Modern Economy, 2011, 2, 412-415
doi:10.4236/me.2011.23045 Published Online July 2011 (http://www.SciRP.org/journal/me)
Are Government Bonds Net Wealth? Some Empirical
Evidence
Tito Belchior Silva Moreira1, Geraldo da Silva e Souza2, Fernando Antônio Ribeiro Soares3
1Department o f Eco nomics, Catholic University of Brasília, Brasília, Brazil
2Department of Stat i s t i c s, University of Brasilia, Brasília, Brazil
3Brazilian Ministry of Defense, Brasília, Braz il
Received March 3, 2011; revised April 25, 2011; accepted May 5, 2011
Abstract
This paper aims to investigate the impact of government debt on economic growth for a balanced panel of
G7 countries over the period 1990-2008. We found empirical evidence that Ricardian Equivalence does not
holds in general. The analysis indicates that only Germany shows a negative association between public debt
and economic growth. The US and France show Ricardian equivalence and UK, Japan, Italy and Canada
show a positive association.
Keywords: Public Debt, Economic Growth, Ricardian Equivalence
1. Introduction
Roughly fifty years ago, [1] wrote a note presenting a
case for the “classic view” that bond financing of public
expenditures – unlike pay-as-you-go financing – places a
burden on future generations. Reference [2], dealing with
an intimately related issue, cast a model in which gov-
ernment debt does not affect the perceived net wealth of
households [3]. David Ricardo pointed out that they
might conceivably treat the future taxes servicing the
government debt as exactly offsetting it. Reference [2]
has shown that maximizing households will actually do
so if they accurately anticipate future taxes, if they face
perfect capital markets, and if they have effectively infi-
nite horizons. The Ricardian Equivalence Proposition
(REP), clearly stated in [2], is said to hold if households
do treat future servicing taxes as an exact offset to the
government debt [4]. Both publications stimulated much
debate about the rule of government bonds in macroeco-
nomics.
The empirical evidence for REP is usually investigated
following two approaches. The first seeks effects of gov-
ernment deficits on interest rates, while the second ana-
lyses the impact of a fiscal policy variable, e.g. public
debt, on the behavior of an aggregated macroeconomic
variable, which could be either consumption or savings,
for example [5]. In this sense, the private agents perceive
a fraction of government bonds as a net wealth.
In the same line of the second approach presented
above, it is possible to test the impact of public debt on
economic growth. Araujo e Martins model (Reference
[6]), a stra ightforward extension of [7-9 ], Martins (1980,
1994, 1995), relying on Samuelson’s pioneering OLG
model [10], is the proper framework for the analysis.
Based on [6], we investigate a possible association be-
tween public debt and economic growth, in the context
of the AK model. We note here that [6] concluded that
an increase in government debt negatively affects the
rate of growth of the capital stock and, consequently,
negatively affects the economic growth.
However, there is another explanation for the positive
association between public debt and economic growth.
The public investment may be complementary to private
investment in so far that, by generating po sitive external-
ities, it creates favorable conditions for the latter. In this
case, public investment can have a complementary effect
(crowding-in) with respect to private investment, espe-
cially when it is made in the areas of infrastructure and
the provision of public goods. The so-called supply-side
impact estimates the effect of public investment on total
factor productivity. One of the first studies in this area
was that of [11], followed by [12-14]. It may be noted
that [15] has developed a model in line with the “new
growth theory”. He shows that public investment has a
strong impact on the marginal productivity of private
capital and labor. This line of research originated a

T. B. S. MOREIRA ET AL.413
number of empirical studies, such as, [16-20].
2. Araujo and Martins Model1
Reference [6] demonstrate that sustained long-run gro-
wth is possible in a one-sector overlapping-generations
framework assuming a convex technology, without in-
come redistribution from old to the young supported by
income taxation and without “pure” altruism à la [2].
Considering an AK production function, and under the
assumption that the agent’s utility function embodies an
absolute bequest motive, the authors derive one clear
policy implication from the model: an increase in gov-
ernment debt negatively affects the rate of growth of the
capital stock as:

11
1
1
111
tt tt
t
KK BK
A
KA








(1)
where Kt is the stock of capital at the beginning of time t,
Bt is the outstanding stock of bonds at the beginning of
period t, A represents the technology and the coefficient

denotes the agent’s preferences. This equation shows
the endogenous rate of growth of the capital stock. The
flow of governmental debt financing as a proportion of
the pre-exiting stock of capital actu ally negatively affects
the rate of capital accumulation.
Substituting tt
K
YA into Equation (1) we obtain:
101
11
tt t
tt
YY B
YY



 (2)
where 01
1
A




 and

111
A
A


 .
Equation (2) has the observ ational representation:
01tt
Yb
t

  
 (3)
where 1
1
tt
tt
YY
YY




,
1
t
tt
B
bY
 and t

is a stochastic
error. We will use this formulation in our statistical exer-
cise.
3. Empirical Results
We use annual data from 1990 to 2008 to assess the Ri-
cardian equivalence and the nature of the association
between government debt and economic growth for the
G7 countries (Canada, France, Germany, Italy, Japan,
United Kingston and United States).
As a proxy for economic growth (t
Y) we use the an-
nual percent change of Gross Domestic Product (GDP) at
constant prices and for the ratio public debt/GDP () we
use the general government net debt as a percent of GDP.
2The source of data is the International Monetary Fund,
World Economic Outlook Database, April 2008. W e use
dummy variables to differentiate the countries. The basis
is US.

t
b
The dynamic panel method of analysis employed here
follows [22] and [23]. Table 1 shows the estimation re-
sults for the basic model:
01,12,23 4,1itititititi it
YYYbb

 
 


 
 (4)
where i

is a random effect for country i and it

is an
error componen t not showing serial correlation of second
order. The test for the presence of second order autocor-
relation has a p-value of 68% and the model seems ade-
quate.
All variables are significant at the 1% level. We note
that in the long run the net effect of t
b and 1t b

is
negative and statistically significant (p-value < 0.1%), as
expected. In this sense, the increment of the ratio public
debt/GDP results in a reductio n of the economic growth.
Now we consider the model:
6
01,12,23 4,11
66 6
,1 ,2
11 1
itititititi i
i
iiitiiitiiiti it
ii i
YYYbb
Db DbDb
  D


 


 
 


 

 


(5)
which assumes different intercepts and net debt coeffi-
cients for each country with a common dynamic eco-
nomic growth component structure.
Table 2 shows the estimation results for Model (5).
The Hausman specification test provides evidence of a
superior fit of Model (5) relative to Model (4). The test
for the presence of second order autocorrelation has a
p-value of 37% and the moment conditions seem ade-
quate.
In the long run the net effect of 1t and 2t
,
t
b bb

is
negative and statistically significant for some countries
and not for others. Table 3 shows the r esults.
France and the US show Ricardian equivalence. Only
Germany has a long run negative net effect of the ratio
debt/GDP in accordance with the model of [6]. In this
Table 1. Estimation of Equation (4).
Variables Coefficients Robust
Standard Error p-values
1t
Y

 0.255 0.077 0.001
2t
Y

 –0.232 0.044 <0.001
t
b –0.164 0.041 <0.001
1t
b

0.162 0.042 <0.001
Constant 2.319 0.486 <0.001
2We also used the government gross debt as a percent of GDP. The
results were similar.
1Reference [6] .

T. B. S. MOREIRA ET AL. 414
Table 2. Estimation of Equation (5).
Variables Coefficients Robust
Standard Error p-values
1t
Y
 0.006 0.085 0.995
2t
Y
 –0.312 0.078 <0.001
t
b –0.597 0.045 <0.001
1t
b 0.916 0.063 <0.001
2t
b –0.328 0.033 <0.001
11t
D
b 0.382 0.036 <0.001
11,1t
D
b –0.719 0.072 <0.001
11, 2t
D
b 0.398 0.047 <0.001
22,t
D
b 0.243 0.018 <0.001
22,1t
D
b –0.522 0.044 <0.001
22,2t
D
b 0.284 0.029 <0.001
33,t
D
b 0.310 0.032 <0.001
33,1t
D
b –0.943 0.081 <0.001
33,2t
D
b 0.511 0.053 <0.001
44,t
D
b 0.408 0.058 <0.001
44,1t
D
b –0.568 0.096 <0.001
44,2t
D
b 0.216 0.052 <0.001
55,t
D
b 0.371 0.029 <0.001
55,1t
D
b –0.793 0.080 <0.001
55,2t
D
b 0.441 0.052 <0.001
66,t
D
b 0.659 0.070 <0.001
66,1t
D
b –0.848 0.078 <0.001
66,2t
D
b 0.314 0.040 <0.001
1
D
–2.856 1.480 0.054
2
D
–0.127 1.823 0.944
3
D
4.939 2.050 0.016
4
D
–7.213 2.096 0.001
5
D
–0.541 1.640 0.742
6
D
–4.133 1.610 0.010
Constant 3.820 1.197 0.001
context, a government debt crowd-out productive in-
vestment as it competes with capital for individuals’
non-consumed output. Canada, Italy, Japan and UK show
positive statistically significant long run net effects.
Table 3. Intercepts and public debt coefficients for Model (5).
Coefficients Long run net effect
Countries Constantt
b 1t b 2t b p-value(*)
Canada (1) 0.96 –0.22 0.20 0 .07 <0.001
France (2) 3.82 –0.36 0.40 –0.05 0.657
Germany (3) 8.76 –0.29 –0.02 0.18 <0.001
Italy (4) –3.39 –0.19 0.35 –0.11 <0.001
Japan (5) 3.82 –0.23 0.13 0.11 0.016
UK (6) –7.95 0.06 0.07 –0.02 <0 .001
US (7) 3.82 –0.60 0.92 –0.33 0.348
(*) Wald test, 0:0
iii
H 


.
4. Conclusions
The empirical results show that the economic growth is
not independent of public debt and that the Ricardian
Equivalence hypothesis is not generally valid. Indeed
only the US and France show Ricardian Equivalence.
Germany follows the model of Araujo and Martins [6]
indicating that there is competition between public and
private investment, so that the former “crowds-out” the
latter.
The other countries of G7 show a positive association
between public debt and economic growth. Theoretically
the net effect should be negative. We point out two major
reasons to explain positive empirical results for Canada,
Italy, Japan and UK. Firstly is that Araujo and Martins
model is valid only for closed economies and the IMF
measurements of government debt comprises all gov-
ernment gross liabilities for both residents and non resi-
dents. Finally the theoretical model assumes the debt
formed exclusively by treasures bill. A suggestion for
further investigation involves an extension of Araujo and
Martins model for an open economy. This line of re-
search should take into account possible financial link-
ages among the countries that might transfer REP to the
exchange rate.
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the Burden of the Debt,” Instituto de Pesquisa Econômica
Aplicada, Brasília, 1979.

T. B. S. MOREIRA ET AL. 415
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