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Essays on the economics of child labor and fertility [Elektronische Ressource] / vorgelegt von Ramona Bruhns (geb. Schrepler)

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Essays on the Economics of ChildLabor and FertilityInaugural-Dissertation zur Erlangung der Doktorwurde˜Fakultat fur Wirtschafts- und Sozialwissenschaften˜ ˜Ruprecht-Karls Universitat Heidelberg˜vorgelegt von:Ramona Bruhns(geb. Schrepler)geboren am 29. Marz 1977, in Timisoara, Rumanien˜ ˜April 2006iiContentsAcknowledgments 1Introduction and Overview 11 Child Labor and Fertility 131.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2 The model framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.3 The Household’s Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.3.1 The unrestricted solution . . . . . . . . . . . . . . . . . . . . . . . . 201.3.2 Unrestricted solutions w.r.t. one variable . . . . . . . . . . . . . . . 221.3.3 The corner solutions w.r.t. both variables . . . . . . . . . . . . . . 241.3.4 The household’s decision . . . . . . . . . . . . . . . . . . . . . . . . 251.4 Economic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.4.1 The critical level of schooling . . . . . . . . . . . . . . . . . . . . . 271.4.2 Low and moderate levels of e–ciency . . . . . . . . . . . . . . . . . 281.4.3 High levels of e–ciency . . . . . . . . . . . . . . . . . . . . . . . . . 301.4.4 Conclusion: Economic growth and steady states . . . . . . . . . . . 301.5 Governmental Intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.5.
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Essays on the Economics of Child
Labor and Fertility
Inaugural-Dissertation zur Erlangung der Doktorwurde˜
Fakultat fur Wirtschafts- und Sozialwissenschaften˜ ˜
Ruprecht-Karls Universitat Heidelberg˜
vorgelegt von:
Ramona Bruhns
(geb. Schrepler)
geboren am 29. Marz 1977, in Timisoara, Rumanien˜ ˜
April 2006ii
Contents
Acknowledgments 1
Introduction and Overview 1
1 Child Labor and Fertility 13
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2 The model framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 The Household’s Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.1 The unrestricted solution . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.2 Unrestricted solutions w.r.t. one variable . . . . . . . . . . . . . . . 22
1.3.3 The corner solutions w.r.t. both variables . . . . . . . . . . . . . . 24
1.3.4 The household’s decision . . . . . . . . . . . . . . . . . . . . . . . . 25
1.4 Economic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.1 The critical level of schooling . . . . . . . . . . . . . . . . . . . . . 27
1.4.2 Low and moderate levels of e–ciency . . . . . . . . . . . . . . . . . 28
1.4.3 High levels of e–ciency . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.4 Conclusion: Economic growth and steady states . . . . . . . . . . . 30
1.5 Governmental Intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.5.1 Regulatory measures . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.2 Fiscal Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.3 Policy Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.5.4 Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
A.1 The corner solution with respect to fertility . . . . . . . . . . . . . 50
A.2 The corner solution with respect to education . . . . . . . . . . . . 52
A.3 The corner solutions w.r.t. both variables . . . . . . . . . . . . . . 53
A.4 Potential Steady States: the unrestricted solution w.r.t. e. . . . . . 56
2 Child Labor, Fertility and Land: Economic growth in developing coun-
tries 62
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.3 The Household’s Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3.1 The unrestricted solution . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3.2 The unrestricted solution w.r.t. education . . . . . . . . . . . . . . 69
2.3.3 The unrestricted solution w.r.t fertility . . . . . . . . . . . . . . . . 70
2.3.4 The corner solutions w.r.t both variables . . . . . . . . . . . . . . . 72Contents iii
2.4 Growth paths: a characterization . . . . . . . . . . . . . . . . . . . . . . . 73
2.4.1 Miscellaneous Paths . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.4.2 Growth paths with a constant total population size . . . . . . . . . 76
2.4.3 Path P6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.4.4 A constant level of e–ciency and e2f0;1g . . . . . . . . . . . . . . 81
2.4.5 Path P8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.5 Conclusion: Paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.5.1 The low-level stationary state . . . . . . . . . . . . . . . . . . . . . 85
2.5.2 The high-level stationary state and growth steady state . . . . . . . 86
2.5.3 Economic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.5.4 Dynamic E–ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.6 Governmental Intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.6.1 Lump-sum transfers . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.6.2 School-attendance subsidies . . . . . . . . . . . . . . . . . . . . . . 93
2.6.3 Governmental Programs . . . . . . . . . . . . . . . . . . . . . . . . 95
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3 The Long-run Efiects of HIV/AIDS in Kenya 98
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.2 Historical Overview and Data: 1920-2000 . . . . . . . . . . . . . . . . . . . 102
3.2.1 Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.2.2 Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.2.3 Educational Attainment . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.5 Projections: The Base Case . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.5.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.5.2 The Benchmark Cases . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.5.3 Scenarios: Household Behavior when expectations are revised with
a delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.6 Variations: Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
13.6.1 Variation 1: The level of N . . . . . . . . . . . . . . . . . . . . . 130min
3.6.2 Variation 2: The level of fi . . . . . . . . . . . . . . . . . . . . . . 132t
3.6.3 Variation 3: The level of z . . . . . . . . . . . . . . . . . . . . . . . 134t
3.7 Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.7.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
3.7.2 Policy: Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.8 The Efiects on Social Welfare . . . . . . . . . . . . . . . . . . . . . . . . . 142
3.9 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
3.9.1 No public spending on health . . . . . . . . . . . . . . . . . . . . . 147
3.9.2 Public Spending on Health . . . . . . . . . . . . . . . . . . . . . . . 150
3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.11 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4 Summary and Conclusions 160
Bibliography 165iv
List of Figures
1 Economically active children aged 10-14: participation rates. Source: ILO 2
1.1 The unrestricted solution with respect to fertility for e„ = 0; for low and
high child-raising costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2 Unrestricted solution with respect to education for difierent costs. . . . . . 23
1.3 unrestricted solution with respect to education with subsidies (for fi„=1=4) 41
2fi(1¡´)1.6a The Household’s Decision and Phase Diagram: z <1 and b< . . . 59nmax
2fi(1¡´)1.6b The Household’s Decision and Phase Diagram: z =1 and b< . . . 59nmax
2fi(1¡´)1.6c The Household’s Decision and Phase Diagram: z >1 and b< . . . 59nmax
2fi(1¡´) 2fi(1¡´)1.6d TheHousehold’sDecisionandPhaseDiagram: z <1andb2[ ; ] 60n nmax min
2fi(1¡´) 2fi(1¡´)1.6e TheHousehold’sDecisionandPhaseDiagram: z =1andb2[ ; ] 60n nmax min
2fi(1¡´) 2fi(1¡´)1.6f TheHousehold’sDecisionandPhaseDiagram: z >1andb2[ ; ] 60n nmax min
2fi(1¡´)1.6g The Household’s Decision and Phase Diagram for z <1 and b> . . 61nmin
2fi(1¡´)1.6h The Household’s Decision and Phase Diagram: z =1 and b> . . . 61nmin
2fi(1¡´)1.6i The Household’s Decision and Phase Diagram: z >1 and b> . . . 61nmin
2.1 Unrestricted solution w.r.t. fertility for a flxed level of e–ciency as a func-
tion of N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71v
List of Tables
1.1 Unrestricted solution w.r.t fertility for e„=0 and e„=1 . . . . . . . . . . . 22
1.2 Unrestricted solution w.r.t education . . . . . . . . . . . . . . . . . . . . . 23
1.3 4U as a function of e–ciency and child-raising costs . . . . . . . . . . . . 24n
1.4 4U as a function of e–ciency and child-raising costs . . . . . . . . . . . . 25e
1.5 Conclusion: Steady-States . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1 Solutions to the household maximization problem . . . . . . . . . . . . . . 69
2.2 Cyclical and Non-Cyclical Steady States . . . . . . . . . . . . . . . . . . . 74
2.3 Steady States: fertility and education . . . . . . . . . . . . . . . . . . . . . 74
3.1 Population Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.2 GDP in Kenya, 1950-2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.3 Educational Attainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
13.4 Households’ choices of e and N . . . . . . . . . . . . . . . . . . . . . . . 115t t
3.5 Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.6 Projections: Population Tables without AIDS . . . . . . . . . . . . . . . . 119
3.7 Projections: Population Tables with AIDS . . . . . . . . . . . . . . . . . . 119
3.8 Survival rates • and mortality rates (1¡• ) in the benchmark cases . . . 119t t
3.9 Benchmark Case I: NO AIDS . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.10 Benchmark Case I: AIDS, perfect foresight . . . . . . . . . . . . . . . . . . 122
3.11 Scenario 1: AIDS, e subject to a binding contract. . . . . . . . . . . . . . 1269
3.12 Scenario 2: AIDS, e revised by the flrst group . . . . . . . . . . . . . . . . 1279
3.13 Scenario 3: e revised by the second group . . . . . . . . . . . . . . . . . . 1299
13.14 Variation 1: The level of N . . . . . . . . . . . . . . . . . . . . . . . . 131min
3.15 Variation 2: Recovery of fi after 2000. . . . . . . . . . . . . . . . . . . . . 133t
3.16 Variation 3: Recovery of z by 2010 . . . . . . . . . . . . . . . . . . . . . . 135t
3.17 The parameter values of the function q (G ;D =1) . . . . . . . . . . . . . 138t t
3.18 The efiects of the policy program A on fertility and education: 2010 . . . . 141
3.19 The efiects of the HIV/AIDS epidemic expressed as a % of the NO AIDS
levels in 2040 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.20 Lost income through premature adult mortality, including unborn individ-
uals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3.21 Lostincomethroughprematureadultmortality,excludingunbornindividuals150
3.22 The efiects of the public spending programA, expressed as a % of the NO
AIDS levels in 2040 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
a3.23 The policy program A: Profltability , including unborn individuals . . . . 154
a3.24 The policy program A: Profltability , excluding unborn individuals . . . . 154
3.25 The Policy Program A: Base Case . . . . . . . . . . . . . . . . . . . . . . 156List of Tables vi
13.26 The Policy Program A: Variation 1: The level of N . . . . . . . . . . . 157min
3.27 The Policy Program A: Variation 2: Recovery of fi . . . . . . . . . . . . . 157t
3.28 The Policy Program A: Variation 3: Recovery of z . . . . . . . . . . . . . 158t
3.29 Lost income through premature adult mortality, including unborn individ-
uals: Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
3.30 Lost income through premature adult mortality, excluding unborn individ-
uals: Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
a3.31 The policy program A, excluding unborn individuals: Profltability . . . . 159vii
Acknowledgments
This dissertation was written while I was an assistant with the Department of Develop-
ment Economics at Heidelberg University’s South Asia Institute. First of all, I would like
to thank my supervisor, Prof. Clive Bell, who introduced me to the flelds of development
economics and growth theory. I proflted greatly from his support and guidance, and from
the feedback at all stages of the project. The present dissertation would have never been
what it is today without his valuable comments, in form, content and language. I also
thank my second adviser, Prof. Hans Gersbach, for many useful and clarifying sugges-
tions. ThanksalsotoProf. EichbergerandProf. Gansforjoiningmydoctoralcommittee.
I would also like to thank the participants at various conferences (SMYE 2003 { 2005,
NEUDC 2003) and research seminars (Heidelberg’s PhD seminar, Cornell University’s
International Colloquium 2004) for illuminating discussions and comments.
I thank Dagmar Vol˜ker for all the fruitful discussions we had since we started study-
ing economics here in Heidelberg, and even more for our friendship which expressed itself
in things small and large. I would also like to thank Annegret and Stefan for letting me
stay with them in Ithaca, for reading through my research proposal, for the grill parties
and extensive talks about skiing. All my colleagues here in Heidelberg { Dagmar, An-
negret, Stefan, Olli, Julian, Anastasios, Birgit and Christina { I thank you for the great
atmosphere at work!
I thank my family for their support, for their belief in me and their encouragement.
I thank Hjalmar for sharing all these years with me, for his patience and trust { and for
much more. Without you, I would have never made it this far!
Finally, I am indebted to my parents, Doina and Andrei, for having had the courage
to start a new life in Germany 15 years ago { without that, I would have never had the
chance to study here, and to write this dissertation.1
Introduction and Overview
Labor has been a part of childhood for all but short times in the development of hu-
mankind. In ancient Greece and Rome, for example, children were often born or sold
into slavery. Although they were sometimes protected by laws which prevented excessive
abuse, few of them enjoyed education, and many had to work in appalling conditions,
e.g. in mines. In Europe in the middle ages, when formal education was a privilege of
the rich, virtually all children worked, helping their parents with the fleldwork, tending
livestockordoinghouseholdchores. Apartfrommonasteries, wherefuturemonkslearned
how to read and write, the only form of education open to most non-noble boys was an
apprenticeship with a craftsman. This started when the child was still very young, by
the age of 7, and ended up to 10 years later. Formal education became available in large
towns during the 15th century. However, as schooling was neither free nor compulsory,
manypoorfamiliescouldnotafiordtoeducatetheirchildren,whohadtoworktosupport
their parents. At the time of the industrial revolution, child labor in its worst forms was
common in the new factories and mills. As many families moved from the land to town
in order to work in the new industries, labor was cheap, and all family members had to
work to make a living. Orphans, however, were even worse ofi, as they had no parents to
protect them from abuse, and sometimes had to work without pay. Great Britain was the
flrst country in modern history to pass a child labor act, the Factory Act of 1833, which
limited working hours and prohibited children younger than 9 years of age from working
at all. Child labor, however, was still a problem in Europe and the United States well
into the 20th century.Introduction and Overview 2
Figure 1: Economically active children aged 10-14: participation rates. Source: ILO
At present, child labor is insigniflcant in most industrial countries, with less than one
out of 3000 children younger than 14 working in Europe, according to the International
Labor O–ce (ILO). The situation is much worse in other countries and regions, partic-
ularly Africa and Asia. About 40% of all children between 10 and 14 years of age were
economically active in Eastern Africa in 2000, the number being somewhat lower for the
wholecontinent,whereaboutthanoneinfourchildrenworked. Ascanbeseenfromflgure
1, the percentage of economically active children is highest in Africa, and about half as
highinAsiaandLatinAmerica. Duringthewholeperiodforwhichdataisavailable,labor
market participation rates were falling, on average, by 3 percentage points per decade.
While it is clear that working in hazardous conditions for long hours with little pay is
undesirable, not all forms of economic activity captured by the numbers in flgure 1 are to
be condemned. The ILO deflnes economic activity as "all market production (paid work)
and certain types of non-market production (unpaid work), including production for own
use. [...] paid or unpaid, the activity or occupation could be in the formal or informal
1sector in urban or rural areas" . While this includes "child labor", "children in hazardous
work"and "children in unconditional worst forms of child labor", it does not include chil-
dren who perform household chores, which are non-economic activities according to the
1Source: Every Child Counts: New Global Estimates on Child Labour, International Labour O–ce,
Geneva, April 2002Introduction and Overview 3
ILO’s deflnition, and therefore do not appear in the its statistics. Note that some forms
of economic activity, such as light work for a few hours a week, can provide families with
the income they need to afiord schooling, and can even be part of the education, e.g. in
apprenticeships. On the other hand, the non-economic activities which are not captured
by the ILO’s estimates are often considerable, and can prevent children from attending
school.
This distinction is not normally made in the theoretical literature on child labor. Most
authors assume thatchildrencaneitherwork, andtherefore contribute to the household’s
income, or go to school, thereby foregoing wages. Non-wage work, such as caring for the
siblings and households chores, is ignored, as is paid work which is part of the child’s
education.
The literature on child labor has been reviewed by Basu (1999) and by Brown, Dear-
dorfi and Stern (2003). During the 1990s and early 2000s, the literature departed from
the analysis of unitary models to consider issues of household bargaining, especially on
an intra-household level (Moehling (1995), Basu and Ray (2002)).
More recent literature addresses the possibility of multiple equilibria. Basu and Van
(1998), for example, assume that child and adult labor are substitutes, and that parents
only send children to work if the household income lies below some exogenous threshold.
They consider an economy with inhomogeneous households, which difier with respect to
the wage levels for which they send all their children to work, so that the total amount of
child labor in an economy will depend on the adult’s wage. The authors then show that
multiple stable equilibria can exist: in one, all children work and wages are low, and in
the other wages are high and children do not work at all. If indeed two such equilibria
exist, a governmental ban on child labor, if enforced, will result in the economy switching
from the low-wage to the high-wage equilibrium, if the former ruled before the ban.

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