Discussion Paper No. 955

PUBLIC DEBT, ECONOMIC GROWTH
AND THE REAL INTEREST RATE:A PANEL VAR APPROACH
TO EU AND OECD COUNTRIES
Kazuo Ogawa
Elmer Sterken
Ichiro Tokutsu

January 2016

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

January 2016

Public Debt, Economic Growth and the Real Interest Rate:
A Panel VAR Approach to EU and OECD Countries*

Kazuo Ogawa
Institute of Social and Economic Research
Osaka University
Elmer Sterken
Department of Economics
University of Groningen
Ichiro Tokutsu
Graduate School of Business Administration
Kobe University* This research was financially supported by KAKENHI Grant-in-Aid for Scientific Research (S)#15H05728, (B) #25285068 and the program of the Joint Usage/Research Center for “Behavioral
Economics” at ISER, Osaka University. The authors would like to thank Michael Abrigo and Inessa
Love for kindly supplying their panel VAR Stata program. Any remaining errors are the sole
responsibility of the authors.

Abstract

We investigate the causal relationship between the public debt to GDP ratio andeconomic growth for 31 EU and OECD countries from 1995 to 2013. A number of studies
have tackled this problem, but very few make the transmission mechanism explicit intheir analysis. We estimate a panel VAR model that incorporates the long-term realinterest rate on government bonds as a vehicle to transmit shocks in both the public debt
to GDP ratio and economic growth. We find no causal link from the public debt to GDP
ratio to the GDP growth rate, irrespective of the levels of public debt. Rather, we find a
causal relation from the GDP growth rate to the public debt to GDP ratio. In high-debt
countries, the direct negative impact of economic growth on public debt is enhanced bya rise in the long-term real interest rate, which in turn decreases interest-sensitive demandand leads to a further increase in the public debt to GDP ratio.

JEL Classification Number: E43, H63, O47
Keywords: Public debt, Economic growth, Interest rate, Panel VAR, Granger causality
Correspondence to:Kazuo Ogawa
Institute of Social and Economic Research, Osaka University,
6-1 Mihogaoka, Ibaraki, Osaka, 567-0047 JAPAN
Tel: +81- 6- 6879-8570 Fax: +81- 6-6878-2766
E-mail: ogawa@iser.osaka-u.ac.jp

11. Introduction
The seminal work of Reinhart and Rogoff (2010) finds that public debt overhang has anegative effect on economic growth when the debt to GDP ratio is high. Their study has
sparked an empirical investigation into the relationship between public debt andeconomic growth. A number of studies have examined nonlinear relationships between
public debt and economic growth where there exists a threshold beyond which public
debt has a negative impact on economic growth. Many studies have found evidence infavor of a nonlinear negative relationship between public debt and growth, but theirresults are sensitive to the time dimension, country coverage, data frequency andeconometric methods applied. 1 Moreover, to the best of our knowledge, no studies
convincingly demonstrate a causal link from public debt to economic growth with atransmission mechanism explicitly taken into consideration.
We employ a vector autoregression (VAR) model, an ideal econometric tool, to analyze
dynamic interrelations among variables. Based on the VAR model, we test the presenceof Granger causality between economic growth, public debt and the long-term realinterest rate on government bonds through which a shock in public debt is transmitted toeconomic growth and vice versa. High levels of public debt cast doubt on the full
repayment of the debt and might lead to a higher risk premium and associated higher
long-term real interest rates, which in turn has a negative impact on economic growth via
a decline in interest-sensitive expenditures.2
Specifically, we estimate a panel VAR model developed by Holtz-Eakin et al. (1988).
The model describes the dynamic relation among public debt, economic growth and thelong-term real interest rate for a panel data set of 31 EU and OECD countries from 1995
to 2013. Interestingly, our sample period covers the recent European sovereign debt crisis.
We find no causal link from the public debt to GDP ratio to the real GDP growth rate,irrespective of the levels of the debt ratio. Rather, we find a causal relation from the GDP
growth rate to the level of public debt for countries with both high levels of debt to GDP
and those with low levels of debt to GDP. Quantitatively, the impact of the GDP growth1

Égert (2015) finds that nonlinear effects change over time, across countries andeconomic conditions. Kourtellos et al. (2013) find that higher public debt results inlower growth for countries in low-democracy regimes. Panizza and Prebistero (2014)
show that once endogeneity is corrected for the link between public debt and growth
disappears. They instrument public debt with the valuation effects brought about by theinteraction between currency debt and movements in the exchange rate. See Panizza andPresbitero (2013) for a survey of empirical studies dealing with the relationship between
public debt and economic growth.
2
The channel through which high public debt adversely affects economic growth isstated in Baldacci and Kumar (2010) and Reinhart et al. (2012).
2

rate on public debt is larger in countries with high levels of debt. This is because thenegative effects of growth on public debt are amplified through the interest channel. A
negative shock to economic growth initially raises the levels of public debt via an increasein government expenditure to boost the economy and a decrease in tax revenues. In
addition to this direct impact of growth on public debt, slowdown in growth raises thelong-term real interest rate, possibly due to a lower inflation rate, which in turn reduces
growth by decreasing interest-sensitive spending and leads to a further increase in public
debt. A rise in the long-term interest rate also increases interest payments on public debt
and thus further raises the level of public debt. We find that a one-standard-deviation
decrease in the real GDP growth rate raises the ratio of public debt to GDP by 3.24 percent
points for high-debt countries but only 1.04 percent points for low-debt countries.
The remainder of the paper is organized as follows. In Section 2 we provide a brief
survey of the recent literature on the relationship between public debt and economic
growth and present our hypothesis on how public debt affects economic growth. We
describe our dataset and present descriptive statistics in Section 3. Section 4 shows ourempirical results. The last section presents our conclusions.
2. Magnitude of and Channels through which Public Debt Affects Growth and Related
Literature
Reinhart and Rogoff’s (2010) seminal paper finds that public debt overhang has anegative effect on economic growth at high levels, often at a ratio of public debt to GDP
above 90 percent. The observations with debt to GDP above 90 percent have mean growth
rates almost 4 percent lower in advanced countries. Their finding is originally based on
descriptive statistics of historical episodes, which has stimulated a number of rigorous
econometric studies.
Panizza and Presbitero (2013) survey the recent literature on the links between public
debt and economic growth and effectively summarize the empirical studies conducted todate by stating that the relationship between public debt and growth is characterized bylarge cross-country heterogeneity and may vary over time within countries.
There are many studies that find evidence in favor of the negative nonlinear
relationship between public debt and growth. For example, Kumar and Woo (2010)
confirm that only high levels of debt (above 90 percent of GDP) exert a significant
negative effect on growth. They find that a 10 percent point increase in the initial debtto-GDP ratio is associated with a slowdown in real per capita GDP growth rate of 0.2
percent points per annum. Cecchetti et al. (2011) also find, in various specifications ofgrowth regressions, that the threshold beyond which government debt has a negative3

impact on growth is approximately 85% of GDP. They find that a 10 percent point
increase in the debt ratio reduces real GDP growth rate by more than one tenth of 1 percent
point. Checherita-Westphal and Rother (2012) find a nonlinear impact of government
debt on long-term growth with a turning point at approximately 90–100% of GDP. Baumet al. (2013) suggest that the short-run impact of debt on GDP growth is positive andhighly statistically significant but decreases to around zero and then loses significancewhen the ratio of public debt to GDP reaches approximately 67%. For high debt-to-GDP
ratios (above 95%), additional debt has a negative impact on economic activity. They findthat a 1 percent point increase in the debt to GDP ratio reduces real GDP growth rate by
0.06 percent point. Afonso and Jalles (2013) find that the threshold value of the debt ratio
is 58% of GDP for the Euro area and a slightly larger value of 79% of GDP for emerging
countries.
However, some studies emphasize that negative relationships between public debt andgrowth depends on the countries and the sample period chosen. Kourtellos et al. (2013)
find that higher public debt results in lower growth only for countries with low-democracy
regimes. Dreger and Reimers (2013) show that the negative impact of the debt to GDP
ratio is limited to the euro area and periods of non-sustainable public debt. They further
note that the negative debt effect diminishes in industrial countries and that debt exerts a
positive impact on economic growth provided that the debt is sustainable. Égert (2015)
finds some evidence in favor of a negative nonlinear relationship between public debt andgrowth. However, he warns that these results are very sensitive to the time period andcountry studied, the data frequency and assumptions on the minimum number ofobservations required in each nonlinear regime. He reports that when non-linearity isdetected, the negative nonlinear effect starts at much lower levels of public debt (between
20% and 60% of GDP). Eberhardt and Presbitero (2015) find some support for a negative
relationship between public debt and long-run growth across countries but no evidence
for a similar debt threshold within countries. Panizza and Prebistero (2014) find that anegative link between public debt and growth disappears once they correct for
endogeneity by accounting for the valuation effects brought about by the interaction
between currency debt and movements in the exchange rate.
Previous empirical studies have mainly focused on detecting a negative relationshipbetween public debt and economic growth, but there are no studies aimed at identifying
the channels through which public debt affects economic growth. One channel throughwhich public debt is transmitted to growth is via the long-term interest rate. Reinhart etal. (2012) argue that this interest rate channel works as follows: sufficiently high levelsof public debt call into question whether debt will be repaid in full, thus leading to a4higher risk premium and its associated higher long-term real interest rate, which in turnlowers economic growth by decreasing interest-sensitive expenditures on investment anddurables. Baldacci and Kumar (2010) confirm this conjecture and find that higher public
debt leads to a significant increase in long-term interest rates, with the precise magnitudedependent on initial fiscal, institutional and other structural conditions. Baum et al. (2013)
also suggest a nonlinear relationship between public debt and the long-term interest rate
and find that additional public debt increases the long-term interest rate above a thresholddebt to GDP ratio of approximately 73.8%. However, Checherita-Westphal and Rother(2012) report that the level of the public debt to GDP ratio is not statistically significant
in determining long-term interest rates in either linear or quadratic forms.3 Reinghart andRogoff (2012) also provide evidence that countries with a public debt overhang do notalways experience a sharp rise in real interest rates. Nonetheless, even if a significant
positive effect of public debt on the long-term interest rate is detected, it does notnecessarily imply that public debt has an adverse impact on economic growth by way ofthis channel. Rather, we have to show that a higher long-term interest rate decreases thegrowth rate, which is unquestionably theoretically correct, but is by no means empirically
self-evident. Therefore, we have to analyze the causal relations among public debt,
economic growth and the long-term real interest rate.
A panel VAR model is a suitable econometric tool to analyze dynamic interactions
among the public debt to GDP ratio, the real GDP growth rate and the real long-term
interest rate, using cross-country data over time. There have been studies that examine
the causal link between public debt and economic growth. Lof and Malinen (2014)
estimate a panel VAR model of the real GDP growth rate and growth rate of total grossgovernment debt and conclude that the negative correlation between sovereign debt andeconomic growth is primarily driven by the impact of growth on sovereign debt rather
than vice versa. Puente-Ajovín and Sanso-Navarro (2015) investigate the presence ofGranger causality between public debt and growth in 16 OECD countries and find that,with the exception of a few countries, there is a causal link from growth to public debt,
not from public debt to growth.
Unfortunately, previous panel VAR studies only analyze the two-variate relationshipbetween public debt and economic growth. In this paper we shed light on the role of longterm interest rates in transmitting a shock in public debt into growth and vice versa by
examining the tri-variate panel VAR model of public debt, economic growth and the long3

Checherita-Westphal and Rother (2012) find nonlinear effects of debt on private saving,
public investment and Total Factor Productivity and conclude that the channels throughwhich public debt has a nonlinear impact on economic growth are precisely by those.
5

term real interest rate, using cross-country panel data.
3. Data
Our sample includes 27 EU countries and 4 OECD countries (Australia, Canada,
Japan and the United States).4 The sample period covers the years of 1995 to 2013. This
selection of countries and range of sample years offsets some of the critique that previous
studies incurred. The 31 countries have a stable democracy and share common goals oftransparency in both fiscal and monetary policy and other essential institutions. The
sample years include economic variation, with economic prosperity (the 1990s) on the
one hand, and the worldwide financial crisis (2007-2013) on the other, but do not containshifts in structural views on the role of government debt. Our sample period is also
suitable for analyzing the relationship between public debt and economic growth during
the recent European sovereign debt crisis. Specifically, in the Greek crisis of 2015, oneof the topics of discussion between the Greek government and the ‘Trojka’ (the European
Commission, the European Central Bank, and the International Monetary Fund) has been
the excessive burden of government debt and additional foreign debt on the real GDP
growth rate. Similar discussions were held during the Irish, Portuguese, and Spanish
rescue plans in the years 2011-2013. We examine the relations among three variables: thereal GDP growth rate, the ratio of public debt to GDP and the long-term real interest rates.
The real GDP growth rate is calculated as the log difference of real GDP in terms of the2010 national currency market price. The ratio of public debt to GDP is defined as thegross debt of the general government divided by nominal GDP. The long-term real interest
rate is calculated as the nominal long-term (in most cases 10 year) government bonds
minus the inflation rate in terms of GDP deflator. The data sources are the Eurostat
database and OECD database.
Table 1 shows the mean of the real GDP growth rate, the public debt ratio and the longterm real interest rate for each country in the sample. The public debt ratio varies more
widely across countries than the GDP growth rate or the long-term interest rate. The debt
to GDP ratio exceeds 100% in five countries: Japan, Greece, Italy, Canada and Belgium,
while it is less than 20% in Estonia (6.14%) and Luxembourg (10.81%). The real GDP
growth rate ranges from 0.5% (Italy) to 4.41% (Estonia), while the long-term real interest
rate ranges from -0.09% (Romania) to 5.13% (Greece).
Figure 1 exhibits a scatter diagram representing the public debt to GDP ratio and thereal GDP growth rate. We observe a negative correlation between the public debt ratio
and the GDP growth rate. The correlation coefficient is -0.3131, and the null hypothesis
4

Croatia is not included in our set.
6

of no correlation is decisively rejected at the 1% significance level. Figure 2 exhibits ascatter diagram representing the public debt to GDP ratio and the long-term real interest
rate. We observe a positive correlation between the public debt to GDP ratio and the longterm real interest rate. The correlation coefficient for the whole sample is 0.2352 and thenull hypothesis of no correlation is also rejected at the 1% significance level. Note thatthe correlation coefficient gives no information about the direction of the causal links
among the variables, thus, we estimate a panel VAR model to analyze the causal
relationships in the next section.
4. Estimation Results
We estimate a panel VAR model using data from 31 countries over the years 1995 to2013. In applying the VAR model to the panel data, we control for individual
heterogeneity by introducing fixed effects. The mean-differencing procedure commonlyused in panel analysis would yield biased estimates due to the presence of lagged
dependent variables among the explanatory variables. Therefore, following Arellano and
Bover (1995), we use forward-mean differencing, commonly known as the Helmert
procedure, to eliminate fixed effects. The virtue of this procedure is that we can use
untransformed lagged regressors as instruments. Indeed, we use the variables lagged by
one and two years. The model is estimated by the System Generalized Methods ofMoments (SGMM).5
The optimal lag order is chosen by the three model selection criteria for SGMM models
proposed by Andrew and Lu (2001). Three criteria are analogous to the Akaike
information criteria (AIC), the Bayesian information criteria (BIC) and the HannanQuinn information criteria (HQIC). We choose the lag length as one. In estimating a panel
VAR model, we include time dummies as exogenous variables to account for aggregate
macro shocks.
(1) Two-variate caseFirst, we estimate a two-variate panel VAR model of the debt-to-GDP ratio and real
GDP growth rate for the whole sample (Case 1). The ordering of the variables is GDP
growth rate and the debt-to-GDP ratio.6 Table 2 shows the Wald statistics to test Granger
causality, whether the stability condition of the panel VAR model is satisfied, and the5

We use the Stata program originally developed by Love and Zicchino (2006) andextended by Abrigo and Love (2015).
6
Estimation results remain unaltered by a change in the ordering of the variables.
7

Hansen test statistics of overidentifying restrictions.7 We find Granger causality from thereal GDP growth rate to the public debt to GDP ratio but not vice versa. Figure 3 depicts
the impulse responses to a one standard deviation shock to the real GDP growth rate andthe debt to GDP ratio together with the associated 90 percent confidence intervals.8 The
debt to GDP ratio is lowered by 1.45 percent points one year after a positive shock to thereal GDP growth rate.
Some might argue that the failure to detect the impact of public debt on economic
growth is due to misspecification of the model. Many studies find a threshold above which
public debt exerts a negative impact on economic growth and below which public debt
has no effect on economic growth. To account for the differential effects of public debt
on economic growth, we split our sample countries by the mean of the debt-to-GDP ratio
into two groups: a high-public-debt group and a low-public-debt group. The high-publicdebt group consists of 16 countries, and the low-public-debt group consists of 15
countries.9 The two-variate panel VAR model is estimated separately for the high-publicdebt group (Case 2) and the low-public-debt group (Case 3). Table 2 shows that there isno causal link from public debt to economic growth for the high-public-debt group,
however, we do observe a weak causal link from the public debt to GDP ratio to economic
growth in the low-public-debt group. We observe Granger causality from economic
growth to public debt for both the high- and low-public-debt groups. Figures 4 and 5
depict the impulse responses for both groups. The impact of economic growth on public
debt is larger for the high-debt group. The debt-to-GDP ratio is lowered by 2.17 percent
points two years after a positive shock to GDP growth rate for the high-debt group, while
the counterpart is 1.50% for the low-debt group. The impact of the debt-to-GDP ratio on
economic growth is quite small for the low-debt group. The GDP growth rate is lowered
by 0.19 percent points three years after a one-standard-deviation positive shock to thedebt-to-GDP ratio.
(2) Tri-variate case

7

Note that a VAR model is stable if all moduli of the eigenvalue of the estimatedmodels are strictly less than unity. See Hamilton (1994) pp. 260-261.
8
Confidence intervals are estimated from 2,000 Monte Carlo simulations from theestimated panel VAR model.
9
The countries in the high-public-debt group are Belgium, Germany, Ireland, Greece,
Spain, France, Italy, Cyprus, Hungary, Malta, the Netherlands, Austria, Portugal,
Canada, Japan and the United States. Those in the low public debt group are Australia,
Bulgaria, Czech Republic, Denmark, Estonia, Latvia, Lithuania, Luxembourg, Poland,
Romania, Slovak Republic, Slovenia, Finland, Sweden and United Kingdom.
8

Next we estimate a tri-variate panel VAR model of the debt-to-GDP ratio, the real GDP
growth rate and the long-term real interest rate for the whole sample (Case 4). The
ordering of the variables is the real GDP growth rate, the debt-to-GDP ratio and the longterm real interest rate.10 Table 3 shows various test statistics of the estimated tri-variate
panel VAR model.
Even if the model is extended to incorporate the possible impact of public debt on
economic growth via the long-term real interest rate, we cannot detect a causal link frompublic debt to economic growth. There is no direct impact of the debt-to-GDP ratio on thereal GDP growth rate. Moreover, we cannot find indirect effects of public debt on
economic growth as we do not detect Granger causality either from the debt-to-GDP ratio
to the long-term real interest rate or from the long-term real interest rate to the GDP
growth rate.
In contrast, we still find a causal link from economic growth to the public debt to GDP
ratio. Additionally, we find a causal link from economic growth to the long-term realinterest rate. A rise in the GDP growth rate leads to a fall in the long-term interest rate,possibly by way of a rise in the inflation rate.
Figure 6 depicts the impulse responses for the tri-variate case. The debt-to-GDP ratio
is lowered by 1.34 percent points two years after a positive shock to the GDP growth rate.
The impact of economic growth on public debt when the interest rate is endogenized isquantitatively similar to the two-variate case (Case 1). The long-term interest rate
decreases by 1.03 percent points one year after a positive shock to the real GDP growthrate.
We estimate a tri-variate panel VAR model separately for the high-public-debt group(Case 5) and low-public-debt group (Case 6). We observe several common causal links
among the variables for both groups in Table 3. First, there is a direct causal link from
economic growth to public debt. Second, there is no causal link from public debt toeconomic growth, irrespective of the levels of debt. Third, an increase in the real GDP
growth rate lowers the long-term real interest rate. Moreover, we uncover additionalcausal links among the variables for the high-public-debt group. One of these additional
links is a causal link from the long-term real interest rate to economic growth. Thisimplies that economic activities are sensitive to a change in the long-term real interest
rate in the high-public-debt group.11 We also find a causal link from the long-term real
10

The estimation results remain essentially unaltered by changing the ordering of thevariables.
11
We also observe a causal link from the long-term real interest rate to economic growth
for the low-public-debt group, but it turns out that the effect of the interest rate on
9interest rate to the debt-to-GDP ratio. A rise in the long-term real interest rate increases
interest payments on public debt and thus raises the debt-to-GDP ratio.
We now summarize the channel through which a negative shock to real GDP growthrate is transmitted to a rise in public debt. For low-debt countries, we observe only the
direct link from the real growth rate to public debt. That is to say, a negative shock to thereal growth rate raises the levels of public debt via an increase in government expenditure
and a decrease in tax revenues. For high-debt countries, an initial negative impact of
economic growth on public debt is further amplified through the interest channel. In otherwords, slowdown in the growth rate raises the long-term real interest rate, possibly due
to a lower inflation rate, which in turn reduces the real growth rate by decreasing interestsensitive demand and leads to a further increase in public debt. A rise in the long-term
real interest rate also increases interest payments on public debt and further raises thelevel of public debt.
Figure 7 schematically compares the transmission mechanisms from economic growth
to public debt between high-debt countries and low-debt countries. Quantitatively
speaking, the impact of the real growth rate on public debt is much larger for high-debt
countries. Figures 8 and 9 show the impulse responses for high- and low-debt countries,
respectively. The debt-to-GDP ratio is lowered by 1.04 percent points three years after apositive shock to GDP growth rate for low-debt countries, while the debt-to-GDP ratio islowered by 3.24 percent points four years after a positive shock to GDP growth rate forhigh-debt countries. In high-debt countries, the impact of economic growth on the debtto-GDP ratio is persistent, and the debt-to-GDP ratio is still 2.27 percent points lower ten
years after the positive shock to economic growth. In high-debt countries, the debt-toGDP ratio increases by 3.12 percent points six years after a positive shock to the longterm interest rate.
Finally, we make a quantitative evaluation of the extent to which the long-term interest
rate amplifies the shock to GDP growth rate by comparing the pattern of the impulse
responses under an endogenous interest rate with the pattern of responses under an
exogenous interest rate (Case 7). Figure 10 shows the impulse responses when the interest
rate is exogenous. The debt-to-GDP ratio decreases only by 1.86 percent points two years
after a shock to GDP growth rate, which is 1.38 percent points smaller than the case of an
endogenous interest rate.
5. Concluding Remarks
In this paper we find a causal link from economic growth to the public debt by
economic growth is positive, contrary to the theoretical prediction.
10

estimating a panel VAR model that accounts for the interest channel through which ashock to economic growth is transmitted to the public debt and vice versa for EU andOECD countries from 1995-2013. However, we fail to find a reverse causality frompublic debt to economic growth. Our findings remain valid even if we split the sample
countries into a high-public-debt group and a low-public-debt group. Our findings showthat the long-term real interest rate plays a vital role in transmitting a shock in economic
growth to public debt for high-public-debt countries.
Although we could not detect a causal link from public debt to economic growth evenfor high-debt countries, public debt might be accumulated for many years once a negative
shock hits the GDP growth rate. This accumulation is due to a rise in the real interest rate,
which in turn decreases interest-sensitive demand and further increases public debt. Rapid
accumulation of public debt might start to adversely affect the economic growth if thefinancial market perceives the level of public debt as ‘unsustainable’, and the long-term
real interest rate responds more sensitively to the levels of public debt. In fact, the longterm interest rate in Greece rose sharply during 2011 and 2012 in response to a rise in thedebt-to-GDP ratio. In contrast, the long-term interest rate in Japan stayed around zerodespite soaring government debt.12
It is important to investigate why the long-term interest rate in one country stays atquite a low level in spite of large public debt, while it sharply rises in another country
under the same circumstances. This essentially is asking what factors determine a‘sustainable’ level of public debt.13 14 Solving this problem will provide a promising
platform for designing an economic policy to stabilize economies despite mounting
public debt.

12

The simple correlation coefficient between the nominal interest rate of 10-year
government bond and the debt-to-GDP ratio during 1995 to 2013 is 0.479 and -0.805 for
Greece and Japan, respectively.
13
Many academic researchers warn that the current debt level in Japan is unsustainable.
For example, see Dekle (2003), Doi and Ihori (2009), Doi, Hoshi and Okimoto (2011),
Ito, Watanabe and Yabu (2011), Sakuragawa and Hosono (2011) and Hoshi and Ito(2012). Broda and Weinstein (2005) argue that the ratio of government debt to GDP would
be stabilized by an increase in tax rates.
14
The countries with enormous public debt can still maintain decent economic growthsince they possess high growth potentials, such as high productivity. In fact, quite a few
countries in the high public debt group have attained high TFP growth rates.
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Behavior: Evidence from Panel VAR,” The Quarterly Review of Economics andFinance, 46(2), pp. 190-210.
Panizza, U. and A.F. Presbitero (2013). “Public Debt and Economic Growth inAdvanced Economies: A Survey,” Swiss Journal of Economics and Statistics, 149(2),pp. 175-204.
Panizza, U. and A.F. Presbitero (2014). “Public Debt and Economic Growth: Is There a
Causal Effect?” Journal of Macroeconomics, 41, pp. 21–41.
Puente-Ajovín, M. and M. Sanso-Navarro (2015). “Granger Causality between Debt
and Growth: Evidence from OECD Countries,” International Review of Economics
and Finance, 35, pp. 66-77.
Reinhart, C.M. and K.S. Rogoff (2010). “Growth in a Time of Debt,” American
Economic Review, 100(2), pp. 573–78.
Reinhart, C.M., Reinhart, V.R. and K.S. Rogoff (2012). “Public Debt Overhangs:
Advanced-Economy Episodes since 1800,” Journal of Economic Perspectives, 26(3),pp. 69–86.
Sakuragawa, M. and K. Hosono (2011). “Fiscal Sustainability in Japan,” Journal of theJapanese and International Economies, 25(4), pp. 434-446.

13

Figure 1 Scatter Diagram of Public Debt Ratio and GDP Growth Rate
0.15

0.1

GDP growth rate

0.05

0
0

0.5

1

1.5

-0.05

-0.1

-0.15

-0.2

Data source: Eurostat and OECD data base

Ratio of public debt to GDP2
y = -0.0281x + 0.0405
R² = 0.0981

2.5

Figure 2 Scatter Diagram of Public Debt Ratio and Long-term RealInterest Rate
0.25

0.2

0.15

Long-term real interest rate

0.1
y = 0.0191x + 0.0128
R² = 0.0553

0.05

0
0

0.5

1

1.5

-0.05

-0.1

-0.15

-0.2

Data source: Eurostat and OECD data basePublic debt ratio

22.5

GDP growth:GDP growth

Public debt: GDP growth

0.03

0.005

0.025

0.003

0.02
0.001

0.015
0.01

-0.001

0.005-0.0030-0.005

0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

p95_rgdp_rgdp

7

8

9

10

9

10

-0.005p5_sdebt2_rgdp

p5_rgdp_rgdp6

mean_rgdp_rgdp

p95_sdebt2_rgdp

mean_sdebt2_rgdp

Public debt: Public debt

GDP growth: Public debt
0.05

0
0

1

2

3

4

5

6

7

8

-0.01

9

10

0.04
0.03
0.02

-0.02

0.01
-0.03

0
-0.01

-0.04
p5_rgdp_sdebt2
mean_rgdp_sdebt2

p95_rgdp_sdebt2

0

1

2

3

4

p5_sdebt2_sdebt2
mean_sdebt2_sdebt2

Notes: impulse variable: response variable

Figure 3 Impulse Responses: Basic Two-variate Case

5

6

7

8

p95_sdebt2_sdebt2

GDP growth: GDP growth
0.03
0.026
0.022
0.018
0.014
0.01
0.006
0.002
-0.002Public debt: GDP growth
0.005
0.003
0.001
-0.001

0

1

2

3

4

5

6

7

8

9

10

9

10

-0.003-0.0050123p5_rgdp_rgdp

4

5

6

7

p95_rgdp_rgdp

8

9

10

p5_sdebt2_rgdp

mean_rgdp_rgdp

p95_sdebt2_rgdp

mean_sdebt2_rgdp

Public debt: Public debt

GDP growth: Public debt
0.05

0
0

1

2

3

4

5

6

7

8

-0.01

9

10

0.04
0.03
0.02

-0.02

0.01
-0.03

0
-0.01

-0.04
p5_rgdp_sdebt2
mean_rgdp_sdebt2

p95_rgdp_sdebt2

0

1

2

3

4

p5_sdebt2_sdebt2

5

6

7

8

p95_sdebt2_sdebt2

mean_sdebt2_sdebt2

Notes: impulse variable: response variable

Figure 4 Impulse Responses: Two-variate Case for High Debt Countries

GDP growth: GDP growth

Public debt: GDP growth

0.03

0.005

0.025

0.003

0.02

0.001

0.015
-0.001

0.01

0

1

2

3

4

5

6

7

8

9

10

9

10

-0.0030.005-0.005

0
0

1

2

3

p5_rgdp_rgdp

4

5

6

7

p95_rgdp_rgdp

8

9

10

p5_sdebt2_rgdp

mean_rgdp_rgdp

p95_sdebt2_rgdp

mean_sdebt2_rgdp

GDP growth: Public debt

Public debt: Public debt

0

0.05
0

1

2

3

4

5

6

7

8

-0.01

9

10

0.04
0.03

-0.02

0.02
0.01

-0.03

0
-0.04

-0.01
p5_rgdp_sdebt2
mean_rgdp_sdebt2

p95_rgdp_sdebt2

0

1

2

3

4

p5_sdebt2_sdebt2

5

6

7

8

p95_sdebt2_sdebt2

mean_sdebt2_sdebt2

Notes: impulse variable: response variable

Figure 5 Impulse Responses: Two-variate Case for Low Debt Countries

Public debt: GDP growth

GDP growth: GDP growth
0.025

0.005

0.02

0.003

0.015

0.001

0.01

-0.001

0.005-0.00300-0.005123p5_rgdp_rgdp

4

5

6

7

p95_rgdp_rgdp

8

9

10

0

1

2

3

4

5

6

7

8

3

4

5

p5_sdebt2_rgdp

6

7

8

9

10

p95_sdebt2_rgdp

9

10

-0.04

-0.01

-0.05

-0.03

0

p95_rgdp_sdebt2

3

4

4

5

6

7

8

9

10

-0.008-0.013-0.018

0.005
0.004
0.003
0.002
0.001
0
-0.001-0.002-0.003-0.004-0.005-0.006

p95_rgdp_rint

mean_rgdp_rint

3

6

7

4

5

6

7

p95_rint_rgdp

8

9

10

mean_rint_rgdp

8

9

10

0

1

p95_sdebt2_sdebt2

2

3

4

5

p5_rint_sdebt2

6

7

8

9

10

9

10

p95_rint_sdebt2

mean_rint_sdebt2

Interest rate: Interest rate
0.025
0.02
0.015

0

1

2

3

4

5

6

7

8

9

10

0.01
0.005
0

p5_sdebt2_rint
p5_rgdp_rint

5

Public debt: Interest rate

0.002
2

3

0.068
0.058
0.048
0.038
0.028
0.018
0.008
-0.002-0.012

mean_sdebt2_sdebt2

GDP growth: Interest rate
12

p5_sdebt2_sdebt2

mean_rgdp_sdebt2

0

1

2

Interest rate: Public debt

0.05

0.01

-0.03

1

p5_rint_rgdp

0.03-0.0030

Public debt: Public debt

-0.02

p5_rgdp_sdebt2

0.01
0.00750.005
0.00250-0.0025-0.005-0.0075-0.01

mean_sdebt2_rgdp

GDP growth: Public debt
02-0.005

mean_rgdp_rgdp

0
-0.01

1

Interest rate: GDP growthp95_sdebt2_rint

mean_sdebt2_rint

Notes: impulse variable: response variable

Figure 6 Impulse Responses: Basic Three-variate Case

-0.005012p5_rint_rint

3

4

5

p95_rint_rint

6

7

8

mean_rint_rintFigure 7 Causal Relationship among the Public Debt, Economic Growth and Interest Rate: Schematic Illustration
1) High debt countries
GDP growth rate−−−

Public debt＋

Long-term realinterest rate2) Low debt countries
GDP growth rate−Long-term realinterest rate−

Public debt

GDP growth: GDP growth

Public debt: GDP growthInterest rate: GDP growth

0.025

0.005

0.01

0.02

0.003

0.0075

0.015

0.001

0.01

-0.001

0.005

0.005

0

0

1

2

3

4

5

6

7

8

9

10

p95_rgdp_rgdp

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

-0.005

9

10

-0.03
-0.04
-0.05
-0.06
-0.07

0

1

p95_rgdp_sdebt2

mean_rgdp_sdebt2

1

2

3

4

5

6

7

8

9

10

-0.008-0.013-0.018p5_rgdp_rint

2

3

4

5

6

7

8

9

10

p95_sdebt2_sdebt2

0.068
0.058
0.048
0.038
0.028
0.018
0.008
-0.002-0.012

p95_rgdp_rint0

mean_rgdp_rint

5

6

7

p95_rint_rgdp

1

2

3

p5_rint_sdebt2

Public debt: Interest rate

GDP growth: Interest rate
0

4

8

9

10

mean_rint_rgdp

Interest rate: Public debt

mean_sdebt2_sdebt2

0.005
0.004
0.003
0.002
0.001
0
-0.001-0.002-0.003-0.004-0.005-0.0063p5_rint_rgdp

p5_sdebt2_sdebt2

0.002

2

-0.01

mean_sdebt2_rgdp

0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03

1

-0.0075
p95_sdebt2_rgdp

Public debt: Public debt

-0.02

p5_rgdp_sdebt2

0-0.005GDP growth: Public debt
0

0

10

-0.0025

mean_rgdp_rgdp

0-0.0032

p5_sdebt2_rgdp
p5_rgdp_rgdp

-0.01

1

-0.0030-0.0050.00254

567p95_rint_sdebt2

8

9

10

mean_rint_sdebt2

Interest rate: Interest rate
0.025
0.02
0.015

0

1

2

3

4

5

6

7

8

9

10

0.01
0.005
0
-0.005p5_sdebt2_rint

p95_sdebt2_rint

mean_sdebt2_rint

Notes: impulse variable: response variable

Figure 8 Impulse Responses: Three-variate Case for High Debt Countries

0

1

2

p5_rint_rint

3

4

5

p95_rint_rint

6

7

8

9

10

mean_rint_rint

Public debt: GDP growth

GDP growth: GDP growthInterest rate: GDP growth

0.025

0.005

0.01

0.02

0.003

0.0075

0.015

0.001

0.00250.01-0.001

0.005

0.005

0

2

3

4

5

6

7

8

9

0
0

1

2

3

4

5

6

7

8

9

10

p95_rgdp_rgdp-0.005

1

2

3

4

5

p5_rgdp_sdebt2

6

7

8

10

0

1

0
2

3

4

5

6

7

8

9

10

-0.005-0.01-0.015-0.02
p5_rgdp_rint

3

4

5

6

7

8

9

10

p95_sdebt2_sdebt20

p95_rgdp_rint

mean_rgdp_rint

5

6

7

p95_rint_rgdp

1

2

3

4

p5_rint_sdebt2

Public debt: Interest rate
0.005
0.004
0.003
0.002
0.001
0
-0.001-0.002-0.003-0.004-0.005-0.006

4

8

9

10

mean_rint_rgdp

Interest rate: Public debt
0.068
0.058
0.048
0.038
0.028
0.018
0.008
-0.002-0.012

mean_sdebt2_sdebt2

GDP growth: Interest rate
12

p5_sdebt2_sdebt2

mean_rgdp_sdebt20p5_rint_rgdp

mean_sdebt2_rgdp

p95_rgdp_sdebt2

0.005

3

-0.01

p95_sdebt2_rgdp

Public debt: Public debt
92-0.0075

mean_rgdp_rgdp

0.05
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03

1

-0.005GDP growth: Public debt
00-0.0025p5_sdebt2_rgdp
p5_rgdp_rgdp

010-0.003-0.0050-0.005-0.01-0.015-0.02-0.025-0.03-0.035-0.04-0.045
-0.05

1

5

6

7

p95_rint_sdebt2

8

9

10

mean_rint_sdebt2

Interest rate: Interest rate
0.025
0.02
0.015

0

1

2

3

4

5

6

7

8

9

0.01

10

0.005
0
-0.005p5_sdebt2_rint

p95_sdebt2_rint

mean_sdebt2_rint

Notes: impulse variable: response variable

Figure 9 Impulse Responses: Three-variate Case for Low Debt Countries

01

p5_rint_rint

2

3

4

5

p95_rint_rint

6

7

8

9

10

mean_rint_rintGDP growth: GDP growth
0.03
0.026
0.022
0.018
0.014
0.01
0.006
0.002
-0.002Public debt: GDP growth
0.005
0.003
0.001
-0.001

0

1

2

3

4

5

6

7

8

9

10

9

10

-0.003-0.0050123p5_rgdp_rgdp

4

5

6

7

p95_rgdp_rgdp

8

9

10

p5_sdebt2_rgdp

mean_rgdp_rgdp

p95_sdebt2_rgdp

mean_sdebt2_rgdp

GDP growth: Public debt

Public debt: Public debt
0.05

0
0

1

2

3

4

5

6

7

8

9

10

0.04
0.03

-0.01

0.02

-0.02

0.01
-0.03

0

-0.04

-0.01
p5_rgdp_sdebt2
mean_rgdp_sdebt2

p95_rgdp_sdebt2

0

1

2

3

4

p5_sdebt2_sdebt2

5

6

7

8

p95_sdebt2_sdebt2

mean_sdebt2_sdebt2

Notes: impulse variable: response variable

Figure 10 Impulse Responses: Two-variate Case for High Debt Countries with Interest Rate Exogenous

Table 1 Summary Statistics by Country(%)

Public debt ratio GDP growth rate
1
Australia
2
Austria3
Belgium
4
Bulgaria
5
Canada6
Cyprus7
Czech Republic
8
Denmark
9
Estonia
10
Finland
11
France12Germany
13
Greece14
Hungary
15
Ireland
16
Italy
17
Japan
18
Latvia19
Lithuania
20
Luxembourg
21
Malta
22
Netherlands
23
Poland24
Portugal25
Romania26
Slovak Republic
27
Slovenia
28
Spain
29
Sweden30
United Kingdom
31
United States
Data source: EuroStat, OECD Database

42.49
70.18
105.71
39.24
105.84
60.07
26.47
47.96
6.14
44.93
68.24
65.54
112.1467.19
57.36
109.56166.07
20.02
25.31
10.81
61.33
57.05
45.79
72.61
21.04
38.87
30.58
57.16
49.49
52.34
85.50

3.21
1.88
1.74
2.23
2.52
2.28
2.25
1.21
4.41
2.30
1.61
1.25
0.87
2.03
4.05
0.50
0.81
4.30
4.39
3.36
2.12
1.82
4.00
1.10
2.56
3.83
2.45
2.11
2.33
2.03
2.41

Long-term realinterest rate
2.70
2.75
2.57
-0.07
2.35
2.96
2.63
2.10
2.24
2.51
2.75
3.00
5.13
2.62
2.78
2.81
2.57
0.68
2.47
1.22
2.15
2.11
3.54
3.17
-0.09
2.19
2.57
2.44
2.75
2.30
2.42

Table 2 Various Test Statistics of Panel VAR Model: Two-variate Case

Case 1Case 2High debt
Countries

Case 3Low debt
countries

ExcludedGranger causality
variables
Wald statistics
GDP growth equation
debt-to-GDP ratio
0.034 (0.854)
Debt-to-GDP ratio equation
GDP growth rate
9.886 (0.002)
GDP growth equation
debt-to-GDP ratio
Debt-to-GDP ratio equation
GDP growth rate
GDP growth equation
debt-to-GDP ratio
Debt-to-GDP ratio equation
GDP growth rate

Notes: The values in parenthesis are p-value.

Stability
conditionsatisfied

0.038 (0.846)

Hansen’s test statistics ofOveridentifying restrictions

5.898(0.207)

satisfied

3.458(0.484)

satisfied

3.611(0.461)4.018 (0.045)

3.053 (0.081)
9.546 (0.002)

Table 3 Various Test Statistics of Panel VAR Model: Three-variate Case

Case 4

Case 5High debt
Countries

ExcludedGranger causality
variables
Wald statistics
GDP growth equation
debt-to-GDP ratio
0.027 (0.869)
long-term interest rate
1.697 (0.193)
Debt-to-GDP ratio equation
GDP growth rate
3.548 (0.060)
long-term interest rate
1.958 (0.162)
Long-term interest rate equation
GDP growth rate
13.655 (0.000)
debt-to-GDP ratio
0.073 (0.788)
GDP growth equation
debt-to-GDP ratio
1.885 (0.170)
long-term interest rate
10.013 (0.002)
Debt-to-GDP ratio equation
GDP growth rate
12.483 (0.000)
long-term interest rate
6.316 (0.012)
Long-term interest rate equation
GDP growth rate
6.687 (0.010)
debt-to-GDP ratio
0.020 (0.887)

Stability
condition

Hansen’s test statistics ofOveridentifying restrictions

satisfied

7.549 (0.580)

satisfied

9.518 (0.391)

Table 3 (continued) Various Test Statistics of Panel VAR Model: Three-variate Case

Case 6
Low debt
Countries

Case 7
High debt countries(long-term interest
rate exogenous)

ExcludedGranger causality
variables
Wald statistics
GDP growth equation
debt-to-GDP ratio
1.029 (0.310)
long-term interest rate
5.629 (0.018)
Debt-to-GDP ratio equation
GDP growth rate
8.955 (0.003)
long-term interest rate
2.437 (0.119)
Long-term interest rate equation
GDP growth rate
8.219 (0.004)
debt-to-GDP ratio
1.452 (0.228)
GDP growth equation
debt-to-GDP ratio
0.492 (0.483)
Debt-to-GDP ratio equation
GDP growth rate
2.582 (0.108)

Notes: The values in parenthesis are p-value.

Stability
condition

Hansen’s test statistics ofOveridentifying restrictions

satisfied

10.870 (0.285)

satisfied

1.817 (0.769)