# A test of fiscal sustainability in the EU countries

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## Abstract

In this paper, we evaluate fiscal sustainability of five regional groups in the EU using the dataset of 26 countries for the period 1950–2014. To this end, we estimate their policy rules in which primary surpluses respond to public debt and examine whether estimated policy rules satisfy the conditions for fiscal solvency. In the baseline solvency tests with time-invariant marginal responses of primary surpluses, we find that estimated policy rules satisfy the solvency condition that the marginal response be positive for the Benelux, northern, and eastern groups but fail to do so for the western and southern groups. When estimating their policy rules separately for eurozone and non-eurozone countries, we find that long-term fiscal sustainability of eurozone countries is more questionable in the sense that non-eurozone countries in all regional groups have significantly positive marginal responses, whereas eurozone countries in most regional groups do not. Finally, more general solvency tests that allow time-varying marginal responses reveal that only the Southern group fails to satisfy the generalized solvency conditions that marginal responses be always nonnegative and positive infinitely often. These findings seem to be consistent with the fact that countries in the Southern group experienced severe fiscal crises.

## Keywords

EU Debt Sustainability Eurozone## JEL Classification

H6 E62 F45## 1 Introduction

The issue of fiscal sustainability has gained increasing attention in the European Union (EU). Many member countries of the EU have been rapidly accumulating public debt especially after the global financial crisis in 2007–2008. This has been particularly true for countries in Southern Europe as Greece, Ireland, Portugal, and Spain, recently experienced serious fiscal crises and had to receive the bailout packages from international organizations. Due to such rapid accumulation of public debt, the average debt to GDP ratio of the EU countries soared from 44.2% in 2006 to 70.6% in 2014, which is well above the 60% benchmark set by the Stability and Growth Pact.^{1}

The growing debt–GDP ratio in the EU might not be worrisome if it resulted from the severe recessions and subsequent fiscal expansions in the last decade. In this case, the rise in the debt–GDP ratio could be only temporary and the countries could be fiscally solvent in the long run. However, the accumulation of public debt can be a serious problem if it reflects the type of fiscal policy that cannot ensure long-term solvency. For example, if the government does not have a systematic mechanism that can reduce the debt–GDP ratio when it is high and rising, public debt may accumulate unboundedly and eventually become unsustainable. As these hypotheses have quite different implications for fiscal sustainability, it is very important to understand which hypothesis better accounts for the accumulation of public debt in the EU.

Motivated by this issue, this paper provides an empirical analysis on the behavior of governments in the EU countries with a particular focus on long-term fiscal solvency. To tackle this issue, we adopt the methodology developed by Bohn (1998, 2005), who showed that a country is fiscally solvent in the long run if the primary surplus–GDP ratio is an increasing linear function of the debt–GDP ratio. Under this type of fiscal rule, a rise in the debt–GDP ratio would induce an increase in a primary surplus, which in turn would restrain the debt–GDP ratio from rising further. Based on this result, Bohn proposed an empirical test for fiscal solvency in which the primary surplus–GDP ratio is regressed on the debt–GDP ratio and other control variables that capture short-run fluctuations in output and government spending. In this test, the condition for long-term fiscal solvency is satisfied if the estimated coefficient on the debt–GDP ratio is positive and statistically significant. Thus, Bohn’s test can provide valuable insights regarding the long-term fiscal solvency.

More specifically, we conduct Bohn’s test with the panel data of 26 member countries of the EU for the period 1950–2014. As our dataset covers a relatively long period and almost all EU countries, key regression coefficients might be different across countries and over time. To account for the potential heterogeneity, we divide our dataset by region and by subperiod. More specifically, we first classify the countries into five groups, i.e., the Benelux, western, northern, southern, and eastern, based on geographic proximity and similarities in economic systems.^{2} As the names imply, those groups represent five regions of Europe. We also divide the sample period for each eurozone country into the pre-eurozone subperiod and the eurozone subperiod, i.e., periods before and after it joined the eurozone.^{3} Based on this division, we modify Bohn’s test by allowing for region-specific and subperiod-specific coefficients. As a result, we can unveil inter-regional and inter-temporal variations in fiscal sustainability of the countries in the EU. To validate this approach, we establish that key regression coefficients tend to be common to countries within each group and in each subperiod later in this paper.

With this methodology, we first estimate the linear policy rule for each regional group in which the marginal response of the primary surplus–GDP ratio to the debt–GDP ratio is constant, assuming that regression coefficients are common to all countries within each group throughout the sample period. We find that the estimated marginal responses are positive and statistically significant for the Benelux, northern, and eastern groups. On the contrary, the estimated marginal responses are statistically insignificant for the western and southern groups. Thus, the linear policy rules of the Benelux, northern, and eastern groups satisfy Bohn’s condition for fiscal solvency whereas those of the western and southern groups do not. This result implies that the estimated policy rules cannot ensure the western and southern groups to be fiscally solvent in the long run. With their marginal responses essentially zero, they do not have a mechanism that prevents excessive accumulation of public debt, as governments would not increase primary surpluses even if public debt soars. Given this type of behavior, it is not surprising that countries in the western and southern groups have seen their debt–GDP ratios rising continually and that all of the southern countries—Italy, Spain, Portugal, Greece, and Cyprus—experienced major fiscal crises recently.

We then investigate whether eurozone countries have improved fiscal sustainability since they joined the eurozone. To answer this question, we estimate the marginal response and other key coefficients separately for (i) non-eurozone countries, (ii) eurozone countries in the pre-eurozone subperiod, and (iii) eurozone countries in the eurozone subperiod in each regional group. This analysis reveals that fiscal solvency is more questionable for eurozone countries, especially in the eurozone subperiod. More specifically, eurozone countries in the western, northern, and eastern groups exhibit statistically insignificant marginal responses in both subperiods. Moreover, eurozone countries in the southern group have reduced marginal responses from a significantly positive value to an insignificant value in the eurozone subperiod. Only for eurozone countries in the Benelux group, estimated marginal responses have been significantly positive in both subperiods. Consequently, the estimated policy rules of eurozone countries in all but one regional group violate the sufficient condition for fiscal solvency when they are in the eurozone. By contrast, non-eurozone countries in all regional groups have maintained significantly positive marginal responses throughout the sample period. These results suggest that the eurozone membership does not seem to improve fiscal solvency despite the rules and regulations to promote fiscal sustainability.

Finally, we perform a generalized solvency test that allows time-varying marginal responses of primary surpluses. In this framework, we estimate the nonlinear policy rules of the regional groups in which marginal responses can change over time with public debt. Then, we ask whether their policy rules satisfy the generalized solvency conditions according to Canzoneri et al. (2001) that marginal responses should be nonnegative all the time and positive infinitely often. Through this analysis, we find that all regional groups other than the southern group are fiscally sustainable in the sense that their policy rules satisfy the generalized solvency conditions. In sum, all of the Benelux, western, northern, and eastern groups pass one or both of our solvency tests, whereas the southern group fails to pass any of them. This finding seems to make sense given that all of the southern countries had serious fiscal problems in the past.

This paper builds upon the literature to test fiscal solvency empirically. As discussed, this paper follows the methodology of Bohn (1998, 2005). His method is quite general because public debt is sustainable regardless of current and future interest rates and the structure of government bonds in stochastic economies, as long as the primary surplus–GDP ratio exhibits a constant positive response to the debt–GDP ratio. In a series of papers, Bohn (1995, 1998, 2002) tested long-term sustainability of US public debt using this framework. Mendoza and Ostry (2008) extended Bohn’s framework to a panel analysis of long-term sustainability for 22 industrial countries and 34 emerging economies. Other than the specific focus on the EU countries, our paper differs from theirs by analyzing a longer sample period and therefore can compare the behavior of primary surpluses between two samples of pre- and post-euro periods, as well as those of eurozone and non-eurozone countries.

Prior to Bohn’s method, several papers in the literature proposed various solvency tests through unit-root tests of some fiscal variables. As the seminal paper in this approach, Hamilton and Flavin (1986) argued that if both primary surpluses and public debt are stationary, then the inter-temporal budget constraint of the government is satisfied. They found this condition satisfied for the USA in 1960–1984, and concluded that US public debt is sustainable. To refine their analysis, Trehan and Walsh (1988, 1991), Hakkio and Rush (1991), and Ahmed and Rogers (1995) derived various stationarity conditions and cointegration relationships of fiscal variables that should hold for fiscal solvency. They found such conditions are satisfied for the USA and hence the USA is fiscally solvent. Their methods, however, are not as general as Bohn’s, because they are based on strong assumptions on the real interest rate and time-series properties of fiscal variables, as we will discuss in detail in Sect. 5. Given the tractability and generality, we adopt Bohn’s method in our baseline solvency tests for the EU countries. For robustness, however, we also conduct the solvency tests discussed so far in Sect. 5.

This paper is organized as follows. Section 2 explains Bohn’s test for fiscal solvency. Section 3 introduces the dataset and our regression models and validates the specifications of our regression models. Section 4 analyzes the results of the solvency tests based on Bohn’s method. Then, Sect. 5 examines the robustness of our baseline results using other types of solvency tests. Finally, Sect. 5 concludes.

## 2 Bohn’s tests for fiscal solvency

^{4}

*t*and real government debt in the beginning of period

*t*, and \( q_{t,t + j} \) is the pricing kernel for assets in period \( t + j \), evaluated in period

*t*. Notice that future primary surpluses are discounted by the pricing kernel that reflects the behavior of private agents.

^{5}

*t*, and \( \mu_{t} \) is a composite of determinants of \( s_{t} \). In this policy rule, \( \rho \) is a constant that represents the marginal response of the primary surplus to government debt, or simply the marginal response. Bohn showed that if \( \rho > 0 \) in the policy rule (2), the IBC (1) is always satisfied under the following assumptions: (i) \( \mu_{t} \) is bounded as a share of GDP; (ii) the present value of GDP is finite; and (iii) financial markets are complete. To put it differently, \( \rho > 0 \) is a sufficient condition for fiscal solvency under these assumptions. When the government follows the linear policy rule (2) with a positive \( \rho \) in all periods, a rise in the debt–GDP ratio leads to an increase in the primary surplus, which in turn tends to reduce the debt–GDP ratio—and through this channel, the debt–GDP ratio can be stabilized in the long run.

In our empirical analysis, we adopt Bohn’s criterion to evaluate fiscal solvency of EU countries. We estimate a regression equation similar to (2) and examine the sign of \( \rho \). A positive and statistically significant \( \rho \) would imply that public debt is sustainable as long as such a policy rule is maintained in the future. By contrast, a significantly negative or statistically insignificant \( \rho \) does not necessarily imply fiscal insolvency, though it is certainly a possibility, as \( \rho > 0 \) is only a sufficient condition. \( \rho \le 0 \) can be compatible with fiscal solvency if one of the above assumptions fail. In addition, even if all of the assumptions are satisfied, (1) might not be the relevant solvency condition if agents’ decision horizons are finite as in overlapping-generations models. It is also possible that private agents anticipate future policy changes that can eventually satisfy the IBC (1), although the current fiscal policy does not. Due to these possibilities, we keep in mind that \( \rho \le 0 \) does not necessarily imply fiscal insolvency in the interpretation of our empirical results.

Prior to Bohn (1998), other papers attempted to examine fiscal solvency using tests for stationarity or cointegration of fiscal variables. However, Bohn’s method is more general, tractable, and reliable compared to those solvency tests in that it is based on the correct IBC (1) and requires fewer assumptions. Therefore, we use Bohn’s method as our main framework to assess fiscal sustainability of the EU countries. For robustness, however, we will review the stationarity-based solvency tests in more detail and apply them to the EU countries in Sect. 5.

## 3 Models for empirical analysis

In this section, we introduce our dataset and regression models. In particular, we classify EU countries in our sample into five regional groups and introduce the baseline regression model in which key parameters are region-specific. Finally, we test the assumption of equal coefficients within each regional group to validate the specifications of our regression models.

### 3.1 Data description

The dataset consists of real GDP and fiscal variables such as government revenue and non-interest expenditure, interest payments, primary surplus, and public debt of 26 member countries of the EU.^{6} To construct our dataset, we first draw the fiscal variables from the annual macroeconomic (AMECO) database of European Commission and real GDP from the World Bank database. We then take advantage of the dataset complied by Mauro et al. (2015) to extend our dataset to 1950 for our sample countries available in their dataset. We make use of all three sources because the AMECO and World Bank provide data for all of our sample countries but for relatively short periods, whereas the dataset of Mauro et al. gives information for only a subset of our sample countries but for relatively long periods. In the end, our dataset covers the period 1950–2014, but the sample period begins in 1950s for 14 countries and in 1990s for 12 countries.^{7}

The classification of EU member countries in the sample

Region | Eurozone | Non-eurozone |
---|---|---|

Benelux (3 countries) | Belgium (1993, 1999), Netherlands (1993, 1999), Luxembourg (1993, 1999) | |

Western (3 countries) | Austria (1995, 1999), France (1993, 1999), Germany (1993, 1999) | |

Northern (5 countries) | Ireland (1993, 1999), Finland (1995, 1999) | Denmark (1993), UK (1993), Sweden (1995) |

Southern (5 countries) | Italy (1993, 1999), Portugal (1993, 1999), Spain (1993, 1999), Greece (1993, 2001), Cyprus (2004, 2008) | |

Eastern (10 countries) | Slovenia (2004, 2007), Slovakia (2004, 2009), Estonia (2004, 2011), Latvia (2004, 2014) | Hungary (2004), Poland (2004), Czech (2004), Romania (2007), Bulgaria (2007), Lithuania (2004, 2015) |

The northern group is made up of the UK, Ireland, and Nordic countries, all of which are located in Northern Europe. Though the UK and Ireland could be somewhat different from Nordic countries in some aspects, we still put them together into a single group following the UN Statistical Division.^{8} Countries in the southern group are located in Southern Europe and have similar characteristics in many aspects. We emphasize that while all countries in the southern group had serious fiscal problems recently, they are classified into a single group based on geographic proximity, rather than based on the fact that they experienced fiscal problems. Finally, the eastern group encompasses former communist countries located in Eastern or Northern Europe. As these countries have a similar history of the transition from communism, we treat them as a single group.

Table 1 also shows whether each country is a member of the eurozone. As of 2014, 17 countries are in the eurozone and 9 countries out of the eurozone in our sample.^{9} As member countries of the eurozone use the euro as a common currency and should comply with a set of regulations on economic policy, they may have altered their economic policy after joining the eurozone. Based on this idea, we will examine the changes in governments’ behavior related to fiscal solvency since countries joined the eurozone in our empirical analysis. For that purpose, we divide the sample period into the pre-eurozone subperiod and the eurozone subperiod for each member country of the eurozone. For original members of the eurozone, the eurozone subperiod starts from 1999; but for countries that joined in later, the eurozone period begins in the year when they actually joined it. Through this division of the sample period, we will be able to analyze how fiscal policy has changed since countries became members of the eurozone.

^{10}Most notably, fiscal positions in the EU have worsened in terms of both the primary surplus and government debt since the eurozone was established. Specifically, the average primary surplus–GDP ratio fell from 0.02 to − 0.29% but the debt–GDP ratio rose from 42.6 to 51.5% between the two subperiods. However, the average total deficit–GDP ratio decreased from 2.92 to 2.72% after 1999, as interest payments on outstanding debt declined during the euro era.

Summary statistics by subperiods (unit: percent)

Variables | Full sample (1950–2014) | Pre-euro era (1950–1998) | Euro era (1999–2014) | ||||||
---|---|---|---|---|---|---|---|---|---|

Obs | Mean | SD | Obs | Mean | SD | Obs | Mean | SD | |

Real GDP growth | 1125 | 3.18 | 3.19 | 709 | 3.69 | 2.77 | 416 | 2.31 | 3.65 |

Fiscal revenue (A) | 1146 | 36.2 | 11.7 | 730 | 32.9 | 12.7 | 416 | 42.0 | 6.3 |

Non-interest expenditure (B) | 1146 | 36.3 | 11.3 | 730 | 32.9 | 12.2 | 416 | 42.3 | 5.9 |

Primary surplus (A–B) | 1146 | − 0.09 | 3.22 | 730 | 0.02 | 3.00 | 416 | − 0.29 | 3.58 |

Interest payments (C) | 1146 | 2.76 | 2.40 | 730 | 2.95 | 2.79 | 416 | 2.43 | 1.45 |

Total surplus (A–B–C) | 1146 | − 2.85 | 3.71 | 730 | − 2.92 | 3.67 | 416 | − 2.72 | 3.77 |

Government debt | 1125 | 45.9 | 31.5 | 709 | 42.6 | 31.2 | 416 | 51.5 | 31.3 |

### 3.2 Regression models

*B*,

*W*,

*E*,

*S*, and

*N*refer to the Benelux, western, eastern, southern, and northern groups, respectively. Given the notation, we introduce our first regression equation as follows.

We will refer to (3) as *the baseline (regression) model* throughout our empirical analysis and focus on the sign of \( \rho^{k} \): if it is positive, we can conclude that the government debt is sustainable in the long run for regional group \( k \). As for the short-term factors, we expect both \( \alpha_{g}^{k} \) and \( \alpha_{y}^{k} \) to be negative. First, \( \alpha_{g}^{k} \) is likely to be negative because temporary government spending raises GVAR but tends to reduce the primary surplus. \( \alpha_{y}^{k} \) is also expected to be negative because, in a recession, YVAR rises but the primary surplus tends to fall due to fiscal expansions such as increased spending and/or reduced tax revenue.

### 3.3 Testing the equality of coefficients within regional groups

Our regression models are based on the assumption of common coefficients within each regional group; so, we discuss the validity of the assumptions to justify the specifications of our regression models. To this end, we estimate all of our regression equations with country-specific coefficients and test if key coefficients are indeed identical across countries within each regional group. To illustrate this test, we describe it for the baseline model in this subsection, though it is applied to all models used in this paper.

Tests of equal coefficients within regional groups for the baseline model

Region | Regression coefficients | |||
---|---|---|---|---|

Debt/GDP (\( \rho^{j} \)) | GVAR (\( \alpha_{y}^{j} \)) | YVAR (\( \alpha_{g}^{j} \)) | ||

Benelux | (1) The number of countries with an equal coefficient | 2/3 countries | 3/3 countries | 3/3 countries |

(2) | 0.295 | 0.816 | 0.424 | |

Western | (1) The number of countries with an equal coefficient | 3/3 countries | 3/3 countries | 3/3 countries |

(2) | 0.169 | 0.825 | 0.474 | |

Northern | (1) The number of countries with an equal coefficient | 4/5 countries | 2/5 countries | 5/5 countries |

(2) | 0.241 | 0.394 | 0.102 | |

Southern | (1) The number of countries with an equal coefficient | 4/5 countries | 5/5 countries | 5/5 countries |

(2) | 0.204 | 0.100 | 0.203 | |

Eastern | (1) The number of countries with an equal coefficient | 8/10 countries | 10/10 countries | 10/10 countries |

(2) | 0.235 | 0.768 | 0.814 |

In addition to the baseline model, we conduct similar tests for the assumptions of equal coefficients for all regression equations used in our empirical analysis. We first estimate each regression model with country-specific coefficients. Then, we test the equality of coefficients for each regional group and each subperiod and examine the maximum number of countries for which the null hypothesis of equal coefficients can be accepted at the 10% significance level. By taking the average of those maxima across all regression models, we find that the null hypothesis of an equal coefficient is accepted on average for 92% of the Benelux countries, 90% of the western countries, 68% of the northern countries, 86% of the southern countries, and 92% of the eastern countries. As most countries in all regional groups have common coefficients in various cases, the test results seem to support the assumption of common coefficients within regional groups and subperiods and justify the use of region-specific coefficients in our regression models. Therefore, we maintain the assumption of common regression coefficients not only for the baseline regression model (3) but also for all other regression models.^{11}

## 4 Results of the tests for fiscal solvency

### 4.1 The baseline model

^{12}In sum, our estimation results seem to suggest that public debt is sustainable in the long run for the Benelux, northern, and eastern groups.

The behavior of the primary surplus to GDP ratio

Dependent variable: primary surplus/GDP | ||||||
---|---|---|---|---|---|---|

Region | Variable | [1] Baseline (Eq. (3)) | [2] Non-eurozone (Eq. (3)) | [3] Eurozone (Eq. (5)) | [4] Nonlinear (Eq. (6)) | |

Pre-eurozone period | Eurozone period | |||||

Benelux | Debt/GDP (\( \rho^{B} \)) | 0.049 (0.011)*** | N/A | 0.047 (0.011)*** | 0.051 (0.020)** | 0.041 (0.018)** |

Square deviation of debt/GDP (\( \beta^{B} \)) | 0.048 (0.041) | |||||

GVAR | − 0.235 (0.076)*** | − 0.157 (0.087)* | − 0.893 (0.123)*** | − 0.225 (0.085)** | ||

YVAR | − 1.074 (0.154)*** | − 0.668 (0.263)** | − 0.994 (0.502)* | − 1.102 (0.169)*** | ||

Western | Debt/GDP (\( \rho^{W} \)) | − 0.012 (0.012) | N/A | − 0.038 (0.030) | − 0.021 (0.027) | − 0.027 (0.109) |

Square deviation of debt/GDP (\( \beta^{W} \)) | 0.138 (0.064)** | |||||

GVAR | − 0.252 (0.071)*** | − 0.239 (0.057)*** | − 1.238 (0.120)*** | − 0.248 (0.074)*** | ||

YVAR | − 0.861 (0.183)*** | − 0.648 (0.294)** | − 0.351 (0.421) | − 0.907 (0.194)*** | ||

Northern | Debt/GDP (\( \rho^{N} \)) | 0.032 (0.004)*** | 0.036 (0.003)*** | 0.032 (0.021) | 0.000 (0.022) | 0.030 (0.007)*** |

Square deviation of debt/GDP (\( \beta^{N} \)) | 0.002 (0.009) | |||||

GVAR | − 0.523 (0.288)* | − 0.260 (0.090)** | − 0.101 (0.361) | − 1.283*** (0.035) | − 0.526 (0.289)* | |

YVAR | − 1.279 (0.232)*** | − 0.679 (0.399) | − 1.088 (0.682) | − 1.859** (0.787) | − 1.285 (0.230)*** | |

Southern | Debt/GDP (\( \rho^{S} \)) | 0.015 (0.009) | N/A | 0.025 (0.013)* | 0.010 (0.015) | 0.014 (0.009) |

Square deviation of debt/GDP (\( \beta^{S} \)) | 0.001 (0.011) | |||||

GVAR | − 0.570 (0.099)*** | − 0.399 (0.118)*** | − 1.010 (0.160)*** | − 0.573 (0.099)*** | ||

YVAR | − 0.789 (0.286)** | − 0.733 (0.296)** | − 0.849 (0.501) | − 0.794 (0.331)** | ||

Eastern | Debt/GDP (\( \rho^{E} \)) | 0.058 (0.018)*** | 0.065 (0.020)** | − 0.017 (0.069) | 0.021 (0.068) | 0.075 (0.030)** |

Square deviation of debt/GDP (\( \beta^{E} \)) | − 0.040 (0.036) | |||||

GVAR | − 0.810 (0.081)*** | − 0.732 (0.126)*** | − 1.001 (0.150)*** | − 0.938 (0.106)*** | − 0.805 (0.081)*** | |

YVAR | − 0.463 (0.158)*** | − 0.340 (0.318) | − 0.454 (0.314) | − 1.058 (0.391)** | − 0.506 (0.167)*** | |

# of observations | 1125 | 306 | 819 | 1125 | ||

# of countries | 26 | 9 | 17 | 26 | ||

| 0.255 | 0.387 | 0.274 | 0.240 |

On the other hand, the long-term fiscal solvency is more questionable for the western and southern groups according to the baseline estimation results. For both groups, estimated \( \rho \) is statistically insignificant. Thus, the null hypothesis \( \rho = 0 \) cannot be rejected for them, which means the sufficient condition for fiscal solvency is violated for those groups. Under this type of fiscal policy, it is possible for public debt to rise for a long period of time because primary surpluses would not respond systematically to the debt–GDP ratio. Given this behavior in the sample period, it is not a coincidence that the western and southern countries have seen their debt–GDP ratios continually rising, as in Fig. 1. As noted earlier, the western and southern groups are the only regions that exhibit clear upward trends in their debt–GDP ratios. It is also hardly surprising that all countries in the southern group, i.e., Italy, Portugal, Spain, Greece, and Cyprus, had serious fiscal problems.

Unlike the regional differences in the marginal response, the coefficients on GVAR and YVAR, \( \alpha_{g}^{k} \) and \( \alpha_{y}^{k} \), are both negative and statistically significant for all regional groups. As we discussed in Sect. 3, these results are quite intuitive as temporary government spending tends to reduce primary surpluses (\( \alpha_{g}^{k} < 0 \)) and primary surpluses exhibit counter-cyclicality with output (\( \alpha_{y}^{k} < 0 \)). Thus, we can conclude that primary surpluses in all regional groups of the EU seem to have responded quite systematically to the temporary fluctuations in government spending and output throughout the sample period.

### 4.2 Effects of eurozone membership on fiscal sustainability

In this subsection, we analyze the effects of the eurozone membership on their fiscal policies. In particular, we compare the behavior of primary surpluses in two aspects: both between eurozone members and non-members and between the pre-eurozone subperiod and the eurozone subperiod. We investigate the impact of the eurozone membership on the fiscal policy because eurozone countries are likely to adjust their fiscal policy due to the rules and regulations intended to promote fiscal sustainability such as the stability and growth pact.

^{13}Also, by comparing key coefficients in (5) with corresponding coefficients in (3) for non-eurozone countries, we can find differences in governments’ behaviors between eurozone countries and non-eurozone countries.

The estimation results are given in Table 4 with column [2] for non-eurozone countries and [3] for eurozone countries.^{14} First, the Benelux and western groups make a stark contrast to each other in the behavior of primary surpluses, as in the baseline results. The marginal response is positive and statistically significant for the Benelux group in both subperiods, whereas it is statistically insignificant for the western group in both subperiods. Hence, the sufficient condition for fiscal solvency is satisfied only for the Benelux countries throughout the whole sample period. It is notable that the western group did not raise their marginal response significantly even after the countries became members of the eurozone. In terms of Bohn’s criterion for fiscal sustainability, the eurozone membership does not seem to improve fiscal solvency of the western group. Overall, these results are consistent with the findings from the baseline model that the Benelux group is characterized with a significantly positive marginal response but the western group with an insignificant marginal response.

Second, the southern group reduced the marginal response after they joined the eurozone, as shown in column [3] of Table 4. In other words, the estimated marginal response is positive and significant in the pre-eurozone subperiod but insignificant in the eurozone subperiod. This means that the sufficient condition for fiscal solvency is satisfied before the southern countries joined the eurozone, but not after. This result again indicates the limited effect of the eurozone membership on promoting fiscal sustainability.

As for the northern and eastern groups, our sample has both members and non-members of the eurozone. Hence, we can compare the marginal responses between the two types of countries. According to Table 4, estimated marginal responses are positive and significant for the countries out of the eurozone for both regional groups but insignificant for countries in the eurozone regardless of subperiod. Therefore, only non-eurozone countries in the northern and eastern groups have conducted fiscal policy in ways that satisfy the sufficient condition for fiscal solvency. Moreover, eurozone countries in these groups did not significantly raise their marginal responses to the extent that would ensure fiscal solvency, after they joined the eurozone. This is additional evidence that the eurozone membership might have been ineffective in inducing countries to conduct more sustainable fiscal policy.

Overall, the eurozone membership does not seem to have a strong positive effect on the marginal response of primary surpluses. According to columns [2] and [3] of Table 4, eurozone countries in most regional groups did not increase their marginal responses even after they joined the eurozone, despite the rules and regulations intended to improve fiscal sustainability. By contrast, non-eurozone countries in the northern and eastern groups have significantly positive marginal responses. Taken together, our findings seem to cast doubt on the role of eurozone membership in enhancing fiscal solvency of the member countries.

## 5 Robustness checks

In this section, we examine robustness of the solvency tests in the previous section. For that purpose, we consider two types of alternative tests for fiscal solvency. In the first test, we allow time-varying marginal responses in policy rules and examine whether estimated policy rules of the regional groups satisfy the generalized solvency conditions according to Canzoneri et al. (2001). The second set of solvency tests are based on the stationarity of key fiscal variables. Although they are not as general and accurate as Bohn’s test, those tests can still provide useful information about fiscal sustainability of the EU countries.

### 5.1 Solvency tests with time-varying marginal responses

Our solvency tests in Sect. 4 are based on linear policy rules in which the marginal response of primary surpluses to public debt is time-invariant. In general, however, the marginal response can change over time or exhibit severe nonlinearity that linear policy rules cannot adequately account for. In such cases, the solvency tests based on the linear policy rules are less informative. In this subsection, therefore, we extend our analysis by allowing for time-varying marginal responses in solvency tests for the EU countries.

In other words, if time-varying marginal responses are always nonnegative (C1), and the marginal responses are expected to be positive infinitely often (C2), then the IBC of the government (1) is satisfied.^{15} Therefore, we can examine whether both (C1) and (C2) are satisfied to test fiscal solvency.

In the baseline regression model (3) with a time-invariant \( \rho \), it is fairly straightforward to check (C1) and (C2): \( \rho > 0 \) satisfies both conditions, whereas \( \rho \le 0 \) violates one or both of them. Thus, the sufficient condition for fiscal solvency provided by Bohn (1998) can be interpreted as a special case of (C1) and (C2) in CCD in the case of a constant \( \rho \). Therefore, the results of our baseline empirical analysis in Sect. 4 are still valid under the more general criteria for fiscal solvency of CCD if policy functions are indeed linear and time-invariant as in (2).

From the formula for \( \rho_{it}^{k} \), we can find two cases in which both (C1) and (C2) are satisfied: (i) \( \rho^{k} > 0 \) and \( \beta^{k} = 0 \), or (ii) \( \beta^{k} > 0 \). In the first case, the marginal response \( \rho_{it}^{k} \) is reduced to \( \rho^{k} \), which is always positive regardless of the debt–GDP ratio. Hence, this case satisfies both (C1) and (C2), and fiscal solvency is ensured for regional group \( k \). In the second case, \( \beta^{k} > 0 \), the marginal response \( \rho_{it}^{k} \) is linearly increasing in the debt–GDP ratio, and therefore will be positive if the debt–GDP ratio is sufficiently high. Due to this mechanism, the marginal response can be positive infinitely often, and (C2) holds in this case. Also, while the marginal response \( \rho_{it}^{k} \) can be negative for a low debt–GDP ratio and hence (C1) is violated, it is unlikely to lead to fiscal insolvency because \( \rho_{it}^{k} \) will turn positive as the debt–GDP ratio increases. Based on this analysis, we estimate the nonlinear response model (7) and investigate the signs of \( \rho^{k} \) and \( \beta^{k} \) for each regional group.^{16}

Estimation results of the nonlinear response model are presented in column [4] of Table 4. For each of Benelux, northern, and eastern groups, \( \rho^{k} \) is positive and statistically significant but \( \beta^{k} \) is statistically insignificant. Therefore, the estimated fiscal rules of these groups fit the case with \( \rho > 0 \) and \( \beta = 0 \), satisfying the solvency conditions (C1) and (C2). This result is certainly consistent with the finding from the baseline regression model that suggests fiscal solvency for them. For the southern group, however, both \( \rho^{S} \) and \( \beta^{S} \) are statistically insignificant. Hence, neither \( \rho > 0 \) and \( \beta = 0 \), nor \( \beta > 0 \) represents their fiscal policy, meaning that both (C1) and (C2) are violated. Consequently, we cannot rule out the possibility of fiscal insolvency for the southern group. Again, this result corroborates the finding from the baseline regression model that southern countries may not be fiscally solvent.

As for the western group, \( \beta^{W} \) is positive and significant but \( \rho^{W} \) is statistically insignificant. Hence, the western group’s fiscal policy implied by these estimates satisfies (C1) and (C2) as it falls into the case \( \beta > 0 \). Hence, western countries are fiscally solvent according to the estimation results of the nonlinear response model. At first glance, this finding appears at odds with their statistically insignificant marginal response in the baseline regression model, which violates Bohn’s sufficient condition for fiscal solvency. To reconcile this apparent inconsistency, notice that both Bohn’s condition and CCD’s conditions are sufficient, rather than necessary, for fiscal solvency. Thus, a country would be fiscally solvent as long as it satisfies at least one of the two conditions. Consequently, we can conclude that the western countries will be fiscally solvent based on the significantly positive \( \beta^{W} \) in the nonlinear response model even though \( \rho^{W} \) is statistically insignificant in the baseline regression model. In particular, the positive \( \beta^{W} \) suggests that the continual accumulation of public debt in western countries shown in Fig. 1 is less worrisome than it looks, because the rising debt–GDP ratio will eventually lead to sufficiently strong marginal responses by (7) to prevent public debt from increasing further. In this sense, we could interpret the statistically insignificant estimate of \( \rho^{W} \) in the baseline regression model as an indication that the debt–GDP ratio may not be high enough to trigger significantly positive marginal responses in the western group.

Summary of solvency tests

Benelux | Western | Northern | Southern | Eastern | |
---|---|---|---|---|---|

| |||||

Real primary surplus (S) | − 1.94** | − 2.37** | − 4.74*** | 0.08 | 5.11 |

Real end-of-period public debt (B) | 1.64 | 0.70 | 1.21 | 2.14 | 2.68 |

Diff. of real non-interest spending (Δ | − 4.70*** | − 5.55*** | − 7.11*** | − 2.52*** | − 0.94 |

Diff. of real government revenue (Δ | − 5.36*** | − 5.91*** | − 8.34*** | − 5.41*** | − 2.53*** |

Diff. of real end-of-period public debt (Δ | − 3.55*** | − 5.80*** | − 4.25*** | − 0.17 | 2.56 |

Real deficit including interest payments (DEF) | − 2.32** | − 1.12 | − 3.34*** | 1.43 | 4.51 |

| |||||

A. Solvency tests based on marginal responses | |||||

(1) Bohn (1998) | Solvent | Uncertain | Solvent | Uncertain | Solvent |

Solvent if marginal response is always positive | |||||

(2) Canzoneri–Cumby–Diba (2001) | Solvent | Solvent | Solvent | Uncertain | Solvent |

Solvent if marginal response is positive infinitely often | |||||

B. Solvency tests based on unit-root tests | |||||

(1) Hamilton–Flavin (1986) | Uncertain | Uncertain | Uncertain | Uncertain | Uncertain |

Solvent if B is stationary when S is stationary | |||||

(2) Trehan–Walsh (1988) | Solvent | Solvent | Solvent | Uncertain | Uncertain |

Solvent if Δ | |||||

(3) Trehan–Walsh (1991) | Solvent | Solvent | Solvent | Uncertain | Uncertain |

Solvent if Δ | |||||

(4) Ahmed–Rogers (1995) | Solvent | Uncertain | Solvent | Uncertain | Uncertain |

Solvent if DEF is stationary when both Δ |

### 5.2 Stationarity-based solvency tests prior to Bohn

So far, we discuss the results of the solvency tests based on the marginal responses of primary surpluses to public debt following Bohn (1998) and CCD (2001). Prior to them, however, other papers investigated fiscal solvency using tests for stationarity of key fiscal variables. In this subsection, we briefly discuss those methods and apply them to analyze fiscal solvency of EU countries.

*r*is a constant real interest rate. All of the solvency tests that we will introduce below are based on the IBC (8), or equivalently, the assumption of the constant real interest rate. However, (8) is not a relevant IBC for fiscal solvency because it is generally different from the true IBC (1), especially in stochastic economies. This means that (8) does not necessarily guarantee fiscal solvency, and, conversely, fiscal solvency does not require (8). In this sense, the solvency tests based on (8) may be flawed to the extent that (8) differs from (1). Moreover, those tests made several technical assumptions on the time-series properties of fiscal variables to derive testable solvency conditions. Therefore, they can be too restrictive in the sense that they are not useful unless such assumptions are satisfied.

Bohn’s method is free of those problems. It provides a reliable framework to test fiscal sustainability since it is based on the correct IBC (1). Also, Bohn’s test is quite general as it does not require any time-series property of \( s_{t} \) or \( d_{t} \): if the primary surplus–GDP ratio is an increasing linear function of the debt–GDP ratio, the government debt is sustainable regardless of their time-series properties and the evolution of interest rates. With these advantages as well as its tractability, therefore, we have used Bohn’s test as our baseline methodology. For robustness of our main findings, however, we now proceed to discuss the solvency tests prior to Bohn (1998) with the caveats discussed so far.

As the seminal paper on testing fiscal solvency, Hamilton and Flavin (1986) showed that if real primary surpluses are stationary, the stationarity of real end-of-the-period government debt ensures (8) to be satisfied. To check whether this criterion is satisfied for the regional groups of the EU countries, we test whether real primary surpluses and real end-of-the-period government debt are stationary using the panel unit-root tests based on augmented Dickey–Fuller (ADF) tests (Choi 2001). In the panel ADF tests, a variable has a unit root for all countries under the null hypothesis, whereas it is stationary at least for one country under the alternative hypothesis. We include a linear trend and two lags of a dependent variable to account for potential serial correlation up to two periods in the unit-root tests.^{17}

We present the results of Hamilton–Flavin solvency tests in Table 5. First, their solvency criterion is violated for the Benelux, western, and northern groups because real end-of-the-period public debt is non-stationary even though real primary surpluses are stationary, as shown in panel (a). For the southern and eastern groups, we are not even able to apply the Hamilton–Flavin solvency criterion because the prerequisite for the test is not satisfied due to the non-stationarity of real primary surpluses. Thus, no regional group can be said to pass the Hamilton–Flavin test for fiscal solvency.

Trehan and Walsh (1988) derived alternative solvency conditions: assuming that both real revenue and real non-interest expenditure of the government are difference stationary, (8) is satisfied if real end-of-the-period government debt is difference stationary or if real budget deficits including interest payments are stationary. Ahmed and Rogers (1995) also showed that the latter is a necessary and sufficient condition for (8) under the difference stationarity of real government revenue and real non-interest expenditure together with other technical assumptions. To take advantage of those solvency criteria, we first check if real government revenue and real non-interest expenditure are difference stationary. This is indeed the case except for the eastern group, as shown in panel (a) of Table 5. Hence, we can apply their solvency criteria by testing the stationarity of real budget deficits including interest payments or the first difference of real end-of-the-period public debt. We find that the former is stationary only for the Benelux and northern groups and the latter is stationary only for the Benelux, western, and northern groups. Therefore, we conclude that those regional groups satisfy the solvency criteria of Trehan and Walsh (1988) or Ahmed and Rogers (1995). For the eastern group, we cannot make a judgment based on their solvency criteria because the first difference of real non-interest expenditure has a unit root, thereby violating the prerequisite for their solvency tests.

Trehan and Walsh (1991) proposed still another solvency criterion: under some assumptions, (8) is satisfied if the first difference of end-of-the-period public debt is stationary.^{18} According to panel (a) of Table 5, it is stationary only for the Benelux, western, and northern groups, which satisfies the Trehan–Walsh condition for fiscal solvency. By contrast, it is unclear whether the southern and eastern groups are fiscally sustainable according to the Trehan–Walsh criterion.

The results of all of our solvency tests are summarized in panel (b) of Table 5. For each test, we also provide the condition for fiscal solvency.^{19} We classify a regional group as “solvent” if the solvency conditions hold, and “uncertain” otherwise. We use the term “uncertain” rather than “insolvent” because most of the solvency conditions are sufficient. From the table, we can see that our main findings from the baseline regression model are mostly confirmed in other solvency tests. In particular, the Benelux and northern groups pass not only Bohn’s test but also most of the other solvency tests, whereas the southern group fails to pass any of the solvency tests. Similarly, the western group is likely to be fiscally solvent because it passes CCD’s solvency tests and two other stationarity-based solvency tests.

The eastern group, however, exhibits dramatic differences in the judgment on fiscal solvency between the two types of solvency tests: its marginal responses satisfy Bohn’s and CCD’s solvency conditions but its fiscal variables do not satisfy any corresponding solvency conditions. However, solvency tests following Bohn and CCD seem more reliable due to the issues of the unit-root-test-based solvency tests discussed above. Furthermore, even if such solvency tests are fully valid, the unit-root tests for the eastern group may have low power due to relatively short-sample periods for eastern countries. For these reasons, the eastern countries are likely to be fiscally solvent based on the results of Bohn’s and CCD’s tests.

## 6 Concluding remarks

In this paper, we test long-term fiscal solvency of five regional groups of the EU by analyzing the behavior of primary surpluses based on Bohn (1998, 2005)’s and other methods. First, we estimate the marginal response of primary surpluses to public debt assuming that it is constant over the sample period 1950–2014. According to this analysis, the marginal response is significantly positive for the Benelux, northern, and eastern groups, but statistically insignificant for the western and southern groups. Thus, Bohn’s sufficient condition for long-term fiscal solvency is satisfied only for the Benelux, northern, and eastern groups. This result seems to make sense as the regional groups with statistically insignificant marginal responses coincide with the group of countries which have seen their debt–GDP ratios growing rapidly and in some cases experienced serious fiscal crises.

Then we compare the behavior of primary surpluses between the two subperiods, before and after joining the eurozone for the current members of the eurozone. We find that estimated policy rules of non-eurozone countries in all regional groups satisfy Bohn’s condition whereas those of eurozone countries in most regional groups do not, especially after they became members of the eurozone. Only the Benelux countries have significantly positive marginal responses both before and after they joined the eurozone. Hence, eurozone countries in all other groups may not have conducted fiscal policy in a way that ensures fiscal solvency in the eurozone subperiod. This finding suggests that the measures imposed by the eurozone to promote fiscal sustainability do not have desired effects.

Finally, we also examine robustness of our main findings using other solvency tests and find that our baseline results are mostly confirmed. Overall, our empirical analysis suggests that the Benelux, northern, and eastern groups are likely to be fiscally sustainable but the southern group may not be so. The estimated policy rule of the western group violates Bohn’s condition but it does satisfy generalized solvency conditions proposed by Canzoneri et al. (2001). Therefore, the western group is likely to be fiscally solvent in the sense that its marginal response will turn positive if the debt–GDP ratio rises further above some threshold.

Although this paper provides a useful test on fiscal sustainability of the EU countries, it has a few limitations. First, even if a solvency test fails for a regional group, we do not know whether it is indeed fiscally insolvent or it simply violates some assumptions of the test despite fiscal solvency. This problem arises because our tests are based on sufficient conditions. Second, we cannot provide reasons for the potential lack of fiscal sustainability as we just offer simple tests of fiscal solvency. It is beyond the scope of this paper to provide a theory or an empirical analysis to address those issues, and hence we leave such work as future research.

## Footnotes

- 1.
The average public debt–GDP ratio is taken over the 26 EU countries in our sample though there are 28 member countries in the EU as of May 2016. We exclude Malta from our analysis because of limited data availability, and Croatia because it joined the EU late in our sample period in 2013.

- 2.
- 3.
Obviously, the division of the sample period is irrelevant to non-eurozone countries.

- 4.
All equations used in this section are derived in detail in Section A of the online appendix.

- 5.
In standard DSGE models, \( q_{t,t + n} = \beta^{n} u^{{\prime }} (c_{t + n} )/u^{{\prime }} (c_{t} ) \) with the standard notation, but it can be defined generally for various dynamic models.

- 6.
As of July 2015, the EU has 28 member countries. Malta is excluded from the sample due to the lack of data availability. Croatia is also excluded as it joined the EU in 2013.

- 7.
For more details on the construction of our dataset and its sources, refer to Section B of the online appendix.

- 8.
- 9.
Notice that Lithuania is classified as a non-eurozone country because it joined the eurozone after the sample period.

- 10.
The division of the two subperiods may not coincide with the division between the pre-eurozone and eurozone subperiods for countries that joined the eurozone after 1999. We divide the sample period in this way in Table 2 for illustration.

- 11.
Our methodology follows Mendoza and Ostry (2008), who estimated the marginal response of primary surpluses to public debt for two groups, industrial countries and emerging economies, with a sample of 56 countries. They tested the assumption of group-specific marginal responses and found that 75% of the countries have the same

*ρ*. They interpret this finding as lending support to their specification. - 12.
To verify this argument, we estimate the following country-specific regression: \( s_{t} = \rho d_{t} + \alpha_{g} {\text{GVAR}}_{t} + \alpha_{y} {\text{YVAR}}_{t} + \varepsilon_{t} \) for Ireland and for the period up to 2007. We find that the estimate of

*ρ*is 0.048 and the corresponding*p*value is 0.020. - 13.
The regression coefficients specific to the eurozone subperiod can be biased because the eurozone subperiod is relatively short and includes the Great Recession. However, we think the short-sample bias is likely to be small because we collect information from the panel of multiple countries to estimate the regression coefficients. Also, time dummies can deal with the influence of the Great Recession at least partly.

- 14.
Notice that no coefficient exists for the Benelux, western, and southern groups in column [2] because all countries in these groups belong to the eurozone.

- 15.
As emphasized by CCD, the condition (C2) can hold for any frequency of positive marginal responses. For example, even if the marginal response is positive once in every 100 years, (C2) would still be satisfied.

- 16.
The nonlinear response model is nonlinear in the sense that it includes a nonlinear explanatory variable, not in the sense that regression coefficients are nonlinear.

- 17.
In our online appendix, we also present the results of other types of panel unit-root tests such as the Im–Pesaran–Shin (2003) tests and the panel Phillips–Perron (PP) tests (Choi 2001). We only report the results of the panel ADF tests because the three types of panel unit-root tests yield similar results. The appendix also includes details on the methodology of the panel unit-root tests.

- 18.
Trehan and Walsh (1991) provided multiple solvency criteria to test fiscal solvency. Here, we examine just one of their solvency criteria, which is drawn from Proposition 2 of their paper.

- 19.
As noted, there can be additional technical assumptions for some solvency tests. We do not specify them here for simplicity. For those assumptions and other details on the solvency tests, refer to the papers cited here.

## Supplementary material

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