Human capital investment and population dynamics [Elektronische Ressource] / vorgelegt von Edgar-Csaba Vogel

Informations

• Publié par: universitat_mannheim
• Publié le: 01 janvier 2010
• Nombre de lectures: 8
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

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 Mod