CHILD LABOUR AND ECONOMIC GROWTH

CHILD LABOUR AND ECONOMIC GROWTH
A Thesis Submitted to the College of
Graduate Studies and Research
In Partial Fulfillment of the Requirements
For the Degree of Master of Arts
In the Department of Economics
University of Saskatchewan
Saskatoon
By
Nardos Kebreab Tesfay
© Copyright Nardos Kebreab Tesfay, June 2003. All rights reserved  ii
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whole or part should be addressed to:
Head of the Department of Economics
University of Saskatchewan
Saskatoon, Saskatchewan
S7N 5A5
Canada  iii
ABSTRACT
This paper examines the relationship between national income and child labour.
We are particularly interested in evaluating the economic role of children at different
stages of development.  Our objective is to show that in the aggregate, at a low level of
development the direction of the relationship between the incidence of child labour and
per capita income is indefinite.  Child labour may increase or decrease with income.
Forecasts of the child labour force participation rate as well as per capita gross domestic
product are made for each country in the sample.  We also forecast future levels of the
primary net enrollment ratio in an effort to provide empirical support for our policy
recommendations.  
Using panel data methodology, we find evidence of an inverted-U, Kuznets-like
relationship between the child labour force participation rate and per capita GDP.  The
relationship is significant for the total sample and the sample for which per capita GDP is
above US$1000.  Holding all else constant, forecast results suggest that for those
countries on upward sloping part of the curve, child labour is a problem that will persist
for many years to come.  The growth rates of per capita GDP required to reach 10 per
cent child labour by the target date, 2029, range from 2 per cent to 15 per cent.     iv
ACKNOWLEDGEMENTS
I would like to take this opportunity to thank Professor Mobinul Huq for
providing me with guidance throughout my research, as well as an excellent suggestion
for a thesis topic.  I especially thank Professor Huq for his willingness to organize and
interpret my frequent rash ideas and loose assumptions.  This will be my final year at the
University of Saskatchewan and so I would also like express my gratitude to Professor
Huq, on behalf of the graduate students, for his genuine concern, most especially for his
rigorous efforts to ensure that we were all funded and well fed.  My thanks to Professor
Cristina Echevarria, Professor Morris Altman and Professor Jim Handy for their
insightful comments and helpful research material.  Heartfelt thanks to Professor
Echevarria and Professor Huq for their guidance and counsel over the years.
I would like to express my profound and humble and gracious thanks to my
family, for their love, guidance and encouragement.  I thank my parents for instilling in
me the value of an education.  Thank you for allowing me to stray from the flock on
occasion and find my own way. Thank you for supporting me throughout.  Thanks to my
father who, by example, taught me to honour the history and struggle of my people, to
not only talk about great things but to do great things as well, and to leave a positive
legacy. I expect injustice will continue to motivate me throughout my lifetime and this is
because of you.  I was just as devastated as you when One Sky lost its funding.  I would
especially like to thank my mum for being the best role model a mother, a woman, a
person can be.  There are no words to express how I feel about what you have done for
me.   None of this, absolutely none of it would be possible without you!  You are every
element I need to survive.  Oh and Simon, I am forever indebted to you for introducing
me to Cat Power.
Nardos Kebreab Tesfay   v
TABLE OF CONTENTS
CHAPTER 1: INTRODUCTION …………………………………………………         1
CHAPTER 2: LITERATURE REVIEW ………………………………………….         5
 2.1 On the Role of Children in Development …………………..................         5
  2.1.1 Old Age Income Support ……………………………………         5
   2.1.1.1 Children as an Alternative to Land Ownership …...         6
   2.1.1.2 Imperfect Capital Markets ………………………...         6
   2.1.1.3 Absence of Welfare Institutions …………………..         7
   2.1.1.4 Absence of a Women’s Labour Market …………..          7
2.1.2 Insurance Against Income Stability ………………………...          8
2.1.3 Children as a Source of Labour …………………………….          8
2.1.3.1 Vicious Circle Hypothesis ...……………………...          8
 2.1.3.2 Unpaid Household Work …………………………        10
 2.1.3.3 Children as Income Earning Assets ………………        11
 2.2 Wealth ………………………………………………………………...        12
 2.3 The Economic History of Child Labour ……………………………...        13
  2.3.1 Early Industrialization and the Employment of Children …..        13
  2.3.2 The Child Labour Market …………………………………..        15
   2.3.2.1 Supply of Child Workers …………………………        15
   2.3.2.2 Demand for Child Workers ………………………        16
   2.3.2.3 Changing Structure of the Labour Market ……….         17
  2.3.3 Child Labour Legislation and Compulsory Schooling …….         18
 2.4 Chapter Summary ……………………………………………………         19
CHAPTER 3: THEORETICAL FRAMEWORK ………………………………          20
 3.1 The Cost of Raising Children in a Developing Country …………….         20
 3.2 Wealth Revisited …………………………………………………….         22
 3.3 A Model of Household Preference ………………………………….         23
  3.3.1 The Quantity – Quality Interaction of Child Demand …….          23
  3.3.2 An Extension of the Becker Model………………………..          26
 3.4 Chapter Summary ……………………………………………………        36  vi
CHAPTER 4: HYPOTHESIS, ESTIMATION PROCEDURE AND DATA  ..            37
 4.1 Hypothesis ………………………………………………………....            37
 4.2 Estimation Procedure ………………………………………………            38
 4.3 Data ………………………………………………………………...            41
 4.4 Chapter Summary ………………………………………………….            47
CHAPTER 5: THE RESULTS ………………………………………………...            48
 5.1 Estimation Results …………………………………………………            48
  5.1.1 Discussion of Results ……………………………………            48
  5.1.2 Evaluation of Results ……………………………………             53
   5.1.2.1 Dickey-Fuller Tests ……………………………            53
   5.1.2.2 Heteroscedasticity Tests ……………………….            54
   5.1.2.3 Autocorrelation Tests ………………………….            54
 5.2 Projection Results …………………………………………………            55
 5.3 Chapter Summary …………………………………………………            61
CHAPTER 6: CONCLUSIONS ……………………………………………...             62
BIBLIOGRAPHY …………………………………………………………….             66  vii
APPENDICES …………………………………………………………………….         72
Appendix A1: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Linear Model (Total Sample) ……………………...........................         73
Appendix A2: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Linear Model (per capita GDP< US$1000) ………………………..        74
Appendix A3: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Linear Model (per capita GDP> US$1000) ……………………......        75
Appendix B1: Child Labour and Per Capita GDP Fixed Effects Regression Results, LogLog Model (Total Sample) …………………………………………        76
Appendix B2: Child Labour and Per Capita GDP Fixed Effects Regression Results, LogLog Model (per capita GDP< US$1000) …………………………..        77
Appendix B3: Child Labour and Per Capita GDP Fixed Effects Regression Results, LogLog Model (per capita GDP> US$1000) ………………………….         78
Appendix C1: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Quadratic Model (Total Sample) ………………………………......        79
Appendix C2: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Quadratic Model (per capita GDP< US$1000) …………………......       80
Appendix C3: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Quadratic Model (per capita GDP> US$1000) ……………………..       81
Appendix D: Augmented Dickey-Fuller Unit Root Test Results ………………….      82
Appendix E: Heteroscedasticity Test Results ………………………………….......     83  viii
LIST OF TABLES
Table 2.1: Child Labour Force Participation Rates
US, 1870-1910 ……………………………………………...                   14
Table 2.2: Child Labour Force Participation Rates
England and Wales, 1850-1910 ……………………………..                  15
Table 4.1:  Descriptive Statistics for Countries
with a High Incidence of Child Labour, 1989-1999 ………..                   42
Table 4.2:  Descriptive Statistics Countries
with a Low Incidence of Child Labour, 1989-1999 …………                  42
Table 4.3:  Percentage Change in Per Capita GDP
and Percent Child Labour, 1989-1999 ……………………....                  43
Table 4.4:  Percentage Change in Per Capita GDP
and Percent Child Labour, 1989-1999 ……………………....                  43
Table 5.1:  Estimation Results for Linear Model ………………………..                  49
Table 5.2:  Estimation Results for Log-Log Model ……………………..                  49
Table 5.3: Estimation Results for Quadratic Model …………………….                  50
Table 5.4:  Forecast Time Period for Child Labour to Reach Target ……                 56
Table 5.5:  Estimated Growth Rate Required to Reach Target by 2029 …                 59
Table 5.6: Primary Net Enrollment Ratio Results for 2029 ……………..                 60  ix
LIST OF FIGURES
Figure 3.1:  Effect of a Change in Child Wage on Child Time Allocation ……..        33
Figure 3.2:  Effect of a Change in Non-Labour Income
on Child Time Allocation ………………………………………….        34
Figure 4.1:  Children Aged 10-14 in the Labour Force,
per capita GDP< US$1000 ………………………………………...        44
Figure 4.2:  Children Aged 10-14 in the Labour Force,
per capita GDP> US$1000 ………………………………………...        44
Figure 4.3:  Average Incidence of Child Labour, 1989-1999 ………………….         45
Figure 5.1:  Forecast Results for Child Labour and Per Capita GDP,
selected countries ………………………………………………….         57
Figure 5.2:  Forecast Child Labour Trend, selected countries ………………….        58       1
CHAPTER 1
INTRODUCTION
 In the year 2000, the International Labour Organization (ILO) estimated that
there were over 200 million child labourers worldwide.  Of these 200 million, 180
million are suspected to be engaged in the worst forms of child labour, which can be
summarized as, ‘those activities . . . [that are] inexcusable under any circumstance and
must be eliminated without delay” (ILO, 2002: 1).  That is to say, approximately 90 per
cent of working children are engaged in labour that is, by nature, detrimental to their
psychological and physical well-being.  These include,
•  labour that is performed by a child who is under the specified minimum age for
that type of work,
•  hazardous work and,
•  children engaged in types of child labour to be abolished.
1
 The elimination of the worst forms of child labour has come to be recognized as
crucial for sustainable social and economic development.  By 1 February 2002, 115
countries had ratified the Worst Forms of Child Labour Convention No. 182.  The
convention recognizes that those forms of child work defined as hazardous to a child’s
well-being or unconditionally at odds with a child’s basic human rights should be
absolutely prohibited by any person under the age of 18 (ILO, 2002: 11).
 Children remain economically active in virtually all economic sectors: in
industry, agriculture, the informal sector and in the household.  The term ‘economic
activity’ refers to the broad nature of children’s work.  It includes all productive
activities, household or market-oriented, undertaken by a child in a paid or unpaid
capacity.  In this study, these general forms of economic activity will be referred to as
                                             
1
 This includes all economically active children aged 5-14, except those aged 12-14 engaged in light
work, as well as children aged 15-17 engaged in hazardous work.   2
child labour, to be distinguished from the unconditional worst forms for abolition
defined as slavery, trafficking, bondage, forced recruitment in armed conflict, other
forms of forced labour as well as various illicit activities (ILO, 2002: 9).  
 The data suggest that child labour and poverty are inextricably linked.
2
    At  the
aggregate level, countries with per capita GDP below US$1000 (adjusted for purchasing
power) have child labour force participation rates as high as 40 to 60 per cent, compared
to less than 10 per cent for countries with significantly higher per capita GDP (World
Development Report, 1989-2001; Yearbook of Labour Statistics, 1989-1999).  However,
current data on the decline in child labour force participation over time is less marked.
In many low income countries, as national incomes have increased over time, we have
observed a substantial decline in child labour.  Although, a significant number of lesser
developed countries have experienced virtually no change, and in several cases an
increase in its incidence between 1989 and 1999.
 Since Basu and Van (1998), the theoretical literature on this subject has grown
substantially.  Most of the research has concentrated on the role of economic growth in
reducing the economic dependence of households and firms on children.  At the
household level, parents send their children to work out of economic necessity.  The
supply of children to the labour market, in turn, perpetuates a cycle of poverty in two
ways,
1. By interfering with the accumulation of human capital, child labour reduces the
adulthood labour market productivity of child workers, thereby discouraging
economic growth and development.
2. By depressing adult wages, child labour results in households becoming more
reliant on children as income earning assets.  
 Our objective is to explain how, at a low level of development, the initial phase
of economic development may result in a decline or a rise in the incidence of child
labour.  We recognize the positive correlation between poverty and child labour.
Theoretically, the rate of child economic activity should decline with income.  The
                                             
2
 For instance, see Krueger (1996).   3
empirical evidence supporting this is substantial.
3
  The implication is such that policies
aimed at stabilizing current and future household income will help to reduce the need
for parents to send their children to work.  However, in poor settings, we may observe a
positive relationship between child labour and income.  This may be an indicator of the
significance of physical child labour and/or child labour earnings to the survival of
households.  As the variance in expected household income increases, the number of
gainfully employed children could increase as well.  Further, we suggest that child
labour is not necessarily a facet of poverty but rather a means by which households can
improve their standard of living by taking advantage of the labour market opportunities
resulting from a greater demand for all labour.  Poverty simply ensures a continuous
supply of children to the labour market.  As household incomes grow and become more
stable, families can more easily satisfy their basic consumption needs and are less
dependent on the labour (earnings) of their children.  They will find that they are better
able to invest in the education of their children.
 It is well documented that in the long run, economic growth will reduce the need
for child labour.  It is also possible that these very forces are responsible for the initial
increase in the incidence of child labour in development.  We recognize the importance
of long run economic forces in curtailing the phenomenon; our concern is with how the
nature and the scope of child employment changes at different stages of development.
The historical experience of advanced, industrial countries suggests that in the early
stages of development, child labour may rise with national income.  Thus, the effect of
economic development on child employment is indefinite.  The question is of an
empirical nature.  
 The primary objective of this study is to estimate the effect of economic growth
and development, as measured by per capita gross domestic product, on the incidence of
child labour.  We hypothesize that at the aggregate level, there may exist an inverted-U
shaped, Kuznets-like relationship between a country’s child labour force participation
rate and its per capita income.  Using panel data methodology, econometric analyses are
carried out on data from 75 developing countries for which child labour is welldocumented, over the period 1989-1999.  The objective is to determine the validity of
                                             
3
 See Anker (2000).   4
the hypothesis by examining the empirical evidence.  Projections are made regarding
future child labour levels.  More specifically, we predict the number of years required to
reach 10 per cent child labour, as defined by the child labour force participation rate; we
also determine the growth rate required to reach 10 per cent child labour by the target
date, 2029.  Forecasts for future primary school enrollment ratios are also made in an
attempt to evaluate the effectiveness of current policies or lack thereof.  
The remainder of this thesis is organized as follows.  We emphasize the
relevance of our contribution by providing a review of the theoretical and empirical
literature on child labour in economic development in Chapter 2.  In Chapter 3, we
introduce the theoretical framework for our hypothesis by presenting a model of
household choice.  Chapter 4 discusses the hypothesis, the estimation procedure and the
data.  In Chapter 5 we present our results, followed by some concluding remarks in
Chapter 6.   5
CHAPTER 2
LITERATURE REVIEW
In this chapter, we discuss the role of children as economic assets and the nature
of children’s work at different stages of development.  We begin with section 2.1 in
which we characterize children’s economic value at a low level of development.  This is
followed by a discussion of the effect of a change in household wealth on the demand
for child services in section 2.2.  We conclude by presenting a summary of the British
and American historical experience in section 2.3.
2.1 On the Role of Children in Development
There are three main categories under which the pecuniary and non-pecuniary
economic benefits children provide to their parents fall.  Children are a source of oldage security, a source of insurance against the risk of income instability and children
provide a source of labour to their parents.
2.1.1 Old Age Income Support
Children are valuable when at least one of the following circumstances hold,
•  property rights are insecure,
•  credit and insurance markets are imperfect,
•  private and public welfare institutions are absent or inefficient,
•  there does not exist a well-developed labour market for women, particularly in
rural areas.
It is the perception of parents that there exist no other reliable means of support in oldage.  Under these circumstances, where mature adults rely on their adult children for
financial security, old-age support is expected to be an important motive for fertility.   6
2.1.1.1 Children as an Alternative to Land Ownership
Children, by virtue of their culturally and economically defined role, can be
relied upon to smooth the consumption of their parents when property rights are
insecure.  Although as a substitute for children, land may not be a perfect security asset.
First, there are some things children can provide that land cannot: health care, physical
and emotional assistance, as well as psychic benefits.  Second, land is costly to
maintain, it requires management and is highly labour intensive.  Weather induced
environmental risks and the associated fluctuations in agricultural yields result in a high
variance of expected income.  Nonetheless, we would expect land ownership to reduce
parental reliance on children as a source of insurance against future disability.
4
 
In the context of insecure property rights, parental dependence on children may
be as significant as would be the case for landless parents.  Nugent and Gillaspy (1983),
and DeVany and Sanchez (1978) find that in the ejidal system of farming, whereby
farmers are granted usufruct rights over the land as opposed to ownership, increasing
ejidal share tends to raise fertility.  Uncertainty over future land use results in high
fertility as a means of retaining control over the land.
2.1.1.2 Imperfect Capital Markets
5
Particularly in rural areas, in the case of an adverse shock to current agricultural
yield, farmers would like to borrow in the current period against future expected
income.  Borrowing in a bad season and saving in a good one allows farm families to
smooth consumption over time.  This will depend on the agent’s ability to borrow.
Unless agents have access to credit by means of sufficient collateral, it is unlikely that
parents can save for their consumption needs in old age.  When there are more reliable
means of consumption smoothing and accumulating assets for use in old age, children
are not as vital for old-age security purposes.  Thus, children are valuable assets in the
context of imperfect credit and insurance markets as a result of,
                                             
4
 The most notable theoretical papers on this subject are Neher (1971), Cain (1983), and Nugent (1985).
Cain (1985) provides empirical confirmation of this.
5
For a complete discussion and review of the literature see Portner (2001), and Rammohan (2001).   7
•  imperfect information on the part of creditors to distinguish the riskiness of
potential clients,
•  a lack of collateral, which restricts the credit options of the poor, who must then
rely on informal sources of credit.
2.1.1.3 The Absence of Welfare Institutions
The development of effective, equitable social security systems can reduce the
reliance of parents on their children as providers of old-age security, and reduce the
demand for children.
6
  If attractive alternative sources of old-age support are available,
the pension motive for fertility will decline.
2.1.1.4 The Absence of a Well-Developed Women’s Labour Market
Where opportunities for women’s employment are not well-developed, the oldage security motive is likely to play a larger role in the household fertility decision.
This is particularly true in rural areas where women’s primary responsibilities are child
rearing, household duties and general subsistence activities.  In this regard, women may
rely on their husbands for economic support and subsequently their children (Nugent,
1985).
The greater the share of the old-age support parents expect from their children,
the greater will be the demand for children to satisfy this motive.
7
  In the context of high
risk settings – high infant and child mortality, uncertainty regarding child loyalty and
the possibility of child default – additional pressures are placed on the household
fertility decision.  When alternative means of saving or investing are unavailable, it is
                                             
6
 Cox and Jimenez (1992) provide empirical confirmation of this in their study of Peru.
7
 For empirical confirmation of this, see Jensen (1990).   8
rational that fertility will remain high in order to guarantee enough surviving, loyal
children to satisfy this need.
8
2.1.2 Insurance Against Income Instability
In the developing world, many families are concerned with consumption risks.
General weather-induced environmental threats such as drought and flooding, property
risks, the possibility of unemployment and illness, and other sources of risk can threaten
a household’s normal consumption stream.  In the absence of efficient insurance
markets, alternative sources of risk coping mechanisms, such as child labour income,
are valuable.
Parents’ fertility decisions can be influenced by the presence of such concerns.
A larger household can spread the risk over more members.  Cain (1981) explores this
issue in his study of three Indian villages and one village in Bangladesh.  He finds
children to be redundant as a source of insurance when alternative means of adjusting
are available.  In harsh risk environments and when the mechanisms of risk adjustment
are ineffective, the insurance value of children acts as an incentive for high fertility.
2.1.3 Children as a Source Labour
 
Children serve as a source of wage labour; in addition, children contribute their
time to household production and maintenance.  The potential importance of children’s
labour and/or their income transfers to the household will be most significant in poor
settings.  
2.1.3.1 The Vicious Circle Hypothesis
In resource-based subsistence economies, where natural resources are managed
as common property, overgrazing, overstocking and exploitation may be a problem.
                                             
8
It should be noted that the types of support children provide range from money remittances to more
time-intensive services.  For instance, aged parents may live with their children.  Thus, children are
expected to satisfy a range of parental needs.     9
When traditional systems of checks and balances that respect the regenerative capacity
of the land fail or begin to erode, communities may be faced with the depletion of their
natural resource base. This is so because the private cost of using these resources falls
short of the full cost.  The polluter absorbs the private cost – the time required to collect
the good – but the full cost is borne by the entire community in terms of poor soil and
water quality, fewer grazing areas and a reduction in firewood availability.
9
If children contribute to the household by collecting resources from common
property sources, physical scarcity of these resources implies that children devote more
time to collection activities.  This could potentially increase the demand for children.
Greater population pressures on the natural resource base will, in turn, further accelerate
the rate of environmental deterioration, increasing the demand for children and so on.
This is known as the vicious circle hypothesis (Nerlove, 1991; Dasgupta, 1993;
Dasgupta and Maler, 1994; Dasgupta, 1995).
10
When children’s tasks are primarily collection and grazing activities, as well as
herding and tending to livestock, natural resource scarcity increases the marginal value
product of children’s time relative to adult’s time.  If the substitution effect dominates
the income effect, worsening environmental conditions will increase the demand for
children.  
. . . .as forests recede up the mountain sides, parents may perceive a
greater benefit of having an additional child to gather firewood . . .
lower quality environments may be associated with a greater livestock
component in total production . . . children may have a comparative
advantage over adults in tending to livestock in contrast to the heavier
labour of planting, tilling and harvesting crops.  Thus, environmental
deterioration may well enhance the marginal productivity of children,
at least relative to total family productivity (Nerlove, 1991: 1341).
Based on this principle, where the polluter does not pay the full cost, parents do
not have to pay the full price of child rearing.  Rather, they share those costs with the
community.  If shared access to community resources continues, where traditional
                                             
9
 The Tragedy of the Commons, a term originally used by Hardin (1968), essentially describes the nature
of this phenomenon.
10
 For empirical confirmation of this see Cleaver and Schreiber (1994), as well as Filmer and Pritchett
(2002).  It should be noted that the probability of the occurrence of this phenomenon may be very small.
There are several empirical studies that contradict the vicious circle argument; McCann (1999) is an
interesting example.  10
methods of control are ineffective, parents may produce too many children which will
place pressure on the environmental resource base.  As community resources are
depleted, the household is provided with an incentive to expand and further depletion of
the environmental resource-base ensues.
11
2.1.3.2 Unpaid Household Work
Particularly among rural families, children are economic assets in developing
countries.  Parents in peasant societies are less concerned with the child rearing costs.
Rather, if the net economic value of children – equal to the economic contribution of
children less their consumption costs – is increasing, the demand for children could
potentially increase.  
Among farm families, children maintain their high economic value the greater
the abundance of land.  That is to say, for small-scale and subsistence farming, the
marginal productivity of child farm labour is increasing in family land size.  The most
prominent empirical confirmation of this is found in Rosenzweig and Evenson (1977),
and Levy (1985).  In their study of rural India, Rosensweig and Evenson (1977)
empirically test the importance of children’s economic contribution on fertility.  They
find land size to be complementary with child labour in that it had a positive and
significant effect on fertility.  This may also be indicative of the positive income effect
on fertility.  At a low level of development, initial increases in income may positively
affect fertility behavior.
More land implies more wealth and increases the potential for economic
activity.  Farmers who cannot afford to hire labour will rely on family labour,
particularly those least mechanized.  The technology for non-market production and
subsistence farming requires only a minimum level of human capital.  Reluctantly,
children are ideal labour inputs in these sectors.  Having more children is a means of
increasing household production.  Although children cannot be expected to cultivate
                                             
11
 However, enclosure of the local commons is not necessarily a solution to the problem. The
privatization of natural resources is often difficult to define and enforce; privatization could leave the
poor at the mercy of landowners, an even greater disadvantage.  Humphries (1990) addresses this issue in
her study of Great Britain.  Also, see Shiva (1993).  11
crops, they are well-suited to the less demanding tasks, thereby freeing adult labour for
the more strenuous activities and for market work.  This is especially true for mothers.
As markets for women’s work outside the home become more developed,
children assume a greater responsibility for household tasks such as maintenance and
child care.  Thus, for sufficiently large families, the early stages of development could
potentially imply greater market activity for all members and greater household
productive activity for children.  It follows that households with more children will be
economically more successful (Nag et al., 1978).  In his study on the economic
activities of children in rural Bangladesh, Cain (1977) finds that high fertility is an
economically rational choice for parents.  Cain estimates that by the age of 12, boys
become net producers and compensate for their cumulative consumption by age 15.
2.1.3.3 Children as Income Earning Assets
Where the economy allows for children’s participation in the workforce, greater
market potential for children will also have an effect on fertility.  Children’s labour
contributions can be an important component of household earnings, amounting to one
third of household income in some cases (Lansky, 1997: 233).   If there is a child labour
market (in agriculture, domestic service, industry and the informal service sector) in
which children receive a wage, parents may bear more children.  This is so because the
net value of child rearing is higher.  Several studies confirm this relationship that
fertility is higher in high child wage regions.  Further, they assert that those variables
positively correlated with returns to child labour (such as agricultural productivity and
the size of agricultural land holdings) have a positive effect on the demand for
children.
12
  An increase in the returns to child labour will increase the supply of child
labourers and raise fertility.
Decisions on family size and child’s time use are jointly made.  The importance
of this relationship is highlighted in Dessy (2000).  Dessy argues that the existence of a
                                             
12
 For empirical confirmation of this see Rosenzweig and Evenson (1977), Rosenzweig (1978), Cain
(1985), Levy (1985), and Rosenzweig (1990).  It should be noted that these economic reasons for having
children do not justify having an indefinitely large number of children as it remains unclear whether a
child’s labour contributions over time compensate for their cumulative consumption.  See Cain (1977),
and Cain (1982) for a discussion of this.  12
child labour market would lower the relative cost of children, which in turn, may raise
the total fertility rate above the level that would have prevailed in the absence of an
earnings potential for children.  Fertility is responsive to these economic incentives.
When child labour is present, the net economic value of children is determined by the
time and commodity costs of child rearing (consumption expenditure and forgone
parental income) as well as the associated benefits (child labour earnings, non-market
production, domestic help, insurance against risk, as well as old-age security).
2.2 Wealth
Often, a child worker’s role in maintaining family income above the poverty line
is significant.  In their study of child labour in India’s urban informal sector, Sharma
and Mittar (1990) found that when child labour income is included, 22.2 per cent of
households fall below the poverty line.  When child labour income is not included in the
sample, 77.8 per cent of households fall below the poverty line (for households with 3
to 4 persons).  Parents send their children to work out of economic hardship.
The connection between child labour and poverty is empirically welldocumented.  In his study of Vietnamese agriculturalists, Edmonds (2002) finds that in
the poorest households, child labour is fairly inelastic with respect to per capita
expenditure.  He finds a flat or increasing relationship with per capita expenditure.  This
is consistent with the significance of child labour income to the survival of households
for households below the poverty line.  Once a threshold level standard of living is
obtained, around 2100 calories per day, child labour begins to decline with expenditure.
Similarly, Swaminathan (1998) presents a case in which high economic growth in the
Bhavnagar, Western India, has been characterized by the persistence of and an increase
in the incidence of child labour over a fifteen year period.
13
Land ownership and other physical assets are often associated with higher
fertility among agricultural populations, particularly among small-scale farmers.  Less
mechanized farming is more labour intensive.  Farmers who rely on their own family’s
                                             
13
 Some of the most prominent studies of the relationship between child labour and poverty can be found
in Rosenzweig and Evenson (1977), Rogers and Standing (1981), Basu and Van (1998), Eswaran (2000),
and Ray (2000).  13
labour will have larger families.  Under such circumstances, an increase in income is
not offset by an increase in the opportunity cost of parent’s time as it is not
accompanied by an increase in adult wage rates or greater adult education.  Thus, the
demand for children can be expected to increase in part due to a wealth effect (with
higher wages farm families are able to afford larger families), but largely due to the
greater opportunity for child employment on the farm and the higher return to child
labour.  The marginal productivity of all household members increases.  This has been
observed in several agricultural societies in India, Bangladesh, Iran, Nepal, The
Philippines and Thailand (World Development Report, 1984).
14
2.3 The Economic History of Child Labour
“…under the early factory system, the employment of masses of children was the
foundation of industry” (Hammond and Hammond, 1978: 144).
2.3.1 Early Industrialization and the Employment of Children
To understand the nature of children’s work in the context of the British and
American experience, we refer to the historical economic literature in which
development is considered to be the movement from a pre-industrial to industrial to
post-industrial economy.  For the remainder of this study, we assume that this
movement from a low level of development to a more advanced stage is characterized
by a shift away from an economy in which production is primarily within the household
for consumption within the household, towards an economy which produces for the
market.  As such, we have defined national income per capita as being a sufficient
indicator of the level of development.  It is important to emphasize here that this may, at
first, appear to be a narrow definition of what constitutes development as we have
neglected both the structure of the economy and the cultural aspects entirely.  However,
for the purpose of this study, this definition will suffice as our objective is to show that
in areas of high output growth, the incidence of child labour may also be high.  The
                                             
14
 There is also some historical evidence from Canada’s early settlement period; see McInnis (1977),
especially Table 5.    14
question then becomes one of identifying the variables which help to explain this
phenomenon.  We will come back to this question in chapter five.
In today’s advanced industrial economies, industrial development was the major
factor in the initial increase in the incidence of child labour.  For instance, in both the
United States and the United Kingdom, women and children composed a significant
proportion of the manufacturing labour force during the industrialization period.  After
the American civil war, the US began a program of rapid industrialization, 1870-1930.
The number of gainful workers aged 10-14 grew during the period 1870-1900, peaking
at 1.75 million children in 1900, followed by a sustained decline.  This is illustrated in
Table 2.1 below.
     Table 2.1   Child Labour Force Participation Rates for the United States, 1870-1910
Gainfully Employed Children aged 10-14
United States, 1870-1910
   
Year Activity
Rate (%)
Real GNP
a
1870 16.00 23.1
1880 19.60 42.4
1890 21.40 52.7
1900 21.70 76.9
1910 17.80 120.1
   
                                a)    GNP at market prices is expressed in millions of dollars, 1958.
*Child employment estimates are taken from US Bureau of the Census (1997), series D75-84.
Historical estimated of GNP are taken from Kendrick and Kuznets, published in Kendrick
(1961).
Similarly, in the United Kingdom, the earnings of women and children became
an important component of family earnings.  Although it is unknown whether children
worked more in the pre-industrial or industrial period, economic historians agree that
during the early industrial period, children’s share of the workforce in many key
industries grew significantly.  In other words, the nature of children’s work changed
with the expansion of the factory system.  Not only were children performing their
household tasks and contributing their time to household production, but as the
economy began to shift from production for consumption within the household to  15
production in the market, they became significant wage earners.  In industrial areas,
children’s earnings were a central component of family income.  Refer to Table 2.2 for
some descriptive statistics.
In addition to these data, Nardinelli (1990) presents some statistics specific to
the textile industry.  In the textile industry alone, the number of children aged 10 to 13
employed in the UK, declined steadily from 1835-1860.  There it began to rise, peaking
in 1874 when the number of children aged 10 to 13 working in English and Welch
textiles reached 122,000 (Nardinelli, 1990: 4).  Other interesting results are presented in
Horrell and Humphries (1995).  In their study of the family economy during the British
industrial revolution, Horrell and Humphries found that the number of children working
in the labour market increased, and that the age of entry into the labour force decreased.
Table 2.2   Child Labour Force Participation Rates for England and Wales, 1850-1910
Gainfully Employed Children aged 10-13
England and Wales, 1850-1910
   
Year Activity
Rate (%)
Real GNP
a
1850 28.30 596
1860 28.60 791
1870 26.30 1,021
1880 19.00 1,379
1890 21.10 1,615
1900 16.90 2,032
1910 14.30 2,328
   
a) Gross National Product (GNP) at market prices is expressed in millions of  
pounds, 1900.  These data are for the United Kingdom, including Ireland.
*Child Employment estimates are taken from Nardinelli (1990); historical estimates of GNP are
taken from Chesnais (1992).  
2.3.2 The Child Labour Market
2.3.2.1 The Supply of Child Workers
 
From the supply side, child employment in key sectors, such as mining and
textiles, was the result of the desire of households to improve their standard of living.   16
In this case, child labour is not necessarily a facet of poverty.  Rather, sending children
to work is a means by which low income families could supplement household income
by taking advantage of the wage opportunities resulting from a greater demand for all
labour.  Although the nature of children’s work during this period is debatable, the
current consensus is such that the incidence of child labour increased during the early
stages of industrialization.
15
2.3.2.2 The Demand for Child Workers
The historical experience of today’s advanced industrial countries suggests that
the structure of demand determines the nature of children’s work.  Under the early
factory system, children’s work was crucial to the success of certain key industries.
Children were found in labour-intensive sectors, limited to low-skill, menial and often
dangerous jobs.  Their labour was cheaper, and could potentially drive down adult male
wages.  As children are substituted for adult male labour, the wages of adult males fall
resulting from a decline in the demand for their services.
Thus, the supply of child labour reduced the need for technological
advancement.  An example of this would be the rural, labour-intensive fruit and
vegetable canneries of California and Maryland.  Accustomed to family and child
labour, these canneries invested only minimally in equipment and plant facilities
compared with urban canneries that completely displaced child labour with full
mechanization (Brown et al., 1992).  In certain industries, children were ideal.  They
were cheap to employ, more docile and easily coerced.  
Goldin and Sokoloff (1982; 1984) describe early American industry as
characterized by a high price for adult male labour as a result of greater agricultural
mechanization.  The initially low relative productivity for female and child labour in
agriculture was instrumental in the disproportionate employment of women and
children in the early textile factories of the American North-East.  Firms substituted
relatively cheap female and child labour for adult male labour.  Their employment was
                                             
15
 The literature on the youthfulness of workers in the first century of British industrialization is massive;
see Thompson (1963), Pinchbeck  and Hewitt (1973), McKendrick (1974), Hammond and Hammond
(1978), and Nardinelli (1990).  17
characterized by increased mechanization in certain industries and greater organization
of labour in others.  Consequently, as industrialization proceeded, the relative wages of
women and children increased with increasing productivity.  Correspondingly, the
labour force participation of these groups rose.  As the wages of women and children
began to approximate those of adult males, firms began to substitute adult male labour
for female and child labour.
2.3.2.3 Changing Structure of the Child Labour Market
The reduction in the supply of child workers was a result of an increase in
family incomes and the declining demand for children is seen as the result of
technological progress and greater capital intensity.  Children’s wages were no longer
crucial to the success of these industries.  The nature of production required a more
highly skilled workforce, thereby altering the age structure of the labour force.
Similarly, in the United Kingdom, the age structure of the labour force had
changed by the late nineteenth century.  Children had little to no role in the new
industries of the era, namely the chemical industry and electricity (Cunningham, 2000:
412).  Children found a demand for their services as messengers and in newspaper
delivery.  This shift was by and large a result of the same long run economic forces.
Technology changes increased the age of entry into the workforce and the
importance of children’s economic contribution to the economic well-being of the
family declined as a result of rising adult male wages.  As standards of living began to
rise, the rational choice was to invest in the education of each child to maximize family
income when each child eventually enters the workforce with the prospects of finding a
better job.  A decline in child mortality rates resulted in fewer births, in part because the
necessity of having many children to compensate for the high risk of child death
diminished.  In addition, when the probability of child survival is high, returns to human
capital become important.  This follows Becker’s family strategy explanation for a
decline in child labour which will be discussed in Chapter 3.
The relative return to investing in education may have begun to exceed the
return from children’s market employment.  More industrial technologies depreciate the  18
value of unskilled labour.  In addition to the increased opportunity cost of parents’ time,
compulsory schooling and factory legislation implied a higher cost of having children.
2.3.3 Child Labour Legislation and Compulsory Schooling
Child labour legislation is another means of controlling the nature of children’s
work as well as the hours they work, provided they can be effectively enforced.
Historical evidence suggests that a high incidence of child labour can persist in the
presence of child labour laws (Weiner, 1991).  In the United States, state laws were
largely ineffective due, in part, to poor enforcement and disorganization.  Legislation
proved effective only once child intensive industries had already begun to decline
(Sanderson, 1974).  
Goldin (1979) tests for the importance of these laws in curbing the employment
of children in the US.  She found the laws to be ineffective; a rise in the father’s wage
was found to reduce the probability of child participation in the labour force.  In a
related study, Moehling (1999) looks at minimum age legislation in the manufacturing
industry in the US.  She finds that minimum age restrictions did not limit the
occupational choices of children in 1900.  Further, she finds that compulsory school
attendance laws increased the likelihood of school attendance for children who would
have otherwise been at home; they had little effect on children who worked in the
labour market.  On the other hand, household income and wealth were found to be
strongly correlated with the likelihood that a child worked.
In England, while it appears as though the Factory Acts contributed to
improving the conditions of children employed in factories, rising family income was
instrumental in maintaining the long run decline in child labour.
16
  Adult wages below a
threshold level will ensure a supply of child labourers, suggesting policies that raise the
wages of adults relative to children are more likely to reduce the supply of child
workers.
17
                                             
16
 For a more complete discussion of the British Factory Acts see Nardinelli (1990).
17
 Some of the relevant and notable policy papers include Grootaert and Kanbur (1995), Basu (1999),
Baland and Robinson (2000), Dessy (2000), Altman (2001), and Hazan and Berdugo (2002).  19
The most effective and easily enforceable child labour law is compulsory
schooling legislation.  There is evidence in Britain that the introduction of compulsory
schooling in 1880 was associated with a decline in child labour force participation, the
reduction in hours worked by children and a rise in the average age of labour force entry
(Cunningham and Viazzo, 1996).
2.4 Chapter Summary
In this chapter, we have presented a discussion of the role of children in the
household at different stages of development.  The value of children, and in turn, the
demand for children, will be determined in part by household wealth.  The ability of
households to smooth consumption over time, and the presence of effective, equitable
public welfare institutions are also important determinants.
Drawing upon the historical experience of advanced industrial countries, both
legal restrictions and economic factors played a role in reducing child labour, although
legislation appears to have been less significant.  The process of industrialization may
have initially increased the demand for and the scope of children’s work, however the
long run economic impact of the industrial revolution resulted in its eventual
elimination.  Thus an increase in the aggregate number of child workers is expected to
be transitory.
Based on the empirical evidence of Edmonds (2002) and Swaminathan (1998),
as well as the American and British historical experience, there is reason to develop a
theoretical model.  In Chapter 3, we discuss the household fertility decision in the
context of Becker’s model of child demand.  Taking into consideration the potential for
a child labour market, an extended version of the model to include the household time
allocation decision is presented.   20
CHAPTER 3
THEORETICAL FRAMEWORK
Thus far, we have presented a theoretical overview of the possible direction of
the relationship between child labour and national income.  We have suggested that the
incidence of child labour may increase or decrease with income depending on the level
of development and the economic relationship between the parents and the child.  In
this chapter, we begin by discussing the net cost or net economic value of children.
Both the money costs as well as the time costs are evaluated and compared at different
stages of development.  We consider the role of such costs in the household fertility
decision.  We present a model of household choice.  First, we discuss the mathematical
model of child demand introduced by Becker which essentially illustrates the case for
an advanced stage of development.  This is followed by an extension of the model to
incorporate child time use in an effort to explain the decision faced by households at a
lower level of development, where there exists an earnings potential for children.  The
objective of this chapter is to illustrate the changing valuation of children at different
stages of development.
3.1 The cost of raising children in a developing country
Relative to advanced industrial countries, the cost of raising children in a
developing country is low as a result of the low money and time costs.  The price of
housing and the price of child rearing inputs are relatively low.  For instance, in more
economically isolated areas where market systems are not fully developed and where
transportation costs are high, child rearing inputs, such as food, clothing and shelter are
locally produced and relatively cheap.  The time cost to parents refers to the cost of the
time spent raising children, and in particular, the value of the mother’s time.  Therefore,  21
the opportunity cost of child rearing primarily refers to the mother’s forgone earnings
and leisure, as well as the lost opportunity to accumulate further education.  A low level
of development is characterized by low human capital and thus, a low level of adult
wages, especially for women.  In addition, the cost of schooling per child is
hypothesized to be high due to the high economic value of children and hence, the high
opportunity cost of investing in a child’s schooling (Becker and Murphy, 1990).
In economies with the above features, increasing income may not imply
declining fertility.  An economy at an early stage of development may be characterized
by a positive relationship between income and fertility.
18
  The low money cost of child
rearing inputs coupled with the low opportunity cost of child rearing perpetuates a high
fertility rate, especially when children are economically active.  At a low level of
development, where the main cost to raising children is the money spent on basic child
rearing inputs, the demand for children will be higher.
19
 
If children’s contribution to the family is significant, the net cost of children is
further depressed.  As discussed, children function as security against future disability,
they perform household tasks, and they may work in the home production sector or in
the market.  When children’s time has economic value, the net cost of children is lower
relative to an economy in which children have no earnings potential, and the total
fertility rate may be higher.  The low cost of child rearing coupled with the high
productivity of children may result in a large family size as the net cost of children is
low.
net cost of children = (present value of expected money cost + present value of
women’s time used to produce and rear children) – (present value of expected
money return + present value of child time services in the home)
At an advanced stage of development, the net cost of raising children is high.
Children are a consumer durable, therefore we assume that children have some other
                                             
18
 This follows directly from Malthus who predicts that the demand for children is highly responsive to
changes in family wealth.  However, Malthus refers to households as being able to afford more children,
higher fertility rates are not the result of households needing more children to survive.
19
 The money cost of child rearing inputs tends to be low in developing countries, see Mueller (1982).  22
intrinsic value that they provide to their parents.
20
  At a very low level of development,
we would expect the net cost of children to be negative.  Children are consumer as well
as producer durables, therefore families receive income or labour from them, and the
money cost of raising children may be very low.
In the long run, with economic development, market production methods
become less compatible with child skills, strengths and abilities.  From the supply side,
children’s contribution to the household becomes less significant and the cost of raising
children begins to rise.  With increases in the rate of return to investment in human
capital, greater market opportunities for women which increase the opportunity cost of
women’s time, and the higher price of child-related goods, there will be pressure for
fertility to fall.  Families substitute away from having many children to investing more
in each child.
3.2 Wealth revisited
The Malthusian theory of population change essentially ignores the quality
aspect of child demand.  Regardless, it is important in that Malthus predicts the high
responsiveness of child demand to changes in income in the early stages of
development (Malthus, 1973).  This low level of development is characterized by a high
birth rate, a high death rate and low per capita income.  An abundance of historical
evidence from advanced industrial countries confirms this hypothesis, particularly with
respect to the rural experience (Knodel, 1974; McInnis, 1977).
Small and middle size farms tend to rely more heavily on manual labour and are
usually family operated.  Greater wealth will increase the economic value of children.
Within this range of farm size, it is expected that fertility will increase.  Large-scale,
commercial farming requires mechanization or an even greater amount of labour, likely
non-familial.  Consequently, the benefit of additional children, beyond this range of
farming is negligible.
                                             
20
 What Becker (1976) terms ‘psychic benefit.’  23
The rural example helps to illustrate the circumstance in which parents cannot
afford to have their children not work.
21
  Beyond a certain income threshold, parents
buy the leisure of their children and withdraw them from the workforce.  However,
below this threshold parents accept the fact that their children must work.  
Parents are not less concerned about the welfare of their children; on the
contrary, parents wish to maximize the quality of their children given the available
resources, just like their wealthier counterparts.  Rather, the costs associated with not
having their children work are too high.  As such, we would expect income elasticity of
child demand to increase with income.  Having a child not work can be thought of as a
commodity or a luxury good that is purchased once a certain income level is attained.
The hypothesis is that when income per capita is low, the incidence of child
labour may grow more rapidly and is potentially an increasing function of per capita
income.  When per capita income is high, the reverse is true, child labour is a
decreasing function of per capita income.  The result is a Kuznets curve or an invertedU shaped function.
As income increases, the variance in expected income increases which may
increase the supply of children to the labour market as well as children’s contribution to
family earnings.  At this stage of development, there is a greater demand for all labour;
in order to keep costs down, employers in key industries search for a cheap source,
namely children.  This high demand for child labour is perpetuated by poverty which
ensures a continued supply of children to the work force.  Children may also be more
productive in the non-market sector and their participation in this sector may increase as
well.
3.3 A Model of Household Preference
3.3.1 The Quantity – Quality Interaction of Child Demand
The negative relationship between wealth and fertility that is observed at a more
advanced stage of development is explained by the quantity-quality theory of child
                                             
21
 Basu (2002) refers to this as the ‘luxury axiom’.  24
demand, formalized mathematically by Becker (1976; 1981).  Declining fertility with
increases in income is essentially an indication that the price of both the quantity and
quality of children is increasing, where the child quality component encompasses all
aspects of child quality such as, health and nutrition, education, safety and stability.
Assumptions:
1. Child mortality rates are so low that the effect of a change in income on child
survival is negligible.
2. All children in the same family have the same quality and that quality is fully
produced by each family with its own market goods.
Features of the model:
1. The shadow price or marginal cost of any commodity includes the money cost
of the goods used to produce the commodity as well as the time cost in
production of that commodity.
2. The shadow price of children with respect to quantity [the cost of an additional
child, holding quality constant] is greater the higher their quality.
3. The shadow price of children with respect to quality [the cost of a unit increase
in quality, holding quantity constant] is higher the greater the number of
children.
It is this rise in both the shadow price of quantity and quality that help to explain
declining fertility and the elimination of a supply of children to the workforce.
Each family maximizes the following utility function,
U = U ( ,  ,  ) n q Z                                                                                                             (3.1)
The quantity of children is represented by the variable, n,  q refers to the quality
of each child and  Z denotes the quantity of all other commodities, otherwise referred to
as a composite commodity.  If we let p represent the constant cost of a unit of quality,
then  p qn ⋅ is the total amount spent on children.
The shadow price of quantity and quality can be explicitly defined as,
π n
= ⋅ p q is the shadow price or marginal cost of n
π q
= ⋅ p n is the shadow price or marginal cost of q  25
The shadow price of quantity is positively related to  q.  The shadow price of
quality is positively related to n.   An increase in quality is more expensive for a larger n
as the increase must apply to more units.  Similarly, an increase in the quantity is more
expensive for higher quality children as higher quality children cost more.
The budget constraint, bound by household resources, can be expressed as
follows,
I p qn  Zz
= ⋅  + π                                                                                                           (3.2)
where:
I is full income
π z
 can be defined as the cost of  Z
Household income (both labour and non-labour) and the interaction between the
quantity and quality of children will determine the household fertility decision and the
nature of child human capital investment.  Both the high price of child rearing inputs
and the high value of parent’s time contribute to the declining demand for children.
Parents shift from raising a large number of children to investing in the quality of a few.
The Lagrangian function for utility maximization subject to the budget
constraint can be written as,
L U n q Z  p qn Z I max z
= − ⋅ + − ( ,  ,  )  [  ] λ π                                                                       (3.3)
where,  λ is the marginal utility of money income
For an interior solution, the first order conditions for maximization yield the
following equilibrium conditions,
∂
∂
λ
λ λπ
U
n
MU p q
MU p q
n
n n
= − ⋅ =
= ⋅ =
0
                                                                                          (3.4)
∂
∂
λ
λ λπ
U
q
MU p n
MU p n
q
q q
= − ⋅ =
= ⋅ =
0
                                                                                          (3.5)
∂
∂
λπ
λπ
U
Z
MU
MU
z z
z z
= − =
=
0
                                                                                                 (3.6)
The equilibrium values can be solved in terms of the shadow prices and income,  26
n d  I = n n q  z
( ,  ,  , ) π π π                                                                                                    (3.7)
q d  I = q n q z
( ,  ,  , ) π π π                                                                                                    (3.8)
Z d  I = z n q  z
( ,  ,  , ) π π π                                                                                                    (3.9)
The empirical evidence confirming a strong negative relationship between the
quantity and quality of children is massive.
22
  The findings suggest that a higher level of
development – higher per capita income – which raises the rate of return to investment
in human capital will bring about a response from parents.  Parents respond to a
reduction in the marginal cost of quality by reducing fertility.  
3.3.2 An Extension of the Becker Model
In this section, we present an extension of the Becker model of general
household production to include child time use.  The model is a continuation of those
hypothesized by Ben-Porath (1973), DeTray (1973), Michael (1973), and Willis (1973).
The origins to this mathematical approach can be found in Mincer (1963), Becker
(1976), and a series of papers collected in Becker (1981).  For simplicity, the dynastic
approach of Becker and Barro (1988), in which parents’ utility depends on the utility of
their children is ignored.
The model is based on the following assumptions,
1) Parents are able to exercise choice over the number of children they have.
2) Households are concerned with the optimal stock of children.  All lifetime
decisions are made at one point on time, the parents’ lifetime.  In such a case, a
one period model will be sufficient to characterize household decision-making.
 We assume that households maximize a utility function composed of a number
of commodities, including both the quantity and quality of children, which require both
time and money as inputs.  That is to say, all commodities consumed by the family are
first produced by members of the household in such a fashion as to maximize household
satisfaction.  These commodities may be produced in a goods-intensive or time-
                                             
22
 The research of Becker (1981) in the United States, Japan, Taiwan and Great Britain has confirmed this
interaction; over time, a large decline in the birth rate has been accompanied by a substantial increase in
the level of schooling.  Other notable papers include Rosenzweig and Wolpin (1980), Rosenzweig and
Schultz (1985), and Rosenzweig and Schultz (1987).  27
intensive manner and can therefore be referred to as activities.  For instance, consider
the activity of child care.  Parents can either purchase child care services or spend the
time required to care for their own children.  
 The child service component,  c, is representative of the fact that parents get
satisfaction from having children.  Not only do children provide some intrinsic benefit
to their parents but they may also contribute their time to the production of these
‘activities’. Children might engage in household production by directly providing
labour to the household; where there is a market for children’s work, they may sell their
time for a wage rate.  Thus, more children and better quality children imply a greater
capacity for households to consume.  
U = U ( , ) Z c                         U U Z c
> > 0 0 ,                                                             (3.10)
where:
c is the stock of child services
Z denotes consumption of a composite commodity
U U Z c
, refer to the first order partial derivative
Each commodity component can be decomposed into the following,
c c q n = ( ,  )                            c c q n
> > 0 0 ,                                                                (3.11)
Z Z x t Z Z
= ( , )                        Z Z x t
> > 0 0 ,                                                              (3.12)
  Recall, q denotes the quality of children and n refers to the quantity of children;
c c q n
, represent the first order partial derivative;  x
z
 denotes the quantity of market
goods required to produce the composite consumption good and  t
z
 is the time required
for production;  Z Z x t
, refer to the first order partial derivatives.
Families get satisfaction from child time services – which include child time
sold to the market to contribute to family earnings and non-market labour – as well as
the quality with which children are raised.  The household is better off with better
quality children.  In addition, with more children the household can acquire more child
time services.  However, utility is constrained by the fact that the quantity and quality of
children are substitutes in consumption.  Parents must choose their desired combination
which will be based on their income and the relative costs of quantity and quality.    28
In addition, each Z commodity has its own production function, which requires
both time and money as inputs.  The more time and money households have the more
market goods they can purchase, the more commodities they can consume and the better
off they will be.  Household members devote some time to produce certain
commodities.  Each household member, for which there is a labour market, sells their
labour for a given wage in order to purchase the market goods required to produce a
given commodity.  Similarly, there are monetary as well as time costs associated with
the production of the child commodity,  c q n ( ,  ) .  The monetary cost of child-rearing
inputs tends to be low, particularly when communities are isolated and self-sufficient;
local communities also bear some of the costs (refer to Chapter 2, section 2.1.3.1 for a
discussion of the vicious circle hypothesis). Nevertheless, child services are also
produced using inputs of market goods and parents’ time,
q q x t = q q
( , )    q q
x t
> > 0 0 ,                                                                        (3.13)
n n x t
n n
= ( , )                n n
x t
> > 0 0 ,                                                                        (3.14)
The variables  xq
 and  x
n
 represent the market goods required for the production
of child quality and quantity, respectively.  Similarly,  tq
 and  t
n
 are the time required to
produce child quality and quantity.  Depending on the characteristics of a particular
household member, wage labour may be significant or insignificant; similarly, the time
devoted to household tasks and non-market production can vary.  For example, the
number of hours adult males spend caring for children may be few, and the amount of
time adult females spend in market work may be insignificant.  Furthermore, young
children are more time-intensive than older children as they require constant
supervision.  In the presence of young children, it is more likely for adolescent girls to
spend a significant proportion of their time caring for their younger siblings (Levinson
and Moe, 1998).
In the context for which this model is formulated, children are a source of labour
and income stability and there may not be a substitute for their services.  In the case of
variable income, this is particularly true when access to insurance and credit markets are
restricted.  Thus, while each family is still faced with the child quality investment
decision, it may be insignificant.  This is further perpetuated by the assumption that in  29
this environment, child schooling, assumed to be a sufficient indicator of child quality,
yields a negligible pecuniary rate of return.  These factors suggest that investment in
each child’s quality is low.
However, as has already been discussed, parents are also interested in having
children to secure their own future consumption needs.  This will, in part, be dependent
on the quality of children, the amount of time devoted to the accumulation of education
and skills as well as the amount of time and resources parents devote to child rearing.
More educated children can command a higher wage.  
Parents are constrained by the tradeoff between the quality and quantity of
children as well as their reliance on children as producer goods.  Therefore, although
parents would like to invest in the quality of their children, family size is crucial to the
survival and success of the household.  As a source of old-age security, the risk of child
default could be just as high for an educated child as an uneducated one.  Further, where
poor health and nutrition and inaccessible medical facilities reduce the probability that a
child will reach adulthood, having many children might be a more rational choice than
investing in a few.
The household is faced with the task of allocating family time, in a single child
household each member is constrained by,
T t  t t t  i m f
i
w
i
z
i
n
i
q
i
= + + +  = ,                                                                     (3.15)
T t t
c
w
c
z
c
= +                                                                                                               (3.16)
The superscript, i, indicates the parent, mother m and father f and c indicates the
child.  The time allocation variables represent the following:  tw
 represents the hours
allocated to the market sector,  t
z
 are the hours spent in non-market productive activity,
t
n
 is the time spent producing children (child quantity) and  tq
 is the time spent engaged
in child rearing (child quality).
This is the total time available exclusive of hours spent maintaining and
accumulating human capital – which may be negligible, and leisure.  In other words, all
time is productive.  Optimal investment in human capital is assumed to be minimal.
The production of children requires some time and money on the part of the mother and
father, as does the quality of children.  It is assumed that children do not engage in child  30
rearing in any capacity.  Thus, the key measure of a household member’s contribution,
and subsequently household utility, is the amount of time spent in productive activities
whether it is market oriented or not.
For a given market wage rate, the model can be expressed in terms of the
household production functions,
max U ( , )  . . Z c s t                                                                                                      (3.17)
Z Z x t Z Z
= ( , )                                                                                                            (3.18)
c c q n = ( ,  )                                                                                                                  (3.19)
q q x t = q q
( , )                                                                                                              (3.20)
n n x t
n n
= ( , )                                                                                                              (3.21)
and the following resource constraints,
I w t  w t  w t  v  p x  p x  p x n
m
w
m f
w
f c
w
c
= + + + = + + ⋅ Z Z  n n  q q
                                            (3.22)
T t  t t t  i m f
i
w
i
z
i
q
i
n
i
= + + +  = ,                                                                     (3.23)
T t t
c
w
c
z
c
= +                                                                                                 (3.24)
t t t t Z z
m
z
f
z
c
= ( ,  , )                                                                                                          (3.25)
t t t t q q q
m
q
f
= ( ,  )                                                                                                           (3.26)
t t t t
n n n
m
n
f
= ( ,  )                                                                                                           (3.27)
The variables,  p p p Z n q
, , are the price of market goods, the price of child
quantity and child quality inputs, respectively;  w w w
m f  c
, , is the wage of the mother,
father and child.  In addition, v refers to the family’s non-labour income or household
wealth, which includes money transfers, property income and income earned from the
sale of home produced goods.
23
Equations 3.22 – 3.24 combine to form the following budget constraint,
expressed in terms of the time spent in market activities,
I p x  p x  p x n
w T  t t t  w T  t  t t  w T t  v
Z Z  n n  q q
m m
z
m
n
m
q
m f f
z
f
n
f
q
f c c
z
c
=  + + ⋅
=  − − −  +  −  −  −  +  −  + ( ) (  ) ( )
                        (3.28)                      
                                             
23
 A given household member will consider the labour income of other household members as part of
their own non-labour income. For instance, a rise in the father’s wage rate is taken by the child as an
increase in the child’s non-labour income.  31
Given the wage rate each household member can command in the market, given
their non-labour income and the maximum time available, each family member will
decide how to allocate time to different activities.  The choice variables are,
t t t t
t t t t
t t
x x x
w
m
z
m
n
m
q
m
w
f
z
f
n
f
q
f
w
c
z
c
Z n q
, , ,
, , ,
,
, ,
The maximization problem can be written as,
max , ( , , ) , ( , , ) , ( , , ) { } [ ] [ ]
. .  (  )  (  )  (  )
U  U Z x t t t t  c q x t t  n x t t
s t p x  p x p x n w T  t t t  w T  t  t  t  w T t  v
Z z z
m
z
f
z
c
q q
m
q
f
n n
m
n
f
Z Z  n n  q q
m m
z
m
n
m
q
m f f
z
f
n
f
q
f c c
z
c
=
+ + ⋅ =  − − − +  − − − +  − +
                                                                                                                            (3.29)
For an interior solution, maximization of the utility function subject to the
budget constraint yields the following first order conditions,
∂
∂
∂
∂
∂
∂
λ
L
x
U
Z
Z
x
p
Z Z
= − = Z
0                                                                                          (3.30)
∂
∂
∂
∂
∂
∂
∂
∂
λ
L
x
U
c
c
n
n
x
p
n n
= − = n
0                                                                                      (3.31)
∂
∂
∂
∂
∂
∂
∂
∂
λ
L
x
U
c
c
q
q
x
p n
q q
q
= − ⋅ = 0                                                                                 (3.32)
∂
∂
∂
∂
∂
∂
∂
∂
λ
L
t
U
Z
Z
t
t
t
w i m f
z
i
z
z
z
i
i
= − =  = 0 ,                                                          (3.33)
∂
∂
∂
∂
∂
∂
∂
∂
λ
L
t
U
Z
Z
t
t
t
w
z
c
z
z
z
c
c
= − = 0                                                                                     (3.34)
∂
∂
∂
∂
∂
∂
∂
∂
λ
L
t
U
c
c
n
n
t
w i m f
n
i
n
i
i
= − =  = 0 ,                                                          (3.35)
∂
∂
∂
∂
∂
∂
∂
∂
λ
L
t
U
c
c
q
q
t
w i m f
q
i
q
i
i
= − =  = 0 ,                                                          (3.36)
∂
∂λ
L
w T t t t  w T t  t t  w T t  v p x p x p x n
m m
z
m
n
m
q
m f f
z
f
n
f
q
f c c
z
c
Z  Z  n n  q q
=  − − −  +  − − −  +  −  + −  −  −  ⋅ = ( ) (  ) ( )  0
                                                                                                (3.37)  32
Equations 3.30 - 3.32 say that when the price of any market good increases, at
the margin, the additional benefit gained from consuming an additional unit of that good
falls short of its cost.  For instance, when the marginal cost of child schooling increases
(such as an increase in the price of child school inputs, transportation costs or
enrollment fees for  each child) the benefit from investing in an additional unit of
schooling for each child is less than the marginal cost.  When the price of any market
good increases, consumption of that good will decline, holding all else constant.
Households will engage in more time-intensive production methods.  Equation 3.33
says that when the market wage of the mother or father rises, at the margin, the
opportunity cost of an additional unit of time spent engaged in home production
increases.  Parents will spend more time in good-intensive productive activities and less
time in non-market production.  Equation 3.35 and 3.36 say that when the wage rate of
the mother or father increases, the opportunity cost of the time spent engaged in child
production and child rearing activities increases.  The production of child quantity and
child quality will be more good-intensive as opposed to time-intensive.  Equation 3.37
ensures that the budget constraint is satisfied.
Of particular interest is equation 3.34; we are concerned with how a child
responds to a change in their market wage rate.  In addition, the responsiveness of
children to a change in their non-labour income is of interest.  In other words, given
t w w w v w
c m f c
= ψ ( ,  , , ) , we would like to evaluate the following comparative static
effects,
   
∂
∂
∂
∂
∂
∂
t
w
T t
w
and
t
v
w
c
c
c
z
c
c
w
c
=
( ) −
1. Refer to Figure 3.1 and Equation 3.34, when the child wage rate increases,
ceteris paribus, the opportunity cost of time spent in non-market related activity
increases.  For a high child wage rate,  whigh
c
 (E1), the marginal benefit from an
additional unit of non-market activity is less than the marginal cost.  Children
will spend less time engaged in non-market activity and more time working in
the market.  If the child wage rate is so low that it falls below the level required
to produce the equality MB=MC,  wlow
c
, children will not work in the market at  33
.  E2
.  E1
Marginal Benefit =
∂
∂
U
t
z
c
child time spent in non-market activities,  t
z
c
whigh
c
wlow
c
child wage rate
all or they will work fewer hours. The marginal benefit of non-market activity
exceeds the child’s foregone earnings.  In Figure 3.1 we have depicted the case
for a child that continues to work in the market, but takes on more household
productive work.
Figure 3.1 Effect of a Change in Child Wage on Child Time Allocation
2. Holding child wage constant, an increase in household wealth or v is represented
by a parallel rightward shift of the marginal benefit curve; families can consume
more Z commodities (including children) and increase utility.  Refer to Figure
3.2 below.  The household is able to purchase more market goods and can afford
to spend less time working.  For an increase in a parent’s wage rate, the
implication for children is such that they will spend less time in the market and
more time in the household, possibly taking leisure and attending school, a pure
income effect.
24
 
                                             
24
 Recall that children take parents’ income as part of their own non-labour income.   34
Marginal Benefit
child time spent in non-market activities,  t
z
c
child wage rate
  Figure 3.2 Effect of a Change in Non-Labour Income on Child Time Allocation
 
 As a result, children’s market work and household productive work may
increase or decrease.  The direction will depend on the child wage rate offered in the
market, the earnings of parents – taken as the child’s non-labour income – as well as
other components of family non-labour income.  Whether a child works in the market or
in the household is determined by the child’s relative productivity.  If the market wage
rate that a child can command exceeds the value of the child’s non-market time, the
child will engage in market production.  The principal effect is a rise in family income.
 As development progresses, greater market opportunities for children may arise.
Further, an increase in expected household income implies greater variation in expected
income.  Children may become even greater assets.  The combination of these factors
increase the opportunity cost of investing in a child’s human capital.  Poverty and
greater productivity of child labour ensure a supply of children to the labour force,
which further increases the cost of child schooling.
Greater productivity of adult males in certain sectors will lead to more market
opportunity for women and children in others.  The greater labour market productivity  35
of women and children in these sectors will increase their labour force participation.
25
 
A rise in the wage rate of adult women will raise family income, we expect the cost of
raising children to rise as the value of women’s time increases.  
The higher opportunity cost of child rearing will reduce fertility such that the
substitution effect dominates the income effect.  However, in the case of a large, poor
family, even as mother’s shift to market production, it is possible that adolescent
children (especially girls) take on more household responsibilities to compensate for
their mother’s lack of presence (Levinson and Moe, 1998).  This will increase the
opportunity cost of schooling for adolescents.
A sustained rise in income and an improved standard of living (including a
decline in infant and child mortality, as well as better health and improved nutrition)
will reduce the economic value of children.  The return to child education begins to
exceed the return to child market employment (a rising opportunity cost of child
labour).  We would expect the labour force participation rate of children to decline and
the demand for higher quality children to rise.  When child mortality is low, having a
large number of children to ensure the survival of some target is no longer a significant
factor in the household fertility decision.  Further, if more children can be expected to
survive into adulthood to earn a living, the rate of return to investing in a child’s human
capital and overall quality will increase.  
Once a certain level of income is reached, such that an acceptable standard of
living is attained, subsequent increases in the wage rate of adult women will further
increase the time cost of children.  This helps to explain the eventual decline in fertility.
This decline in the supply of children to the labour market is accompanied by a
declining demand for child labour services resulting from the changing structure of
production.
 
                                             
25
 For a discussion of the increase in demand for all labour market participants in early industrialization,
see Goldin and Sokoloff (1982; 1984).  36
3.4 Chapter Summary
The declining importance of children in industry combined with increasing
female wage rates and the rising price of child rearing inputs, all contribute to the rising
cost of child quantity and the decline in child demand.  Moreover, a decline in the
economic value of children in the home and in agriculture will increase the cost of
children, in turn, reducing the demand for them.  These factors also reduce the cost of
quality and increase the demand for these commodities relative to quantity.  Thus, it is
the long-run economic forces of technological change, rising income, the higher price of
raising children and the corresponding declining relative cost of child quality that
explain the changing economic role of children over time.  
Chapter 4 begins our empirical study.  Our hypothesis is presented more
formally, as well, the estimation procedure is discussed.  Some interesting statistics,
which further demonstrate the relevance of our theory, are also presented.  37
CHAPTER 4
THE HYPOTHESIS, ESTIMATION PROCEDURE AND THE DATA
In this chapter we begin by summarizing our hypothesis more formally,
followed by a thorough discussion of the estimation procedure.  We introduce some
descriptive statistics motivating the study in order to demonstrate the relevance of the
question at hand.
4.1  Hypothesis
In Chapter 2 and Chapter 3, we have discussed the importance of family income
as a determinant of child labour.  Our empirical test is based on the subsequent
relationship between per capita income and the child labour force participation rate.
Thus, the theory is embedded in the following relation,
% (  ) child labour f per capita income =
Theoretically, there is some uncertainty as to the direction of the relationship.
We have explored the conventional view that the incidence of child labour should
decline with per capita income; we have accounted for the possibility that child labour
may increase with per capita income.  Consequently, within a theoretical framework,
the direction of the relationship is indeterminate.  Our question becomes one of an
empirical nature.
The nature of the inverted-U relation is such that at a very low level of
development, economic growth implies the opportunity for more market activities for
all participants in an economy, including children.  By productive activities, I am
referring to the productive activities within the home and in the market sector.  At a
higher level of development, the productive activities of children, excluding the
accumulation of human capital, begin to decline and continues on this path as family  38
incomes grow and become more stable.  The direction of the relationship is an empirical
question.  
4.2  Estimation Procedure
The validity of the inverted-U hypothesis can be tested by estimating the
following empirical specifications,
%cl Y = + β1 2
β                                                                                                           (4.1)
%cl Y =
+
α
β
  [expressed in terms of the natural logarithm,  ln(% ) ln ln cl Y = + α β ]       (4.2)                      
%cl Y Y = +  + β β  β 1 2  3
2
                                                                                                (4.3)
The dependent variable, %cl , is defined as the aggregate percentage of child
labour.  The ILO defines this as the number of children aged 10 to 14 active in the
labour force divided by the number of children aged 10 to 14, expressed as a
percentage.  The explanatory variable is per capita GDP (and per capita GDP squared).  
We test for three empirical specifications. First, we test for a monotonic
relationship (Equation 4.1).  The sign of the income parameter is expected to be
negative.  We test for a negative exponential relationship (Equation 4.2); again, the sign
of the income parameter is expected to be negative.  If Equation 4.2 is found to provide
a better explanation given the data, this indicates that the incidence of child labour
exhibits a downward trend and the inverted-U relationship does not explain the
available data.  Last, we test for a non-linear quadratic relationship (Equation 4.3).  For
the inverted-U hypothesis to hold,  β2
>0 and  β3
<0 must be true.
Using panel data methodology, we propose to estimate a fixed effects
specification by pooled least squares (Hsiao, 1986; Judge et al, 1988).  The crosssectional specific components are assumed to be fixed parameters.  That is to say, each
country has a unique constant term which captures the location specific factors.  The
equations can be written as,
%cl D Y it j
j
N
= + + jt it it
=
∑ β β µ 1
1
2
                                                                                     (4.4)   39
ln(% ) ln ln( ) cl D Y it j
j
N
= + + jt it it
=
∑ α β  µ
1
                                                                      (4.5)
%cl D Y Y it j
j
N
= + + + jt it it it
=
∑ β β β µ 1
1
2 3
2
                                                                        (4.6)                  
µ σ it µ
~ ( ,  ) iid 0
2
∀ i =1, . . . ,N  where N refers to the number of cross-sectional units
∀ t =1, . . . ,T  the number of annual time periods
β1 j
 are the cross-section fixed effects
The dummy variables take on the value of 0 or 1 corresponding to the country
that is being observed,
D
if j i
if j i
jt
=
=
≠






1
0
The fixed effects specification is most appropriate to absorb any permanent
differences across countries – such as government policy and legislation.  Further,
because the sample is not randomly drawn, we do not assume the cross-sectional
specific effects to differ as a result of sampling error.  Equation 4.4 will be referred to as
the linear model, we will refer to Equation 4.5 as the log-log model and Equation 4.6 as
the quadratic model.
The model is then estimated with an additional component which includes the
following covariates,
1.  Population Statistic: Crude Birth Rate (CBR), a simple statistic which
measures the number of live births per 1000 population occurring during that
year, usually estimated at mid-year.
2.  Education Statistic: Primary Net Enrollment Ratio (NER), which is the ratio
of number of children of official primary school age – as defined by the
national education system – who are enrolled in school to the population of
the corresponding official primary school age.  Although the literacy rate
may have more explanatory power of the basic level of education, our
concern is not with the level human capital per se but rather, child time use.  40
 The signs of the coefficients are sensitive to the level of income.  In this regard,
in order to clearly observe the responsiveness of child employment to aggregate per
capita income, it is necessary to group countries according to income level and estimate
the model as follows,
1. Estimate the model for the entire sample.
2. Estimate the model for those countries with per capita GDP less than US$1000
(the bottom 20 per cent of the sample).
3. Estimate the model for those countries with per capita GDP greater than
US$1000.
 To check for stationarity of the time series, we perform the Dickey-Fuller (DF)
test for unit roots.  If the trend exhibits some stochastic process the GDP time series is
non-stationary.  It is necessary to carry out a differenced series until we obtain a
stationary one.
 The model is tested for heteroscedasticity.  Although the OLS parameter
estimates will no longer be efficient, the presence of heteroscedasticity does not destroy
the unbiasedness and consistency properties.  In order to ensure reliable inference, if
heteroscedasticity does exist, it is necessary to compute a heteroscedasticity-consistent
covariance matrix, derived by White.
 Provided we do not go too far into the future, the growth rate of per capita GDP
is used to forecast future per capita GDP in certain key regions which are then used to
predict future child labour levels.  These data are then used to determine the time
required to reduce the incidence of child labour to 10 per cent, assuming government
policy, child labour laws and compulsory schooling legislation remain unchanged.  We
also forecast future primary school enrollment ratios.   41
4.3 Data
 Panel data for 75 developing countries were taken from the United Nations, the
World Bank and the International Labour Organization for the period 1989-1999.  Data
on the following variables were obtained,
•  Per capita GDP, adjusted for purchasing power.
•  Percentage of economically active children, aged 10-14.
•  Crude Birth Rate
•  Net Primary Enrollment Ratio
 Data for Gross Domestic Product adjusted for purchasing power and expressed
in US dollars are found in The World Development Report (1989-2001), published by
the World Bank.  A country’s child labour force participation rate is defined as the
number of children aged 10-14 active in the labour force divided by the number of
children aged 10-14, expressed as a percentage.  These data are found in The Yearbook
of Labour Statistics (1989-1999), published by the International Labour Office.  Data
for the net enrollment ratio, defined as the ratio of the number of children of official
primary school age – as defined by the national education system – who are enrolled in
school to the population of the corresponding official school age, are found in  The
Human Development Report (1989-1999).  As well, statistics for the crude birth rate,
which measures the number of live births per 1000 population occurring during that
year are found in  The Human Development Report (1989-1999), published by the
United Nations Development Programme.
 Tables 4.1 – 4.4 below give some descriptive statistics for the data used in the
estimation of equations 4.4 - 4.6.  Tables 4.1 and 4.2 illustrate the range of child labour
force participation rates across countries.  Those countries with a very high incidence of
child labour tend to have high birth rates and low primary school enrollment ratios.
Correspondingly, these are countries for which average per capita GDP is below
US$1000.  Table 4.2 presents some statistics for countries that have been experiencing a
steady decline in the incidence of child labour for a significant amount of time.  These
countries have much higher average school enrollment ratios, and lower fertility rates.
In addition, average per capita GDP is significantly higher.  42
Table 4.1   Descriptive Statistics, Selected Countries with a High Incidence of Child Labour, 1989-1999
Country %cl  CBR  Primary
NER
Per capita
GDP
       
Bangladesh 35 33 66 1148
Burkina Faso 55 46 27 758
Chad 37 45 37 699
Ethiopia 42 48 28 496
Mali  54 51 25 635
Tanzania 40 41 48 818
Uganda 46 47 54 518
       
  * Data is averaged for the period 1989-1999; source: see above.
Table 4.2   Descriptive Statistics, Selected Countries with a Low Incidence of Child Labour, 1989-1999
Country %cl  CBR  Primary
NER
Per capita
GDP
       
Argentina 6 20 99 7817
Costa Rica 6 24 89 5092
Ecuador 8 28 96 2809
Iran 5 33 92 4142
Malaysia 3 27 97 6806
Mauritius 3 18 95 6838
Peru 3 28 94 3559
       
  *Data is averaged for the period 1989-1999; source: see above.
 Tables 4.3 and 4.4 give some insight into the nature of this empirical question.
Table 4.3 provides some statistics which confirm the conventional view that there exists
an inverse relationship between income and the incidence of child labour.  In Table 4.4
we present some statistics which suggest that this theory does not explain what is
happening in all countries and may be incomplete.  These data are for countries in
which per capita income increases significantly over the period, while the incidence of
child labour either increases as well, or remains relatively unchanged.  These
observations account for 25 per cent of the sample.  43
Table 4.3   Percentage Change in Per Capita GDP and Percent Child Labour, 1989-1999
Country  % ∆ GDP % ∆ cl Country % ∆ GDP % ∆ cl
         
Argentina +62 -4 Mauritania +28 -4
Bangladesh +44 -14 Mauritius +35 -2
Brazil +22 -4 Mexico +26 -6
Burk. Faso +31 -20 Myanmar +52 -3
Cambodia +22 -2 Nicaragua +32 -5
China +19 -4 Niger +13 -2
Costa Rica +24 -3 Panama +36 -2
C. d’Ivoire +11 -5 PNG +19 -3
Dom. Rep  +5 -3 Paraguay +35 -17
Gabon +25 -4 Philippines +41 -5
Ghana +44 -2 Portugal +59 -5
Guatemala +28 -3 Senegal +10 -4
Guinea +66 -3 Sri Lanka +26 -3
Honduras +33 -3 Thailand +36 -2
Indonesia +17 -4 Togo +44 -4
Iran +40 -3 Turkey +35 -18
Lesotho +20 -3 Uganda +56 -3
Madagascar +10 -4 Uruguay +30 -18
Mali +17 -4 Vietnam +43 -17
         
*Burkina Faso is abbreviated as Burk. Faso; Cote d’Ivoire is abbreviated as C. d’Ivoire;
Dominican Republic is abbreviated as Dom. Rep; PNG refers to Papau New Guinea.  Source:
author’s calculations using data sources described above.
Table 4.4   Percentage Change in Per Capita GDP and Percent Child Labour, 1989-1999
Country  % ∆ GDP % ∆ cl Country % ∆ GDP % ∆ cl
         
Bolivia +30 +3 Haiti +32 -1
Botswana +47 +6 India +58 +6
Chad +29 0 Malaysia +29 +1
Colombia +29 +3 Namibia +72 +9
Egypt +41 +2 Nepal +26 +20
El Salvador +53 +4 Peru +38 -1
Ethiopia +35 -1 Sudan +26 +14
Gambia +37 +17 Zimbabwe +41 +20
         
*Author’s calculations using data sources described above.  44
Ethiopia and Chad experience a considerable increase in per capita GDP; however the
decline in child labour is virtually insignificant.  Nepal and Zimbabwe experience a
significant growth in the incidence of child labour.
Figure 4.1 and Figure 4.2 plot per cent child labour for 1999 against average per
capita GDP.  Figure 4.2 illustrates that once a threshold income level is reached,
approximately US$1000, the incidence of child labour begins to decline more steadily.
As conventional wisdom would suggest, child labour declines with income.  For per
capita GDP below US$1000, this relationship is not well defined.
 
0
10
20
30
40
50
60
0 500 1000 1500
average per capita GDP (1989-1999)
per cent child labour (1999)
       
Figure 4.1   Children aged 10-14 in the Labour Force, per capita GDP < US$1000
26
 
0
5
10
15
20
25
30
35
40
45
50
0 5000 10000 15000 20000
average per capita GDP (1989-1999)
per cent child labour (1999)
Figure 4.2   Children aged 10-14 in the Labour Force, per capita GDP > US$1000
27
                                             
26
 Author’s calculations using data sources described above.
27
 Ibid.  45
Figure 4.3 summarizes the average incidence of child labour by region.  In
absolute terms, the Asia-Pacific region accounts for some 127 million working children
(approximately 70 per cent of the total), followed by sub-Saharan Africa with 23 per
cent of the total (ILO, 2002: 20).  In terms of the number of child labourers in relation
to the population of children, the problem is most severe in sub-Saharan Africa.
Nor th A f r ic a
and The
Middle Eas t
South and
South Eas t
A s ia
s ub-Saharan
A f  rica
South and
Latin Amer ic a
Central Asia
0
5
10
15
20
25
30
per cent child labour
     Figure 4.3   Average Incidence of Child Labour, 1989-1999
28
 
Compared to Asia and the Pacific where 19 per cent of all children under the age
of 15 work, in sub-Saharan Africa 29 per cent of all children are working (ILO, 2002:
20).  Table 4.1 above also illustrates this phenomenon.  Some of the poorest countries
have child labour force participation rates in excess of 40 per cent.  In some cases these
figures exceed the female labour force participation rates.
Many of the activities that children engage in are crucial to the survival of the
household, a significant proportion of which produce no wage income.  Several surveys
of low-income rural households in the developing world suggest that children often
work in the labour force in an unpaid capacity.  Many children work within the home
and are not part of the labour force, this is particularly true for girls.  Consequently,
reporting a child wage rate is often unheard of, suggesting that children’s work is
narrowly defined.  As such, the above data which suggests a capacity for child labour to
increase could be a reflection of,
                                             
28
 Source: author’s calculations.  46
1. Underreporting of the number of children working due to measurement
problems.
29
2. An expansion in the demand for and/or the supply of child workers.
 As a result, official data sources may understate not only the scope of the
problem but the nature of it as well.  For these reasons, time-use studies appear to be the
most effective means of evaluating the role of children as producers.  That is to say, the
most important measure of a child’s contribution to the household is the relative amount
of time spent in various activities.
30
 
However, if we view the official ILO statistics as a subset of the entire child
labour phenomenon, these data are not entirely useless.  There is no sufficient public
data that reflects the true extent of children’s participation in the household and in the
informal sector.  The ILO statistics tend to be more general and representative of what
is happening in the market sector.  Furthermore, these data may be incomplete in the
sense that they reflect what is happening in certain areas more accurately than in others,
and hence there is a bias.  Whether this bias is systematic or not is unknown.  The
extreme importance of this question must be emphasized, as policy recommendations
will be based on the data.
Swaminathan (1998) has presented a case in which even after accounting for
some underestimation, the Census of India reports a significant rise in the absolute
number of child workers in Gujarat, Western India between 1981 and 1995.  During the
period, state domestic product increased by over 200 per cent (Swaminathan, 1998:
1516).  In addition to Swaminathan, Edmonds (2002) finds that among Vietnamese
agriculturalists, child labour in the poorest households is either increasing in per capita
expenditure or remains relatively unchanged as per capita expenditure increases.  These
examples coupled with the historical experience of today’s advanced industrial
countries, provide us with reason to investigate further.
                                             
29
 For literature on underreporting in the context of children’s work, see Bliss (1904); for a discussion of
this issue in the context of women’s work, see Cloud and Garret (1996), and Goldin (1995).  The debate
surrounding what should constitute a child worker is ongoing.  For an overview of the measurement
dispute, see Ashagrie (1993), Basu (1999), Smolin (1999), and Anker (2000).
30
 This is discussed in Moe and Levinson (1998) and Levinson (1991).  47
4.4 Chapter Summary
In this chapter our hypothesis as well as the motivation behind our choice of
model specification is presented and explained.  In addition, we have provided some
descriptive statistics to illustrate the relevance of this question.  In the following chapter
we will determine which model provides the best fit for the available data. Our
estimation results are summarized followed by a discussion of the policy implication of
our findings.   48
CHAPTER 5
THE RESULTS
In this Chapter, we test the validity of the theoretical discussion presented in
Chapter 2 and Chapter 3.  Equations 4.4 – 4.6 are estimated, the results obtained from
these regressions are interpreted.  We determine which model provides the best fit and
discuss the policy implications of our results.  Projections are made for future levels of
child labour and per capita GDP, as well as primary school enrollment.  These data are
then used to substantiate our hypothesis and to provide support for our policy
suggestions, discussed in Chapter 6.  We emphasize that the question of the direction of
the relationship is indefinite and is a matter of an empirical nature.
5.1 Estimation Results
5.1.1 Discussion of Results
 The results presented here were obtained by estimating equations 4.4 - 4.6 for
the three categories previously outlined.  Equation 4.6 is modified to include the
additional covariates introduced in Chapter 4, the crude birth rate (CBR) and the
primary net enrollment ratio (NER).  Cross-sectional specific fixed effects are also used.
Pooled least squares regression results are presented in Tables 5.1, 5.2 and 5.3 below.
Recall, Y represents per capita GDP and Y
2
refers to per capita GDP squared. The fixed
effects are summarized in Appendix A - C.  49
Table 5.1   Estimation Results for the Linear Model (Equation 4.4)
Dependant
Variable
Estimated Coefficients
a
per cent economically
active children
Y = per capita GDP
b
  R
2 N NT Income
Elasticity
Total -0.120
(-0.95)
0.94 75 825 -0.012
Per Capita GDP<1000 -2.204
(-1.74)
0.95 15 165 -0.047
Per Capita GDP>1000 -0.107
(-0.83)
0.90 60 660 -0.031
         
a) t-statistics reported in parentheses
b) GDP expressed in thousands
Table 5.2   Estimation Results for the Log-Log Model (Equation 4.5)
Dependant
Variable
Estimated Coefficients
a
ln per cent
economically active
children
ln Y
R
2 N NT Income
Elasticity
Total -0.017
(-0.38)
0.91 75 825 -0.017
Per Capita GDP<1000 -0.012
(-0.52)
0.97 15 165 -0.012
Per Capita GDP>1000 0.013
(0.23)
0.91 51 561 -0.013
         
a) t-statistics reported in parentheses
      50
    Table 5.3   Estimation Results for the Quadratic Model (Equation 4.6)
Dependant
Variable
Estimated Coefficients
a
per cent
economically
active children
Y
c
Y
2 CBR  NER
R
2 N NT Average
Income
Elasticity
b
Turning
Point
Total
 0.563
(1.68)
-0.05
(-2.60)
  0.94 75 825 0.036 $5, 630
 0.772
(2.42)
-0.061
(-3.31)
0.096
(2.51)
 0.94 75 825 0.052 $6,330
 0.698
(1.94)
-0.055
(-2.78)
0.170
(4.48)
-0.029
(-1.39)
0.95 60 660 0.046 $6,350
Per Capita GDP<1000
 -5.242
(-0.81)
1.913
(0.50)
  0.95 15 165 -0.047 $1,370
 -6.928
(-1.10)
3.210
(0.86)
0.182
(2.33)
 0.95  15 165 -0.038 $1,080
 -11.337
(-1.19)
5.099
(0.81)
0.140
(1.51)
-0.065
(-2.72)
0.92 13 143 -0.073 $450
Per Capita GDP>1000
 0.658
(1.93)
-0.056
(-2.83)
  0.90 60 660 0.039 $5,880
 0.843
(2.59)
-0.065
(-3.47)
0.085
(2.01)
 0.90 60 660 0.068 $6,490
 0.706
(1.97)
-0.056
(-2.87)
0.168
(3.90)
0.005
(0.12)
0.92 47 517 0.070 $6,300
                 
a) t-statistics reported in parentheses
b) evaluated at the mean
c) GDP expressed in thousands
 First, consider the linear model.  While the sign of the income parameter
suggests a negative, monotonic relationship between per cent child labour and per
capita GDP, the t-statistics are very small and insignificant at more than the 10 per cent
level.  The results from the log-log model suggest a downward trend for child labour as
per capita GDP increases.  However, the income parameters are statistically
insignificant.  According to this criterion, the evidence for a negative, non-monotonic
relation between child labour and per capita GDP is weak.
Upon inspection of the regression results from the quadratic specification, there
does appear to be evidence of a non-monotonic relationship between child labour and
the level of development.  For each sample, a quadratic relationship with per capita  51
GDP is tested.  Although it is difficult to infer much about the individual coefficients
due to the presence of multicollinearity, we are able to make some observations.  
To begin with, we look at the case in which per capita GDP is below US$1000.
For the poorest 20 per cent of the sample, there is a negative correlation between
income and the incidence of child labour, a relationship that weakens as income
increases for this group.  We would expect the incidence of child labour to increase with
development, especially for this group.  However, the sample size is very small and
underreporting is likely to be most prevalent here.  In addition, neither income terms are
significant.    The incidence of child labour displays the opposite, although insignificant,
pattern.  Therefore, these results do not discredit our theory.
For the total sample, the coefficients of the income parameters have the
appropriate signs.  The income parameter is significant at the 5 per cent level.  The
squared income term is significant at less than the 1 per cent level.  Taking into
consideration that per capita GDP is expressed in thousands, the estimated coefficients
are very small and economically insignificant.  This brings into question the role of both
government as well as different aspects of development in the determination of child
labour levels.  For instance, consider Figure 4.2.  In the middle income range we find
countries with virtually the same level of per capita GDP but varying levels of child
labour.  Formal recognition of where children work and identification of the variables
that help to explain why children work will provide us with further insight.  The turning
point for child labour, as implied by estimated Equation 4.6, occurs at per capita GDP
US$5,630.
Consider the group for which per capita GDP is greater than US$1000.   The
relationship between the incidence of child labour and per capita GDP is positive
quadratic, thereby supporting the inverted-U hypothesis.  The first income parameter is
significant at the 1 per cent level.  The squared term is significant at less than the 1 per
cent level.  Once again, the income coefficients are very small.  Approximately 70 per
cent of the countries for which growth in GDP is accompanied by growth in the
incidence of child labour are in this group.  This explains why the relationship is
strongest here.  Those within this group are among the first to participate in the
developmental process.  Information regarding labour market opportunities is more  52
readily available, labour market opportunities are more accessible.  It follows that child
labour force participation declines a little later than for the total sample.  Conditions
begin to improve after a per capita income level of US$5,880 is obtained.  However, the
countries experiencing an increase in the incidence of child labour compose only 24 per
cent of this group.  This indicates that in areas where child labour persists and continues
to grow, we may have to wait a very long time before it begins to decline steadily.  
When the population statistic and the education statistic are included, the income
parameters remain significant.  In particular, the squared income term remains
significant for the total sample as well as the group for which per capita GDP is above
US$1000.  One problem with regard to the inclusion of different aspects of
development is that they are highly collinear with GDP, making it difficult to infer
about causal direction and impact.  Our general results are summarized below.
1. We find that for all income groups, the crude birth rate is positively and
significantly related to the pattern of child labour.  However, its effects
on child labour are likely to be non-linear.  
2. The inclusion of the primary net enrollment ratio as an explanatory
variable does not provide any explanatory power for the per capita
income above US$1000 group.  This higher income group is more likely
to react to incentives for secondary school enrollment as opposed to
primary.  For the total sample and the low-income group, child labour
and the primary net enrollment ratio are significantly, negatively
correlated.  Children who spend more hours working in the market will
have less time available to devote to the accumulation of human capital.
Children who work are effectively less likely to attend school.
The equations provide a better explanation for some groups than for others.  As
a result, the existence of a threshold value of per capita GDP is sensitive to the sample
composition and specific functional form.  This is understandable as both the shape and
curvature of the U will depend on the policy choices made by relevant parties: firms,
governments and households.  Therefore, the U hypothesis is not necessarily inevitable
but rather a matter of (policy) choice.  Eventually, GDP per capita is associated with a
decline in child labour.  53
The income terms in all models are jointly significant at the one per cent level of
significance.  We perform the following F-test of significance using ESS = explained
sum of squares and RSS = residual sum of squares; k denotes the number of parameters
and n refers to the sample size,
F
ESS k
RSS n k
= F k  n  k
−
−
− −
1
~ (  ,  ) α
1                                                                               (5.1)
 Upon inspection of the t-statistics and the coefficient of determination, the
quadratic model appears to be the best fit.  Further, given the nature of the data, we
would expect neither the linear model nor the log-log model to provide the greatest
explanatory power.  As the data does appear to exhibit some non-monotonic process,
the linear model is not the appropriate choice.  Similarly, 25 per cent of the sample
experience some growth in child labour force participation, in addition, this study is
only for an 11 year period; therefore, the log-log model is also likely to be
inappropriate.
 For the total sample, the log-log model reports an income elasticity of -0.017.
This suggests that a one per cent increase in GDP per capita will result in a decrease in
the incidence of child labour by approximately 0.017 per cent.  The linear model reports
an average income elasticity of -0.012, similar to the log-log results.  For the quadratic
model, we find an income elasticity of 0.036.  This says that if per capita GDP increases
by one per cent the incidence of child labour will increase by 0.036 per cent.
5.1.2 Evaluation of Results
5.1.2.1 Dickey-Fuller Tests
 
 Standard inference procedures assume stationarity of the regressors.  We run the
Augmented Dickey-Fuller (ADF) test of stationarity on the following forms,
∆ cl t cl cl e
t t i t i
i
m
= +  +  +  + − − t
=
α α  δ  γ 0 1  1 ∑
1
                                                                      (5.2)
∆ Y t Y Y e
t t i t i
i
m
= +  +  +  + − − t
=
α α  δ  γ 0 1  1 ∑
1
                                                                         (5.3)  54
where:
m denotes the number of lagged terms
t =1, . . . . ,11 representing 1989-1999
δ = − ρ 1 is the first difference operator
e
t
 is white noise
 
 We fail to reject the null hypothesis of the existence of a unit root,  δ =0, based
on MacKinnon’s critical value criterion.
31
  Consequently, the data should be
differenced.  First to third differencing results in stationarity for a few of the series; for
many of the series, fifth differencing is not sufficient.  Differencing to this degree
results in errors.  Thus, we are constrained by the limitations of the data, in particular,
the sample period.
5.1.2.2 Heteroscedasticity Tests
 
 Based on the results of White’s test for heteroscedasticity, we find
heteroscedasticity to be a problem in our model.
32
  As a result, White’s
heteroscedasticity-consistent covariance matrix is computed in order to obtain accurate
standard errors.  The corrected t-statistics were reported in Table 5.1 - 5.3 above.
5.1.2.3 Autocorrelation Tests
 
 Upon inspection of the DW statistic (< 1.5 for all samples), specification errors
exist, in particular positive serial correlation.  If autocorrelation exists the problem can
be reduced by first differencing, making inference more reliable. If both
heteroscedasticity and autocorrelation exist, the autoregressive conditional
heteroscedasticity or ARCH model is generally used.  However, our data is for the
period 1989-1999, for such a short period serial correlation should not be a problem;
moreover, we are constrained by the degrees of freedom.
                                             
31
 Refer to Appendix D for a sample of the ADF test results.
32
 Refer to Appendix E for White’s Heteroscedasticity test results.  55
5.2 Projection Results
 
 The middle 60 per cent of the sample comprise approximately 70 per cent of the
countries that experience an increase in per capita GDP with a corresponding increase
in the incidence of child labour or no change whatsoever.  With this in mind, for the
total sample, we can forecast future values of per capita GDP which are then used to
forecast future child labour levels.  The average growth rate of per capita GDP is used
to forecast future values of GDP per capita,
GDP GDP r
t
t
= + 0
( ) 1                                                                                                  (5.4)
GDPt
 is per capita GDP at time t,  GDP0
 is the initial value of per capita GDP (base
year value) and r is the average rate of growth of per capita GDP.
The natural logarithm of equation 5.4 can be written as,
ln ln ln( ) GDP GDP t r
t
= + + 0
1                                                                                    (5.5)
We estimate,
lnGDP t
$ $
t
= + β β 0 1
                                                                                                      (5.6)
where:
β
β
0 0
1
1
=
= +
ln
ln( )
GDP
r
Our results are as follows,
ln . .
( )  ( .  ) ( .  )  .
GDP t
se r
t
= +
=
7 420 0 027
0 061 0 009 0 011
2
                                                                    (5.7)
 An average growth rate of 2.74 per cent is obtained.  Our target level of child
labour is 10 per cent.  For those countries that have not yet met this goal, we determine
what level of GDP is required to do so.  Using 1999 as the base year, these computed
values are substituted into equation 5.4 to estimate the number of years it will take to
reach the target provided each country grows at the average rate and there are no
changes in policy.  This approach suggests that it could take from 20 to over 150 years.
The results are summarized in Table 5.4 below.                          Table 5.4   Forecast Time Period for Child Labour to Reach the Target
33
20-39 years  40-59 years  60-79 years  80-99 years  100-119 years  120-139 years  140-159 years
Botswana  Dominican   India  Cote d’Ivoire  Bangladesh  Angola  Burundi
Brazil Guatemala Bolivia Lesotho Cambodia Benin Ethiopia
El Salvador  Namibia  Ghana  Pakistan Cameroon Burkina Faso
G-B
b
Gabon Nicaragua
PNG
a Gambia Chad Malawi
Thailand Zimbabwe Yemen Guinea Congo Malawi
Haiti Kenya Mozambique
Mauritania Madagascar Niger
Myanmar Nigeria Rwanda
Nepal Sierra Leone Tanzania
Senegal Uganda
Sudan Zambia
Togo
a) Papau New Guinea
b) Guinea-Bissau
For instance, consider the example of Ethiopia, a country that has persistently had
one of the highest child labour force participation rates.  Using our estimation results
from Equation 4.6, we determine what level of GDP is required to reach 10 per cent child
labour.  Keep in mind that Ethiopia currently has an aggregate child labour force
participation rate in excess of 40 per cent, over the 11 year period there has been no
significant change in this rate.  Moreover, we are assuming that all else remains constant
and that the average relationship is a sufficient indicator of what is happening in Ethiopia.
We find that at this rate, Ethiopia would require US$29,000 per capita GDP which
translates into 146 years assuming the Ethiopian economy grows at the average rate of
2.74 per cent.
34
This suggest that many countries that lie on the upward sloping part of the
inverted-U curve will remain there for a  long time provided there are no changes to
government policy.  Figures 5.1 and 5.2 below illustrate the implication of these results,
for selected countries.  For instance, Ethiopia will not see a steady decline in child labour
until per capita GDP US$6,590, which could take 90 years.
                                               
33
 Source: author’s forecast results.
34
We compute the time it takes to reach 10 per cent child labour in Ethiopia as follows,
t
GDP GDP
r
t
=
−
+
=
−
=
ln ln
ln( $)
ln ln .
ln( . )
1999
1
29 0 6
1027
146
56Forecast Results: Botswana
5
0
15
10
0 5 10 15 20
forecast per capita GDP
( ni thousands)
t n r ce e p st acer of
r bou ild la hc
Forecast Resul ts: Chad
35
35.5
36
36.5
37
37.5
0 5 10 15
forecast per capita GDP
( n tho i usands)
t n r ce e p st ac re of
r bou ild la hc
Forecast Resul ts: Ethiopia
46
44
42
40
0 5 10 15 20
forecast per capita GDP
( n t i housands)
t n ce r  e p st ca re of
our d lab il hc
Forecast Resul ts: India
5
0
15
10
0 5 10 15 20
forecast per capita GDP
( n t i housands)
t n r ce e p t sac re of
ur bo ild la hc
F gu i re 5.1  Forecast Results for Child Labour and Per Capita GDP, se el cted countries
57F gu i re 5.2  Forecast Child Labour Trend, se el cted count r ei s
Forecast Chi dl Labour Trend: Bo wt sana
5
0
15
10
0 20 40 60
years
nt  e c r e p t sacer fo
r abou l dli hc
Forecast Chi dl Labour Trend: Chad
35
35.5
36
36.5
37
37.5
0 50 100 150
years
nt  e c r e p t sacer fo
bour a l dli hc
Forecast Chi d Lab l our Trend: E ht oi p ai
45
44
43
42
41
40
0 50 100 150
years
nt e c per t sacer of
r abou l dli hc
Forecast Chi dl Labour Trend: Ind ai
5
0
15
10
0 50 100
years
t n ce r e p st ca er of
r abou l dli hc
58The implication is that without any significant change in policy, child labour
will persist for decades to come.
35
   These results appear to be overly pessimistic and
simplistic.  Most countries that lie on the upward sloping part of the curve have growth
rates that are significantly higher than the average, many in excess of 5 per cent.
Contrastingly, on the opposite end of the spectrum, countries with child labour force
participation rates between 1 and 5 per cent have much lower growth rates.
In this regard, we calculate the growth rate required to reach the target within 30
years, by 2029.  The computed growth rates range from 2 to 15 per cent.  The results are
summarized in Table 5.5 below.  For instance, by setting t =30, we find that the growth
rate required to reach 10 per cent child labour in Ethiopia is 14 per cent.  However, the
target does appear to be attainable for some of the countries, in particular those with
estimated growth rates between 0 and 8 per cent, depicted in the  first two columns of
Table 5.5.
                           Table 5.5  Estimated Growth Rate Required to Reach the Target by 2029
36
0-5 per cent  5-8 per cent  8-10 per cent  10-12 per cent  12-14 per cent  14-16 per cent
Botswana Bolivia Cameroon Bangladesh Angola Burundi
Brazil Ghana Cote d’Ivoire Cambodia Benin Ethiopia
Dominican India Guinea Congo Burkina Faso Mali
El Salvador  Nicaragua Haiti  Gambia  Chad  Mozambique
Gabon Pakistan Lesotho Myanmar
G-B
b Tanzania
Guatemala
PNG
a Mauritania Nepal Kenya
Namibia Thailand Sudan Senegal Madagascar
Zimbabwe Yemen Togo Malawi
Uganda Niger
Zambia Nigeria
Rwanda
Sierra Leone
a) Papau New Guinea
b) Guinea-Bissau
Similarly, we forecast the primary net enrollment ratio for the target date, 2029,
for each country.  The results are summarized in Table 5.6 below.  Primary net
                                               
35
 However, it should be noted that we have estimated far into the future, respectively.  Forecasting errors
increase rapidly.
36
 Source: author’s forecast results.
59enrollment ratios are rising for all countries, although the average growth rate is quite
low, approximately 0.1 per cent.  Our estimation results, presented in section 5.1.1,
indicate that for the poorest 20 per cent of the sample, a 1 per cent increase in the
primary net enrollment ratio will reduce the child labour force participation rate by
0.065 per cent.  Using this result, we compute what primary net enrollment ratio is
required to reduce child labour to 10 per cent by the target date. For each country in the
sample, we compute the level of per capita income in 2029, t = 30, using the growth
equation.  We substitute this into the quadratic equation to determine the child labour
force participation rate in 2029.   The difference between this result and %cl = 10 is
computed.  This value and the coefficient of the primary net enrollment ratio are then
used to determine the required primary net enrollment ratio to reach 10 per cent child
labour by 2029.  The estimated values we obtain are very high, in excess of 100 per cent
in most cases.
37
  Our findings suggest that as  a policy instrument, primary school
enrollment alone may not be a sufficient means to reach the target.  
 
    Table 5.6   Primary Net Enrollment Ratio Forecast Results for 2029
38
20-39% 40-59% 60-79% 80-100%
Angola Benin Bangladesh Bolivia Mongolia
Burkina Faso Cote d’Ivoire  Cameroon Botswana Namibia
Burundi Guinea Bissau Gambia Brazil Nicaragua
Chad Senegal Iran Colombia Panama
Ethiopia Tanzania Kenya Costa Rica Paraguay
Guinea Uganda Lesotho Dom. Rep Peru
Haiti Madagascar Egypt Rwanda
Mali Mauritania El Salvador Syria
Mozambique Morocco Honduras Turkey
Niger Nepal Iran Uruguay
PNG Mauritius
Togo
Zambia
*Dominican Republic is abbreviated as Dom. Rep; PNG refers to Papau New Guinea.
                                               
37
 For instance, consider the country of Tanzania.  Assuming Tanzania’s economy grows according to the
average rate, per capita GDP is estimated to be US$1,063 in 2029.  This is substituted into the quadratic
equation from which we obtain a child labour force participation rate of 15.52 per cent, which exceeds the
target level by 5.52 per cent.  This difference divided by the coefficient of the NER variable, -0.065, gives
the required primary net enrollment ratio required to satisfy the target level of child labour by 2029; in
this case the required primary NER is 84 per cent.
38
 Source: author’s forecast results.
605.3     Chapter Summary
 
In this chapter we have presented the regression results obtained from estimating
equations 4.4 – 4.6.  We find the quadratic model to be the best fit.  The inverted-U
hypothesis is strong and significant for the total sample as well as for the group in
which GDP per capita is greater than US$1000.
Our estimated equations and projection results suggest that assuming each
country grows according to the average growth rate, without any significant changes in
policy, child labour will persist for many years to come.  The importance of primary
school enrollment and hence, the monitoring of child time use is also highlighted.  The
results suggest that the poorest 20 per  cent are likely to respond to educational
incentives, in particular primary school incentives.  Our projection results for the net
enrollment ratio suggest that increasing  NER alone will not sufficiently reduce child
labour, incentive based schemes will be more  effective.  That is to say, educational
subsidies must be accompanied by income supplementation programs.  Our results also
highlight the positive correlation between fertility and child labour.  In Chapter 6, we
discuss the policy implications of our findings in the context of the current consensus
within the field and present some opportunities for further research.
61CHAPTER 6
CONCLUSION
In this paper, we develop a theoretical framework for analyzing the nature and
scope of child labour at different stages of development.   In Chapter 2 we look at the
role of children as producer goods in a developing country context, as well as the role of
children as consumer goods.  Using household utility theory, in Chapter 3 we develop a
model of household choice.  First, we discuss the role of children at an advanced stage
of development using Becker’s mathematical formulation of the quantity-quality
interaction with regard to child demand.  We then modify the model to include
household time allocation in order to illustrate the case for a lower level of
development.  We test the validity of the  hypothesis that in the aggregate, we may
observe a rise in the incidence of child labour in the early stages of development, until
some threshold level of income is achieved.  Upon reaching this threshold, the
incidence of child labour declines more steadily.  The results are presented in Chapter 5.
Regressions are run on different models with percent child labour as the
dependent variable and per capita GDP as the explanatory variable.  We find that the
quadratic model provides the best fit.  We find evidence of an inverted-U shaped
relation for the total sample as well as for those countries in which per capita GDP is
greater than US$1000.  Moreover, the income elasticities at the mean suggest that as per
capita GDP increases, the incidence of child labour increases provided there are no
effective changes in policy.  The small size of the income parameters suggests that other
aspects of development are important determinants of child labour levels.  Government
policy may also provide children with a voice until we are able to model the role of
children more effectively.  For the bottom 20 per cent of the sample, those countries
with per capita GDP below US$1000, we find the opposite, though insignificant pattern.
That is to say, the child labour force participation rate is inversely correlated with per
62capita GDP, although the income parameters are insignificant at more than the 10 per
cent level and are therefore of no consequence.
Forecasts for per capita GDP, percent child labour, as well as the net primary
enrollment ratio are obtained.  Without significant and effective changes in policy, the
incidence of child labour will continue to rise in many countries for several decades to
come.  It follows that, ceteris paribus, in these countries economic growth alone, as
measured by per capita GDP, may not be a sufficient means by which to reduce child
labour, or eliminate it altogether.  It could take more than 150 years to reduce average
child labour force participation to 10 per cent.  To reach this target by 2029, the
required growth rates range from 2 to 15 per cent.  It may be impossible to generate an
outcome in which the level of child labour is significantly reduced unless measures are
taken to stabilize household income.  Measures taken towards improving the
distribution of income will be most effective.  That is to say, increasing the level of
income may not reduce the number of gainfully employed children; redistribution
efforts are more likely to have the desired effect.
Our results complement the findings of  much of the related research which
imply that by reducing income variability, policies that raise the wage of adults relative
to children are more likely to  reduce the supply of child workers.
39
  Providing some
form of assistance to poor households through income supplementation schemes might
be a sufficient short term solution when improving conditions in the adult labour market
is not an option.  This is true only if the resources are available and if parents believe
that policymakers are credible.  The relaxation of credit constraints and targeting
coordination failures within credit markets is important.  Credit markets could replace
children as a source of insurance against unstable current and future income.
40
The introduction of a formal system of  social security may help to reduce the
need for children, a traditional mechanism of support for the elderly.  Effective credit
markets will provide parents a means by which to save for their consumption needs in
old age.  The establishment of institutions  that substitute for the services children
provide to their parents is crucial in order to reduce parental dependence on child
                                               
39
 As noted in Chapter  2,  refer to Grootaert and Kanbur  (1995), Basu (1999), Baland and Robinson
(2000), Dessy (2000), Altman (2001), and Hazan and Berdugo (2002).
40
 See Ranjan (2001), and Dehejia and Gatti (2002).
63services.  Access to credit markets will enable parents to save for their own future
consumption needs.  
In addition, effective monitoring of child time use is necessary.  As Weiner
(1991) notes, no country has successfully eliminated child labour without regulating the
use of children’s time.  While the historical experience of Britain and the United States
suggests that child labour levels had already begun to decline before compulsory
schooling was introduced, such legislation could have a positive impact, provided it is
designed appropriately and easily enforceable.  However, this must be done in such a
way as not to harm families economically.  For instance, incentive-based educational
opportunities could stimulate child enrollment ratios and reduce the number of gainfully
employed children without economically hurting their families.  Moreover, while
banning, boycotting and bullying have shown to have negative effects on child workers
and their families, regulating children’s working conditions could prove to be
beneficial. Such initiatives will also provide an incentive for firms to adopt better
technologies.
Our results also illustrate the positive  correlation between fertility and child
labour.  Studies have shown that higher education for mothers is associated with fewer,
healthier children.
41
  This could potentially increase household resources devoted to
each child.  Subsidizing the  education of both women and  children will substantially
benefit households and communities.
There are several opportunities for further  research.  It would be interesting to
test for this relationship using more specialized econometric as well as forecasting
models, provided more extensive microeconomic data is available.  Specifically,
regional analyses of countries that have experienced significant growth in certain key
areas would provide us with the means by which to make more relevant inference and
hence, more context appropriate policy recommendations.   For instance, it would be
interesting to observe how this relationship is characterized in Western India – a region
of India that has experienced growth in both state domestic product and child labour –
compared with other Indian provinces.
                                               
41
 See Cochrane (1983), Farooq et al. (1987),  Strauss  (1990), Ahmad (1991), Thomas (1991), and
Ainsworth et al. (1995).
64This study also highlights the need for economic models to include children
rather than lump them into the category  of the household.  Those models that do
explicitly consider the role of children in the household tend not to accurately reflect the
nature of their role; this is particularly true in the context of resource allocation models.
The static model presented in this paper is only a first step.   We have looked at
household utility of child time spent in different activities at a point in time.  There are
many limitations to this approach, where household decisions regarding child time use,
child demand and resource allocation are made at one point in time and by one
household member representing the family.   For instance, fertility theory and human
capital investment theory are modeled such that decision-making takes place over time.
Thus, a dynamic model would allow us to combine these ideas in order to develop more
relevant and effective policy.  It would be interesting to examine this question using a
dynamic approach to intra-household bargaining, thereby taking into consideration the
role of children as strategic decision-makers over time.  Effective evaluation of child
time use is important.  That is to say, the next step would be to examine the utility of
child time use for children and for the household over time.  
When children are recognized as producers, it is often perceived as the result of
a combination of poverty and their weak  economic and social position. Children are
rarely considered to be legitimate social and economic actors; rather, they are assumed
to be recipients of orders given by the  head of household.  Even bargaining models,
whereby household members and other relevant parties are modeled to act according to
some strategic interest, tend to neglect  children as having any bargaining power
whatsoever.  This is another limitation to the approach we have taken.  The recognition
of children as participants in family decision-making will lead to further insight into
childhood and future adulthood wellbeing.
Studies of industrial structures and production processes in different economic
sectors are also important.  We must explore these issues in order to identify the
determinants of child labour.  Other concerns include the effects of war and parental
illness, and the role of government policy.
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71APPENDICES
72Appendix A1: Child Labour and Per Capita GDP Fixed Effects Regression Results, Linear Model
(Total Sample)
Country Fixed E ects Country Fixed E ect
Angola 27.69 Malaysia 3.77
Argentina 5.41 Mali 54.62
Bangladesh 35.32 Mauritania 24.36
Benin 36.53 Mauritius 5.25
Bolivia 15.28 Mexico 11.86
Botswana 13.47 Mongolia 2.64
Brazil   19.32  Morocco  5.84
Burkina Faso 54.91  Mozambique  34.28
Burundi 42.99 Myanmar 24.75
Cambodia 25.03 Namibia 15.80
Cameroon 25.60 Nepal 35.40
Chad 36.09 Nicaragua 13.87
China 11.87 Niger 45.36
Colombia 5.50 Nigeria 26.05
Congo 26.62 Pakistan 14.77
Costa Rica  6.77  Panama 4.66
Cote d’Ivoire  20.83  PNG  19.77
Dominican Republic 15.36  Paraguay 10.34
Ecuador 7.39 Peru 3.08
Egypt   9.57  Philippines  9.16
El Salvador 11.77  Portugal 3.58
Ethiopia 43.05 Rwanda 42.17
Gabon 18.30 Senegal 31.01
Gambia 27.22 Sierra Leone 15.45
Ghana 13.38 Sri Lanka 2.89
Guatemala 14.58 Sudan 22.60
Guinea 34.08 Syria 6.16
Guinea-Bissau 39.28 Tanzania 39.43
Haiti 24.40 Thailand 14.25
Honduras 10.60 Togo 29.22
India 10.63 Turkey 20.00
Indonesia 9.90 Uganda 45.40
Iran 5.23 Uruguay 8.70
Iraq 3.65 Vietnam 10.07
Kenya 40.87 Yemen 20.49
Lesotho 22.55 Zambia 16.75
Madagascar 36.09 Zimbabwe 19.25
Malawi 34.90
73Appendix A2: Child Labour and Per Capita GDP Fixed Effects Regression Results, Linear Model
(per capita GDP< US$1000)
Country Fixed E ects
Burkina Faso 56.55
Burundi 44.32
Chad 37.77
Ethiopia 43.99
Guinea-Bissau 40.89
Madagascar 37.64
Malawi 36.33
Mali 55.84
Mozambique 36.05
Myanmar 26.67
Niger 46.88
Rwanda 43.47
Sierra Leone  16.94
Tanzania   40.65
Zambia 18.63
74Appendix A3: Child Labour and Per Capita GDP Fixed Effects Regression Results, Linear Model
(per capita GDP> US$1000)
Country Fixed E ects Country Fixed E ect
Angola 27.68 Lesotho 22.53
Argentina 5.30 Malaysia 3.66
Bangladesh 35.31 Mauritania 24.34
Benin 36.51 Mauritius 5.22
Bolivia 15.25 Mexico 11.76
Botswana 13.39 Mongolia 2.61
Brazil   19.24  Morocco  5.79
Cambodia 25.04 Namibia 15.75
Cameroon 25.57 Nepal 35.39
China 11.84 Nicaragua 13.85
Colombia 5.43 Nigeria 26.03
Congo 26.59 Pakistan 14.75
Costa Rica  6.69  Panama 4.57
Cote d’Ivoire  20.81  PNG  19.70
Dominican Republic 15.31  Paraguay 10.29
Ecuador 7.33 Peru 3.02
Egypt   9.53  Philippines  9.12
El Salvador 11.74  Portugal 3.42
Gabon 18.23 Senegal 30.98
Gambia 27.21 Sri Lanka 2.85
Ghana 13.35 Sudan 22.59
Guatemala 14.54 Syria 6.10
Guinea 34.05 Thailand 14.17
Haiti 24.39 Togo 29.21
Honduras 10.57 Turkey 19.93
India 10.60 Uganda 45.38
Indonesia 9.86 Uruguay 8.60
Iran 5.16 Vietnam 10.05
Iraq 3.61 Yemen 20.48
Kenya 40.86 Zimbabwe 19.23
75Appendix B1: Child Labour and Per Capita GDP Fixed Effects Regression Results, Log-Log Model
(Total Sample)
Country Fixed E ects Country Fixed E ect
Angola 3.44 Malaysia 1.17
Argentina 1.58 Mali 4.11
Bangladesh 3.67 Mauritania 3.31
Benin 3.68 Mauritius 1.52
Bolivia 2.76 Mexico 2.49
Botswana 2.66 Mongolia 0.95
Brazil   3.07  Morocco  1.77
Burkina Faso 4.11  Mozambique  3.65
Burundi 3.86 Myanmar 3.20
Cambodia 3.34 Namibia 2.79
Cameroon 3.36 Nepal 3.64
Chad 3.70 Nicaragua 2.72
China 2.57 Niger 3.93
Colombia 1.67 Nigeria 3.35
Congo 3.40 Pakistan 2.80
Costa Rica  1.94  Panama 1.51
Cote d’Ivoire  3.15  PNG  3.10
Dominican Republic 2.80  Paraguay 2.33
Ecuador 2.05 Peru 1.05
Egypt   2.34  Philippines  2.29
El Salvador 2.55  Portugal 0.66
Ethiopia 3.86 Rwanda 3.84
Gabon 3.01 Senegal 3.55
Gambia 3.35 Sierra Leone 2.85
Ghana 2.70 Sri Lanka 0.91
Guatemala 2.78 Sudan 3.19
Guinea 3.64 Syria 1.85
Guinea-Bissau 3.78 Tanzania 3.78
Haiti 3.31 Thailand 2.74
Honduras 2.45 Togo 3.49
India 2.40 Turkey 3.06
Indonesia 2.38 Uganda 3.93
Iran 1.65 Uruguay 1.63
Iraq 1.30 Vietnam 2.35
Kenya 3.82 Yemen 3.13
Lesotho 3.23 Zambia 2.93
Madagascar 3.70 Zimbabwe 2.87
Malawi 3.66
76Appendix B2: Child Labour and Per Capita GDP Fixed Effects Regression Results, Log-Log Model
(per capita GDP< US$1000)
Country Fixed E ects
Burkina Faso 4.07
Burundi 3.83
Chad 3.66
Ethiopia 3.83
Guinea-Bissau 3.75
Madagascar 3.66
Malawi 3.63
Mali 4.07
Mozambique 3.61
Myanmar 3.28
Niger 3.89
Rwanda 3.81
Sierra Leone  2.81
Tanzania   3.75
Zambia 2.89
77Appendix B3: Child Labour and Per Capita GDP Fixed Effects Regression Results, Log-Log Model
(per capita GDP> US$1000)
Country Fixed E ects Country Fixed E ect
Angola 3.22 Indonesia 2.14
Argentina 1.31 Iran 1.40
Bangladesh 3.46 Iraq 1.06
Benin 3.46 Kenya 3.61
Bolivia 2.53 Lesotho 3.01
Botswana 2.40 Malaysia 0.90
Brazil   2.81  Mauritania  3.09
Cambodia 3.12 Mauritius 1.24
Cameroon 3.13 Mexico 2.22
China 2.34 Mongolia 0.72
Colombia 1.41 Morocco 1.53
Congo 3.17 Namibia 2.54
Costa Rica  1.68  Nepal 3.43
Cote d’Ivoire  2.93  Nicaragua  2.49
Dominican Republic 2.55  Nigeria  3.16
Ecuador 1.80 Pakistan 2.57
Egypt   2.10  Syria  1.25
El Salvador 2.32  Thailand 2.87
Gabon 2.76 Togo 2.09
Gambia 3.14 Turkey 0.81
Ghana 2.48 Uganda 2.05
Guatemala 2.54 Uruguay 0.38
Guinea 3.43 Vietnam 3.33
Haiti 3.10 Yemen 0.67
Honduras 2.23 Zimbabwe 2.97
India 2.18
78Appendix C1: Child Labour and Per Capita GDP Fixed Effects Regression Results,
 Quadratic Model
(Total Sample)
Country Fixed E ects Country Fixed E ect
Angola 26.93 Malaysia 1.54
Argentina 3.47 Mali 54.23
Bangladesh 34.58 Mauritania 23.48
Benin 35.70 Mauritius 3.84
Bolivia 13.98 Mexico 9.55
Botswana 11.31 Mongolia 1.37
Brazil   17.07  Morocco  4.18
Burkina Faso 54.41  Mozambique  33.74
Burundi 42.57 Myanmar 24.16
Cambodia 24.31 Namibia 14.07
Cameroon 24.45 Nepal 34.72
Chad 35.59 Nicaragua 12.73
China 10.39 Niger 44.89
Colombia 3.27 Nigeria 25.32
Congo 25.42 Pakistan 13.65
Costa Rica  4.53  Panama 2.49
Cote d’Ivoire  19.86  PNG  18.44
Dominican Republic 13.53  Paraguay 8.55
Ecuador 5.50 Peru 1.27
Egypt   7.90  Philippines  7.63
El Salvador 10.33  Portugal 2.75
Ethiopia 42.76 Rwanda 41.76
Gabon 16.26 Senegal 30.06
Gambia 26.55 Sierra Leone 14.99
Ghana 12.41 Sri Lanka 1.36
Guatemala 12.87 Sudan 21.84
Guinea 33.28 Syria 4.18
Guinea-Bissau 38.78 Tanzania 39.05
Haiti 23.72 Thailand 12.03
Honduras 9.45 Togo 28.53
India 9.76 Turkey 17.81
Indonesia 8.33 Uganda 44.74
Iran 3.11 Uruguay 6.45
Iraq 2.01 Vietnam 9.26
Kenya 40.12 Yemen 19.81
Lesotho 21.62 Zambia 16.17
Madagascar 35.61 Zimbabwe 18.04
Malawi 34.46
79Appendix C2: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Quadratic Model
(per capita GDP< US$1000)
Country Fixed Effects
Burkina Faso 57.73
Burundi 45.47
Chad 38.84
Ethiopia 44.96
Guinea-Bissau 42.08
Madagascar 38.83
Malawi 37.50
Mali 56.96
Mozambique 37.20
Myanmar 27.71
Niger 48.07
Rwanda 44.60
Sierra Leone  18.02
Tanzania   41.76
Zambia 19.78
80Appendix C3: Child Labour and Per Capita GDP Fixed Effects Regression Results,
Quadratic Model
(per capita GDP> US$1000)
Country Fixed E ects Country Fixed E ect
Angola 26.82 Lesotho 21.48
Argentina 3.12 Malaysia 1.14
Bangladesh 34.48 Mauritania 23.35
Benin 35.58 Mauritius 3.49
Bolivia 13.78 Mexico 9.16
Botswana 10.98 Mongolia 1.18
Brazil   16.71  Morocco  3.94
Cambodia 24.20 Namibia 13.80
Cameroon 24.29 Nepal 34.63
China 10.18 Nicaragua 12.56
Colombia 2.91 Nigeria 25.21
Congo 25.25 Pakistan 13.49
Costa Rica  4.17  Panama 2.15
Cote d’Ivoire  19.72  PNG  18.26
Dominican Republic 13.26  Paraguay 8.28
Ecuador 5.21 Peru 1.00
Egypt   7.66  Philippines  7.40
El Salvador 10.12  Portugal 2.45
Gabon 15.95 Senegal 29.93
Gambia 26.45 Sri Lanka 1.13
Ghana 12.28 Sudan 21.73
Guatemala 12.61 Syria 3.88
Guinea 33.16 Thailand 11.68
Haiti 23.63 Togo 28.44
Honduras 9.28 Turkey 17.47
India 9.63 Uganda 44.65
Indonesia 8.09 Uruguay 6.06
Iran 2.78 Vietnam 9.14
Iraq 1.77 Yemen 19.71
Kenya 40.00 Zimbabwe 17.86
81Appendix D: Example of an Augmented Dickey Fuller Unit Root Test on Per Capita GDP, Ethiopia
ADF Statistic   -2.42 1% critical value  -5.48
5% critical value  -4.08
10% critical value  -3.49
Variable Coefficient Standard Error  t-statistic  Probability
X3V(-1) -0.835 0.345 -2.417 0.0603
D(X3V(-1)) -0.322 0.276 -1.165 0.2966
C 0.224 0.102 2.192 0.0799
@Trend (1989) 0.029 0.009 3.292 0.0217
R-squared 0.745
82Appendix E: White’s Test for Heteroscedasticity
White’s Test: Based on the auxiliary regression of the squared residuals from the initial
model on the explanatory variables, their squared values and cross-products,
n R ⋅ df
2 2
~ χ
The degrees of freedom correspond to the number of regressors.
We obtain a  value of 55.34 which exceeds the critical value; therefore we reject the
null hypothesis of homoscedasticity.
χ
2
83