Knowledge codification and endogenous growth theory [Elektronische Ressource] / vorgelegt von Maik T. Schneider

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Knowledge Codification andEndogenous Growth TheoryInaugural-Dissertation zur Erlangung der Würde einesDoktors der Wirtschaftswissenschaften (Dr. rer. pol.)an der Wirtschafts- und Sozialwissenschaftlichen Fakultätder Ruprecht-Karls-Universität Heidelbergvorgelegt im August 2006 vonMaik T. Schneidergeboren in Schwäbisch HallAcknowledgementsThis dissertation would not have been accomplished without the assistance and encour-agement of a number of people. In particular, I owe sincere gratitude to my advisorProf. Dr. Hans Gersbach for his continuous support, advice, and perceptive comments,which contributed greatly to this thesis. Within discussions I have benefitted a lot fromhis extensive scientific expertise. I also thank Prof. Timo Goeschl, Ph.D. for co-advisingon this work and his valuable suggestions.My thanks go to all participants and professors of the Graduate Program “Environ-mental and Resource Economics” and former members of the Interdisciplinary Institutefor Environmental Economics of the University of Heidelberg for personal and practicalassistance and numerous inspiring discussions. In particular, I would like to mentionDr. Stefan Baumgärtner, Dr. Christian Becker, Svenja Espenhorst, Christoph Heinzel,Dr. Olaf Hölzer, Friderike Hofmeister, Benjamin Lünenbürger, Felix Mühe, Dr. MartinQuaas, and Dr. Markus Schaller.

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Knowledge Codification and
Endogenous Growth Theory
Inaugural-Dissertation zur Erlangung der Würde eines
Doktors der Wirtschaftswissenschaften (Dr. rer. pol.)
an der Wirtschafts- und Sozialwissenschaftlichen Fakultät
der Ruprecht-Karls-Universität Heidelberg
vorgelegt im August 2006 von
Maik T. Schneider
geboren in Schwäbisch HallAcknowledgements
This dissertation would not have been accomplished without the assistance and encour-
agement of a number of people. In particular, I owe sincere gratitude to my advisor
Prof. Dr. Hans Gersbach for his continuous support, advice, and perceptive comments,
which contributed greatly to this thesis. Within discussions I have benefitted a lot from
his extensive scientific expertise. I also thank Prof. Timo Goeschl, Ph.D. for co-advising
on this work and his valuable suggestions.
My thanks go to all participants and professors of the Graduate Program “Environ-
mental and Resource Economics” and former members of the Interdisciplinary Institute
for Environmental Economics of the University of Heidelberg for personal and practical
assistance and numerous inspiring discussions. In particular, I would like to mention
Dr. Stefan Baumgärtner, Dr. Christian Becker, Svenja Espenhorst, Christoph Heinzel,
Dr. Olaf Hölzer, Friderike Hofmeister, Benjamin Lünenbürger, Felix Mühe, Dr. Martin
Quaas, and Dr. Markus Schaller. Further I wish to express much appreciation for
neighborly atmosphere and stimulative conversations to Christian Traeger, with whom
I shared an office for most of the time. Equal appreciation goes to Dr. Ralph Winkler,
my latter office mate. Moreover, I am indebted to him for substantial remarks and
concrete help during the last stage of this dissertation. My gratitude extends to Oliver
Grimm, Grischa Perino, and my sister Nadine Schneider for proof-reading and helpful
comments. Ialsogratefullyacknowledgethefinancialsupportofadoctoralfellowshipby
theDeutscheForschungsgemeinschaft(GermanResearchFoundation)withintheGradu-
ate Program “Environmental and Resource Economics” of the Universities of Heidelberg
and Mannheim.
Special thanks go to my parents, who kept me grounded and always proved a reliable
support. Likewise I wish to acknowledge my partner Angelika Förster for her empathy
and companionship, especially during the harder times of the last years, as well as her
unfaltering faith in me.
Heidelberg, August 2006 Maik T. Schneider
iiiivContents
1 Introduction 1
1.1 Purpose of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Empirical Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Theoretical Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Premises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Key Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 The Economic Problem and Modelling Strategy . . . . . . . . . . . . . . 6
1.7 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
I A Basic Endogenous Growth Model With Imperfect Knowl-
edge Transfer 11
2 Knowledge and Knowledge Codification 13
2.1 General Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 A Formal Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 The Model Specification 21
3.1 The Production Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 The Intermediate Goods Sector . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 The Decision Process . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Research and Intermediate Goods Production . . . . . . . . . . . 24
3.2.3 Second-Stage Profit Maximization . . . . . . . . . . . . . . . . . . 27
3.3 The Costs of Knowledge Codification . . . . . . . . . . . . . . . . . . . . 27
3.4 The Problem of the Household . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Sequence of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Equilibria and General Dynamics 35
4.1 Sequential Markets Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Codification Behavior of the Economy 41
5.1 Constant Number of Ideas per Researcher and Period . . . . . . . . . . . 49
5.2 Standing on the Shoulders of Giants. . . . . . . . . . . . . . . . . . . . . 55
6 Conclusions 63
vContents
7 Appendix 65
7.1 Sufficient Conditions for the Household’s Optimization Problem . . . . . 65
7.2 Allocation of Labor in Temporary Equilibrium . . . . . . . . . . . . . . . 66
7.3 Existence of Non-Trivial Steady States . . . . . . . . . . . . . . . . . . . 68
7.3.1 Φ = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3.2 Φ = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.4 Proof of Proposition 5.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
II Notes on the Robustness of the Results 79
8 Robustness with Respect to Assumptions on Technological Change 81
8.1 The New Production Function of Intermediate Goods . . . . . . . . . . . 81
8.2 Sequential Markets Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 82
8.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
8.4 Knowledge Codification. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.4.1 Constant Number of Ideas per Researcher and Period: Φ = 0 . . . 91
8.4.2 Standing on the Shoulders of Giants: Φ = 1 . . . . . . . . . . . . 95
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8A Appendix of Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8A.1 Sufficient Conditions for the Household’s Optimization Problem . 102
8A.2 Existence of Non-Trivial Steady States . . . . . . . . . . . . . . . 103
8A.3 Influence of Knowledge Codification on the Return on Physical
Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
9 A Generalization 109
9.1 General Properties of the Model . . . . . . . . . . . . . . . . . . . . . . . 109
9.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
9A Appendix of Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
˜9A.1 Equivalence of the Dynamical Systems with (Φ,Φ) = (1,1) and
˜(Φ,Φ) = (1,0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9A.2 Steady-State Behavior without Knowledge Codification . . . . . . 116
10 Oligopolistic Intermediate Sectors 119
10.1 Outline of the Model Structure . . . . . . . . . . . . . . . . . . . . . . . 119
10.1.1 Knowledge and Information . . . . . . . . . . . . . . . . . . . . . 119
10.1.2 Final Goods Production . . . . . . . . . . . . . . . . . . . . . . . 120
10.1.3 The Intermediate Goods Sectors . . . . . . . . . . . . . . . . . . . 120
10.1.4 The Problem of the Household . . . . . . . . . . . . . . . . . . . . 122
10.1.5 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
10.2 Dynamics and Knowledge Codification . . . . . . . . . . . . . . . . . . . 125
10.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
viContents
III RelationtoStandardEndogenousGrowthTheoryandSocial
Optimality 131
11 Relation to Romer’s Model of Endogenous Technological Change 133
11.1 What are the Differences to the Romer Model?. . . . . . . . . . . . . . . 133
11.2 An Interpretation of the Romer Model . . . . . . . . . . . . . . . . . . . 135
11.3 The Modified Romer Model . . . . . . . . . . . . . . . . . . . . . . . . . 136
11.3.1 The Production Sector . . . . . . . . . . . . . . . . . . . . . . . . 136
11.3.2 Knowledge Dynamics and the Research Sector . . . . . . . . . . . 137
11.3.3 The Intermediate Goods Sector . . . . . . . . . . . . . . . . . . . 140
11.3.4 The Problem of the Household . . . . . . . . . . . . . . . . . . . . 141
11.3.5 The Costs of Knowledge Codification . . . . . . . . . . . . . . . . 143
11.3.6 Sequence of Events . . . . . . . . . . . . . . . . . . . . . . . . . . 143
11.3.7 Sequential Markets Equilibrium . . . . . . . . . . . . . . . . . . . 144
11.3.8 Dynamics and Knowledge Codification . . . . . . . . . . . . . . . 147
11.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
12 Social Optimality 151
12.1 The Command Optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
12.2 Is the Sequential Markets Equilibrium Dynamically (In-)Efficient? . . . . 160
12.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
12A Appendix of Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
13 Final Conclusions 169
Bibliography 175
viiContents
viiiList of Figures
2.1 Knowledge and Information . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 The Structure of the Overlapping Generations Model . . . . . . . . . . . 33
ixList of Figures
x