Public Debt and Endogenous Growth

185 Pages·2003·3.326 MB·English

by  PD Dr. Michael Bräuninger (auth.)

Public Debt and Endogenous Growth
Contributions to Economics
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Michael Bräuninger
Public Debt
and Endogenous Growth
With 89 Figures
and 10 Tables
Springer-Verlag Berlin Heidelberg GmbH
Series Editors
Werner A. Müller
Martina Bihn
Author
PD Dr. Michael Bräuninger
Institut für Theoretische Volkswirtschaftslehre
Universität der Bundeswehr Hamburg
Holstenhofweg 85
22043 Hamburg
Germany
[email protected]
ISSN 1431-1933
ISBN 978-3-7908-0056-2 ISBN 978-3-642-57420-7 (eBook)
DOI 10.1007/978-3-642-57420-7
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Preface
This book considers public debt dynamics in various endogenous growth mod
els, namely the AK model and explicit models of innovation and human cap
ital accumulation. Furthermore, the closed economy, the small open economy
and a two-country world are analysed. In the closed economy model, the focus
is on budget deficit and public debt dynamics and their influence on capital
growth and output growth. Then, in the open economy model, the effects
on foreign debt growth are considered. In a two-country setting, public debt
growth in one country affects growth in the other country. In each scenario the
government either fixes the deficit ratio or the tax rate. For both strategies
the steady state is derived and stability is analysed. Then, dynamics induced
by various shocks and policy measures are explored. Many diagrams illustrate
the dynamics.
I greatly benefited from comments by Michael Carlberg. In addition, Alkis
Otto and Justus Haucap discussed with me many parts of the book. I wish to
thank them all.
Hamburg, February 2003 Michael Briiuninger
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Part I The Closed Economy with AK Production
2 The Solow Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5
2.1 Introduction............................................ 5
2.2 Fixing the Deficit Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6
2.2.1 The Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6
2.2.2 Stability......................................... 12
2.2.3 Some Shocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
2.2.4 Summary......................................... 18
2.3 Fixing the Tax Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18
2.3.1 The Model ....................................... 18
2.3.2 Stability......................................... 21
2.3.3 Some Shocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22
2.3.4 Summary......................................... 27
2.4 The Optimal Deficit Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27
2.4.1 The Model ....................................... 27
2.4.2 Stability......................................... 32
2.4.3 Some Shocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 33
2.4.4 Summary......................................... 37
viii Contents
3 The Overlapping Generations Model. . . . . . . . . . . . . . . . . . . . . .. 39
3.1 Introduction ............................................ 39
3.2 Fixing the Deficit Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40
3.2.1 The Model ....................................... 40
3.2.2 Stability......................................... 46
3.2.3 A Balanced Budget. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48
3.2.4 An Increase in the Deficit Ratio. . . . . . . . . . . . . . . . . . . .. 49
3.2.5 Summary......................................... 50
3.3 Fixing the Tax Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
3.3.1 The Model ....................................... 52
3.3.2 Stability......................................... 55
3.3.3 Summary......................................... 57
Part II Human Capital and Innovations in the Closed Economy
4 The Augmented Solow Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.1 Introduction ............................................ 61
4.2 Fixing the Deficit Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
4.2.1 The Model ....................................... 62
4.2.2 Stability......................................... 67
4.2.3 Some Shocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
4.2.4 Summary......................................... 75
4.3 Fixing the Tax Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76
4.3.1 The Model ....................................... 76
4.3.2 A Tax Cut ....................................... 79
4.3.3 Summary......................................... 81
5 The Romer Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
5.1 Introduction............................................ 83
5.2 Fixing the Deficit Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
5.2.1 The Model ....................................... 83
5.2.2 Stability......................................... 93
5.2.3 Some Shocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94
5.2.4 Summary......................................... 99
Contents ix
5.3 Fixing the Tax Rate ..................................... 101
5.3.1 The Model ....................................... 101
5.3.2 A Tax Cut ....................................... 109
5.3.3 Summary ......................................... 110
Part III The Open Economy with AK Production
6 The Solow Model of the Small Open Economy ............. 113
6.1 Introduction ............................................ 113
6.2 Fixing the Deficit Ratio .................................. 114
6.2.1 Perfect Capital Mobility ............................ 114
6.2.2 The High-Productivity Country ..................... 115
6.2.3 Some Shocks ...................................... 118
6.2.4 The Low-Productivity Country ...................... 121
6.2.5 Stability ......................................... 125
6.2.6 Some Shocks ...................................... 126
6.2.7 Summary ......................................... 129
6.3 Fixing the Tax Rate ..................................... 130
6.3.1 The High-Productivity Country ..................... 130
6.3.2 The Low-Productivity Country ...................... 134
6.3.3 Summary ......................................... 139
7 The Solow Model of a Two-Country World ................ 141
7.1 Introduction ............................................ 141
7.2 Fixing the Deficit Ratio .................................. 142
7.2.1 The Model ....................................... 142
7.2.2 Stability ......................................... 147
7.2.3 Some Shocks ...................................... 150
7.2.4 Summary ......................................... 153
7.3 Fixing the Tax Rate ..................................... 155
7.3.1 The Model ....................................... 155
7.3.2 A Tax Cut ....................................... 157
7.3.3 Summary ......................................... 158
x Contents
8 Conclusion ................................................ 159
8.1 The Closed Economy with AK Production ................. 159
8.2 Human Capital and Innovations in the Closed Economy ...... 162
8.3 The Open Economy with AK Production .................. 164
9 Result ..................................................... 169
Symbols ................................................... 171
References ................................................. 173
M. Brauninger Public Debt and Endogenous Growth
© Physica-Verlag Heidelberg 2003