Heterogeneity in the debt-growth nexus: Evidence from EMU countries  
 
 

Marta Gómez-Puiga*, Simón Sosvilla-Riverob 

aDepartment of Economics and Riskcenter, Universitat de Barcelona.  
08034 Barcelona, Spain 

bComplutense Institute for International Studies, Universidad Complutense de Madrid. 
28223 Madrid, Spain 

 
Revised version 

July 2017 
 
 
 
 
 
 

Abstract 
 
The objective of this paper is to examine whether the threshold beyond which a public debt change 
may have a detrimental effect on economic growth changes across euro area countries during the 
1961-2015 period. In contrast with previous studies, we do not use panel estimation techniques, but 
implement a time-series analysis for each country based on the growth literature. The results suggest 
that in all the countries but Belgium a debt increase begins to have detrimental effects on growth 
well before the SGP debt ceiling (a debt ratio of around 40% and 50% in central and peripheral 
countries, respectively) is reached. So, although austerity policies should be applied in EMU 
countries – since according to our results debt reduction barely exerts any significant beneficial 
impact on EMU countries’ growth – they should be accompanied by structural reforms that can 
increase their potential GDP. Moreover, as our results suggest that the harmful impact of a debt 
change on growth does not occur beyond the same threshold and with the same intensity in all 
EMU countries, a focus on average ratios and impacts may be unsuitable for defining policies. 
Specifically, our findings suggest that the pace of fiscal adjustment should be lower in Greece and 
Spain than in the other countries. 

 
 
Keywords: Public debt, economic growth, heterogeneity, multiple structural breaks, euro 
area, peripheral EMU countries, central EMU countries.  
 
JEL Classification Codes: C22, F33, H63, O40, O52 

                                                 
* Corresponding author. Tel.: +34 934020113; fax: +34 934039082. 
E-mail addresses: marta.gomezpuig@ub.edu (M. Gómez-Puig), sosvilla@ccee.ucm.es (S. Sosvilla-Rivero)  
 

mailto:marta.gomezpuig@ub.edu
mailto:sosvilla@ccee.ucm.es


2 
 

“At the present stage of development in Economics it is probably an advantage to have 

different groups looking at the same problem from different viewpoints, so that their 

conclusions can be compared and possibly then form the basis for a new compressive model”  

Granger (1990, 1) 

 

 

1. Introduction  

Nine years after the onset of the Great Recession, recovery remains tepid and bumpy in the 

European Economic and Monetary Union (EMU), and the prospects remain uncertain. 

The recent economic crisis led to an unprecedented increase in public debt across euro area 

countries1, raising serious concerns about its impact after a debt crisis that even called into 

question the stability of the euro. Troubled sovereign borrowers received financial rescue 

packages which were conditional on fiscal austerity and on the implementation of structural 

reforms to improve competitiveness.  

In the light of the events of the last few years, there is widespread agreement about the 

potentially adverse consequences for the economies of EMU countries of their unparalleled 

levels of public debt. However, few macroeconomic policy debates have generated as much 

controversy as the current austerity argument [see Alesina and Ardagna (2010), Alesina et al. 

(2015), Guajardo et al. (2011) or Jordà and Taylor (2016)] and, as Europe stagnates, the 

disagreement appears to be far from over. The core of the debate revolves around 

identifying the right stabilization policies to implement or, in a context of low economic 

growth, establishing the right pace of adjustment: austerity measures may prove positive in 

the long run, but they are likely to have negative effects on demand and production during 

the adjustment period [see Cottarelli and Jaramillo (2013), Delong and Summers (2012), or 

Perotti (2012)].  

Overall, the theoretical literature finds that there is cause to take into account the effects of 

very high debt on capital stock and growth, since it tends to point to a negative link 

between the public debt-to-Gross Domestic Product (GDP) ratio and the steady-state 

growth rate of GDP (see, for instance, Aizenman et al., 2007). The conventional view is 

that while debt can stimulate aggregate demand and output in the short run [see Barro 

(1990) or Elmendorf and Mankiw (1999)], in the long run it may crowd out capital and 

                                                 
1 On average, public debt reached levels about 100% of Gross Domestic Product (GDP) – its highest level in 50 years – 
by the end of 2013. 



3 
 

reduce output (Salotti and Trecroci, 2016). Moreover, the literature provides a variety of 

reasons to explain why the higher the level of public debt, the more negative its effects. 

Greiner (2014) points out that growth-impeding long-run effects are caused by changes in 

market participants’ expectations at high levels of public debt, leading to an increase in 

interest rates and a decrease in investment; Teles and Mussolini (2014) stress that, as 

uncertainty rises, additional fiscal flexibility for productive government spending is 

reduced, with a negative effect on growth; whilst Cochrane (2011) emphasizes that the 

higher the levels of public debt, the greater their negative effects due to a climate of 

uncertainty in which economic actors expect future confiscation, in the form of either 

increasing inflation or distortionary taxation.  

Against this background, the analysis in this paper will focus on the short-run effects of 

debt changes on economic growth in EMU countries with the objective to bring some light 

to the current austerity debate in a context of unprecedented debt levels. Therefore, we 

pose the following research questions: Does the effect of changes in the debt-to-GDP ratio 

on the short-run growth rate depend on the level of debt and the sign of the debt change? 

What is the debt-to-GDP threshold beyond which expansionary fiscal policies (a debt 

increase) have a negative impact on euro area economies’ rates of growth? Does the short-

term effect of a debt variation on economic performance differ across euro area countries? 

If a heterogeneous nexus between debt and growth is found, should stabilization policies to 

consolidate public finances or the pace of adjustment within euro area countries differ?  

These are important policy questions that need to be answered, but the results from the 

empirical literature in the EMU context do not provide a conclusive response since, despite 

the severe sovereign debt crisis, few papers have examined the relationship between debt 

and growth for euro area countries and the scant literature so far has mostly disregarded 

country heterogeneity in this relationship. Checherita-Westphal and Rother (2012) analyse 

the empirics of the debt-growth nexus using a standard growth model and panel data 

techniques and find that, during the 1970-2008 period, the turning point beyond which 

government debt negatively affects growth is 90-100% of GDP. Baum et al. (2013), who 

focused on the 1990-2010 period, detected a similar threshold by employing a dynamic 

approach (while the short-run impact of debt on per capita GDP growth is positive and 

significant, it decreases to zero beyond debt-to-GDP ratios of 67%, and at ratios above 

95% additional debt has a negative impact on output growth). In contrast, Dreger and 

Reimers (2013)’s analysis is based on the distinction between sustainable and non-

sustainable debt periods. Their results show that the negative impact of the debt-to-GDP 



4 
 

ratio on growth in the euro area is limited to periods of non-sustainable public debt; 

instead, debt will exert a positive impact on growth given that it is sustainable. The three 

former studies are synthesized and extended by Antonakakis (2014). Like them he uses a 

panel approach, but in addition to debt non-linearities he also examines the role of debt 

sustainability in economic growth in the euro area.  

Overall, the empirical literature mentioned above supports the presence of a common debt 

threshold across (similar) countries like those in the euro area favouring that so far the 

policy debate mostly ignored country heterogeneity in fiscal rules implementation.  

However, on the one hand, some recent literature has stressed that the effects of fiscal 

consolidation on economic activity, not only differ between core and peripheral countries 

(Anderson et al., 2014), but also across peripheral economies (Aldici et al., 2016). On the 

other hand, the latest literature on the debt-growth relationship suggests that the presence 

of a tipping point does not mean that it has to be common across countries.  

Indeed, the review paper by Panizza and Presbitero (2013) triggered a new wave of studies 

analysing the heterogeneous growth effects of public debt2. According to Mitze and Matz 

(2015), whilst a “first generation” of empirical cross-country studies predominantly 

predicted an inverted U-shape relationship between public debt and economic growth, with 

a negative impact on growth particularly in highly indebted countries, more recently a 

“second generation” of empirical contributions has challenged those findings on various 

grounds, including uncontrolled sample heterogeneity. The “first generation” of papers 

include the works by Reinhart and Rogoff (2010), Pattillo et al. (2011), Lof and Malinen 

(2014) and Woo and Kumar (2015); whilst the “second generation” include Ghosh et al. 

(2013), Markus and Rainer (2016), Chudik et al. (2017), Pescatori et al. (2014) or  

Edberhardt and Presbitero (2015).  

The latter authors propose a variety of reasons for the heterogeneity across countries in the 

debt-growth nexus. Ghosh et al. (2013) show that the turning point may be a function of 

countries’ structural characteristics and GDP growth. Markus and Rainer (2016) point out 

that, due to specific institutional characteristics concerning fiscal flexibility, fiscal 

                                                 
2 See, e.g., Eberhardt and Presbitero (2015), who investigate the debt-growth relationship in 118 developing, emerging 
and advanced economies and find some evidence for nonlinearity, but state that there is no evidence at all for a common 
threshold level in all countries over time; Égert (2015), who presents empirical evidence suggesting that 90% (the 
threshold suggested in the seminal paper by Reinhart and Rogoff, 2010) is not a magic number since it may be lower and 
nonlinearity may change across different samples and specifications, or Gómez-Puig and Sosvilla-Rivero (2015), who 
examine the bi-directional causality between debt and growth in a sample of eleven EMU countries and find that public 
debt has a negative effect over growth from an endogenously determined breakpoint and above a debt threshold that 
differs depending on the country.  
 



5 
 

effectiveness and fiscal consistency, different economic systems entail different degrees of 

fiscal uncertainty, which to a large extent shape the investment climate at comparable levels 

of public debt and thus constitute a source of heterogeneity in the relationship between 

high public debt levels and long-run economic growth. Chudik et al. (2017) and Pescatori et 

al. (2014) identify the debt trajectory as a source of heterogeneity in the debt-growth 

relationship, suggesting that high but falling public debt levels are growth-neutral while 

high and rising debt levels are detrimental for economic activity. Finally, according to 

Eberhardt and Presbitero (2015), there are many possible reasons for the differences in the 

relationships between public debt and growth across countries. First, production 

technology may differ across countries, and thus also the relationship between debt and 

growth. Second, the capacity to tolerate high levels of debt may depend on a number of 

country-specific characteristics, related to past crises and the macro and institutional 

framework. Third, vulnerability to public debt may depend not only on levels of debt, but 

also on its composition (domestic versus external, foreign or domestic currency-

denominated, long-term versus short-term public debt), which may also differ significantly 

across countries. 

Nevertheless, our study of the empirical evidence revealed hardly any analyses of the 

potential heterogeneity in the debt-growth nexus across euro area countries since the scarce 

literature on this topic belongs to the “first generation” of papers. Thus, to the best of our 

knowledge, this is the first paper to examine explicitly whether the debt-growth 

relationship may differ across EMU countries depending on their particular idiosyncrasies. 

The study of whether the relationship between public debt and economic growth may vary 

across countries has a significant bearing in the euro area context because, if the impact of 

debt on growth differs according to country, a focus on the average relation may be 

misleading for the definition of policy in individual countries –especially in an environment 

in which some EMU countries are already obliged to apply adjustment plans that re-

establish competitiveness and fiscal balance.  

Hence, this paper aims to fill the existing gap in the literature by explicitly taking into 

account the possible heterogeneity in the relationship between debt and growth across euro 

area countries. Our paper, then, is closely related to the work by Eberhardt and Presbitero 

(2015) and covers a very similar period but, in contrast with their analysis, it centres on the 

short-run effects of debt on economic growth, focuses on a different sample of countries 

and applies a different methodology. Whereas those authors used total public debt data 

from 118 developing, emerging and advanced economies, we centre on 11 euro area 



6 
 

countries. And with regard to the econometric methodology, instead of using panel 

estimation techniques that allow for heterogeneous limits across countries, we explore the 

time series dimension of the issue to obtain further evidence based on the historical 

experience of each country in the sample in order to detect potential heterogeneities in the 

relationship across euro area countries. In so doing, by taking into consideration the 

stationary or non-stationary nature of the variables under study, we can properly use 

hypothesis tests to examine the statistical significance of the estimated coefficients.   

The rest of the paper is organized as follows. Section 2 presents the rationale for our 

empirical approach on the basis of the results of some preliminary descriptive analyses. 

Section 3 introduces the analytical framework. Section 4 describes the data used in the 

analysis. Empirical results are presented in Section 5 and some extensions are incorporated 

in order to explore the possibility of asymmetric effects and to identify threshold effects. 

Finally, some concluding remarks and policy implications are provided in Section 6.  

2. Preliminary descriptive analysis 

In the following, we provide some descriptive analyses highlighting the cross-country 

heterogeneity in the relationship between debt and growth in euro area countries. Figure 1 

shows the evolution of net sovereign debt-to-GDP and real GDP per capita growth in the 

11 countries in our sample (Austria, Belgium, Finland, France, Germany, Greece, Ireland, 

Italy, the Netherlands, Portugal and Spain) over the sample period 1961-2015.   

[Insert Figure 1 around here] 

Some interesting insights can be drawn from Figure 1, which shows that the debt-to-GDP 

ratio reached its peak at the end of the sample period in all the countries in our sample, 

with the exceptions of Belgium, Finland, and the Netherlands where the highest ratio 

coincided with the economic crisis of the early 1990s. So, leaving these three countries 

aside, the recent economic and financial crisis led to an unprecedented increase in public 

debt-to-GDP ratios in the majority of EMU countries, even though their evolution over 

the 1961-2015 period exhibits different patterns. While in Ireland, Italy and Spain the 

notable rise in debt accumulation in 2007-2008 was preceded by a deleverage period; in 

Austria, France, Germany, Greece and Portugal debt presented an upward trend 

throughout the period, albeit at different speeds. With respect to GDP growth, although 

the evolution of the business cycle is quite similar in all EMU countries, the impact of the 



7 
 

recessions (five according to the CEPR Euro Area Business Cycle Dating Committee3: 

1974:Q4-1975:Q1; 1980:Q2-1983:Q3; 1992:Q2-1993:Q3; 2008:Q2-2009:Q2; and 2011:Q4-

2013:Q3) clearly diverges across countries. 

All in all, Figure 1 indicates that the evolution of the two variables studied (net public debt-

to-GDP and GDP per capita growth) presents very different patterns across euro area 

countries. This suggests that an individual analysis of their relationship over time may 

capture the potential heterogeneity across countries and provide more useful information 

than a country-group analysis applying panel techniques.   

Obviously, the above results are by no means conclusive, but they may challenge some of 

the implicit assumptions adopted in most of the previous literature regarding the 

relationship between debt and growth in similar countries, like those in the euro area. They 

thus provide a good reason to examine whether there may be some differences in this 

relationship across EMU countries depending on their level of economic development, 

their industrial structure, or the institutional environment.  

3. Analytical framework 

Economic models are inevitably incomplete characterizations of the complicated reality of 

economic life: “like rays of light they illuminate a part of a whole and leave the rest in dark” 

Hicks (1981, p.232). Therefore, formulating a sufficiently general initial model to capture all 

the substantively relevant influences is a fundamental problem facing all empirical 

modelling exercises (Doornik and Hendry, 2015). 

The crucial decision in all empirical studies concerns the set of variables for which 

observations should be collected and then analysed, which will be a small subset of all the 

variables in the economy. Following both the relevant economic theory and the previous 

empirical results, our strategy incorporates the specification and estimation of a growth 

equation based on the growth literature (e.g., Barro and Sala-i-Martin, 2004) augmented by 

public debt to assess whether the latter has an impact on growth over and above other 

determinants. 

The initial empirical specification is derived from the neoclassical growth model of Solow, 

where the growth rate of real per capita GDP (gt) for a given country is: 

                                                 
3 The CEPR Euro Area Business Cycle Dating Committee establishes the chronology of recessions and expansions of the 
eleven original euro area member countries plus Greece for 1970-1998, and of the euro area as a whole from 1999 
onwards (see Centre for Economic Policy Research, 2014). 
 



8 
 

                                      1
1

n

t t i it t t
i

g y X dα γ δ β ε−
=

= + + + +∑    (1) 

where yt-1 is the logarithm of initial real per capita GDP (to capture the “catch-up effect” or 

conditional convergence of the economy to its steady state), Xit (i=1, …, n) is a set of 

explanatory regressors and dt is the net public debt-to-GDP ratio. 

Regarding Xt, we consider a set of explanatory variables that have been shown to be 

consistently associated with growth in the literature: population growth rate as a percentage 

(POPGRt); the ratio of gross capital formation to GDP (GCFt); life expectancy at birth, a 

proxy for the level of human capital (HKt)4; openness to trade, measured by the absolute 

sum of exports and imports over GDP (OPENt); and the GDP deflator inflation rate, a 

measure of macroeconomic instability and uncertainty (INFt). 

In the economic growth literature, the rate of growth of labour used in the production 

process and the accumulation of physical capital (investment) are the key determinants of 

growth (Solow, 1956 or Frankel, 1962). So, population growth (POPGRt) and the ratio of 

gross fixed capital formation to real GDP (GCFt) are used to proxy country size and the 

rate of labour growth and the accumulation of the physical capital stock respectively. The 

empirical evidence suggests that the relationship between population and economic growth 

is mixed and varies between countries. Some empirical studies suggest that the relationship 

is negative and insignificant (Levine and Renelt, 1992); others find a negative and 

significant association (Mankiw et al., 1992); whilst still others present evidence of a positive 

relationship (Sachs and Warner, 1997). The population growth rate, then, has been found 

to exhibit either a positive or a negative relationship with economic growth. However, 

according to many literature reports, a positive and statistically significant impact of 

physical capital stock (investment) on economic growth is expected5.   

A proxy of human capital (HKt) is included to reflect the notion that countries with an 

abundance of human capital are more likely to be able to attract investors, absorb ideas 

from the rest of the world, and engage in innovation activities (Grossman and Helpman, 

                                                 
4 This proxy is also used by Sachs and Warner (1997). Other proxies commonly used for human capital such as years of 
secondary education and school enrollment in secondary were only available from 1980. Additionally, the proxy years of 
secondary education did not change during the sample period. As shown in Jayachandran and Lleras-Muney (2009), 
longer life expectancy encourages human capital accumulation, since a longer time horizon increases the value of 
investments that pay out over time. Moreover, better health and greater education are complementary with longer life 
expectancy (Becker, 2007). Indeed, life expectancy at birth correlates strongly with the index of human capital per person 
provided by the Penn World Table (version 8.0, Feenstra et al., 2013), based on years of schooling (Barro and Lee, 2013) 
and returns to education (Psacharopoulos, 1994). 
5 Investment and growth may also be associated through the savings ratio (Keynes, 1936).  

 



9 
 

1991). Whilst some studies have found a positive relationship between human capital and 

economic growth (Radelet et al., 2001), others have found a negative relationship (Barro, 

2003). Consequently, the effect of human capital on economic growth is expected to be 

either positive or negative. Trade openness (OPENt) is posited to boost productivity 

through transfers of knowledge and efficiency gains (Seghezza and Baldwin, 2008). Since 

most of the empirical literature [Romer (1992), Barro and Sala-i-Martin (1995), or Edwards 

(1998), among others] provides evidence of the positive impact of openness on growth, a 

positive sign is expected for this variable. Finally, with regard to the inflation rate (INFt), it 

has been argued that inflation is a good macroeconomic indicator of how the government 

manages the economy [see Fischer (1993) or Barro (2003), among other authors] and that 

low inflation brings about economic efficiency because, through the price mechanism, 

economies are able to allocate scarce resources to their best economic use (World Bank, 

1990). Nonetheless, the a priori expectation may be either a positive or negative association 

between inflation and economic growth. This uncertain a priori effect is supported by the 

different arguments presented in the literature regarding the relationship between these two 

variables. Whilst some authors defend a negative relationship, others support a positive 

one. So, on the one hand, the former group includes De Gregorio (1993), who suggests 

that inflation can increase the cost of capital, reducing capital accumulation and lowering its 

productivity and thus inhibiting long-run growth; Friedman (1977), who conjectures that 

inflation uncertainty would reduce the effectiveness of the price mechanism to coordinate 

economic activities, decreasing the output growth rate; and Fischer (1993) or Bruno and 

Easterly (1998), who stress the negative relationship between inflation and growth 

especially via its impact on the efficiency of physical capital. On the other hand, the latter 

group includes Tobin (1965), who argues that higher anticipated inflation can increase 

capital per head as households shift their (portfolio) assets away from real money balances 

(non-interest-bearing money) toward real capital (more productive forms) and Dotsey and 

Sarte (2000), who contend that inflation makes the return to money balances uncertain and 

reduces the demand for real money balances and consumption; this increases precautionary 

savings and, in response to higher anticipated inflation, the investment pool enhances 

economic growth. 

4. Data  

We use annual data for eleven EMU countries: both central (Austria, Belgium, Finland, 

France, Germany and the Netherlands) and peripheral (Greece, Ireland, Italy, Portugal and 



10 
 

Spain)6. We use long spans of data covering the 1961-2015 period (i.e., a total of 54 annual 

observations) to explore the dimension of historical specificity and to capture the 

underlying relationship between the variables under study. 

To maintain as much homogeneity as possible for a sample of 11 countries over the course 

of five decades, we use the World Bank’s World Development Indicators7 as our primary 

source. We then strengthen our data with the use of supplementary information from the 

International Monetary Fund (International Financial Statistics and World Economic 

Outlook, October 2016) and the European Commission´s AMECO database. As 

mentioned above, we use per capita GDP at 2010 market prices, population growth rate, 

the ratio of gross capital formation to GDP, an index of human capital, openness to trade 

and GDP deflator inflation. The precise definitions and sources of the variables are 

presented in Appendix 1. 

5. Empirical Results8 

5.1. Time series properties 

Our approach focuses on time series analyses of yearly data for individual countries which 

can help us to document the possible differences in their experiences. This approach is 

likely to provide an accurate idea of what underlies the debt-growth nexus in EMU 

countries. 

Since the appropriate econometric treatment of a model depends crucially on the pattern of 

stationarity and non-stationarity of the variables under study, before carrying out the 

estimation we test for the order of integration of the variables by means of the Augmented 

Dickey-Fuller (ADF) tests. This step is necessary to ensure that all our variables in the 

regression equation have the same order of integration, given the non-stationarity that most 

macroeconomic data exhibit. The results decisively reject the null hypothesis of unit root at 

conventional significance levels for gt, INFt, POPGRt and GCFt (indicating that they are 

                                                 
6 This distinction between European central and peripheral countries has been used extensively in the empirical literature. 
The two groups we consider roughly correspond to the distinction made by the European Commission (1995) between 
countries whose currencies continuously participated in the European Exchange Rate Mechanism (ERM) from its 
inception and which maintained broadly stable bilateral exchange rates with each other over the sample period, and those 
countries whose currencies either entered the ERM later or suspended their participation in the ERM, as well as 
fluctuating widely in value relative to the Deutschmark. These two groups are also roughly the ones found in Jacquemin 
and Sapir (1996), who applied multivariate analysis techniques to a wide set of structural and macroeconomic indicators, 
to form a homogeneous group of countries. Moreover, these two groups are basically the same as the ones found in 
Ledesma-Rodríguez et al. (2005) according to economic agents’ perceptions of the commitment to maintain the exchange 
rate around a central parity in the ERM, and those identified by Sosvilla-Rivero and Morales-Zumaquero (2012) using 
cluster analysis when analyzing the permanent and transitory volatilities of EMU sovereign yields. 
7 http://data.worldbank.org/data-catalog/world-development-indicators 
8 We summarize the results by pointing out the main regularities. The reader is asked to browse through Tables 1 to 6 to 
find evidence for particular country of her/his special interest.  



11 
 

stationary in levels, i. e., I(0)), while we do not reject the null for yt, dt, OPENt and HKt 

(suggesting that these variables can be treated as first-difference stationary, i. e., I(1))9. 

Then, following Cheung and Chinn’s (1997) suggestion, we confirm these results using the 

Kwiatkowski et al. (1992) (KPSS) tests, where the null is a stationary process against the 

alternative of a unit root10. As can be seen in Figure 1 the growth rates are clearly stationary 

I(0), whereas dt appears to be I(1), highlighting the point made above. 

5.2. A basic empirical model 

Given that our dependent variable is stationary (i. e., its statistical properties such as mean, 

variance, autocorrelation, etc. remain constant over time), we cannot explain it with non-

stationary variables (whose statistical properties change over time). Additionally, if the 

variables in the regression model are not stationary, then the standard assumptions for 

asymptotic analysis will not be valid and we cannot undertake hypothesis tests about the 

regression parameters. Therefore, by differencing the non-stationary variables we transform 

them into stationary variables11. 

As a result of the time series properties of our data, the baseline empirical model is as 

follows:  

1 1 2 3 4 5t t t t t t t t tg g INF HK OPEN POPGR GCF dφ δ δ δ δ δ β ε−= + + ∆ + ∆ + + + ∆ +   (2) 

where Δ denotes the first difference operator.  

Note that model (2) is quite different from model (1), which is commonly used in the 

literature, especially regarding the variables yt-1, HK, OPEN and d, since we find that they 

are non-stationary and therefore enter our model in first differences. As argued in 

Asimakopoulos and Karavias (2016), by rewriting equation (1) as (3) 

1
1 1

l l
s s ns ns

t t i it i it t t
i i

g y X X dα γ δ δ β ε−
= =

= + + + + +∑ ∑      (3) 

(where s
itX  and ns

itX denote the stationary and non-stationary explanatory variables 

respectively), we can compare (3) with our equation (2), which has 1 1t tg y− −= ∆ instead of 

1ty − , td∆  instead of td  and ns
itX∆  instead of ns

itX as explanatory variables due to non-
                                                 
9 These results (which are not shown here in order to save space, but are available from the authors upon request) were 
confirmed using Phillips-Perron (1998) unit root tests controlling for serial correlation and the Elliott, Rothenberg, and 
Stock (1996) Point Optimal and Ng and Perron (2001) unit root tests for testing non-stationarity against the alternative of 
high persistence. These additional results are also available from the authors. 
10 The results are not shown here due to space restrictions but are available from the authors upon request. 
11 Note that if the public debt-to-GDP ratio series contains a unit root, that would imply that the results of many previous 
studies (some of which had been used as a basis for policy recommendations) are spurious.  



12 
 

stationarity. The interpretation of the estimated parameters is the same in both models, but 

that ofφ , 2 ,δ 3δ and β changes12. 

5.3. Exploring the possibility of asymmetric effects  

To explore the possibility of an asymmetric effect on positive and negative debt variations 

on economic growth for each country, we use the following alternative empirical 

specification to capture this possibility: 

1 1 2 3 4 5

1 2( 0) ( 0)
t t t t t t t

t t t t t

g g INF HK OPEN POPGR GCF
d I d d I d
φ δ δ δ δ δ

β β ε
−= + + ∆ + ∆ + +

+ ∆ ∆ > + ∆ ∆ < +
   (4) 

where I is an indicator function that takes the value 1 if the condition is fulfilled (i. e., if Δdt 

is positive or negative) and zero otherwise. The indicator function has the effect of splitting 

the debt change variable into two, allowing for its impact to differ depending on the sign of 

the change (i. e., debt accumulation and debt relief).  

We employ a data-based method for obtaining a parsimony representation of the data 

generating process (DGP): the general-to-specific approach (Hendry, 1995). General-to-

specific modelling seeks to mimic reduction by commencing from a general congruent 

specification which is simplified to a minimal representation consistent with the desired 

criteria and the data evidence. Starting from a general unrestricted model that contains all 

the variables likely to be relevant (based on the specification presented in equation 2) and 

lags long enough to be able to capture a constant parameter representation, standard 

testing procedures eliminate statistically-insignificant variables. Diagnostic tests check the 

validity of the reductions, ensuring a consistent final selection which produces a 

parsimonious and interpretable econometric model that is data admissible, presents well-

behaved residuals and uses conditioning variables that are weakly exogenous (see Faust and 

Whiteman, 1997)13. With a judicious choice of parameters and variables this approach 

generates a well-specified model which embeds the economic theory and can deliver the 

parameters of interest14. 

Given the strong potential for endogeneity of the debt variable, especially reverse causation 

(low or negative growth rates of per-capita GDP are likely to induce higher debt burdens), 

                                                 
12 The estimation results for the basic empirical model are not shown here to save space, but they are available from the 
authors upon request. As pointed out by an anonymous referee, the use of the three models could be distracting and 
conflicting.  
13 Phillips (1988) contends that the general-to-specific methodology performs a set of corrections that make it an optimal 
procedure under weak exogeneity. 
14 An impressive record has been built up for the usefulness of empirical model discovery via general-to-specific searches 
(see Hendry, 2000). 



13 
 

we use 2SLS (two-stage least squares) instrumental variable techniques to estimate the 

finally selected model. Following the common practice with macroeconomic data, we use 

lagged terms of regressors as instruments15. Panel A in Table 1 reports the results. It can be 

observed that all explanatory variables turn out to be significant and their signs are in 

concordance with the literature. The degree of country’s openness to trade, both the 

proxies used to measure human and physical capital and population growth have a positive 

impact on real GDP per capita growth, whilst the inflation rate and the ratio of public debt 

over GDP exert a negative effect16. 

[Insert Table 1 around here] 

The results reported in Panel A in Table 1 support the existence of an asymmetric effect 

between debt accumulation and debt reduction over growth, since the negative coefficient 

on the former (-0.35 on average) is, in absolute values, always higher than the negative 

coefficient on the latter (-0.16 on average), suggesting that the negative marginal effect of 

an increase in debt exceeds the positive marginal impact of a debt relief17. However, this 

asymmetric effect clearly differs between countries. The difference between the two 

marginal impacts ranges from a value of -0.46 in the case of Ireland to one of -0.03 in the 

case of Finland; Ireland, France, Germany, Portugal and Belgium are the countries where 

the asymmetry is higher. Interestingly, we do not find clear differences in patterns between 

central and peripheral countries, since the decrease in the absolute value of the marginal 

impact in the case of debt reduction varies within each group of countries and its average is 

-0.2 in both cases.  

As can be seen in Panel B in Table 1, the estimated models seem to pass diagnostic tests 

such as normality of error term, second-order residual autocorrelation and 

heteroskedasticity (χ2
N, χ2

SC and χ2
H respectively). The overall regression fit is satisfactory, 

as measured by the adjusted R2 value (ranging from 0.5069 for Austria to 0.6991 for Spain). 

Finally, if we focus on the marginal impact of a debt reduction over growth in peripheral 

countries − where some countries (Portugal, Ireland and Greece) received financial rescue 

packages conditional on fiscal austerity and the implementation of structural reforms, and 
                                                 
15 Following the usual practice, to test whether lagged variables are relevant and valid instrument, we initially examine the 
first-stage regression, checking sign, significance and plausible magnitude of the coefficients on the instrument. Given the 
“weak instrument” problem, we apply the "rule of thumb” of a t-stats bigger than 2 (at least 10). We then examine the 
“reduced form” regression, checking that for the sign and magnitudes of coefficients. Finally, since we have more than 
one instrument, we test validity/exclusion restrictions using the Sargan (1958)’s test.   
16 As pointed out in Section 4.1, a positive effect was expected for the variables measuring openness to trade and physical 
capital, while a negative effect was expected for the ratio of public debt. However, according to the literature the expected 
effect of human capital, population growth and inflation rate might either be positive or negative. 
17 Note that an estimated negative coefficient for ΔdtI(Δdt<0) suggests a positive impact on growth, since such negative 
coefficient is multiplied by a negative number.  



14 
 

others (Spain) received financial assistance to recapitalize its banks with conditions on 

implementing structural reforms –, we see that, precisely in these four countries, this 

impact presents very low values (-0.18, -0.10, -0.05 and -0.05 in Portugal, Ireland, Greece 

and Spain, respectively), highlighting that the effect of austerity policies for boosting 

economy in those countries is limited.  

These results are in accordance with most of the recent literature which has studied 

whether the consolidation of public finances in the euro area through the reduction of 

fiscal expenditures and an increase in taxes contributed to GDP growth. Dreger and 

Reimers (2016) point out that the lack of public investment may have restricted private 

investment and thus GDP growth. Fatás and Summers (2016) provide support for the 

presence of strong hysteresis effects of fiscal policy, suggesting that attempts to reduce 

debt via fiscal consolidations have very likely resulted in a higher debt-to-GDP ratio 

through their long-term negative impact on output. Jordà and Taylor (2016)’s estimates 

indicate that in a slump austerity generally prolongs the pain, much more so than in a 

boom.  

Some of the literature has focused its analysis on the peripheral countries hit harder by the 

crisis. Aldici et al. (2016) look at the feasibility of the fiscal adjustment comparing the 

macroeconomic conditions in each country and emphasizing the role of the fiscal 

multipliers in the process. Their results also point to the slump in investment as the key 

negative factor behind the collapse in demand in all cases. Moreover, they suggest that one 

of the reasons why the recession was particularly deep in Greece was that the fall in 

investment was not even partially offset by higher exports, in contrast to Portugal and 

Ireland. Anderson et al. (2014) contend that structural reforms in core countries could be 

expected to offset the near-term negative impact on activity arising from the required fiscal 

consolidation. However, for the periphery, their results suggest that it would take several 

years before structural reforms could return the level of output to its pre-consolidation 

path. Inspecting the adjustment programs in place during the past few years in Portugal, 

Reis (2015) concludes that if success is assessed as making another debt crisis unlikely in 

the near future, the program delivered; however, if instead it is judged in terms of a 

rebound of the economy from its prolonged depression, then there is little to celebrate. 

Finally, Rosnick and Weisbrot (2015), who focus on the Spanish economy, find that the 

data do not support the thesis that the current economic recovery is the result of a return 

of market, consumer, and investor confidence due to fiscal consolidation; for them, a more 

likely explanation is a slowdown and possibly even the end of fiscal consolidation, 



15 
 

combined with more favourable external factors. These authors corroborate our results 

that fiscal consolidation in Ireland, Greece, Portugal and Spain barely affected economic 

recovery. 

5.4. Identifying threshold effects  

Identifying a threshold effect for each economy under study would inform policy makers 

of the presence of a country-specific tipping point, which would be useful information for 

guiding macroeconomic policies and fiscal adjustments. To this end, we use the following 

alternative specification: 

1 1 2 3 4 5
* *

1 2( ) ( )
t t t t t t t

t t t t t

g g INF HK OPEN POPGR GCF
d I d d d I d d
φ δ δ δ δ δ

γ γ ε
−= + + ∆ + ∆ + +

+ ∆ ≤ + ∆ > +
   (5) 

where I is an indicator function that takes the value 1 if the condition is fulfilled (i. e., if td  

is either below or above a specific threshold value d*) and zero otherwise18. Again, the 

indicator function has the effect of splitting the debt change variable into two, allowing for 

its impact to differ depending on whether de debt ratio is below or above a given tipping 

point.  

Following the common practice in the empirical literature, the assignment to one or the 

other regime is determined by the debt-to-GDP ratio, allowing us to compare our results 

with previous papers which have adopted this ratio as the primary variable of interest. We 

evaluate all possible values for *,d selecting for each country the value that minimizes the 

sum of squared residuals from the regression as the relevant one19. 

[Insert Table 2 around here] 

We apply the 2SLS estimator proposed by Caner and Hansen (2004) using lagged terms of 

regressors as instruments. The results in Panel A in Table 2 show the debt-to-GDP 

threshold beyond which a debt increase starts to be detrimental for growth. It is striking 

that we do not find a common debt threshold in the EMU countries under study: it differs 

notably from country to country, ranging from 61% in Belgium to 21% in France. 

Furthermore, with the exceptions of Belgium (61%) and Germany (55%), the average value 

of the debt threshold is higher in peripheral (48%) than in central countries (41%). 

However, the average negative marginal impact of a debt increase beyond that point on 

                                                 
18 Cecchetti et al. (2011) and Baum et al. (2013), among others, use the same indicator function to capture thresholds 
effects.   
19 We also explored the possibility of multiple thresholds, but the data was unable to identify a second significant 
threshold during the sample period.   



16 
 

growth is much higher in central (-0.59) than in peripheral countries (-0.24). Therefore, 

these results suggest that with the exceptions of Belgium and Germany, peripheral 

countries have a little more room to increase their public indebtedness than central ones 

before it starts to have a detrimental effect on growth. Furthermore, beyond the tipping 

point the harmful effect of a debt increase on economic performance is much higher in 

central than in peripheral countries which may explain “the debt intolerance” exhibited by 

some core EMU countries20.  

All in all, the average threshold (44%) for the eleven countries under study is much lower 

than the figure obtained in the literature for euro area countries by means of panel data 

techniques. Checherita-Westphal and Rother (2012) find that, between 1970 and 2008, the 

turning point was 90-100% of GDP, while Baum et al. (2013), who focused on the 1990-

2010 period, detected a similar threshold (95%) using a dynamic approach. The different 

results should be assessed with due caution and should be examined in the context of the 

distinct methodological approach implemented in this paper, since we adopt a times series 

analysis instead of a panel data approach and we deal appropriately with the different order 

of integration of the relevant variables, using changes in debt-to-GDP ratio as the primary 

variable of interest.   

However, in our view, our results are much more consistent than the ones just mentioned 

with the Stability and Growth Pact’s (SGP)21 debt ceiling of 60% of GDP. Otherwise, if 

the tipping point (beyond which government debt negatively affects growth) was 90-100% 

of GDP, what would be the justification for requiring governments, under penalty of fines, 

to reduce their debt ratios if they surpassed the 60% reference value? Still, the accuracy of 

the fiscal limits included in the SGP has been surrounded by considerable controversy in 

the literature, and there is no agreement on its efficiency.  

In an empirical study of whether it pays off (in terms of economic growth) to fulfil the 

convergence criteria on the public budget and participation in the euro area, Bökemeier and 

Clemens (2016)’s results show that growth is higher if the debt-to-GDP ratio is below 60%. 

Similarly, Checherita-Westphal et al. (2014) estimate that euro area governments should 

maintain a debt-to-GDP target of 50% if they wish to maximize growth. However, other 

                                                 
20 As can be seen in Panel B in Table 2, the regressions fit reasonably well, as they pass the diagnostic tests against non-
normal errors, autocorrelation and heteroskedasticity.   
21 The revised Stability and Growth Pact (European Economy, 2011) includes the clause that if the fiscal position falls 
short of the Medium-Term Objectives (MTOs), countries must implement more ambitious adjustment plans in order to 
meet them. In addition, for countries with debt ratios above 60% of GDP, an excessive deficit procedure can be launched 
if the debt ratio is deemed not to be decreasing at a satisfactory rate – meaning that the debt ratio must diminish annually 
by at least 1/20th of the difference between the actual debt ratio and 60% of GDP reference value. 
 



17 
 

authors consider that a profound reform of the SGP is needed to make it work in the 

future. Ioannou and Stracca (2014) present evidence that the SGP has had no significant 

beneficial impact on the fiscal and economic performance of euro area countries; while 

Teulings (2016) shows that an episode of increased dynamic inefficiency, like the one 

driven by the Great Recession and the increased financial volatility, would require a higher 

debt level than those considered in the SGP. 

In this context, the conclusions that can be drawn from our analysis at this point are also 

mixed. On the one hand, in all the countries under study but Belgium, a debt increase 

begins to have detrimental effects on growth well before the SGP debt ceiling, meaning 

that fiscal policies should stay within a safe zone (i.e., a debt ratio of around 50% and 40% 

in peripheral and central countries respectively) below the official fiscal limit. So, with 

average debt levels of 100% in euro area countries, deleverage (austerity policies) should be 

applied; but, according to our results, debt reduction exerts barely any significant beneficial 

impact on euro area countries’ economic performance. Therefore, in our view, adjustment 

programmes should be accompanied by structural reforms that might increase the 

adjustment capacity or the potential GDP in euro area countries (see Aldici et. al. 2016). 

Otherwise, after years of experience with fiscal austerity which have reaffirmed its 

ineffectiveness as a primary instrument of debt reduction, according to other authors (see 

Mody (2013), among them) the current policy dilemmas might only be solved in a 

framework that allows orderly debt restructuring. 

Finally, it is interesting to note that in eight out of the 11 countries in our sample (Austria, 

Finland, France, Germany, Greece, Ireland, Portugal and Spain), the years when the 

detected thresholds ratios are recorded coincide with the minimum value of the index of 

the fiscal stance proposed by Polito and Wickens (2012, 2014). This suggests that after a 

severe worsening of fiscal policy, an additional increase in the debt-to-GDP ratio would 

not stimulate economic growth. This reading is consistent with the claim made in Polito 

and Wickens (2012) that the main causes of fluctuations in their index are variations in the 

gap between expenditures and revenues. 

5.5. Comparing results  

In order to compare the results obtained from the asymmetric model and the threshold 

model, we perform stochastic dynamic simulations of the estimated models to assess how 

each explanatory variable contributes to the explanation of the average growth rate of real 



18 
 

per capita GDP during the 1981-2015 period.  Table 3 reports the results for each country 

under study22. 

[Insert Table 3 around here] 

As can be seen, the absolute value of the average negative contribution of a debt increase 

to growth is similar (-0.2) in the asymmetric and the threshold model. However, while in 

the asymmetric model the average negative contribution is somewhat higher in central 

countries (-0.3) rather than in peripheral ones (-0.2), in the threshold model the average 

negative contribution does not change between the two groups of countries.    

To compare the two models further, we perform dynamic multi-step forecasts of gt. within 

the sample using previously forecasted values of gt, and evaluate these forecasts based upon 

the model with the actual data. Table 4 shows the forecasting performance of our 

competing models. We evaluated their forecasting performance using five different 

measures of forecast accuracy: The Root Mean Squared Error (RMSE), the Mean Absolute 

Error (MAE), the Mean Absolute Percentage Error (MAPE), and two Theil Inequality 

coefficients (U1 for forecast accuracy and U2 for forecast quality). These statistics all 

provide a measure of the distance of the true from the forecasted values.  

[Insert Table 4 around here] 

The results presented in Table 4 indicate that in most of the countries the threshold model 

reports higher forecast accuracy. The exceptions are Austria, Italy, and the Netherlands, 

where the asymmetric model presents better forecast quality jointly with Germany and 

Finland, where both the threshold and the asymmetric model seem to be just as good. 

Therefore, when analyzing the contribution of a debt increase in economic growth (Table 

3), we will rely on the results obtained from the threshold model in the case of Belgium, 

France, Greece, Ireland, Portugal and Spain; while in Austria, Italy and the Netherlands, we 

will use the results from the asymmetric model. In the case of Germany and Finland, we 

will take both into account. In Finland, the negative contribution of a debt increase to 

growth is very similar in both models (-0.18 and -0.20). However, in Germany, in absolute 

terms, the contribution is higher in the asymmetric model (-0.45) rather than in the 

threshold one (-0.22). Therefore, the average negative contribution of a debt increase in  

euro area countries economic performance is slightly higher when using the value from the 

asymmetric model in these two countries (-0.3 compared to -0.2, if the value from the 

                                                 
22 To save space, we only comment on the results for variations in the debt-to-GDP ratio.   



19 
 

threshold model is used). Moreover, while the average negative contribution of a debt 

increase in euro peripheral countries’ growth is -0.2, it ranges from -0.25 until -0.29 in 

central countries depending on the value used in Finland and Germany.  

Focusing on the behaviour of the contribution of a debt increase to economic growth 

within each group of countries (central and peripheral), we do find important differences. 

France, Germany, Belgium and Finland are the central countries with the highest negative 

contribution of a debt increase (their values range from -0.85 to -0.2), while the 

Netherlands and Austria have the lowest (-0.02 and -0.005 respectively). In the case of 

peripheral countries, Ireland, Italy and Portugal are the ones with the highest negative 

contribution (-0.34, -0.34 and -0.18), while in Greece and Spain it is significantly lower (-

0.10 and -0.06 respectively).  

Even though we agree that it is imperative to lower public debt over time, these results, 

combined with those displayed in Table 1, reinforce the idea that European policymakers 

need to be aware that the effect of debt on economic performance differs according to 

EMU country, as does the effect of fiscal adjustments on growth prospects. Therefore, we 

think that the pace of adjustment should differ between countries. In particular, according 

to our results, the five peripheral countries under study should be split in three groups with 

regard to the implementation of policy measures. The first would include Spain and 

Greece, Portugal would be the sole member of the second, and the third group might be 

formed by Italy and Ireland.   

In Spain and Greece, not only is the debt threshold above 50% (close to 60% in the Greek 

case), but the negative contribution of a debt increase to economic growth is also very low. 

In Portugal public debt reaches its tipping point at a lower value (close to 40%) but the 

negative contribution of higher sovereign indebtedness to economic performance is still 

small (-0.18). Finally, in Italy and Ireland the debt threshold ranges from 40% to 50% and 

the negative contribution of a debt increase is high (-0.34).  

Consequently, in the Greek and Spanish cases (whose economies have been severely hit by 

the crisis), our findings suggest that the pace of fiscal adjustment should be lower than in 

the other three countries. However, in Ireland and Italy (the countries with the highest 

detrimental effect of a sovereign debt increase on growth) a faster fiscal adjustment should 

be applied. Besides, in order to support growth when fiscal policy is tightened, we also 

agree that there is a need for reforms in goods, service, and labour markets to improve 

economic efficiency and boost potential growth, thus serving as important tools in the 



20 
 

fiscal adjustment process. Policies enhancing both stability and growth are possible in the 

EMU; some of them have already been implemented, and others are at an advanced stage 

of development. 

5.6. Robustness check 23 

Given that the sample period includes the inception of the EMU in January 1999, we 

conduct robustness checks by splitting the sample before and during EMU in order to 

examine whether the introduction of the fiscal discipline rules that came along with the 

common currency might have influenced the relationship between a debt change and 

economic growth from that date. The estimated coefficients for a debt change in the two 

periods corresponding to the asymmetric and the threshold model are shown in Tables 5 

and 6, respectively. 

[Insert Tables 5 and 6 around here] 

The estimation results shown in these tables remain robust across both models, being once 

again the coefficients on debt variations statistically significant with the same sign, 

confirming the presence of asymmetric and threshold effects before and during the EMU. 

As can be seen in Table 5, when we compare the marginal impact on growth of debt 

accumulation and relief, before and after the beginning of the monetary union, the Wald 

test of significant differences in the estimated coefficients shows that the null hypothesis of 

no difference between pre-EMU and EMU coefficients associated with debt accumulation 

( 1̂β ) is rejected at the 1% significance level in Germany and at the 10% significance level in 

Ireland and the Netherlands, while there is no statistically significant difference between 

pre-EMU and EMU coefficients associated with debt relief ( 2β̂ ) except for Ireland and 

Italy (at the 5% significance level), and for Finland (at the 10% significance level).  

Moreover, in all the above cases but Ireland, the marginal impact of a debt change 

decreases with the introduction of the euro, suggesting that the fiscal discipline associated 

with the Stability and Growth Pact and the Excessive Deficit Procedure had somewhat 

mitigated the capacity of fiscal policies to influence economic growth. As said, Ireland 

seems to be an exception since the negative effect of a debt accumulation on economic 

growth is higher during the EMU period than before the introduction of the common 

currency.  

                                                 
23 We are grateful to an anonymous referee for suggesting this analysis. 



21 
 

Regarding the threshold model24, the Wald tests in Table 6 indicate that the marginal 

impact of a debt change on economic growth is only statistically different in the two 

periods at the 10% level in Germany above the determined tipping point (55% which is 

reached in 1995). Concretely, in that country, again the negative marginal impact of a debt 

increase beyond the threshold decreases with the introduction of the euro.  

All in all, the results from this robustness check suggest that the fiscal discipline and the 

multilateral surveillance of budget positions that were introduced with the inception of the 

EMU have moderated the impact of fiscal policies on economic growth, but only to some 

extent [as contend by Ioannou and Stracca (2014) or Teulings (2016), among others], since 

the coefficient estimates of both asymmetric and threshold models do not reveal 

statistically significant differences for most of the countries under study, given further 

support to the findings in the previous sub-sections.   

6. Concluding remarks 

In this paper, we propose a new approach to analyse the debt-growth nexus, a relationship 

which has spawned a multitude of studies using a wide range of methodologies and 

conclusions. The previous work rests largely on the results from panel data studies, but we 

argue that more can be learned from appropriate time series analyses for individual 

countries in order to record their heterogeneous experiences. In doing so, we do not 

discount the importance of the panel data approach, which has some relevant theoretical 

implications; rather, we question the way in which these results are presented, and indeed 

the way in which they are used by policymakers. 

Therefore, this paper builds upon the existing literature studying the effect of public debt-

to-GDP ratio on economic growth, focusing on the time series dimension of the issue to 

obtain further evidence based on the historical experience of 11 EMU member countries 

during the 1961-2015 period to detect potential heterogeneities in the relationship across 

the euro area. As in every empirical analysis, the results must be treated with some caution 

since they are based on a set of countries over a certain period and on a given econometric 

methodology. This is particularly true of the comparison of the results with those of 

previous papers, since we adopt a time series analysis instead of a panel data approach, and 

                                                 
24 Note that, during the EMU subsample, only for Ireland and Spain there are observations where the debt-to-GDP ratio 
is below the estimated threshold *( ).td d≤  Therefore, we can only test the null hypothesis Pr

1 1ˆ ˆe EMU EMUγ γ− =  for these two 
countries. 



22 
 

since we use changes in debt-to-GDP ratio as the primary variable of interest instead of the 

level of debt-to-GDP ratio25.   

The results presented in this paper should be of value to macro-prudential policymakers, as 

they provide evidence that in all the countries under study (with the exception of Belgium) 

a debt increase begins to have detrimental effects on growth well before the SGP debt 

ceiling is reached, meaning that fiscal policies should stay within a safe zone (a debt ratio 

around 40% and 50% in central and peripheral countries respectively) below the official 

fiscal limit. So, with average debt levels of 100% in euro area countries, deleverage 

(austerity policies) should be applied, but according to our results debt reduction does not 

exert any significant benefit on euro area countries’ economic performance. Therefore, in 

our view, adjustment programmes should be accompanied by structural reforms able to 

increase the adjustment capacity or the potential GDP in euro area countries. Otherwise, 

the current policy dilemmas might only be solved (see Mody, 2013) in a framework that 

allows orderly debt restructuring.  

Moreover, since our results provide support for the idea that the harmful impact of debt 

on growth does not occur beyond the same debt ratio threshold and with the same 

intensity in all EMU countries, a focus on average ratios and impacts may be misleading for 

the definition of policy in individual countries. This is especially true in an environment in 

which some EMU countries must already apply adjustment plans that re-establish 

competitiveness and fiscal balance. Specifically, our findings suggest that the pace of fiscal 

adjustment should be lower in Greece and Spain than in the other three peripheral 

countries. 

Finally, our findings may also provide useful inputs for further research since, as Coase 

(1988, 71) states “the inspiration is most likely to come through the stimulus provided by 

the patterns, puzzles and anomalies revealed by the systematic gathering of data, 

particularly when the prime need is to break our existing habits of thought”. Concretely, in 

view of the encouraging results of the present study, an extension of the present research 

might explore which are the channels (e.g., the equilibrium real interest rate, the sovereign 

risk premium or the expected future tax rates, among them) that drive the debt-growth 

relationship. Although this analysis is beyond the scope of the present paper, due to its 

relevance, it is in our near future research agenda.   

                                                 
25 To the best of our knowledge, there is no any previous study which has yet examined the statistical property of the 
public debt-to-GDP ratio series and taken into consideration its stationarity property in the analysis of the debt-growth 
nexus.   



23 
 

Acknowledgements 

The authors wish to thank two anonymous referees for their helpful comments and 

suggestions on a previous draft of this article, which have enabled us to introduce 

substantial improvements. The paper has also benefited from discussion with Christopher 

Martin, Bruce Morley, Vanja Piljak, Nikolaos Sakkas and the participants at the First 

Catalan Economic Society Conference in Barcelona and the 15th INFINITI Conference 

on International Finance in Valencia. Simón Sosvilla-Rivero thanks the Department of 

Economics for their hospitality during a research visit at the University of Bath. 

Responsibility for any remaining errors rests with the authors. 

Funding 

This paper is based upon work supported by the Instituto de Estudios Fiscales [grant IEF 

015/2017], the Bank of Spain [grant PR71/15-20229], the Spanish Ministry of Education, 

Culture and Sport [grant PRX16/00261] and the Spanish Ministry of Economy and 

Competitiveness [grant ECO2016-76203-C2-2-P]. 

 

 

 

 



24 
 

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                                    Appendix 1: Definition of the explanatory variables and data sources 
 

Variable Description Source 
Real growth rate (gt) Growth rate of real per capita GDP (annual %)   World Development Indicators (World Bank), 

extended to 2015 using  World Economic 
Outlook, October 2016 (IMF) 

Level of Output (yt) Per capita Gross domestic product at 2010 market prices AMECO, extended to 2015 using  World 
Economic Outlook, October 2016 (IMF) 

Public debt-to-GDP ratio (dt) Ratio of net public debt to GDP AMECO and International Monetary Fund 

Population growth (POPGRt) Population growth (annual %) World Development Indicators (World Bank),  
extended to 2015 using World Economic 

Outlook, October 2016 (IMF) 
GCF-to-GDP ratio (GCFt) Ratio of gross capital formation to GDP World Development Indicators (World Bank) 

Human capital (HKt) Life expectancy at birth, total (years) World Development Indicators (World Bank) 

Openness (OPENt) Absolute sum of exports and imports over GDP World Development Indicators (World Bank),  
extended to 2015 using  World Economic 

Outlook, October 2016 (IMF) 
Inflation (INFt) Growth rate of GDP deflator (annual %) World Development Indicators (World Bank),  

extended to 2015 using  World Economic 
Outlook, October 2016 (IMF) 



30 
 

      Figure 1. Sovereign Debt-to-GDP and GDP per capita growth evolution in EMU countries: 1961-2015 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
           

Note. Source AMECO and WDI 

 
-4

-2

0

2

4

6

8

0

20

40

60

80

100

120

140

160

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

wt
h

Pu
bli

c D
eb

t-t
o-

GD
P

BELGIUM

Public Debt-to-GDP Real GDP per capita growth  -10

-5

0

5

10

15

0

10

20

30

40

50

60

70

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

wt
h

Pu
bli

c D
eb

t-t
o-

GD
P

FINLAND

Public Debt-to-GDP Real GDP per capita growth  

-4

-2

0

2

4

6

8

0

20

40

60

80

100

120

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

wt
h

Pu
bli

c D
eb

t-t
o-

GD
P

FRANCE

Public Debt-to-GDP Real GDP per capita growth  
-6

-4

-2

0

2

4

6

8

0

10

20

30

40

50

60

70

80

90

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P p

er
 ca

pit
a g

ro
wt

h

Pu
bli

c D
eb

t-t
o-G

DP

GERMANY

Public Debt-to-GDP Real GDP per capita growth  
-6

-4

-2

0

2

4

6

8

0

10

20

30

40

50

60

70

80

90

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P p

er
 ca

pit
a g

ro
wt

h

Pu
bli

c D
eb

t-t
o-G

DP

THE NETHERLANDS

Public Debt-to-GDP Real GDP per capita growth  

-10

-5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

wt
h

Pu
bli

c D
eb

t-t
o-

GD
P

IRELAND

Public Debt-to-GDP Real GDP per capita growth  
-8

-6

-4

-2

0

2

4

6

8

10

0

20

40

60

80

100

120

140

160

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P p

er
 ca

pit
a g

ro
wt

h

Pu
bli

c D
eb

t-t
o-G

DP

ITALY

Public Debt-to-GDP Real GDP per capita growth  -10

-5

0

5

10

15

0

20

40

60

80

100

120

140

160

180

200

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

 G
DP

 p
er

 ca
pit

a 
gr

ow
th

Pu
bli

c D
eb

t-t
o-

GD
P

GREECE

Public Debt-to-GDP Real GDP per capita growth  

-10

-5

0

5

10

15

0

20

40

60

80

100

120

140

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

w
th

Pu
bl

ic 
De

bt
-to

-G
DP

PORTUGAL

Public Debt-to-GDP Real GDP per capita growth  
-6

-4

-2

0

2

4

6

8

10

12

0

20

40

60

80

100

120

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

w
th

Pu
bl

ic 
De

bt
-to

-G
DP

SPAIN

Public Debt-to-GDP Real GDP per capita growth  

-6

-4

-2

0

2

4

6

8

0

10

20

30

40

50

60

70

80

1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Re
al 

GD
P 

pe
r c

ap
ita

 g
ro

wt
h

Pu
bli

c D
eb

t-t
o-

GD
P

AUSTRIA

Public Debt-to-GDP Real GDP per capita growth



Table 1: Asymmetric model estimation results 
 

Panel A: Estimation results 

  AT BE FI FR GE GR IE IT NL PT SP 

gt-1  0.3559*  
 (3.0788) 

0.1870** 
(2.5262) 

 0.1073 * 
 (2.8123) 

0.3912*  
(3.5921) 

0.0742**  
 (2.5679) 

0.3480* 
(2.7614)  

0.2401**  
(2.4153)  

0.3559*   
(3.0331) 

0.2898** 
(2.3412) 

0.2708**  
(2.3516) 

0.6603*  
 (3.0222) 

INFt -0.0652* 
(-2.9961) 

-0.0106** 
(-2.4834) 

-0.0161** 
(-2.3312) 

-0.0688** 
(-2.3550) 

-0.1253** 
(-2.2652) 

-0.1799** 
(-2.6431) 

-0.1262* 
(-2.8015) 

-0.0359** 
(-2.3328) 

-0.0777** 
(-2.4357) 

-0.1074** 
(-2.5315) 

-0.0386* 
(-2.8881) 

ΔHKt 1.6174** 
(2.3552) 

0.3891** 
(2.4215) 

0.8188* 
(2.7420) 

0.8502* 
(3.8110) 

0.5722** 
(2.3291) 

6.0990**  
 (2.3261) 

3.1679 
(2.3716) 

0.3697** 
(2.4171) 

0.1124** 
(2.3232) 

1.3625** 
(2.4571) 

0.7463* 
(2.8221) 

ΔOPEN t 0.2495*  
 (3.2762)  

0.1166* 
(3.4623) 

 0.3001*  
(3.3361) 

0.1827* 
(2.4207) 

0.3193*  
 (3.9825)  

 0.0679** 
(2.4801) 

0.0347 
(2.6916) 

0.3259* 
(2.8812) 

0.0998* 
(2.8415) 

0.0652* 
(2.7661) 

0.2256** 
(2.4551) 

POPGROt 
0.8097** 
(2.3115) 

2.2881** 
(2.5923) 

3.1118* 
(2.7812) 

0.5730* 
(2.5134) 

0.3691* 
(2.6681) 

1.5568** 
(2.3341) 

0.1370 
(2.3527) 

1.3890** 
(2.3862) 

1.2397** 
(2.3281) 

1.4770* 
(2.9188) 

0.9190** 
(2.5662) 

GCFt 
0.5343** 
(2.4962) 

0.1312* 
(3.8324) 

0.1661* 
(4.1012) 

0.0564* 
(3.2123) 

0.0755** 
(2.4618) 

0.4923** 
(2.3516) 

0.2046 
(2.8801) 

0.1319* 
(3.1715) 

0.7081* 
(3.2661) 

0.1396* 
(4.2320) 

0.0810** 
(2.4617) 

ΔdtI(Δdt>0) -0.1457** 
(-2.5634) 

-0.2408* 
(-2.6921) 

-0.5437* 
(-4.5723) 

-0.6297* 
(-2.5815) 

-0.4169** 
(-3.3752) 

-0.1010** 
(-2.5171) 

-0.5607 
(-4.7312) 

-0.4481* 
(-2.7143) 

-0.2516* 
(-2.6661) 

-0.3996* 
(-3.7512) 

-0.1507** 
(-2.5810) 

ΔdtI(Δdt<0) -0.0864** 
(-2.3998) 

-0.0309** 
(-2.3042) 

-0.5154** 
(-2.2314) 

-0.1813* 
(-2.3551) 

-0.0772** 
(-2.3684) 

-0.0533** 
(-2.5215) 

-0.1018 
(-2.6017) 

-0.3263* 
(-2.6551) 

-0.1249** 
(-2.4345) 

-0.1847** 
(-2.6222) 

-0.0456** 
(-2.3516) 

  
Panel B: Model Diagnostics                        

  AT BE FI FR GE GR IE IT NL PT SP 

Adjusted R2 0.5066 0.5699 0.6628 0.6362 0.6311 0.5993 0.6759 0.6516 0.6714 0.6315 0.6991 

DW Test 2.3432 2.3579 2.4382 2.2609 2.4112 2.3516 2.2541 2.2603 2.2412 2.4211 2.3722 

χ2
N  1.8019 

[0.4062] 
2.6446 

[0.2663] 
3.1147 

[0.2107] 
1.5031 

[0.4717] 
0.3633 

[0.8339] 
3.2498 

[0.1969] 
1.6654 

[0.4349] 
1.6246 

[0.4438] 
1.2961 

[0.5231] 
0.4881 

[0.7843] 
1.1778 

[0.5599] 

χ2
SC 0.7221 

[0.6972] 
0.6737 

[0.5991] 
0.6935 

[0.7070] 
2.3360 

[0.3110] 
0.4703 

[0.8231] 
0.5918 

[0.7439] 
0.7039 

[0.7033] 
3.2015 

[0.2017] 
1.9344 

[0.3802] 
0.3406 

[0.8434] 
3.4576 

[0.1775] 

χ2
H 9.7357 

[0.2841] 
6.7833 

[0.7457] 
6.6370 

[0.5763] 
5.3963 

[0.6117] 
6.4655 

[0.4973] 
2.6931 

[0.9521] 
8.7579 

[0.2707] 
7.3818 

[0.4961] 
10.3646 
[0.2404] 

4.8097 
[0.7777] 

10.5802 
[0.2266] 

  
Notes:  AT, BE, FI, FR, GE, GR, IE, IT, NL, PT and SP stand for Austria, Belgium, Finland, France, Germany, Greece, Ireland, 

Italy, the Netherlands, Portugal and Spain respectively. 
 In the ordinary brackets below the parameter estimates, the corresponding t-statistics are shown, based on the 

heteroskedasticity and autocorrelation consistent standard errors proposed by Newey and West (1987). 
 χ2N, χ2SC and χ2H are the Jarque-Bera test for normality, the Breusch-Godfrey LM test for second-order serial correlation 

and the Breusch-Pagan-Godfrey test for heteroskedasticity. In the square brackets, the associated probability values are 
given. 

               * and ** denote significance at the 1% and 5% level, respectively.  



32 
 

Table 2:  Threshold model estimation results 
 

Panel A: Estimation results 

  AT BE FI FR GE GR IE IT NL PT SP 

gt-1  0.3648* 
 (3.1862) 

0.0907* 
(2.8003) 

 0.0932*  
 (2.7241) 

0.3842*  
(3.7111) 

0.0942*  
 (2.7181) 

0.4042* 
(3.2924)  

0.3397*  
(2.7037) 

0.3736*  
(3.2115) 

0.3436* 
(2.8661) 

0.2879**  
(2.4514) 

0.6492*  
 (3.1016) 

INFt -0.0610* 
(-2.9272) 

-0.0161** 
(-2.2725) 

-0.0278** 
(-2.6015) 

-0.0647** 
(-2.3243) 

-0.1662* 
(-2.6891) 

-0.1635** 
(-2.5342) 

-0.1133** 
(-2.4715) 

-0.0043** 
(-2.3451) 

-0.0380* 
(-2.6655) 

-0.0774** 
(-2.3771) 

-0.0434** 
(-2.3561) 

ΔHKt 1.7884** 
(2.6473) 

0.1510** 
(2.3815) 

1.0678* 
(2.9711) 

1.3752** 
(2.3371) 

1.4776* 
(2.8560) 

4.5210*  
 (2.7027) 

6.2846* 
(3.1442) 

0.5810** 
(2.6261) 

0.2169** 
(2.3241) 

1.3216** 
(2.4241) 

0.7288** 
(2.3230) 

ΔOPEN t 0.2392*  
 (3.1217)  

0.0981* 
(3.1434) 

 0.2838*  
(4.1922) 

0.1658** 
(2.3548) 

0.2855*  
 (3.6808)  

 0.0560** 
(2.4128) 

0.1218** 
(2.6525) 

0.3615* 
(3.2331) 

0.1057* 
(3.0910) 

0.1006** 
(2.3346) 

0.2405* 
(2.6919) 

POPGROt 
0.8572** 
(2.3587) 

2.5998* 
(3.1942) 

2.6089*** 
(2.5020) 

1.9275** 
(2.6321) 

0.3057** 
(2.4766) 

1.7582** 
(2.5006) 

0.2476** 
(2.5771) 

1.2511** 
(2.5927) 

1.4051* 
(2.7316) 

1.9496* 
(2.8416) 

0.8891* 
(2.5802) 

GCFt 
0.6005* 
(2.6678) 

0.1198* 
(4.6411) 

0.1600* 
(4.2623) 

0.0512** 
(2.3243) 

0.0549* 
(2.8793) 

0.4746** 
(2.3616) 

0.0911** 
(2.3711) 

0.0843** 
(2.6116) 

0.6847* 
(3.1671) * 

0.1278* 
(4.2111) 

0.0790** 
(2.6234) 

ΔdtI(dt>d*) -0.1778* 
(-2.7815) 

-0.7263* 
(-3.7814) 

-0.7716* 
(-5.0371) 

-1.0077* 
(-3.6276) 

-0.6148* 
(-3.6115) 

-0.1502* 
(-2.9015) 

-0.3130* 
(-3.1051) 

-0.1786* 
(-2.7912) 

-0.2698* 
(-2.8334) 

-0.3773* 
(-4.2510) 

-0.1879* 
(-2.7711) 

ΔdtI(dt<d*) 0.0579* 
(2.7145) 

0.1256** 
(2.4920) 

0.4932* 
(3.9631) 

0.1714** 
(2.4142) 

0.1959* 
(2.8436) 

0.2559* 
 (2.8771) 

0.2130* 
(3.8233) 

0.0648* 
(2.6818) 

0.1647** 
(2.5671) 

0.0485** 
(2.3516) 

0.0211** 
(2.2414) 

d* 
 

28% 
[1977] 

61% 
[1970] 

40% 
[1992] 

21% 
[1978] 

55% 
[1995] 

59% 
[1989] 

50% 
[1976] 

41% 
[1971] 

38% 
[1974] 

37% 
[1981] 

52% 
[1993] 

  
Panel B: Model Diagnostics                        

  AT BE FI FR GE GR IE IT NL PT SP 

Adjusted R2 0.5066 0.5644 0.6778 0.6706 0.6541 0.6021 0.6954 0.6567 0.6759 0.6379 0.7168 

DW Test 2.3432 2.3426 2.4117 2.2476 2.4415 2.3853 2.2678 2.2655 2.2541 2.4083 2.3421 

χ2
N  1.68281 

[0.4311] 
0.7051 

[0.6720] 
1.4800 

[0.4771] 
2.8600 

[0.2393] 
0.0537 

[0.9735] 
3.1281 

[0.1969] 
1.3685 

[0.5045] 
0.9928 

[0.6215] 
0.7728 

[0.6795] 
0.4881 

[0.7843] 
1.1778 

[0.5599] 

χ2
SC 1.8910 

[0.3885] 
2.5622 

[0.2777] 
0.6935 

[0.7070] 
1.0346 

[0.5961] 
0.4403 

[0.8024] 
0.8994 

[0.6378] 
0.5570 

[0.7569] 
3.1207 

[0.2101] 
2.8994 

[0.2353] 
0.2147 

[0.8982] 
4.1838 

[0.1235] 

χ2
H 4.6661 

[0.7926] 
6.7833 

[0.7457] 
8.9735 

[0.3445] 
5.3963 

[0.6117] 
9.0188 

[0.3407] 
6.3616 

[0.6068] 
9.0652 

[0.3368] 
11.3425 
[0.1830] 

12.1291 
[0.1455] 

5.0279 
[0.7546] 

8.5501 
[0.3817] 

  
Notes:  AT, BE, FI, FR, GE, GR, IE, IT, NL, PT and SP stand for Austria, Belgium, Finland, France, Germany, Greece, Ireland, 

Italy, the Netherlands, Portugal and Spain respectively. 
 d* indicates the estimated threshold in the debt/GDP ratio and, in the square brackets below them, we present the year 

when the threshold is reached.   
 In the ordinary brackets below the parameter estimates, the corresponding t-statistics are shown, based on the 

heteroskedasticity and autocorrelation consistent standard errors proposed by Newey and West (1987). 
 χ2N, χ2SC and χ2H are the Jarque-Bera test for normality, the Breusch-Godfrey LM test for second-order serial correlation 

and the Breusch-Pagan-Godfrey test for heteroskedasticity. In the square brackets, the associated probability values are 
given. 
* and ** denote significance at the 1% and 5% level, respectively. 



33 
 

Table 3: Contribution of each explanatory variable to the growth rate 

  AT BE FI FR GE GR IE IT NL PT SP 

         Asymmetric model 
   gt-1 

INFt  
ΔHKt  

ΔOPEN t  
POPGROt 

GCFt 
           ΔdtI(Δdt>0) 
          ΔdtI(Δdt<0) 

      
      Explained 

 
0.0016 
-0.0005 
0.7171 
0.0040 
0.0082 
0.2733 
-0.0045 
0.0006 

 
2.1381 

 
0.1056 
-0.0108 
0.0183 
0.0502 
0.2102 
0.7456 
-0.1298 
0.0108 

 
2.2719 

 
0.0450 
-0.0132 
0.0322 
0.0424 
0.3765 
0.6363 
-0.2032 
0.0842 

 
2.5073 

 
0.5658 
-0.1778 
0.1257 
0.0806 
0.2347 
0.8484 
-0.7330 
0.0555 

 
2.1618 

 
0.1125 
-0.3927 
0.0886 
0.2588 
0.0644 
1.2937 
-0.4532 
0.0279 

 
2.0855 

 
0.0565 
-0.0522 
0.1013 
0.0034 
0.0716 
0.8304 
-0.0132 
0.0018 

 
2.1618 

 
0.1944 
-0.1380 
0.2010 
0.0185 
0.0303 
1.0688 
-0.4406 
0.0655 

 
3.2127 

 
0.2238 
-0.0492 
0.0257 
0.0615 
0.1541 
0.8669 
-0.3362 
0.0532 

 
2.0469 

 
0.0319 
-0.0212 
0.0009 
0.0082 
0.0501 
0.9412 
-0.0181 
0.0070 

 
1.9592 

 
0.2119 
-0.1262 
0.1152 
0.0147 
0.1120 
0.9263 
-0.2837 
0.0297 

 
2.9446 

 
0.4080 
-0.0466 
0.0432 
0.0469 
0.1638 
0.4568 
-0.0830 
0.0110 

 
2.5073 

   Threshold model 
   gt-1 

INFt  
ΔHKt  

ΔOPEN t  
POPGROt 

GCFt 
           Δdt(dt<d*) 
          ΔdtI(dt>d*) 

   
        Explained 

 
0.0015 
-0.0004 
0.7145 
0.0035 
0.0079 
0.2766 
0.0001 
-0.0036 

 
2.1886 

 
0.0617 
-0.0191 
0.0083 
0.0509 
0.2876 
0.8200 
0.0091 
-0.2191 

 
2.2672 

 
0.0448 
-0.0262 
0.0481 
0.0460 
0.3620 
0.7029 
0.0033 
-0.1810 

 
2.5081 

 
0.4573 
-0.1375 
0.1674 
0.0602 
0.6496 
0.6327 
0.0242 
-0.8539 

 
2.1536 

 
0.1510 
-0.5497 
0.2414 
0.2443 
0.0563 
0.9930 
0.0810 
-0.2173 

 
2.1127 

 
0.0733 
-0.0530 
0.0839 
0.0051 
0.0904 
0.8951 
0.0088 
-0.1016 

 
2.1652 

 
0.3202 
-0.1442 
0.4642 
0.0759 
0.0638 
0.5539 
0.0079 
-0.3418 

 
3.7336 

 
0.2513 
-0.0063 
0.0432 
0.0730 
0.1485 
0.5923 
0.0027 
-0.1047 

 
2.0817 

 
0.0406 
-0.0103 
0.0018 
0.0087 
0.0567 
0.9093 
0.0059 
-0.0127 

 
1.9385 

 
0.2094 
-0.0846 
0.1039 
0.0211 
0.1375 
0.7885 
0.0019 
-0.1778 

 
2.9631 

 
0.4058 
-0.0531 
0.0427 
0.0506 
0.1603 
0.4508 
0.0002 
-0.0573 

 
2.5370 

 
 

Observed 
 

2.3619 
 

2.2357 
 

2.5387 
 

2.1517 
 

2.0488 
 

2.1517 
 

3.7567 
 

1.9941 
 

2.0417 
 

2.9489 
 

2.5387 
 
Notes:  AT, BE, FI, FR, GE, GR, IE, IT, NL, PT and SP stand for Austria, Belgium, Finland, France, Germany, Greece, Ireland, 

Italy, the Netherlands, Portugal and Spain respectively. 
 The contributions are normalized to 1. 
 
  



34 
 

Table 4: Forecast accuracy  

  AT BE FI FR GE GR IE IT NL PT SP 

         Asymmetric model 
 
RMSE 
MAE 

MAPE 
SMAPE 

Theil´s U1 
Theil´s U2 

 

 
 

1.6822 
1.2728 

245.7643 
68.9455 
0.3014 
0.4092 

 
 

1.4986 
1.1977 

107.4667 
64.2291 
0.2680 
0.3261 

 
 

1.7829 
1.4308 

228.8803 
60.9822 
0.2322 
0.5765 

 
 

1.3404 
1.1123 

118.2404 
65.9260 
0.2476 
0.8058 

 
 

1.3729 
1.0684 

128.8657 
64.9815 
0.2526 
0.6856 

 
 

3.4865 
2.7963 

224.1046 
93.0946 
0.4214 
0.8778 

 
 

2.1692 
1.6385 

80.2761 
66.1567 
0.1950 
0.2470 

 
 

1.9725 
1.6361 

183.8302 
82.3025 
0.3397 
0.2457 

 
 

1.3721 
1.1049 

63.3426 
68.3219 
0.2584 
0.5860 

 
 

2.3637 
1.9034 

194.9332 
71.5568 
0.2714 
0.5292 

 
 

1.9586 
1.5217 

98.0630 
75.5680 
0.2922 
0.5312 

         Threshold model 
 
RMSE 
MAE 

MAPE 
SMAPE 

Theil´s U1 
Theil´s U2 

 

 
 

1.7144 
1.3341 

274.6975 
68.6044 
0.3069 
0.3883 

 
 

1.3415 
1.0917 

98.7810 
57.7618 
0.2351 
0.4181 

 
 

1.7637 
1.4445 

226.2982 
62.4967 
0.2297 
0.6191 

 
 

1.2649 
1.0925 

108.1447 
67.3532 
0.2312 
0.7518 

 
 

1.3267 
1.0988 

131.18176 
60.7439 
0.2377 
0.8515 

 
 

3.4515 
2.6898 

239.1299 
83.9547 
0.4052 
0.9860 

 
 

1.9649 
1.6428 

152.8034 
63.4062 
0.1742 
0.1375 

 
 

1.9945 
1.6918 

224.6151 
80.6154 
0.3561 
0.3945 

 
 

1.5905 
1.2960 

88.5590 
75.0829 
0.3021 
0.6890 

 
 

2.3166 
1.8343 

175.5161 
70.7161 
0.2533 
0.4181 

 
 

1.8654 
1.4344 

91.5161 
64.617 
0.2671 
0.4366 

 
 
Notes:  AT, BE, FI, FR, GE, GR, IE, IT, NL, PT and SP stand for Austria, Belgium, Finland, France, Germany, Greece, Ireland, 

Italy, the Netherlands, Portugal and Spain respectively. 
 RMSE is the Root Mean Square Error, MAE is the Mean Absolute Error, MAPE is the Mean Absolute Percentage Error, 

Theil’s U1 is the Theil Inequality coefficient of forecast accuracy, and Theil’s U2 is the Theil Inequality coefficient of 
forecast quality. Bold values indicate the forecast that performed the best under each of the evaluation statistics. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 



Table 5:  Asymmetric model: Pre- EMU and EMU estimation analysis 
 

  AT BE FI FR GE GR IE IT NL PT SP 
 

Pre-EMU 
Pr

1̂
e EMUβ −

 
-0.0912**  
 (-2.8521) 

-0.1837** 
(-2.6412) 

- 0.7750*  
 (-2.7671) 

-0.6873*  
(-2.9212) 

-0.5771*  
 (-2.6719) 

-0.3347* 
(-2.7721)  

-0.5045*  
(-2.7411) 

-0.5892*   
(-2.7612) 

-0.4527* 
(-2.7356) 

-0.3869  
(-2.7223) 

-0.1683*  
 (-2.7544) 

 Pr
2

ˆ e EMUβ −
 

-0.0393* 
(-2.9151) 

-0.0885** 
(-2.5716) 

-0.6005** 
(-2.6512) 

-0.1068* 
(-2.6616) 

-0.1810** 
(-2.6155) 

-0.0994* 
(-2.6812) 

-0.2291* 
(-2.8312) 

-0.4766* 
(-2.6574) 

-0.2441* 
(-2.6671) 

-0.1351** 
(-2.6515) 

-0.0526* 
(-2.8112) 

 
EMU 1̂

EMUβ  
-0.2485** 
(-2.5512) 

-0.2888** 
(-2.5613) 

-0.8632** 
(-2.7817) 

-0.3863* 
(-2.8615) 

-0.1331* 
(-2.5667) 

-0.3229*  
 (-2.7662) 

-0.7365* 
(-2.7262) 

-0.3800* 
(-2.7132) 

-0.1236* 
(-2.7761) 

-0.4209* 
(-2.7659) 

-0.1334* 
(-2.8231) 

 
2

ˆ EMUβ  
-0.1695*  

 (-2.7412)  
-0.2199* 
(-2.7671) 

 -0.3018*  
(-2.7771) 

-0.0775* 
(-2.6551) 

-0.0603*  
 (-2.8235)  

 -0.0429* 
(2.6761) 

-0.0134* 
(-2.6566) 

-0.1530* 
(-2.8278) 

-0.0578* 
(-2.8145) 

-0.1701* 
(2.8113) 

-0.0370* 
(-2.7548) 

 
Differences in  

coefficients 
Pr

1 1
ˆ ˆe EMU EMUβ β− =  

0.0911 
[0.7628] 

0.8694 
[0.3511] 

0.0793 
[0.7783] 

1.5980 
[0.2062] 

7.9275* 
[0.0049] 

0.0009 
[09757] 

2.8860*** 
[0.0894] 

0.2566 
[0.6125] 

3.4028*** 
[0.0651] 

0.0295 
[0.8636] 

0.0124 
[0.9113] 

 Pr
2 2

ˆ ˆe EMU EMUβ β− =  
0.3876 

[0.5336] 
0.2891 

[0.5908] 
3.6572*** 
[0.0558] 

0.0616 
[0.8040] 

0.8127 
[0.3673] 

0.0997 
[0.7522] 

5.4691** 
[0.0194] 

5.2223** 
[0.0225] 

0.0709 
[0.7900] 

0.0006 
[0.9811] 

0.0191 
[0.8902] 

 
Notes:  

1̂β and 
2β̂ are, respectively, the estimated coefficients capturing in equation (4) the effects on economic growth of positive and negative debt variations. 

In the ordinary brackets below the parameter estimates, the corresponding t-statistics are shown, based on the heteroskedasticity and autocorrelation consistent standard errors proposed by Newey and 
West (1987).  
Wald tests are Chi-square test statistics for significant differences in estimated coefficients. In the square brackets, the associated probability values are given. 
*, ** and *** denote significance at the 1%, 5% and 10% level, respectively.  

 



36 
 

 
Table 6:  Threshold model: Pre- EMU and EMU estimation analysis 

 
  AT BE FI FR GE GR IE IT NL PT SP 

 
Pre-EMU 

Pr
1̂

e EMUγ −  
0.0823* 
(2.8434) 

0.1035* 
(2.6876) 

0.4572* 
(2.7656) 

0.1301* 
(2.7769) 

0.2610* 
(2.9122) 

0.2046* 
(2.8142) 

0.1827* 
(2.8551) 

0.0262* 
(2.7671) 

0.1880* 
(2.9162) 

0.0480 
(2.8112) 

0.0228* 
(2.8661) 

 Pr
2ˆ

e EMUγ −  -0.1823*  
 (-2.7761) 

-0.6140* 
(-2.7767) 

-0.8708* 
 (-2.8273) 

-1.0449* 
(-2.8762) 

-0.9881*  
 (-2.8655) 

-0.2403* 
(-2.7884)  

-0.4914*  
(-2.7991) 

-0.3218*   
(-2.8431) 

-0.2706* 
(-2.8342) 

-0.3519 
(-2.7861) 

-0.2079*  
 (-2.7781) 

 
EMU 1̂

EMUγ       
      

 
0.2070* 
(2.7761)    0.0335* 

(2.7882) 
 

2ˆ
EMUγ  

-0.1380* 
(-2.7856) 

-0.8604* 
(-2.8243) 

-0.8165**  
(-2.8456) 

-1.2790* 
(-2.9541) 

-0.6321*  
 (-2.8555) 

-0.1059* 
(-2.9341) 

-0.3729* 
(-2.8661) 

-0.3074* 
(-2.8442) 

-0.1706* 
(-2.9541) 

-0.2939 
(-2.7984) 

-0.1268* 
(-2.8771) 

 
Differences in  

coefficients 

Pr
1 1ˆ ˆe EMU EMUγ γ− =        0.4280 

[0.5130]    0.0223 
[0.9620] 

 Pr
2 2ˆ ˆe EMU EMUγ γ− =  

0.1457 
[07027] 

0.8319 
[0.3617] 

0.0686 
[0.7933] 

0.2717 
[0.6022] 

3.0918*** 
[0.0787] 

0.5818 
[0.4456] 

0.1621 
[0.6873] 

0.0167 
[0.8972] 

0.3323 
[0.5643] 

0.1088 
[0.7416] 

0.3742 
[0.5407] 

 
Notes:  

1̂γ and 2γ̂ are, respectively, the estimated coefficients capturing in equation (5) the effects on economic growth of debt variations below or above the detected threshold value. 

During the EMU subsample, only for Ireland and Spain there are observations where *,td d≤ so we can only test the null hypothesis Pr
1 1ˆ ˆe EMU EMUγ γ− = for these two countries. 

In the ordinary brackets below the parameter estimates, the corresponding t-statistics are shown, based on the heteroskedasticity and autocorrelation consistent standard errors proposed by Newey and 
West (1987).  
Wald tests are Chi-square test statistics for significant differences in estimated coefficients. In the square brackets, the associated probability values are given. 
*, ** and *** denote significance at the 1%, 5% and 10% level, respectively.