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Human Capital Investment and
Population Dynamics
Inauguraldissertation
zur Erlangung des akademischen Grades
eines Doktors der Wirtschaftswissenschaften
der Universit˜at Mannheim
vorgelegt von
Edgar-Csaba Vogel
Mannheim, 2010Dekan: Prof. Tom Krebs, Ph.D.
Referent: Prof. Axel B˜orsch-Supan, Ph.D.
Korreferent: Prof. Dr. Andreas Irmen
Datum der mundlic˜ hen Prufung:˜ 1. Juli 2010
iiAcknowledgments
The fact that this thesis has only a single author suggests that this is the achievement of
only oneperson. Thisis, however, onlypart ofthe truth. Without the helpand supportof
manyothersitwouldhavebeenmuchharder{ifnotimpossible{toflnishthisdissertation.
Therefore, I want to take the chance to thank all those who deserve the credit for their
support through the last years.
First, I would like to thank my supervisor, Prof. Axel B˜orsch-Supan, for his help and
support. Ilearnedverymuchfromhiscommentsandsuggestionsandmyworkwasinspired
by his critical and unconventional way of thinking about research. Further, I am greatly
indebted to Prof. Alexander Ludwig for his continuous support and encouraging words.
Working together was a real pleasure. The joint work and our discussions shaped my
way of thinking and doing research. The fruits of this cooperation are chapters 4 and 5.
Moreover I thank Prof. Andreas Irmen for numerous discussions and comments. Special
thanks go to Thomas Schelkle for the productive cooperation on chapter 5.
Next, I would like to thank my fellow colleagues and friends at the CDSE { especially
the class of 2005. We had tough times but also a lot of fun and their company during
di–cult passages of the doctoral voyage was of invaluable help. It was a real pleasure to
spend time together, in- and outside of our o–ces. I also would like to thank my fellow
colleagues at MEA for their support and encouraging comments which provided an ideal
atmosphere for doing research. Last but not least I would like to thank my family and
friends for supporting me thorough. Finally, I express my gratitude to my parents who
supported me throughout. I would never have made it without the their love and endless
support. Therefore, I dedicate this thesis to them.
iiiContents
Acknowledgments iii
1 General Introduction 1
1.1 FromMalthustoModernGrowth: ChildLabor,SchoolingandHumanCapital 2
1.2 Why Schooling Became Optimal . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Demographics in a Simple OLG Economy . . . . . . . . . . . . . . . . . . 5
1.4 Demographic Change, Human Capital and Welfare . . . . . . . . . . . . . 6
2 From Malthus to Modern Growth: Child Labor, Schooling and Human
Capital 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Household Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Solution to the Household’s Problem . . . . . . . . . . . . . . . . . 19
2.3.3 The Steady State Solution . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 The Macroeconomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 General Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.1 Technological Progress . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.2 Survival Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
vvi CONTENTS
2.5.3 The Dynamical System . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5.4 A Calibration Exercise . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.A Appendix: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Human Capital and the Demographic Transition: Why Schooling Be-
came Optimal 47
3.1 Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Life Expectancy, Schooling and Fertility . . . . . . . . . . . . . . . . . . . 50
3.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1 Timing and Conventions . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.2 Aggregate Production . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.3 Human Capital of Adults . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.4 The Price of Education . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.5 Household Preferences and Constraints . . . . . . . . . . . . . . . . 56
3.3.6 Individual Maximization Problem . . . . . . . . . . . . . . . . . . . 58
3.3.7 The Choice of Private vs. Public Schooling . . . . . . . . . . . . . . 63
3.3.8 Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 The Dynamic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.1 Life Expectancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.2 Schooling Choice in General Equilibrium . . . . . . . . . . . . . . . 67
3.4.3 Population Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.4 Technological Progress . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4.5 An Illustrative Simulation . . . . . . . . . . . . . . . . . . . . . . . 71
3.5 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.A Appendix: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75CONTENTS vii
4 Mortality, Fertility, Education and Capital Accumulation in a Simple
OLG Economy 81
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.2 Markets for Annuities . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.3 Household Optimization . . . . . . . . . . . . . . . . . . . . . . . . 86
4.2.4 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2.5 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.6 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.7 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.1 Analytical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.2 Role of Annuity Markets . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.A Appendix: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.B Appendix: Numerical Results without Annuity Markets . . . . . . . . . . . 117
5 Demographic Change, Human Capital and Welfare 121
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.2.1 Timing, Demographics and Notation . . . . . . . . . . . . . . . . . 124
5.2.2 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2.3 Formation of Human Capital . . . . . . . . . . . . . . . . . . . . . 126
5.2.4 The Pension System . . . . . . . . . . . . . . . . . . . . . . . . . . 126viii CONTENTS
5.2.5 Firms and Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.2.6 Thought Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.3 Calibration and Computation . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.2 Household Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.3.3 Individual Productivity Proflles . . . . . . . . . . . . . . . . . . . . 129
5.3.4 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.3.5 The Pension System . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.3.6 Computational Method . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.4.1 Backfltting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.4.2 Transitional Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.A Appendix: General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.A.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.A.2 Backfltting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.A.3 Labor Supply Elasticities . . . . . . . . . . . . . . . . . . . . . . . . 145
5.A.4 Transitional Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.A.5 Demographic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.B Appendix: Computational Details . . . . . . . . . . . . . . . . . . . . . . . 160
5.B.1 Household Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.B.2 The Aggregate Model. . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.B.3 Calibration of Structural Model Parameters . . . . . . . . . . . . . 167Chapter 1
General Introduction
This thesis consists of four self-contained papers linked by one common topic: the interac-
tion of human capital, fertility and the macroeconomic environment. We start by looking
ataneconomycharacterizedbydismalsocialandeconomicconditions: lowlifeexpectancy,
high mortality, little investment into human capital, low income, and high fertility. In the
flrsttwochapters, weexaminethedevelopmentpathfromaMalthusiantraptoaSolowian
economy and make an attempt to provide possible explanations which forces could have
potentially shaped this process. To focus only on the link between human capital, fertility
and survival probabilities, we deliberately ignore the issue of physical capital accumula-
tion which will be brought back in chapters 4 and 5. Then we move on to an economy
with fundamentally difierent conditions. We look at the problems of an aging but devel-
oped economy. The challenges faced by these economies are radically difierent from those
described above. Now, the problem is not that short lives and frequent diseases make in-
vestmentintohumancapitaleconomicallyunviablebutratherthatlonglivingandhealthy
centenarians exert flnancial pressure on our social security systems. The disincentive to
invest into human capital stems now from high taxation rather than from a short planning
horizon. Capital dilution due to high fertility rates is no longer the problem but we worry
thatcurrentlylowfertilityratesmayendangertheflscalsustainabilityofthepay-as-you-go
pension systems and lead to distributional con icts between old and young. No matter
at which situation we look, it is evident that the answer is likely to be dominated by the
interaction of these variables.
12 CHAPTER 1. GENERAL INTRODUCTION
The following sections contain a short non-technical summary of each chapter. Proofs and
technical details are provided directly at the end of each chapter. Due to the fact that
a part of the literature is common to all chapters, references are provided in one single
chapter at the end of the thesis.
1.1 From Malthus to Modern Growth: Child Labor,
Schooling and Human Capital
Chapter2developsadynamicgeneralequilibriummodeloffertility,humancapitalaccumu-
lation, childlaboranduncertainchildsurvivalfocusingonthequalitativeandquantitative
efiect of declining child mortality on household decisions and economic development. Due
to uncertainty about child survival, parents have a precautionary demand for children.
Rising survival probability leads to falling fertility, eventually to investment into schooling
and the demise of child labor. Child labor can be an obstacle to development since it low-
ers the incentives of parents to educate children. Furthermore, we argue that the decline
of precautionary child demand as a consequence of falling mortality is not su–cient to
generate a demographic transition. Falling mortality can only explain a relatively small
part of the fertility decline. A sizable reduction in fertility can only be achieved by human
capital investment and the induced quantity-quality trade ofi.
The modeling environment follows the literature by allowing families to choose their con-
sumption level, number and quality of their children. Children’s quality is measured by
theleveloftheirhumancapitalwhichistheresultoftimeinvestmentintoahumancapital
formation technology. At the same time, parents choose the level of child labor: children
can thus contribute to their families’ income. They can simultaneously work and go to
school, as long as their total time budget is not exhausted. For the parents’ utility func-
tion we assume that it is increasing in their own consumption, the number and quality
of their surviving children but decreasing in the level of children’s labor supply. Thus,
parents face a trade-ofi between higher consumption and the disutility from child labor.
Further, by having working children, they sacriflce some potential utility gain from en-
dowing them with human capital. Since the survival of children is uncertain, parens have
a precautionary demand for children. This means that in times of high child mortality,

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