Sustainability and Optimality of Public Debt

220 Pages·2013·0.998 MB·English

by  Michael Carlberg, Arne Hansen (auth.)

S ustainability and Optimality of Public Debt

Michael Carlberg • Arne Hansen
Sustainability and Optimality
of Public Debt
Second Edition
Prof. Dr. Michael Carlberg
Dr. Arne Hansen
Department of Economics
Helmut Schmidt University
Hamburg, Germany

Originally published under: Carlberg, M. within the series: Contributions to Economics

ISBN 978-3-642-32966-1 ISBN 978-3-642-32967-8 (eBook)
DOI 10.1007/978-3-642-32967-8
Springer Heidelberg New York Dordrecht London
Library of Congress Control Number: 2012954557

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Preface

Public debt seems to be one of the most important and controversial issues of
our time. In many countries, large and persistent budget deficits have continu-
ously raised the ratio of public debt to GDP. After balanced budgets and even
surpluses in the late 1990s, the United States has returned to deficits in recent
years. As a result, the US debt ratio has been growing steadily. In the extreme
case of Japan, public debt has grown to more than twice the size of GDP.
Meanwhile, the German debt ratio has doubled since reunification. These devel-
opments raise serious concerns about debt sustainability. Consequently, there are
increased political efforts to reduce future deficits. For instance, see the
Maastricht Treaty, the Stability and Growth Pact and, more recently, the contro-
versy over balanced-budget rules in Europe. Against this background, the present
book provides a theoretical analysis regarding the sustainability and optimality of
public debt.

Michael Carlberg
Arne Hansen

Contents in Brief

1 Introduction....................................................................................................3

2 A Brief Survey of the Literature..................................................................5

Part I The Closed Economy....................................................................9

3 The Solow Model........................................................................................11

4 Overlapping Generations............................................................................77

5 Infinite Horizon..........................................................................................104

Part II The Small Open Economy....................................................131

6 The Solow Model......................................................................................133

7 Overlapping Generations..........................................................................151

Part III Two Countries..........................................................................161

8 The Solow Model......................................................................................163

9 Synopsis......................................................................................................179

10 Conclusion..................................................................................................187

11 Result...........................................................................................................197

Symbols.............................................................................................................199

References.........................................................................................................201

Contents

1 Introduction..................................................................................................3

2 A Brief Survey of the Literature..............................................................5

Part I The Closed Economy....................................................................9

3 The Solow Model........................................................................................11

3.1 Fixing the Deficit Ratio...........................................................................11
3.1.1 A Simple Model...........................................................................11
3.1.2 The Short-Run Equilibrium.........................................................12
3.1.3 The Long-Run Equilibrium.........................................................14
3.1.4 The Optimal Deficit Ratio............................................................18
3.1.5 The Optimal Saving Ratio...........................................................20
3.1.6 Stability........................................................................................21
3.1.7 Some Shocks................................................................................23
3.1.8 A Budget Surplus.........................................................................29
3.1.9 A Numerical Example..................................................................32
3.1.10 Summary......................................................................................37

3.2 Fixing the Tax Rate.................................................................................38
3.2.1 A Simple Model...........................................................................38
3.2.2 The Short-Run Equilibrium.........................................................39
3.2.3 The Long-Run Equilibrium.........................................................40
3.2.4 Stability........................................................................................45
3.2.5 Some Shocks................................................................................48
3.2.6 The Optimal Tax Rate..................................................................56
3.2.7 The Optimal Saving Ratio...........................................................57
3.2.8 A Numerical Example..................................................................58
3.2.9 Summary......................................................................................59