (see
Table 2). To ensure comparability across the three areas,
only variables that appear in all of the three areas were
included in the analysis. As the extent of land owned by
the families in the suburb area (Thammennakulama) was
much less than that of rural villages, it was not included
as a common component of assets. Although the amount
of jewellery or gold owned by families was a good
component of wealth, it was practically diffi cult to get
information about such assets which is the same as for
Table 1: Distribution of Children (Age 18-21 yrs) by Level of
Schooling
Level of
schooling
Kala
Medawachchi
Halmillewa Thammennakulama Total
Less than
A/L
21 19 14 54
A/L 17 11 49 77
2_if _Y* > 1
1_if_ Y* ≤ 1
Yij
* =
Pr(y = 1|X) = Pr(y* > 1|X)
Pr(y = 1|X) = Pr(ε > -(α + βX)|X)
Human capital formation within families: a study in the North Central Province of Sri Lanka
June/Dec 2010/2011Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
51
income. However, since we have 12 asset type variables,
it gives a 12-dimensioned space, which is impossible to
imagine by just a simple visualization.
The following equation was used to calculate the asset
index.
MCAPi = Ri1W1 + Ri2W2 +…+ RijWj +… + RinWn
Where MCAPi is the ith household’s composite asset
index, Rij is the response of family i to category j, and Wj
is the MCA weight for dimension one applied to category
j. The statistical software ‘MINITAB’ was employed to
calculate the weights.
Then the main problem was the choosing of weights
for each item of assets. For this purpose, there are
two effi cient and unbiased techniques in statistics
namely, ‘principle component analysis’ and ‘multiple
correspondent analysis’. In most of the studies, principal
components or factor analysis (PCA) is widely used
for the construction of asset indices. However, PCA
is essentially designed for continuous variables as it
assumes a normal distribution of indicator variables. In
contrast, multiple correspondence analysis (MCA) makes
fewer assumptions about the underlying distributions
of indicator variables and is more suited to discrete or
categorical variables. Hence, the MCA rather than PCA
in constructing the asset index was employed in the
analysis. Using the weights obtained through MCA, the
assets index was calculated separately for each family so
that it was possible to even rank them on the basis of the
value of the index. However, as positive values add to
the assets index while negative values decrease the assets
score, in some families there was a problem of having
negative index values. To obtain positive asset values, a
value equal to the greatest negative value was added to
each of the asset index values, so that the lowest value
becomes zero. A further small magnitude was added to
make the lowest value non-zero. The transformation
entailed adding 0.1785 to the asset index.
Child’s gender: The child’s gender was considered here
as a child characteristic that separates the child by gender
difference. Gender is a dichotomous variable that takes
the value of 1 for females and 2 for males. Totally, 63
boys and 68 girls were qualifi ed to be selected from the
three villages.
Age of parents: Age of parents which is a continuous
variable, consists of two variables namely, father’s age
and mother’s age. The age of parents when the informant
child is at the age range 18-21 was considered for the
study. This can be considered as a proxy indicator of the
modernity of parents, which may be an important factor
affecting the education of children.
Number of senior siblings: This variable includes the
number of all male and female children who are older
than the informant child. This is a discrete variable that
represents the number of matured members that the
informant child has in the family.
Number of junior siblings: The number of all male and
female children who are younger than the informant child
was taken into account. This is a discrete variable which
was included with the intention of identifying whether
their infl uence is different from that of elder siblings.
Number of other members: This variable was included
in the model with the purpose of separating the nuclear
family from the extended family. The members who are
permanently living in the same household, but not the
members of the nuclear family, for instance, father-in-
law, mother-in-law, any other relative or non-relative
residents, were included in this variable. This is a discrete
variable.
Residence of the family (Area): In order to specify
the residence of the family, dummies for three areas
Table 2: Components of the Assets Index and the Weights Obtained
from Multiple Correspondent Analysis
Asst
No.
Component/
Variable
No. of
Levels
Level Particulars Weight
(Coordinates)
1 Size of house 3 Hsize 1 (< 500 sq.ft) -1.850
Hsize 2 (501- 1000 sq.ft) -0.144
Hsize 3 (>1000 sq.ft) 0.566
2 Roof condition 2 Rcond 1 (Temporary) -1.796
Rcond 2 (Permanent) 0.343
3 Floor condition 2 Fcond 1 (Temporary) -1.582
Fcond 2 (Permanent) 0.450
4 Wall condition 2 Wcond 1 (Temporary) -1.788
Wcond 2 (Permanent) 0.341
5 Toilet condition 3 Tcond 1 (No permanent toilet) -2.262
Tcond 2 (Permanent-Pit) 0.101
Tcond 3 (Permanent-Flush) 1.074
6 Motor vehicles 2 MV 1 (Does not own) -0.136
MV 2 (Owns a motor vehicle) 0.855
7 Land vehicles 2 LV 1 =(Does not own) -0.017
LV 2 (Owns a land vehicle) 0.129
8 Motor-cycles 2 MB 1 =(Does not own) -0.562
MB 2 (Owns a motor-cycle) 0.588
9 Color
televisions
3 TV 1 (Does not own a TV) -1.009
TV 2 (Owns a black & white
TV)
0.324
TV 3 = (Owns a colour TV) 1.302
10 Refrigerators 2 Frig 1 (Does not own) -0.621
Frig 2 (Owns a refrigerator) 0.713
11 Father’s
education
3 FE 1 (< Ordinary Level) -0.508
FE 2 (Advanced Level) 0.452
FE 3 ( > Advanced Level) 1.127
12 Mother’s
education
3 ME 1 (< Ordinary Level) -0.582
ME 2 (Advanced Level) 0.502
ME 3 (> Advanced Level) 1.136
D P S Chandrakumara
June/Dec 2010/2011 Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
52
were included. The nominal values of 1 for Kala-
Medawachchiya (traditional rural area), 2 for Halmillewa
(rural settlement area) and 3 for Thammannakulama
(suburb area) were assigned in order to distinguish the
effect of residence.
Parental occupation: Two dummy variables were created
to determine the parental professional status. First of all,
parental occupation was split into father and mother.
Next, based on the type of their main economic activity,
each category was split into fi ve nominal variables,
viz., (i) No permanent job, (ii) Agriculture and animal
husbandry (own) (iii) Mason/carpentry, labourer, minor
workers, drivers, armed forces including the police, (iv)
Business (v) teaching, government and private sector
executives. The aim of dividing the parents’ occupation
into groups was to approximate the nature of economic
activities of the family.
Data Collection
The estimation requires data that provide information on
the characteristics of children, parents and others. The
primary data was collected through a household survey.
A sample of 131 children from 131 families was drawn
from three villages in the North Central Province (NCP)
of Sri Lanka.
The sampling and data collection procedure followed
several steps. First, the North Central Province (NCP)
was selected for the study because of three reasons: (i)
as part of a bigger project that functioned at NCP; by
choosing this province, it was possible to get advantages,
both scientifi c as well as economic; (ii) ability to manage
data collection process personally, as it was required due
to the sensitive nature of the subject; (iii) the possibility
for generalization; being a province which has both rural
and urban characteristics within the same district, it is
possible to generalize the results for a large part of the
population of the country. Second, Anuradhapura was
selected as it is a district that adequately represents
different aspects that needed to be covered by the study
such as urban-rural divide, high-low family income,
different professions, schools of different grades.
However, the other district, Polonnaruwa in the NCP
did not have any characteristics that varied from the
Anuradhapura district. Third, two Divisional Secretariat
Divisions (DSDs) of the Anuradhapura district, Galnewa
and Nuwaragam Palatha (East) were selected, as Galnewa
represents rural characteristics while Nuwaragam Palatha
(East) represents urban and suburb characteristics.
Fourth, Thammennakulama of Nuwaragam Palatha
(East) was selected because of its non-extremist
suburb characteristics: not highly commercialized or
sophisticated. However, from the Galnewa DS division
that represents rural families, two G.N. divisions -
Karuwalagaswewa and Kala-Madawachchiya - were
selected to represent 18 rural settlement G.N. divisions
and 12 rural traditional G.N. divisions respectively. Fifth,
one village from each G.N. division (Halmillewa and
Kala-Madawachchiya) was selected depending on the
appropriateness of the sampling. Finally, all the children,
in the age range of 18-21, of selected GN Divisions were
identifi ed. The age range was determined at that level
because it was necessary to identify children who reached
the Advanced Level class and children who dropped
out before reaching this level. Accordingly, by that age
range, the children either must have attained Advanced
Level, if they continued schooling, or dropped out so that
the full length of their education up to Advanced Level
can be practically identifi ed. As the number of children
who belong to the required age range is not so high in all
three villages, all the children who were within that range
were taken as informants.
Data collection from the selected children and their parents
was completed by three visits to houses in each village.
At the fi rst visit, families with children in the required
age range, the number of children available in each house
and other basic information were collected. Moreover,
appointments to meet them for the second round were
also arranged through the fi rst visit. The second visit was
arranged only for the families where there were children
in the required age range. All the complicated information
needed for the quantitative analysis regarding the
informant child and his/her family was collected during
second visit by using a semi-structured questionnaire.
The semi-structured questionnaire used in the second
visit was divided into two parts: PART–A and PART–B.
PART-A was to cover family information while PART–B
collected information with regard to the child in
question. A pilot survey was carried out in each area to
test the questionnaire prior to fi nal data collection and
then adjusted to test the content of the data collection
instrument. Finally, the sample consisted of 131 children
who were aged between 18 to 21 and do not have serious
disabilities, live with their biological parents, have full
information on individual and family characteristics up
to Advanced Level education and represent the three
main types of areas in the North Central Province of Sri
Lanka.
Table 3: Size of Sample by Area
Area Area characteristics Number of
children aged
18-21
Number of
children
interviewed
1. Thammennakulama Suburb 57 41
2. Halmillewa Mahaweli settlement 37 30
3. Kala-
Medawachchiya Traditional village 78 60
Total 172 131
Human capital formation within families: a study in the North Central Province of Sri Lanka
June/Dec 2010/2011Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
53
Figure 1: Sampling Procedure
NCP
Anuradhapura
District
Polonnaruwa
District
Nuwaragam Palatha
(East) DSD - suburb
(out of two urban DSDs)
Thammennakulama
GND
(out of 29 GNDs)
Thammennakulama
population block
Karuwalagaswewa:
Halmillawewa population
block
Children in the age
range 18-21
131 children from 131
families
Kala-Medawachchi
sampling block
Karuwalagaswewa
(out of 17 GNDs belonging
to Mahaweli settlements)
Negama GND
(out of 12 GNDs belonging to
traditional villages)
Galnewa DSD - Rural
(out of twenty DSDs)
D P S Chandrakumara
June/Dec 2010/2011 Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
54
ANALYSIS AND RESULTS
Identifi cation of Relevant Variables (through
correlation tests)
In order to uncover the relevant factors for the model,
the researcher examined the correlation that the level
of education of children have with each explanatory
variable which was initially considered for the model.
As the dependent variable and most of the explanatory
variables are categorical, Spearman Correlations were
tested. At this step, eleven exploratory variables were
included for the correlation test. This revealed that out of
all the variables, the two variables, ‘gender of the child
(GNR)’ and ‘number of family members (NFM)’ had no
correlation with the education level of children to at least
5 per cent level of signifi cance. Hence, the remaining
nine variables FAij, MAij, FPij, MPij, NJSij, NSSij, NOMij,
ASIij, AREAij (ROFij) are correlated with the dependent
variable at the range of 1– 5 per cent level of signifi cance
(p < .01 - .05).
Minimizing Multicolinearity (through correlation
tests)
When the data is the result of an uncontrolled experiment
or primary data collection, it may cause many of the
different variables to move together in systematic
ways. When this is the case, the variables are said to be
collinear or multicollinear when several variables are
involved in the econometric testing. This will impose
a problem when evaluating the results, since it may
not be possible to capture the economic relationship
or the parameters of interest. It may also cause lack of
signifi cance of individual independent variables while
the overall model may be strongly signifi cant. Moreover,
it results in wrong signs and magnitudes of regression
coeffi cient estimates and consequently in incorrect
conclusions about relationships between independent
variables. These problems are highly related to this
study since it involves a number of different variables.
To eliminate multicollinearity, one way is to represent
the highly correlated variables by one of the variables.
Another way is to transform the variables to eliminate
multicollinearity.
The simple and clear-cut way to detect collinear
relationships is to test for the correlation coeffi cients
between pairs of variables. In order to fi lter out
multicollinearity in this study, fi rstly the correlation
coeffi cients between each independent variable was
calculated. In the cases where there are variables with
a high degree of collinearity, only one of those variables
was selected so that it represented the other variable/s.
However, the variables essential for the model were
included in the model despite the collinearity. Although
there is collinearity between NJSij and NSSij, neither of
the variables were removed from the model because it
was necessary to include both junior and senior siblings
for a model of family. Even if another two variables, ASIij
and NJSij show multi-collinearity to a certain extent,
these two were also brought forward to be included in
the model because it was necessary for the model to
be meaningful. The two variables, FPij and MPij were
removed from the analysis at this stage because those
variables can be properly represented by ASIij without
a problem to the family model. Since there was multi-
collinearity between father’s age and mother’s age, the
latter (mother’s age) was removed from the analysis and
represented by the father’s age.
Binary Logistic Analysis and Results
For the logistic regression, the level of education
was recorded into either A/L or below that, since
binary response was required. The case processing
summary (Table 4) displays the total number of cases
or observations included in the analysis as 131 and the
number of missing cases as zero. The dependent variable
encoding in Table 5 shows the original and internal values
of the dichotomous variable. Although the original value
that has been given for the dependent variable is 1 if the
child in question is below A/L, and 2 if he/she reached
A/L, the internal values of the model are respectively 0
and 1.
Table 4: Case Processing Summary
Unweighted Cases (a) N Percent
Included in analysis-selected cases 131 100.0
Missing cases 0 0
Total 131 100.0
Unselected cases 0 0
Total 131 100.0
a If weight is in effect, see classifi cation table for the total number of cases.
Table 5: Dependent Variable Encoding
Original Value Internal Value
1 (Below A/L) 0
2 (A/L) 1
The model building process included six variables at
the fi rst step namely, father’s age (FA), total number
of other members (TOM), assets index (ASI), area
Human capital formation within families: a study in the North Central Province of Sri Lanka
June/Dec 2010/2011Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
55
(AREA), number of senior siblings (NSS) and number
of junior siblings (NJS) of the child in question. Among
these, ‘AREA’ was a categorical variable that has
three categorical codes such as 1, 2 and 3 for the three
sampling areas, Kala-Medawachchiya, Halmillewa and
Thammennakulama respectively (Table 6).
Predictive variables were added in a forward stepwise
method, known as the Wald method. The signifi cance of
the models in each step is evaluated using Chi-square
statistics (Table 7). A variable has to be signifi cant at
0.10 level before it can enter into the model, while it has
to be signifi cant at 0.15 for it to remain in the model. The
Table shows that the models in each step up to step 4 are
signifi cant (Sig < 0.01).
The R squared in ordinary multiple linear regression
provides an indication of how much variation in the
observed values of the predicted variable is explained by
the model. However, the Cox & Snell R squared is a form
of R squared which arises in logistic regression, and the
Nagelkerke R squared is a transformation of the Cox &
Snell R squared so that it lies in the interval between zero
and one, as is the case in the ordinary multiple regression
R squared.
Table 6: Categorical Variables Codings
Frequency Parameter coding
(1) (2)
AREA ij 1 30 1.000 .000
2 38 .000 1.000
3 63 .000 .000
Table 7: Omnibus Tests of Model Coeffi cients
Chi-square df Sig.
Step 1 Step
Block
Model
52.651
52.651
52.651
1
1
1
.000
.000
.000
Step 2 Step
Block
Model
29.550
82.201
82.201
1
2
2
.000
.000
.000
Step 3 Step
Block
Model
8.720
90.920
90.920
1
3
3
.003
.000
.000
Step 4 Step
Block
Model
4.283
95.204
95.204
1
4
4
.038
.000
.000
The Nagelkerke R square (Table 8) shows that about
45 per cent of the variation in the outcome variable
(probability to reach or not to reach to A/L) is explained
by the model in step 1, while 70 per cent of this variation
is explained by this logistic model in step 4.
The Hosmer-Lemeshow test displays (Table 9) how
closely the observed and predicted probabilities match.
It provides a formal test to fi nd whether the predicted
probabilities match the observed probabilities. This test
should be greater than 5 per cent to indicate a good fi t
based on the difference between observed and predicted
frequencies. A larger p-value indicates a better match or
insuffi ciency of evidence to claim that the model does
not fi t the data adequately. If the p-value is less than the
accepted α-level, the test would reject the null hypothesis
of an adequate fi t. Accordingly, the model is best at the
third step when the ‘number of junior siblings’ are not
included. However, as the model should explain the
role of different members of the family, the researcher
decided to include the ‘number of junior siblings’ also
into the model. Therefore, the model at step 4 was taken
as appropriate in explaining the human capital formation
within the family.
In addition, Table 8 gives a classifi cation for the models
fi tted, and illustrates the predictive accuracy of the logistic
regression models from step 1 to step 4. It shows that the
model in step 4 was able to predict ‘not reaching A/L’
83.3 per cent, and ‘reaching A/L’ 90.9 per cent correctly,
while the overall success rate in predicting the children
reaching ‘A/L’ was 87.8 per cent. This result shows that
the model, with prediction variables FA, NSS, NJS and
ASI, does a good job at explaining the variability amongst
individuals with regard to reaching ‘A/L’.
/
Table 8: Model Summary
Step -2 Log
likelihood
Cox & Snell R
Square
Nagelkerke
R Square
1 124.895a.331 .466
2 95.345b.466 .628
3 86.625b.500 .674
4 82.342b.517 .696
a. Estimation terminated at literation number 5 because parameter estimates changed by less
than .001.
b. Estimation terminated at literation number 5 because parameter estimates changed by less
than .001.
Table 9: Hosmer and Lemeshow test
Step Chi-square df Sig.
1 24.132 8 .002
2 12.823 8 .118
3 3.471 8 .901
4 9.052 8 .338
Table 10: Classifi cation table
Observed Predicted
Eij Precentage
Correct
1 2
Step 1 Eij 1
2
Overall Percentage
36
9
18
68
66.7
88.3
79.4
Step 2 Eij 1
2
Overall Percentage
42
8
12
69
77.8
89.6
84.7
Step 3 Eij 1
2
Overall Percentage
42
7
12
70
77.8
90.9
85.5
Step 4 Eij 1
2
Overall Percentage
45
7
9
70
83.3
90.9
87.8
a. The cut value is. 500
D P S Chandrakumara
June/Dec 2010/2011 Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
56
Furthermore, each estimated coeffi cient of the logit model
was tested using the Wald statistics for being signifi cantly
different from zero. The signifi cance should be less than 5
per cent. The Wald statistics is calculated by dividing the
coeffi cient (B in Table 11) by its corresponding standard
error, and squaring the result. It provides an indication of
whether or not the coeffi cient is signifi cant for the model.
The Wald statistic and its signifi cance given in Table 11
indicate that all fi tted coeffi cients are signifi cant (sig <
0.05).
Exp (B) represents an odds ratio. In general, it measures the
extent to which the odds in favour of a positive response
are raised when the level of the associated explanatory
variable is raised from the reference level to the level
specifi ed in the table of results. In this study, it measures
the extent to which the odds in favour of reaching A/L
are raised when the levels of each explanatory variable
is raised from the reference level (low) to the highest
level (high). Thus, for this study, fi rstly, it would seem
that a high level of NSS is very signifi cant in increasing
younger children’s retention in education. This conclusion
is supported by the 95 per cent confi dence for Exp (B)
of 3.43 with the limits of 2.27 (lower) and 8.64 (upper).
Secondly, the important factor is the ASI that shows an
odds ratio of 1.38 within the limits 1.21 (lower) and 1.59
(upper). The two variables, FA and NJS take the third and
fourth places respectively when it is determined in terms
of the odds ratio.
The Wald statistic has a Chi-squared distribution on
degrees of freedom indicated in the column headed ‘df’.
The column headed ‘Sig.’ is a p-value associated with
the Wald statistic. Table 11 shows that all the variables,
NSS, ASI, FA and NJS are signifi cant at 5 per cent level,
whereas NSS and ASI are signifi cant at 1 per cent level.
This means that NSS and ASI are highly signifi cant.
The logistic regression table, Table 11 (variables in the
equation) shows the estimated coeffi cients, standard
error, Wald statistic, z-values, p-values, odds ratio and
95 per cent confi dence interval for the odds ratio. From
the output, it can be seen that the estimated coeffi cients
for FA, ASI, NJS and NSS have p-values less than
0.05, indicating that there is suffi cient evidence that the
coeffi cients are not zero using an α-level of 0.05. The
estimated coeffi cient of -.104 for father’s age represents
the change in the log of p (< A/L) / p (A/L) with a 1
unit (one year) increase in father’s age, with the other
factors held constant. The estimated coeffi cient of -.609
for number of junior siblings represents the change in
the log p (< A/L / p (A/L) with a 1 unit increase in junior
siblings, with the other factors held constant. It shows
that the effect of both of these factors on the level of
education is negative. The estimated coeffi cient of 1.489
for the number of senior siblings represents the change
in the log of p (< A/L / p (A/L) with a 1 unit increase
in senior siblings, with the other factors held constant.
The estimated coeffi cient of .327 for the assets index
represents the change in the log of p (< A/L / p (A/L) with
a 1 unit increase in the assets index, with the other factors
held constant. Both of these factors have a positive effect
on the education of children.
Although there is evidence that the estimated coeffi cients
for ASI is not zero, the odds ratio is 1.39 indicating that
a one unit increase in ASI increases a child’s education
by 1.39 times. The highest positive contributor to a
child’s education in a family is the NSS. The odds ratio
shows that the increase of one additional senior sibling
of a family increases a child’s education by 4.43 times.
For FA and NJS, the negative coeffi cients and the odds
ratios indicate that one unit (one year) increase in father’s
age and one unit increase in junior siblings, decrease the
child’s education by 0.90 and 0.54 respectively.
In a logistic regression it is not the actual education level
that is predicted, but rather a function, known as the
logit function, which is predicted. If this function may
be represented by E (p) then as indicated in Table 11, the
equation for step 4 in the logistic regression is:
In order to use the model to predict whether an individual
is reaching or not reaching A/L based on their scores
on NSS, NJS, ASI and FA, the equation fi rst required
transformation. The logit function E(p) is a function
of p, where p indicates reaching or not reaching A/L.
The function is given by log (p/1-p). Transforming
the equation, for model 4 the regression equation is as
follows:
Table 11: Dependent Variable Encoding
B S.E. Wald df Sig. Exp (B) 95.0% C.I for
EXP (B)
Lower Upper
Step ASlij
1a Constant
.307
-3.853
.056
.809
30.101
22.705
1
1
.000
.000
1.360
.021
1.218 1.517
Step NSSij
2b ASlij
Constant
1.392
.347
-5.693
.300
.066
1.090
21.490
27.325
27.289
1
1
1
.000
.000
.000
. 4.024
1.415
.003
2.233
1.242
7.248
1.612
Step FAij
3c NSSij
ASlij
Constant
-.118
1.652
.339
.150
.045
.343
.069
2.354
6.763
23.211
24.292
.004
1
1
1
1
.009
.000
.000
.949
.889
5.216
1.403
1.162
.814
2.664
1.226
.971
10.213
1.606
Step FAij
4d NJSij
NSSij
ASIij
Constant
-.104
-.609
1.489
.327
.433
.048
.304
.341
.070
2.496
4.671
4.028
19.104
21.946
.030
1
1
1
1
1
.031
.045
.000
.000
.862
.901
.544
4.432
1.387
1.542
.820
.300
2.273
1.210
.990
.986
8.642
1.590
a. Variable (s) entered on step 1 : ASlij
b. Variable (s) entered on step 2 : NSSij
c. Variable (s) entered on step 3 : FAij
d. Variable (s) entered on step 4 : NJSij
E(p) = .433 - .104FA -.609NJS + 1.489NSS + .327ASI
p =
e.433-.104FA-.609NJS+1.489NSS+.327 ASI
1 + e.433-.104FA-.609NJS+1.489NSS+.327ASI
Human capital formation within families: a study in the North Central Province of Sri Lanka
June/Dec 2010/2011Sri Lanka Journal of Social Sciences 33/34 (1 & 2)
57
In the equation, p represents the probability of the binary
response being 1, i.e. of reaching A/L. Based on Table 11,
if p is greater than 0.5, it indicates reaching A/L, while a
‘p’ of less than 0.5 indicates not reaching A/L. The results
in this section provide support for the two hypotheses
indicating that high and low scores on reaching A/L or
the level of education can be predicted with statistical
signifi cance by the scores on the NSS and ASI and NJS, FA.
The -2Log Likelihood (-2LL) is a measure of badness-of-fi t,
illustrating error remaining in the model after accounting
for all independent variables. The -2LL of 1567.256
indicates that there is no signifi cant error remaining in the
model. The Hosmer Lemeshow Goodness-of-Fit test is
the most useful measure of test which assesses the overall
model by testing the null hypothesis that all logistic
regression coeffi cients besides the constants are zero. The
model’s Hosmer Lemeshow Goodness of Fit chi-square
is 9.052 with a signifi cance of .338, indicating a good fi t.
The results of the quantitative analysis further confi rm
most of the fi ndings of other studies which were reviewed
in the literature on this subject. In addition, the results
show that there is a special pattern that creates human
capital through education within a family. The family
assets, which mostly consists of parents' assets and senior
children positively affect the education of children while
junior children make a negative impact on the education of
senior children within a family. Further, the analysis fi nds
that the parents’ age has a negative relationship on their
children’s education level. This implies that the children
of older parents would not continue education unless they
are positively affected by senior siblings or family assets.
CONCLUSIONS
Testing the two hypotheses of the study was helpful in
achieving the objectives of the study and to address the
research question effectively.
The null hypothesis in hypothesis 1, ‘The wealth level of
family does not have an infl uence on the education level
of children of the family’, was rejected. While accepting
the alternative hypothesis, it suggests that family wealth
works as an effective factor that uplifts the intra-family
human capital. The empirical model suggests that a
one unit increase in ASI increases a child’s education
by 1.39 times. The family assets level was also closely
related to the parents’ education level and the occupation.
The null hypothesis in Hypothesis II, ‘Existence
of elder siblings does not have an infl uence on
the education level of younger siblings’ was also
rejected. While accepting the alternative hypothesis,
it suggests that ‘Existence of elder siblings causes the
increase of the education level of younger siblings’.
Furthermore, the results suggest that the existence of
senior siblings is the strongest factor that determines
the human capital formation within a family. The
logistic analysis shows that when it is analyzed by
the odds ratio, one unit increase in senior siblings of
a family increases a child’s education by 4.43 times.
Furthermore, while testing Hypothesis II, it was
possible to identify that positive effects are created
from senior to junior siblings, while negative
effects are created from junior to senior siblings.
According to the Logistic Analysis, the odds ratio
indicates that a one unit increase in junior siblings
decreases the education of senior siblings by 0.54.
In addition, to the above conclusions drawn for the
variables which had a direct relationship with the
hypotheses, the following conclusions are also important
in understanding the role of family in human capital
formation:
a) Father’s age, which represented parents’ age, shows
a negative association with the education level of
children. A one year increase in father’s age decreases
the child’s education by 0.90.
b) It also reveals that children’s education level has no
signifi cant association with the rural urban locality.
Finally, it seems that the role of family in human capital
formation through education is highly effective and
crucial. As an economic unit in the society, the role it
plays cannot be replaced by any other way as it has
the basic responsibility in controlling the behaviour of
children including their education. Hence, the model
found by the study is useful in the public policy decisions
on human capital formation through education. The
study shows how family factors can be used in forming
human capital within families if the government uses this
strategy for reducing poverty.
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