Alfred Greiner · Bettina Fincke
Public Debt,
Sustainability
and Economic
Growth
Theory and Empirics
Public Debt, Sustainability and Economic Growth
Alfred Greiner • Bettina Fincke
Public Debt, Sustainability
and Economic Growth
Theory and Empirics
123
Alfred Greiner
Faculty of Economics
Bielefeld University
Bielefeld
Germany
Bettina Fincke
Faculty of Economics
Bielefeld University
Bielefeld
Germany
ISBN 978-3-319-09347-5
ISBN 978-3-319-09348-2 (eBook)
DOI 10.1007/978-3-319-09348-2
Springer Cham Heidelberg New York Dordrecht London
Library of Congress Control Number: 2014952604
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Preface
The financial crises that had begun as a sub-prime crisis in the USA in 2007
had plunged a great many economies throughout the world into deep economic
recessions. It seemed that the slump had been overcome by 2010 when some
countries reached their pre-crisis level of production. However, the sub-prime crisis
turned into a public debt crisis because the bail-out of private financial institutions
by governments led to a drastic increase of national debt to GDP ratios in some
countries. Particularly in the euro area, economies still face severe problems and
must be supported by other countries. This illustrates drastically that public debt
does affect the evolution of market economies and the question arises which
mechanisms one can identify that make public debt influence the real side of an
economy. Whereas economic consequences of taxation can be readily derived, that
does not hold for public debt since the latter does not have immediate consequences
as concerns the allocation of resources. With this book, we intend to contribute to the
research on how public debt affects the growth process of market economies in the
medium- to long-run. In particular, we want to work out the mechanisms that make
public debt affect the allocation of resources and that are not so easily understood
as the economic effects of distortionary taxation.
Our book partly builds on papers by ourselves and extends our earlier book
(Greiner and Fincke 2009). Thus, we develop new theoretical models of endogenous
growth, we update empirical estimations and we present new empirical evidence as
regards the relation between public debt and economic growth. The advantage of a
monograph, compared to publications in the form of research papers, is that a book
publication allows to get more into the details and also to be more precise about
the effects that ensue when certain assumptions are changed and replaced by other
ones, so that one can say more about the robustness of the results derived. Moreover,
this book works out fundamental properties of public debt within basic models of
endogenous economic growth. Therefore, it is also suited as a textbook for graduate
students studying the relation between public debt, public deficits and the allocation
of resources in an intertemporal context. We also owe our thanks to Peter Flaschel,
v
vi
Preface
Göran Kauermann, Uwe Köller and Willi Semmler from whom we have benefited
through earlier joint work and stimulating discussions. Further, we are indebted to
Gaby Windhorst for typing some sections of the manuscript.
Parts of the material in this book have been presented at conferences, workshops
and university seminars. Valuable comments that are gratefully acknowledged
were provided by participants in the International Workshop on Advances in
Macrodynamics at Bielefeld University, in the Conference on The Institutional
and Social Dynamics of Growth and Distribution, Lucca, Italy, in the World Bank
workshop on Modeling Fiscal Policy, Public Expenditure and Growth Linkages,
Washington, D.C., in the Symposium on Nonlinear Dynamics and Econometrics,
London, in the Workshop on Public Debt and Economic Growth of the
European Commission, Economic and Financial Affairs, Brussels, in the DIW
annual workshop on macroeconometric modelling, Berlin, at the UECE Conference
on Economic and Financial Adjustments in Europe, Lisbon, at the SPERI Annual
Conference Beyond Austerity vs Growth: The Future of the European Political
Economy, Sheffield, as well as in seminars at the Université du Luxembourg, at the
Vienna University of Technology and at the Université Paris 1 Panthéon-Sorbonne.
Bielefeld, Germany
June 2014
Alfred Greiner
Bettina Fincke
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
1
2 Sustainable Public Debt: Theory and Empirical Evidence . . . . . . . . . . . . . .
2.1 Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.1.1 Public Debt and the Primary Surplus . . . . . .. . . . . . . . . . . . . . . . . . . .
2.1.2 Conditions for Sustainability of Public Debt .. . . . . . . . . . . . . . . . .
2.2 Empirics: Japan, Germany and the USA . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.2.1 Descriptive Historical Approach .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.2.2 Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.3 Empirical Results for Euro Area Countries . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.3.1 France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.3.2 Ireland, Portugal and Spain.. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.3.3 Greece and Italy.. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.4 The Impact of the 2007 Financial Crisis: Portugal and Spain . . . . . . . .
2.5 Empirical Evidence for Developing Countries . . . .. . . . . . . . . . . . . . . . . . . .
2.5.1 The Estimation Strategy .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
2.5.2 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
5
5
6
7
11
12
15
29
31
32
33
35
43
44
45
67
71
3 Debt and Growth: A Basic Endogenous Growth Model . . . . . . . . . . . . . . . .
3.1 The Growth Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.1.1 The Household Sector . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.1.2 The Productive Sector . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.1.3 The Government . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.1.4 Analysis of the Model Structure . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.1.5 Welfare Effects of Debt Policy .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.2 Debt Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.2.1 Structure of the Model .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.2.2 The Differential Equations . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
81
83
83
84
85
86
94
97
97
99
vii
viii
Contents
3.2.3 Balanced Government Budget . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.2.4 Permanent Public Deficits . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.3 The Interaction of Fiscal and Monetary Policy .. . .. . . . . . . . . . . . . . . . . . . .
3.3.1 The Household Sector . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.3.2 The Productive Sector . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.3.3 The Public Sector . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.3.4 The Balanced Growth Path . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.3.5 Analysis of the Model . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.4 Effects of Wage Rigidities and Unemployment . . .. . . . . . . . . . . . . . . . . . . .
3.4.1 The Structure of the Growth Model.. . . . . . .. . . . . . . . . . . . . . . . . . . .
3.4.2 The Balanced Growth Path . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
3.4.3 Stability of the Economy . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
100
101
105
106
108
108
109
110
116
118
122
126
128
131
4 Productive Government Spending, Public Debt and Growth . . . . . . . . . .
4.1 The Endogenous Growth Model with Full Employment .. . . . . . . . . . . . .
4.1.1 Households .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.1.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.1.3 The Government . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.1.4 Equilibrium Conditions and the Balanced Growth Path . . . . . .
4.1.5 Analyzing the Model . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.2 Effects of a Progressive Income Tax . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.2.1 The Model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.2.2 The Household and the Productive Sector .. . . . . . . . . . . . . . . . . . . .
4.2.3 Implications of the Model . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.3 Productive Public Spending as a Flow . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.3.1 The Private Sector . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.3.2 The Government . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.3.3 Analysis of the Model . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.4 The Role of Wage Rigidity and Unemployment.. .. . . . . . . . . . . . . . . . . . . .
4.4.1 The Endogenous Growth Model . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.4.2 Analysis of the Model with Wage Flexibility . . . . . . . . . . . . . . . . .
4.4.3 The Model with Wage Rigidities. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
4.4.4 Discussion and Comparison to the Model
Without Unemployment .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
147
149
149
150
150
151
153
161
162
162
165
169
169
170
171
177
177
183
188
5 Government Debt and Human Capital Formation . .. . . . . . . . . . . . . . . . . . . .
5.1 The Structure of the Growth Model with Human Capital .. . . . . . . . . . . .
5.1.1 The Household and the Productive Sector .. . . . . . . . . . . . . . . . . . . .
5.1.2 Human Capital Formation .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
5.1.3 The Government . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
5.1.4 Equilibrium Conditions and the Balanced Growth Path . . . . . .
5.1.5 Analysis of the Model . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
205
206
206
208
208
209
210
190
192
195
Contents
ix
5.2 A More Elaborate Model with Human Capital . . . .. . . . . . . . . . . . . . . . . . . .
5.2.1 The Structure of the Growth Model.. . . . . . .. . . . . . . . . . . . . . . . . . . .
5.2.2 Analyzing the Model . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
215
216
221
227
229
6 Debt and Growth: Empirical Evidence . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
6.1 The Estimation Procedure and the Data. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
6.2 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
233
235
238
244
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 245
A Non-parametric Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 249
B Basic Theorems from Optimal Control Theory . . . . . .. . . . . . . . . . . . . . . . . . . . 251
C The Hopf Bifurcation Theorem . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 255
Data Sources .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 257
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 259
Index . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 267
List of Figures
Fig. 2.1
Fig. 2.2
Fig. 2.3
Fig. 2.4
Fig. 2.5
Fig. 2.6
Fig. 2.7
Fig. 2.8
Fig. 2.9
Fig. 2.10
Fig. 2.11
Fig. 2.12
Fig. 2.13
Fig. 2.14
Fig. 2.15
Fig. 2.16
Fig. 2.17
Japanese National government debt as percentage
of GDP (1955–2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
German National government debt as percentage
of GDP (1950–2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
US Federal debt at the end of year as percentage
of GDP (1940–2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Deviation sm.t/ from the average coefficient
for b.t 1/ for Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
General government net financial liabilities, Japan
(1970–2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Deviation sm.t/ from the average coefficient
for b.t 1/ accounting for assets for Japan . . . .. . . . . . . . . . . . . . . . . . . .
Deviation sm.t/ from the average coefficient
for b.t 1/ for Germany . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Deviation sm.t/ from the average coefficient
for b.t 1/ for the US . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Iberian interest rates compared to German bonds
(1979–2012) in % . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Primary surplus to GDP ratio for Portugal and Spain . . . . . . . . . . . . . .
Debt to GDP ratio for Portugal and Spain . . . . . .. . . . . . . . . . . . . . . . . . . .
Primary surplus and debt to GDP ratio for Spain
(1980–2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Primary surplus and debt ratio for Spain (1980–2012)
separated by decades . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Smooth term Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Smooth term Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Public debt to GDP ratio for Botswana (1978–2003) . . . . . . . . . . . . . .
Primary surplus to GDP ratio for Botswana
(1978–2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
12
13
15
18
19
21
23
25
36
37
37
38
39
42
42
46
46
xi
xii
List of Figures
Fig. 2.18 Deviation sm(t) from the average coefficient for b.t 1/
for Botswana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.19 Budget deficit of Botswana (1978–2003) . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.20 Public debt to GDP ratio for Costa Rica (1970–2002) . . . . . . . . . . . . .
Fig. 2.21 Primary surplus to GDP ratio for Costa Rica
(1970–2002) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.22 Deviation sm(t) from the average coefficient for b.t 1/
for Costa Rica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.23 Budget deficit of Costa Rica (1970–2002) . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.24 Public debt to GDP ratio for Mauritius (1973–2005) . . . . . . . . . . . . . .
Fig. 2.25 Primary surplus to GDP ratio for Mauritius
(1973–2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.26 Deviation sm(t) from the average coefficient for b.t 1/
for Mauritius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.27 Budget deficit of Mauritius (1973–2005) . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.28 Public debt to GDP ratio for Panama (1970–2000) . . . . . . . . . . . . . . . .
Fig. 2.29 Primary surplus to GDP ratio for Panama (1970–2000) . . . . . . . . . . .
Fig. 2.30 Deviation sm(t) from the average coefficient for b.t 1/
for Panama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.31 Budget deficit of Panama (1970–2000) . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.32 Public debt to GDP ratio for Rwanda (1978–2004) . . . . . . . . . . . . . . . .
Fig. 2.33 Primary surplus to GDP ratio for Rwanda (1978–2004) . . . . . . . . . . .
Fig. 2.34 Deviation sm(t) from the average coefficient for b.t 1/
for Rwanda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.35 Budget deficit of Rwanda (1978–2004) . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.36 Rwanda’s received grants relative to GDP (1978–2004) . . . . . . . . . . .
Fig. 2.37 Public debt to GDP ratio for Tunisia (1972–1998) . . . . . . . . . . . . . . . . .
Fig. 2.38 Primary surplus to GDP ratio for Tunisia (1972–1998).. . . . . . . . . . . .
Fig. 2.39 Deviation sm(t) from the average coefficient for b.t 1/
for Tunisia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.40 Budget deficit of Tunisia (1972–1998) . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Fig. 2.41 Plot of variables and smooth term sm(t) for France . . . . . . . . . . . . . . . .
Fig. 2.42 Plot of variables and smooth term sm(t) for Ireland .. . . . . . . . . . . . . . .
Fig. 2.43 Plot of variables and smooth term sm(t) for Portugal . . . . . . . . . . . . . .
Fig. 2.44 Plot of variables and smooth term sm(t) for Spain . . . . . . . . . . . . . . . . .
Fig. 2.45 Plot of variables and smooth term sm(t) for Greece . . . . . . . . . . . . . . . .
Fig. 2.46 Plot of variables and smooth term sm(t) for Italy . . . . . . . . . . . . . . . . . .
48
49
50
50
52
53
53
54
55
56
57
57
58
60
60
61
62
63
64
64
65
66
67
74
75
76
77
78
79
Fig. 3.1
Limit cycle in the .b z c/ phase space
with D 3:7127 103 . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 104
Fig. 4.1
Transitional growth rates of consumption, private
capital and public capital after a transition from
scenario (iii) to scenario (i) at t D 0 .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 158
Average tax rate (constant) and marginal tax rate
(rising) as a function of . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 168
Fig. 4.2
List of Figures
xiii
Fig. 4.3
Fig. 4.4
Two saddle point stable BGPs for 1= > 1, > 0 . . . . . . . . . . . . . . . . . 175
Limit cycle in the .x b c/ phase space. . . . . .. . . . . . . . . . . . . . . . . . . . 187
Fig. 6.1
Fig. 6.2
Fig. 6.3
Fig. 6.4
Fig. 6.5
Fig. 6.6
Fig. 6.7
Fig. 6.8
Three-years growth rate . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Public debt to GDP ratio . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Pool, q D 5.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Pool, q D 3.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Pool, q D 1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Spline, q D 5.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Spline, q D 3.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Spline, q D 1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
236
237
239
240
240
241
241
242
List of Tables
Table 2.1
Table 2.2
Table 2.3
Table 2.4
Table 2.5
Table 2.6
Table 2.7
Table 2.8
Table 2.9
Table 2.10
Table 2.11
Table 2.12
Table 2.13
Table 2.14
Table 2.15
Table 2.16
Table 2.17
Table 2.18
Table 2.19
Table 2.20
Table 2.21
Equation (2.9) for Japan . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) without YVar, Japan . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) without GVar, Japan .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) with b only, Japan . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) for Japan (net debt) .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Without YVar, JAP (net debt) .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Without GVar, JAP (net debt) . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
With b only, JAP (net debt) .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) for Germany . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) without YVar, GER . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) without GVar, GER . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) with b only, GER . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) for the USA . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) without YVar, USA . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) without GVar, USA . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Equation (2.9) with b only, USA . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
ADF test for Japan (gross debt) . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
ADF test for Japan (net debt) .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
ADF test for the USA . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
ADF test for Germany . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Coefficients for Eq. (2.14) for France with data
from 1975 to 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.22 Coefficients for Eq. (2.14) for Ireland with data
from 1975 to 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.23 Coefficients for Eq. (2.14) for Portugal with data
from 1977 to 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.24 Coefficients for Eq. (2.14) for Spain with data
from 1980 to 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
17
17
18
18
20
20
20
20
22
22
22
22
24
24
24
24
28
28
28
28
31
33
33
33
xv
xvi
List of Tables
Table 2.25 Coefficients for Eq. (2.14) for Greece with data from
1976 to 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.26 Coefficients for Eq. (2.14) for Italy with data from
1972 to 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.27 Interest rate and growth rate gap for Portugal and Spain .. . . . . . . . .
Table 2.28 Estimation results Spain (1980–2010) . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.29 Estimation results Spain (1980–2011) . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.30 Estimation results Portugal . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.31 Estimation results Spain . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.32 Coefficients for Eq. (2.16) for Botswana . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.33 ADF test results for Botswana. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.34 Coefficients for Eq. (2.16) for Costa Rica. . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.35 ADF test results for Costa Rica . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.36 Coefficients for Eq. (2.16) for Mauritius . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.37 ADF test results for Mauritius .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.38 Coefficients for Eq. (2.16) for Panama .. . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.39 ADF test results for Panama .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.40 Coefficients for Eq. (2.16) for Rwanda. . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.41 ADF test results for Rwanda . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.42 Coefficients for Eq. (2.16) for Tunisia . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 2.43 ADF test results for Tunisia . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 3.7
Table 3.8
Table 3.9
Welfare F for the different budgetary rules
with D 0:25 and b.0/ D 0:32 . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
The balanced growth rate, g, the debt to capital ratio,
v, and the inflation rate, , for different values of the
reaction coefficient, , on the BGP . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
The balanced growth rate, g, the debt to capital ratio,
v, and the inflation rate, , for different values of the
nominal money growth rate, , on the BGP . . .. . . . . . . . . . . . . . . . . . . .
The balanced growth rate, g, the debt to capital ratio,
v, and the inflation rate, , for different nominal
money growth rates, , on the BGP with a balanced
government budget .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Welfare, F , for different nominal money growth
rates, , with a balanced government budget . .. . . . . . . . . . . . . . . . . . . .
Welfare, F , for different values of the nominal money
growth rate, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Welfare, F , for different values of the reaction
coefficient, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Welfare, F , for a balanced government budget
compared to permanent deficits . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Welfare F for the different budgetary rules
with D 0:25 and b.0/ D 0:5. .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
34
34
36
40
40
41
41
47
48
51
52
55
56
58
59
61
62
65
66
96
112
113
114
115
115
115
116
137
List of Tables
xvii
Table 3.10 Welfare F for the different budgetary rules
with D 1 and b.0/ D 0:32. .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 137
Table 3.11 Welfare F for the different budgetary rules with
D 1 and b.0/ D 0:5 . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 138
Table 4.1
Balanced growth rate and the debt to private capital
ratio for different with D 0:05 . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.2 Balanced growth rate and the debt to private capital
ratio for different with D 0:25 . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.3 Welfare in scenario (iii) and welfare resulting from
a transition to scenario (ii) and scenario (i), respectively . . . . . . . . .
Table 4.4 Welfare in scenario (i) and welfare resulting from
a transition to scenario (iii) with b ? > 0 . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.5 Welfare in scenario (i), scenario (ii) and scenario (iii)
for given initial conditions x.0/ D 0:03 and b.0/ D 0:02 . . . . . . . .
Table 4.6 Long-run growth rate, endogenous variables
on the BGP and eigenvalues for different values of "
and with D 0:015 . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.7 Long-run growth rate, endogenous variables on the
BGP and eigenvalues for different values of " and
with D 0:015.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.8 BGPs for 1= < 1 and < 0 . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.9 Balanced growth rate, g, and eigenvalues for different
with D 0:01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.10 Balanced growth rate, g, and eigenvalues for different
with D 0:05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Table 4.11 Balanced growth rate, g, unemployment rate, u,
and eigenvalues for different values of with D 0:01 . . . . . . . . .
Table 4.12 Balanced growth rate, g, unemployment rate, u,
and eigenvalues for different values of with D 0:05 . . . . . . . . .
Table 5.1
Table 5.2
Table 5.3
Table 5.4
Table 5.5
Long-run growth rate and endogenous variables
on the BGP for different and small values of
with ˇh D 0:75 .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Long-run growth rate and endogenous variables
on the BGP for different and small values of
with ˇh D 0:5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Long-run growth rate and endogenous variables
on the BGP for different and large values of
with ˇh D 0:75 .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Long-run growth rate and endogenous variables
on the BGP for different and large values of
with ˇh D 0:5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Welfare in scenario (i), scenario (ii),
and scenario (iii) for given initial conditions
q.0/ D 0:0032; p.0/ D 0:1; z.0/ D 0:035 . . .. . . . . . . . . . . . . . . . . . . .
156
157
160
160
161
168
169
176
186
186
189
190
212
212
213
213
227
xviii
Table 5.6
Table 5.7
Table 5.8
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
List of Tables
Welfare in scenario (iii) on the BGP and welfare
resulting from a transition to scenario (ii), and
scenario (i), respectively .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 227
Balanced growth rate, g, debt to capital ratio
on the BGP, b ? , and the signs of the eigenvalues
of the Jacobian for different values of and .. . . . . . . . . . . . . . . . . . . 232
Balanced growth rate, g, growth rate of public debt,
gb , and the signs of the eigenvalues of the Jacobian
for D 0 and for different values of . . . . . . . .. . . . . . . . . . . . . . . . . . . . 232
Plain panel estimation results. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Spline estimation results, plain model . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Panel estimation results, pooled OLS . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Panel estimation results, random effects . . . . . . .. . . . . . . . . . . . . . . . . . . .
Model selection tests . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .
239
241
242
243
244
Chapter 1
Introduction
After World War II, in particular during the 1970s, the politico-economic principles
had been largely dominated by the Keynesian approach according to which
governments must play an active role in stabilizing market economies. The latter
can be achieved by public expenditures in order to raise aggregate demand, with the
spending being financed by public deficits. Particularly, in times of low aggregate
demand and high unemployment the government must become active in order to
restore the full employment equilibrium which, then, allows to reduce outstanding
public debt. In addition, according to that view public debt does not pose a problem
if the government runs into debt in the home country. This holds because no
resources are lost and public deficits just imply a reallocation of resources from
taxpayers to bondholders.
Another reason to resort to debt-financing is inter-generational redistribution.
The aspect of inter-generational redistribution is also the justification for the
so-called golden rule of public finance. According to that rule, governments should
finance public investments that yield long-term benefits by public deficits in order
to make future generations contribute to the financing. Since future generations
will benefit from today’s investment, their contribution to the financing is justified.
Otherwise, the current generation would have to bear all the costs but benefit only
to a certain degree which is considered as unfair.
As a consequence of the predominant Keynesian view, public debt rose
considerably in the fourth quarter of the last century and, what is more, the increase
in public debt was even larger than the growth rate of the gross domestic product
(GDP), mainly in many European countries, so that the ratio of public debt to GDP
grew, too. Even in the euro area, where countries participating in the European
Economic and Monetary Union have signed the Maastricht treaty stating that the
public deficit and the public debt relative to GDP must not exceed 3 and 60 %,
respectively, quite a many economies have difficulties with their debt service
and some even had to be bailed out by the European Stability Mechanism to
prevent bankruptcy. This raises the question of whether and, more generally, under
© Springer International Publishing Switzerland 2015
A. Greiner, B. Fincke, Public Debt, Sustainability and Economic Growth,
DOI 10.1007/978-3-319-09348-2__1
1
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