Fiscal Sustainability of Eurozone Governments : An Empirical Review of the Past Decade

We provide an empirical review of fiscal sustainability of Eurozone governments by using quarterly data on debt to Gross Domestic Product (GDP) and primary deficit to GDP over the period 1999 to 2010. We verify the conditions of fiscal sustainability, defined by the government’s present value borrowing constraint, by applying unit root tests that involve one, two, or multiple structural breaks. We select the best performing model of structural breaks and group Eurozone governments with respect to fiscal sustainability.


Introduction
In the 1990s, the European Union (EU) countries established the Economic and Monetary Union (EMU or Eurozone, henceforth) and adopted the Euro as a common currency.The EU member states have accepted various criteria, the so-called 'Maastricht convergence criteria', for the entrance to the Eurozone.The Maastricht public finance criteria have been included in the Stability and Growth Pact (SGP).In the SGP, the member states of the EMU committed themselves to strict public financial rules: a maximum government debt to Gross Domestic Product (GDP) of 60% and a maximum budget deficit to GDP of 3%.The European Commission (EC) has been responsible for enforcing the SGP and verifying the quality of statistical data reported by national governments.In 1998, 11 EU member states had met the Maastricht criteria, and the Eurozone initiated with the official launch of the Euro on 1 January 1999 with the following member states: Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain.Since 1999 other EU-member states have joined the EMU: Greece in 2001;Slovenia in 2007;Cyprus, Malta and Slovakia in 2008;Estonia in 2011;Latvia in 2014.The present article is motivated by the fact that several governments of the Eurozone have experienced high deficit and an increasing level of public debt as a consequence of the 2008 subprime mortgage crisis of the United States (US) and the subsequent global economic and financial meltdown.This has initiated debates about fiscal sustainability, crisis management and the prevention of future crises in the Eurozone.See Gros and Mayer (2010), and Marzinotto, Pisani-Ferry, and Sapir (2010).Due to the global development of financial markets experienced in the past decades, financial institutions and governments have become significantly interrelated.Consequently, an indebted national government may affect negatively the financial sector.On the other hand, a financial sector with large losses, for example due to an outsized real estate bubble, may generate default of public finances.See Dabrowski (2010), Gros (2010), and Lachman (2010).Several authors report that the sovereign debt crisis for some countries of the Eurozone has been related with the significant and unsustainable debt accumulation of the private sector (e.g., Ireland and Spain), while in other countries with the governments' mismanagement of public finances (e.g., Greece and Portugal).See De Grauwe (2010), Gros (2010), Arghyrou and Tsoukalas (2011), Featherstone (2011), and Mamadouh and van der Wusten (2011).
We provide an empirical analysis of Eurozone government debt sustainability based on historical data.We use different unit root tests for the debt to GDP and primary deficit to GDP to evaluate the fiscal sustainability of Eurozone governments over the past decade.These unit root tests may involve one, two, or multiple structural breaks.Our framework extends the classical test of fiscal sustainability of Hamilton and Flavin (1986), where the Augmented Dickey-Fuller (ADF, 1979) unit root test is applied.The tests proposed in this article may have more statistical power in periods of economic crisis than the ADF test.Furthermore, they estimate breakpoint dates endogenously, providing additional information about the evolution of fiscal ratios and fiscal sustainability.
The statistical findings presented in this article provide an empirical review of government finances from 1999 to 2010.The results reported show how the evolution of fiscal ratios may have affected sovereign debt investors' beliefs about government debt sustainability and sovereign credit risk in the Eurozone over the past decade.
The remaining part of this article is organized as follows.Section 2 describes the economic foundation of fiscal sustainability tests: the government's present value borrowing constraint.Section 3 reviews the fiscal data applied.Section 4 summarizes the classical ADF test results on fiscal sustainability.Section 5 reports the extended unit root test results on fiscal sustainability.Robustness analysis results are reported in Section 6.Finally, we summarize and conclude in Section 7.

Fiscal Sustainability
In the existing literature, several papers argue that the government is subject to a present value borrowing constraint (e.g., Hamilton & Flavin,1986;Trehan & Walsh, 1991;Alfonso & Rault, 2007;Hallett & Lewis, 2007), which establishes that the present value of the current stock of sovereign debt is identical to the present value of future fiscal balances.The government's borrowing constraint can be derived as follows.The current sovereign debt level, can be expressed as the sum of the debt in the previous period, the corresponding interest payments, and the current primary deficit, : Dividing this equation by the GDP denoted by , we get (2) where denotes the GDP growth rate.It can be derived from these equations that the government's present value borrowing constraint at 0 for an infinite time horizon is given by where / and / .The present value borrowing constraint has been used to define the concept of fiscal sustainability in the literature.Moreover, it has also motivated statistical tests of fiscal sustainability, since fiscal sustainability requires both and to be non-explosive according to Equation (3).
Several authors have proposed the application of unit root tests for fiscal variables to verify fiscal sustainability (e.g., Hamilton & Flavin 1986;Trehan & Walsh 1991;Alfonso & Rault, 2007).Hamilton and Flavin (1986) use ADF unit root tests to verify the sustainability of US government debt.Trehan and Walsh (1991), in a unit root test framework, state: 'We call a budget process sustainable if the expected present discounted value of the implied future stock of debt converges to zero.' Furthermore, Alfonso and Rault (2007) state that the stationarity of government debt is a required for the fiscal sustainability of EU governments.Using different unit root tests, these authors conclude that: 'Sustainability of a given fiscal position requires that all national debt be eventually repaid.The debt ratio must be non-explosive and must ultimately converge on some finite limit.'

Sovereign Debt and Deficit Data
We use data on quarterly public debt to GDP and primary deficit to GDP ratios for the period 1990 to 2010 obtained from the Eurostat Statistics Database of the EC.Since the quarterly deficit to GDP ratios exhibit significant seasonality effects, we use the Holt-Winters exponential smoothing method to remove the seasonality component from these data (see Holt, 1959;Winters, 1960).The list of countries analyzed, the corresponding period observed for each state and some descriptive statistics for debt to GDP and smoothed primary deficit to GDP data are presented in Tables 1 and 2, respectively.In this article, we focus on the 17 member states which joined the Eurozone before 2014.
Table 1 shows that the debt to GDP ratio is heterogeneous within the Eurozone.Greece has the maximum value of debt to GDP (142.80%), while Estonia presents the lowest debt to GDP ratio (3.40%) over the sample period.Table 1 also shows that the countries with the highest mean debt to GDP ratio are Italy (110.34%),Greece (108.60%) and Belgium (100.78%).Moreover, the highest standard deviations (SDs) of debt to GDP over the period analyzed are exhibited by: Ireland (17.91%),Portugal (12.29%) and Greece (11.67%), reflecting substantial changes in the public debt levels over the period 2000 to 2010.
Table 2 exhibits that the statistics of the smoothed primary deficit to GDP ratio are very different in each country of the Eurozone.Ireland has the maximum value of primary deficit to GDP (29.53%), while Finland presents the lowest deficit to GDP ratio (-9.24%) over the sample period.Table 2 also shows that the countries with the highest mean deficit to GDP ratio are Slovakia (2.39%), Portugal (2.14%) and Greece (2.01%).Moreover, the highest SDs of deficit to GDP over the period analyzed are exhibited by: Ireland (9.02%), Spain (6.09%) and Greece (4.20%), evidencing high volatility in the government deficit to GDP levels during the last decade.(Holt, 1959;Winters, 1960).The columns Start and End show the first and last quarter observed for each country, respectively., Med, Max, Min, SD, Skew and Kurt denote sample size, median, maximum, minimum, standard deviation, skewness, and kurtosis, respectively.

Classical Test of Fiscal Sustainability
We study the fiscal sustainability of Eurozone governments by testing if government debt to GDP and primary deficit to GDP ratios are stationarity or explosive over the period 1990 to 2010.We perform different unit root tests for these fiscal ratios.The null hypothesis, H 0 of these tests is that fiscal data form an unstable unit root process, while according to the alternative hypothesis, H 1 fiscal ratios are covariance stationary.See the definitions of covariance stationary and unit root processes in Hamilton (1994).
In the remaining part of this article, is used to denote both debt to GDP and primary deficit to GDP ratios.The initial unit root test employed is the ADF test with a constant term.The ADF test is performed by estimating the following regression model: where ∆ denotes the first difference of , the deterministic terms are given by 1, augmentation terms, ∆ with 1, … , , are added to eliminate possible serial correlation and is an i.i.d.error term with zero mean and finite variance.
The first column of Tables 3 and 4 presents the ADF test statistics for debt to GDP and primary deficit to GDP, respectively.These tables show that the unit root null hypothesis can be rejected only for Austria for both fiscal ratios.Therefore, according to the approach of Hamilton and Flavin (1986), the evolution of the debt to GDP ratio is not compatible with fiscal sustainability for the other 16 member states of the Eurozone.We conclude that 16 countries from the 17 EMU states have unsustainable public finances according to the ADF test., where R 2 corresponds to the R-squared of the regressions of Equations ( 4) and ( 5).Moreover, is the sample size and denotes the number of parameters in each equation.Bold numbers indicate the model with the highest value.*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively., where R 2 corresponds to the R-squared of the regressions of Equations ( 4) and ( 5).Moreover, is the sample size and denotes the number of parameters in each equation.Bold numbers indicate the model with the highest value.*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Extended Tests of Fiscal Sustainability
The financial, economic and public debt crises in the Eurozone of the last years implied structural breaks in public finance ratios in several countries.These motivate the application of more general unit root tests that account for structural changes in the public finances of Eurozone member states.The unit root tests with structural breaks considered in this article verify a weaker form of fiscal sustainability since they imply non-stationary time series under both H 0 and H 1 hypotheses.However, they may evidence stationary behavior around the estimated structural change dates when the H 0 unit root hypothesis is rejected, which would imply predictable fiscal time series.Moreover, the extended unit root tests proposed in this article identify the dates of structural changes over the period 1990 to 2010 in an endogenous manner.
In the following, we briefly review existing unit root tests that incorporate structural changes.There are several unit root tests in the econometric literature which consider the possibility of one structural break in the data series.Perron (1989) considers a unit root test with one structural break with known (exogenous) breakpoint date.This paper has been extended by Zivot and Andrews (1992) who determine the structural breakpoint date endogenously.Additional works that estimate the time of the break endogenously in unit root tests are Perron (1997) and Vogelsang and Perron (1998).Lee and Strazicich (LS, henceforth, 2004) argue that one important issue regarding these endogenous break point unit root tests is that they omit the possibility of a unit root with break under the null hypothesis.Therefore, spurious rejections of H 0 may occur, questioning the statistical validity of these tests.Furthermore, unit root tests with a single structural break do not take into account that several changes may occur in the level of the variable of interest.This fact has motivated Lumsdaine and Papell (1997) to extend the analysis of Zivot and Andrews (1992) to include two structural breaks.However, Lumsdaine and Pappel (1997) have not considered structural breaks under the null hypothesis in their model.Therefore, spurious rejections may occur as it was noted previously.LS (2004) andLS (2003) have addressed the problem of spurious rejection of H 0 by introducing unit root tests with one and two breaks, respectively, considering structural break(s) under the null hypothesis.The LS tests applied in this article allow for structural change(s) in the model's constant term.Moreover, these structural breakpoint dates are identified endogenously in these tests.In the LS (2003LS ( , 2004) ) tests, the following equation is estimated: where and .The parameters denote coefficients estimated by a regression of ∆ on ∆ .Moreover, k augmentation terms, ∆ with 1, … , , are included to correct for serial correlation of the error terms e t .See LS (2004) for the selection of the number of augmentation terms, in Equation (5).In LS ( 2004), 1, , ′ and ∆ 1, ∆ ′.Therefore, this model includes one date of structural change in the constant parameter.In LS (2003), 1, , , ′ and ∆ 1, ∆ , ∆ ′.Thus, this specification considers two different dates of structural changes in the constant parameter.
The unit root test results and the quarters of structural changes estimated by these models are shown in Tables 3  and 4 for the debt to GDP and deficit to GDP ratios, respectively.In order to choose the most appropriate model for the EMU fiscal data, we have computed the adjusted R-squared, , for the test equation of the ADF andLS (2003, 2004) unit root tests.Table 3 and 4 report these metrics, indicating the best model by bold numbers.We can see in Tables 3 and 4 that the of the ADF test is lower than the model performance metric of LS (2003,2004) in all cases.This confirms the application of structural changes when public finances of the Eurozone are analyzed over the period 1999 to 2010.In the following, we focus on the implications of the best econometric model identified by the highest estimates for each country.
Tables 3 and 4 for debt to GDP and deficit to GDP, respectively, report the number of structural changes and the corresponding breakpoint dates.For the debt to GDP variable, one structural break is found for Cyprus (2008Q2), Luxembourg (2008Q3), Malta (2006Q1), Slovenia (2009Q1) and Spain (2008 Q4).Moreover, two dates of structural changes in debt to GDP are evidenced for the rest of the Eurozone states.For the deficit to GDP variable, one structural break is estimated for Greece (2009 Q2) andPortugal (2008 Q3).For the rest of the EMU countries, two breaks are found in the deficit to GDP time series.
We find breaking level stationary debt to GDP for the following governments: Austria, Belgium, Estonia, Finland, France, Germany, Italy, and the Netherlands.These countries represent a suddenly increased and then stabilized level of debt to GDP.On the other hand, breaking level unit root process is found for government debt to GDP for Cyprus, Greece, Ireland, Luxembourg, Malta, Portugal, Slovakia, Slovenia, and Spain.In these countries, the debt to GDP time series is explosive according to the breaking level unit root tests.Furthermore, the best performing unit root test evidences breaking level unit root deficit to GDP for Greece, Ireland, and Portugal.For other EMU states, we find breaking level stationary deficit to GDP process.

Robustness Analysis
The unit root test results reported in Tables 3 and 4 show that, in several cases, the model with two structural breaks has the highest value.However, unit root tests with more than two structural breaks may explain better the evolution of the fiscal variables.To verify the robustness of the results for the unit root test with two structural breaks, we employed a unit root test with three structural breaks, extending the framework of LS (2003).We estimated Equation ( 5) with 1, , , , ′ and ∆ 1, ∆ , ∆ , ∆ ′ .The critical values of this test are obtained by 5000 replications of the model in a way similar to LS (2003).We perform the test with three structural breaks for the countries where the LS (2003) model has the highest value.In the testing procedure, we use the and dates estimated by the LS ( 2003) model (see Tables 3  and 4), while is determined endogenously.This approach is similar to the idea of Bai and Perron (1998), who test for versus 1 breaks conditioning on the locations of l breaks.See also Bai and Perron (2003) and Wang and Zivot (2000).Furthermore, conditioning on two previously estimated breaks, reduces the computation time substantially.We find that the of the three-break unit root test is lower than the of the two-break test for all governments.Therefore, two breakpoints are preferred to three breakpoints according to the metric.

Summary and Conclusions
We use different unit root tests to assess fiscal sustainability of all member states of the Eurozone over the period 1999 to 2010.We apply different unit root tests for sovereign debt to GDP and primary deficit to GDP ratios to verify the conditions of fiscal sustainability derived from the government's present value borrowing constraint.The classical ADF test has not evidenced fiscal sustainability for 16 of the 17 EMU member states.However, this test does not consider the possibility of structural breaks.Therefore, we have considered the unit root tests involving structural breaks, as suggested by LS (2003LS ( , 2004)).These tests include one or two structural changes in the fiscal variables to capture shifts in public finances over the crisis period.The specifications proposed by LS (2003LS ( , 2004) ) have shown better performance than the ADF test when comparing the model selection metric of the different formulations.The LS (2003,2004) tests identify endogenously the dates of structural changes for both the debt to GDP and primary deficit to GDP variables.We have tested for multiple structural breaks and have found that models with one or two structural breaks are superior according to the measure.Based on the unit root test results, we classify the EMU governments into three groups: a) Explosive debt to GDP and deficit to GDP governments: Greece, Ireland, and Portugal.b) Explosive debt to GDP and breaking level stationary deficit to GDP governments: Cyprus, Luxembourg, Malta, Slovakia, Slovenia, and Spain.c) Breaking level stationary debt to GDP and deficit to GDP governments: Austria, Belgium, Estonia, Finland, France, Germany, Italy, and the Netherlands.
These results provide an empirical review of sovereign debt sustainability from 1999 to 2010 for the Eurozone.
The statistical tests involving structural changes identify the breakpoint dates and they can be used to forecast the evolution of future government debt to GDP and primary deficit to GDP in the Eurozone states.The results reported show how the evolution of fiscal ratios may have affected sovereign debt investors' beliefs about government debt sustainability and sovereign credit risk in the Eurozone over the past decade.Furthermore, these results provide a clear insight on the correlation between fiscal sustainability of Eurozone countries and the EMU sovereign debt crisis.

Table 1 .
Descriptive statistics of the government debt to GDP ratio The scale of the data series is in percentage points.The columns Start and End show the first and last quarter observed for each country, respectively., Med, Max, Min, SD, Skew and Kurt denote sample size, median, maximum, minimum, standard deviation, skewness, and kurtosis, respectively.

Table 2 .
Descriptive statistics of the smoothed primary deficit to GDP ratio The scale of the data series is in percentage points.Deficit to GDP data have been smoothed by using the Holt-Winters exponential smoothing technique

Table 3 .
Unit root tests with constant term for the government debt to GDP ratio

Table 4 .
Unit root tests with constant term for the smoothed primary deficit to GDP ratio