A new test for fiscal sustainability with endogenous sovereign bond yields: Evidence for EU economies

Economic Modelling 82 (2019) 136–151

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Economic Modelling journal homepage: www.journals.elsevier.com/economic-modelling

A new test for fiscal sustainability with endogenous sovereign bond yields: Evidence for EU economies☆ Joanna Mackiewicz-Łyziak a, *, Tomasz Łyziak b a b

Faculty of Economic Sciences, University of Warsaw, ul. Długa 44/50, 00-241 Warsaw, Poland Institute of Economics, Polish Academy of Sciences, Poland

A R T I C L E I N F O

A B S T R A C T

JEL classification: E62 E43 C54

In this paper we develop a new test for fiscal sustainability and propose a synthetic fiscal sustainability indicator. Conventional tests based on fiscal reaction functions assume a constant real interest rate. However, many empirical studies find evidence on a positive response of long-term rates to sovereign debt levels. We take this evidence into account and endogenize the long-term real interest rate in testing fiscal sustainability. We apply the new test for the European economies. We find that considering the response of interest rate to debt may change the assessment of fiscal sustainability. More specifically, our results indicate that fiscal sustainability is at risk in a number of European Union economies, even if the results of traditional approaches suggest sustainable fiscal policy.

Keywords: Fiscal policy Fiscal rules Long-term bond yields European Union

1. Introduction Since the beginning of the debt crisis in Europe a lot of attention has been paid to the issue of fiscal sustainability. Rapidly increasing public indebtedness raised questions about solvency of several European governments. The situation was even more alarming in the face of aging populations in most European economies and expected need to increase public spending in response to this demographic process. Empirical studies on fiscal sustainability in Europe provided, however, reassuring results. The studies, usually based either on Bohn's (1998) concept of fiscal reaction functions or on statistical analysis of time series of public debt, concluded that in general fiscal policy in European countries was sustainable. Some examples in chronological order are as follows. Bajo-Rubio et al. (2009) showed that, with exception of Finland, fiscal policy in the EMU countries was sustainable. Similar results obtained Fincke and Greiner (2012) for selected Eurozone countries. Theofilakou and Stournaras (2012) complemented fiscal reaction functions with financial markets pressure and concluded that fiscal policy in EMU countries was sustainable. Betty and Shiamptanis (2013), for 11 euro area countries, verified additional conditions for the fiscal rule, concluding that the public debt would not be explosive. for the In the panel analysis covering 17 eurozone countries Weichenrieder and

Zimmer (2014) found that fiscal policy in these countries was sustainable and became more prudent after the introduction of euro. Although there were also studies showing that in many advanced European countries fiscal policy was unsustainable (e.g. Afonso and Jalles, 2012), the overall picture from the existing empirical literature seems to be rather optimistic. There are significantly less studies covering Central and Eastern European countries. Yet, the existing evidence suggest fiscal sustainability also in this group of European economies (see for example Krajewski et al., 2016; B€ okemeier and Stoian, 2018). The approach to test for fiscal sustainability using fiscal reaction functions was criticized by Ghosh et al. (2013), as explained in more detail in the next section. They developed the concept of non-linear fiscal reaction functions and noticed that the risk premium may increase to infinity after public debt in a given country exceeds its limit. Their analysis was conducted for several advanced economies, for which the assumption about a risk-free interest rate paid on outstanding debt until reaching the debt limit, is justified. It seems however, as we notice in this paper, that for many countries the risk premium may start to increase as debt grows even at moderate debt levels. The main contribution of our paper is, therefore, the extension of the analysis of fiscal sustainability with such a possibility. We propose a new test for fiscal sustainability and a synthetic fiscal sustainability indicator (FSI) that allows for endogenous

☆

The authors are very grateful to two anonymous Reviewers and to Professor Ryszard Kokoszczy nski for their helpful suggestions and comments. The authors also gratefully acknowledge the financial support of the National Science Centre (Poland) under decision no. DEC-2015/17/B/HS4/00297. * Corresponding author. E-mail addresses: [email protected] (J. Mackiewicz-Łyziak), [email protected] (T. Łyziak). https://doi.org/10.1016/j.econmod.2019.01.001 Received 15 October 2018; Received in revised form 31 December 2018; Accepted 4 January 2019 Available online 9 January 2019 0264-9993/© 2019 Elsevier B.V. All rights reserved.

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Economic Modelling 82 (2019) 136–151

the literature on the intertemporal government budget constraint and fiscal sustainability. Bohn's (1998) analytical framework is also based on this assumption, although in this case such an assumption seems justified given that his analysis was focused on the U.S. economy. In many other economies the assumption of constant real interest rate, not reacting to fiscal variables, is doubtful. On the contrary, as the interest rate incorporates a risk premium, it may increase in line with the increase in debt. There is a rich empirical evidence confirming this relationship (cf. Barrios et al., 2009; Baldacci and Kumar, 2010; Maltritz, 2012; Afonso and Rault, 2015). An increase in debt that increases interest rates leads to a rise in interest payments and this, in turn requires a larger primary surplus to stabilize debt. Therefore with an endogenous interest rate the parameter α larger than 0 is clearly not a sufficient condition for the debt being sustainable. The issue of the endogenous interest rate has been addressed in Ghosh et al. (2013). They developed a theoretical framework with a positive probability of default and a default risk premium being a positive, increasing and convex function of this probability of default. They introduced a concept of the debt limit – the level of debt above which the government is no longer able to service its obligations. At this point the risk premium raises to infinity. The difference between the debt limit and actual debt is called the fiscal space. Ghosh et al. (2013) assumed a non-linear fiscal reaction function of the form:

long-term real interest rate, i.e. rising with the level of debt. We perform this test for 27 European Union (EU) countries – more and less developed1 – and find that in many of these economies the long-term real sovereign bond yields positively respond to the increase in debt. Taking into account that the interest payments may increase not only because of increase in debt but also due to an increase in interest rate paid on this debt, makes the conclusions about fiscal sustainability different from those drawn on the basis of standard fiscal reaction functions, which assume that the interest rate is constant. Another policy-relevant contribution of our study is the assessment how fiscal policy sustainability was evolving over the time, especially during the global financial crisis and euro area debt crisis. It suggests that monitoring our indicator of fiscal sustainability can offer important insights for policy makers. The remainder of the paper is organized as follows. In the next section theoretical approach to assessing fiscal sustainability is explained in detail and the condition for sustainability in the proposed new test is derived. The third section presents methods of estimations and data. In the fourth section we discuss the results of our test for fiscal sustainability in 27 EU economies and compare obtained results with other fiscal sustainability measures. Further, we check the evolution of fiscal sustainability performing rolling-window estimations and time-varyingcoefficient (TVC) methods. Finally, the last section offers conclusions and discussion of possible policy implications. 2. Theoretical background

pbt ¼ μ þ f ðdt1 Þ þ εt

Until the seminal paper of Bohn (1998), empirical literature on fiscal sustainability was based on testing statistical properties of fiscal time-series. Tests for unit roots in debt or deficit series or for cointegration between public revenues and expenditures were proposed and applied inter alia by Hamilton and Flavin (1986), Trehan and Walsh (1991), Quintos (1995) and Bravo and Silvestre (2002). Stationarity or difference-stationarity of debt or deficit as well as cointegration between revenues and spending were interpreted as conditions for the intertemporal budget constraint being satisfied, and hence fiscal sustainability. Bohn (1998, 2007) criticized this approach. Firstly, he showed that tests for unit roots have low power in rejecting non-stationarity of debt series. Based on such tests a researcher may conclude about a lack of fiscal sustainability, while in reality the debt may be stationary.2 Secondly, he proved that the debt series integrated in any finite order constitutes a sufficient condition for the intertemporal budget constraint to be satisfied. Instead of testing for stationarity he proposed analysis of the behavior of the government by estimating fiscal reaction functions of the following form: pbt ¼ αdt þ βZt þ εt

(2)

where μ incorporates all determinants of primary balance other than lagged debt and f ðdÞ is a continuously differentiable function describing the response of primary balance to lagged debt.3 They showed that a sufficient condition for debt sustainability is that the responsiveness of primary balance to debt, α, be greater than the interest rate – GDP growth rate differential. In the case of the a linear fiscal reaction function, as assumed in Bohn (1998), this condition can be expressed as follows:

α > r*  g

(3)

where r* is a risk-free interest rate and g denotes the rate of growth of real GDP (treated as constant). In their framework Ghosh et al. (2013) assume that the government is able to borrow at a risk-free interest rate until the debt limit is reached. Beyond that level the risk premium grows to infinity. The assumption about the risk-free rate may be reasonable in the case of advanced economies which were analyzed in Ghosh et al. (2013). Governments in many other emerging and transition countries face, however, higher costs of borrowing and the risk premium is positive.4 Moreover, as mentioned above, there is evidence that the risk premium grows with the level of debt, so that the difference between the real interest rate r and the GDP growth rate g is not constant, but growing, even at moderate debt levels. In such a case, the condition described in (3) is not a sufficient condition for fiscal sustainability, because interest payments grow faster than primary balance and the debt explodes (other things being equal). Our point is illustrated in Fig. 1, which presents a simple stylized simulation of debt paths assuming constant vs. endogenous interest rate under specific and realistic assumptions related to initial values of debt, primary balance, interest rate and GDP growth rate. Simulation results show that with a constant interest rate the public debt stabilizes in the long-run, but with endogenous interest rate, reacting to fiscal policy performance, the public debt indeed explodes. In order to take into account the possibility of endogenous interest rate, we assume that the long-term interest rate that each country pays on

(1)

where pb is the primary balance in relation to GDP, d is the government debt-to-GDP ratio, Z is a set of other determinants of the primary balance, α measures the responsiveness of primary balance to debt, and ε is an error term. Bohn (1998, 2007) showed that a positive coefficient α is a sufficient condition for fiscal sustainability, regardless of the results of tests for debt stationarity. This approach to studying fiscal sustainability has become very popular in the empirical literature. Many studies for different countries estimated parameter α to assess fiscal sustainability. However, the above interpretation of α strongly relies on the assumption that the interest rate on government bonds is constant or deviates from the long-run mean in a random way. This is a standard approach to treating the interest rate in

1 Among 28 EU member states only Estonia is not included in our analysis due to a lack of data on long-term sovereign bond yields. 2 Bohn's conclusions were confirmed in further empirical studies (see for example Chen, 2014).

3 The description of the properties of the function can be found in Ghosh et al. (2013). 4 This issue was noticed by Paret (2017) in the study on fiscal sustainability in emerging market countries.

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Fig. 1. Simulation of the debt path with constant and endogenous interest rate. Source: own calculations.

In this case interest payments become a square function of debt. We define the function of interest payments-primary balance differential, z:

than the old ones but more vulnerable to the investors sentiment. Therefore, instead of applying panel analysis we consider each country separately. In the first step we estimate for each country a system of equations consisting of the fiscal reaction function and the relationship between the long-term interest rates and public debt. The fiscal reaction function estimated is of the following form:


 zðdÞ ¼ r* þ βd  g d  μ  αd

pbt ¼ α0 þ α1 pbt4 þ α2 dt4 þ

its debt consists of the risk-free interest rate, r*, and the default risk that depends on the level of debt: rt ¼ r* þ βdt

(4)

(5)

(8)

where pbt4 is the primary balance in terms of GDP lagged by four quarters, dt4 is the debt-to-GDP ratio lagged by four quarters, Xi;t is the set of macroeconomic variables, used commonly in empirical studies as controls, that include output gap, the government expenditures gap, inflation and trade openness. Our baseline specification includes output gap and government expenditures gap as control variables. Similar specification of the fiscal reaction function has been used by Mendoza and Ostry (2008), among others. In additional estimations we add other control variables used in the literature, but the results are similar to these from baseline specification.5 We estimate equation (8) using two-stage least squares method, as suggested by Celasun and Kang (2006).6 We deal with possible endogeneity caused by the fact that the output gap may be affected by the fiscal variables. We use pbt4 , dt4 , government expenditures gap, as well as current and lagged values of the output gap in the whole European EU EU y t1 as instruments.7 Union: b y t and b Contrary to the approach taken in Ghosh et al. (2013) we do not assume non-linear fiscal reaction functions. Since we estimate them for individual countries using relatively short time-series we consider linear function a good approximation of behavior of fiscal authorities. In the period under consideration no country in the sample experienced the

(6)

The condition (6) states that fiscal sustainability requires parameter α to compensate additionally for the risk premium that is increasing with debt. For the countries that are able to borrow at a risk-free rate, this condition reduces to (3). In the remaining countries, the reaction of primary balance to debt has to be accordingly stronger to sustain sustainability. The degree of fiscal sustainability can be, therefore, verified with a synthetic fiscal sustainability indicator (FSI), based on equation (6) and defined as follows: FSI ¼ α  r*  2βd þ g

γ i Xi;t þ εt

i¼1

Fiscal sustainability is achieved if the difference between interest payments and primary balance is decreasing, i.e.: z' ðdÞ ¼ r * þ 2βd  g  α < 0 ⇔ α > r* þ 2βd  g

4 X

(7)

Positive values of FSI indicate prudent fiscal policy, whose response to public debt is sufficiently strong to absorb the effects of pricing debt in financial markets. Its negative values suggest that fiscal policy sustainability is at risk. 3. Methodological approach and data Taking into account the possibility described in the previous section, i.e. a positive response of risk premium to public debt, we propose a new test to assess empirically fiscal sustainability. The procedure consists of three steps, including a joint estimation of conventional Bohn's (1998) fiscal reaction function and the response of long-term interest rate (risk premium) to public debt, verification of condition (6) on the basis of estimated parameters α and β and finally, testing if the fiscal sustainability indicator is positive. We apply this procedure to 27 EU countries. This group is not homogenous and comprises more and less advanced economies. The new member states that joined the EU after 2004 are in general less indebted

5 In order to check for the robustness of our results, we estimate equation (8) adding inflation and trade openness to the set of control variables (used by Ghosh et al., 2013), as well as with output gap alone. The estimates of proved to be very robust to the selection of the control variables. The results are presented in Table A.3. in the Appendix. 6 In addition, we estimate equation (8) using GMM with the same set of instruments. We found the results to be robust to the estimation method. 7 We checked the validity of instruments using Sargan test for overidentifying restrictions and F-test on the joint significance of instruments in the first stage regression.

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fully eliminate the problem but alleviates it to a large extend. Following the suggestion of Bohn (1998) that the fiscal reaction function should include not only debt but also other determinants of primary balance, we add output gap as a business cycle indicator. Output gap is calculated as the difference of the logarithm of real output (chained linked volumes, index 2010 ¼ 100, seasonally and calendar adjusted data, ESA2010) and the trend obtained using the Hodrick-Prescott filter. Similarly, government expenditure gap is calculated as a difference of seasonally adjusted series of total government expenditures (as percentage of GDP) and its trend obtained using the Hodrick-Prescott filter. Data on nominal long-term (10-year maturity) government bonds interest rates are taken from the European Central Bank. We calculate real long-term interest rates using data on inflation expressed as annual growth rate of the HICP index. The source of the data is Eurostat. Monthly data has been transformed into quarterly data using quarterly averages. In order to test for the stationarity of the variables we performed Augmented Dickey-Fuller and Phillips-Perron tests. The results are presented in Table A.1 in the Appendix. With exception of Bulgaria, the tests suggest non-stationary debt in all the countries. For the primary balance and the interest rate the results are mixed. However, taking into account the critique of Bohn (1998, 2007), explained in the previous section, we allow for the possibility that the results of the stationarity tests may be misleading.

whole spectrum of debt values. The second equation of the system is the response of the real longterm interest rate to the level of public debt, with a set of control variables: rt ¼ β0 þ β1 dt1 þ β2 r Ger þ β3 gt þ εt t

(9)

where r Ger is German real long-term interest rate, which may be treated t as a proxy of a risk-free rate and incorporates all factors that may influence the level of interest rates and are not country-specific. The above equation follows closely the theoretical model and is consistent with empirical studies showing that fiscal variables affect long-term yields on government bonds in European economies (cf. Afonso et al., 2015; Barrios et al., 2009; Schuknecht et al., 2009; Bernoth et al., 2012). The equation (9) includes two country-specific variables: public debt that represents the default risk, and the rate of growth of real GDP, g, which measures cyclical conditions and strength of the economy.8 For similar reasons as described above we assume linear form of this function. In the case of countries for which the estimated coefficient α2 is negative or statistically not different from zero we conclude about lack of fiscal sustainability. For the remaining countries we check the estimates of coefficient β1. Positive and statistically significant estimates of this coefficient indicate a positive default risk premium, associated with the stance of fiscal policy. For these countries we test condition (6), using mean value of the real long-term interest rate in Germany as a proxy for the risk-free interest rate. For countries without default risk we test condition (3). Finally, the procedure ends with the Wald test verifying the equality of both sides of condition (6) or (3). Even if calculated values of parameters suggest that condition (6)/(3) is satisfied, if we cannot reject hypothesis about equality of both sides of this condition, we cannot state fiscal sustainability. We estimate equations (8) and (9) using quarterly data from 2000q1 (or 1996q19) to 2017q2 for 27 European Union countries. In addition, to analyse stability of the estimated relationships over time, we conduct rolling-window estimations and time-varying-coefficient (TVC) estimations. This analysis is particularly important given that the sample period covers the global financial crisis and the debt crisis in the euro area that could heavily influence the fiscal reaction functions as well as pricing in the financial markets. In the case of the rolling-window estimations, due to a limited number of observations, we use a window size of 40 quarters. In the case of time-varying-coefficient approach, we use the state-space representation, in which the measurement part is given by equations (8) and (9), while the signal equations describe the time-varying coefficients of the above equations as random walk processes without drift. Fiscal data come from the Eurostat quarterly government finance statistics. The public debt variable is a general government gross debt stock expressed as a percentage of GDP, calculated according to ESA2010 methodology. The primary balance (in percent of GDP) is calculated as the sum of the budget balance and interest payments, also ESA2010 methodology. As the fiscal variables are subject of strong seasonality they have been seasonally adjusted using Census X-13 (debt) and Census X-12 (primary balance) method. The level of fiscal variables depends on the rhythm of a fiscal year. This is visible in quarterly data therefore when estimating fiscal reaction functions yearly data would be preferable. We use quarterly data to increase the number of observations since time series of yearly data would be too short. Seasonal adjustment may not

4. Results 4.1. Whole sample results The results of the fiscal sustainability test described above performed for the EU economies are presented in Table 1.10 Column I of the Table 1 provides estimates of coefficient α2 of the basic specification of equation (8), representing the responsiveness of primary balance to debt.11 In the classical approach of Bohn (1998) positive and statistically significant value of this parameter is interpreted as an indicator of sustainable fiscal policy. We obtained such a result for 20 out of 27 analysed economies. There was only one country – France, with negative and statistically significant estimate of α2. For six countries, i.e. Ireland, Luxembourg, Malta, the Netherlands, Austria, and Finland, the coefficient is not significantly different from zero. In the case of these countries we conclude about the lack of fiscal sustainability, in accordance with the standard interpretation of Bohn (1998). For 15 out of 20 countries with positive value of α2 we observe a positive and statistically significant response of the long-term interest rate to debt (coefficient β2, column II), i.e. a positive default risk premium. This group of economies comprises Bulgaria, the Czech Republic, Greece, Spain, Croatia, Italy, Cyprus, Latvia, Lithuania, Hungary, Poland, Portugal, Romania, Slovenia and Sweden. With exception of Sweden all the countries are either new member states from Central and Eastern Europe or highly indebted southern countries. This confirms our intuition that investors may treat these economies differently than core Eurozone countries with sovereign bond yields in the former economies responding to growing public debt, making the interest payments higher and thus further deteriorating their fiscal position. Hence, to test for fiscal sustainability in these countries we verify condition (6). We report the value of the right-hand-side of this condition (limit) in column III of Table 1. To calculate it we use mean values of all the variables in the analysed period. We proxy the risk-free interest rate r* with a mean real long-term interest

8 In order to check for the robustness of our results we added additional control variables, i.e. VIX, primary balance and trade openness to equation (9). We found that the extended set of controls did not change our conclusions about the impact of public debt on long-term yields. The detailed results available on request. 9 The longer time-series are available for Belgium, Hungary, Spain and Sweden.

10

The rest of estimated coefficients of equations (8) and (9) not reported in Table 1., is presented in Table A.2. in Appendix. 11 Estimates of parameter α2 obtained for all other specifications of equation (8) and using two different estimation methods are presented in Appendix in Table A.3. 139

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Table 1 Results of test for fiscal sustainability for 27 EU countries.

Belgium Bulgaria Czech Rep. Denmark Germany Ireland Greece Spain France Croatia Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Romania Slovenia Slovakia Finland Sweden UK

α2 (I)

β(II)

Limit r * þ 2βd  g(III)

H0: α ¼ r * þ 2βd  g Prob(Chi-sq) (IV)

Assessment of fiscal sustainability (V)

0.09*** (0.01) 0.08*** (0.02) 0.20*** (0.02) 0.12*** (0.03) 0.08*** (0.02) 0.02 (0.02) 0.04*** (0.01) 0.03** (0.01) 0.01*** (0.00) 0.06*** (0.01) 0.01*** (0.00) 0.07*** (0.02) 0.05*** (0.02) 0.06*** (0.02) 0.01 (0.02) 0.11*** (0.02) 0.00 (0.00) 0.00 (0.00) 0.004 (0.02) 0.13*** (0.05) 0.04*** (0.01) 0.10*** (0.03) 0.03*** (0.01) 0.10*** (0.02) 0.00 (0.00) 0.10*** (0.01) 0.02** (0.01)

0.01 (0.01) 0.19*** (0.04) 0.14*** (0.03) 0.01 (0.02) – 0.05*** (0.01) 0.08***(0.02) 0.05*** (0.01) 0.003 (0.01) 0.08*** (0.02) 0.03*** (0.01) 0.07*** (0.01) 0.43*** (0.03) 0.32*** (0.03) 0.14*** (0.03) 0.14*** (0.04) 0.08** (0.04) 0.03 (0.02) 0.02 (0.01) 0.05*** (0.01) 0.04***(0.00) 0.18*** (0.05) 0.03*** (0.01) 0.02 (0.03) 0.01 (0.01) 0.05*** (0.02) 0.02 (0.01)

0.00 0.10 0.09 0.00 0.005 0.03 0.23 0.06 0.01 0.09 0.08 0.10 0.20 0.16 0.02 0.19 0.09 0.003 0.00 0.02 0.07 0.08 0.01 0.03 0.003 0.04 0.001

0.00 0.32 0.00 0.00 0.02 0.75 0.00 0.01 0.00 0.02 0.00 0.20 0.00 0.00 0.09 0.00 0.00 0.31 0.84 0.01 0.00 0.45 0.60 0.00 0.26 0.00 0.00

þ – þ þ þ – – – – – – – – – – – – – – þ – /þ /þ – – þ þ

Standard errors in parenthesis. *** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level. Source: own calculations.

rate in Germany.12 For the remaining countries, i.e. with negative or statistically insignificant β, we check condition (3). The right-hand side value of the condition in this case is calculated as the difference between the mean long-term real interest rate and the mean rate of growth of real GDP. In column IV we present the results of the Wald test for equality of both sides of the condition (6) or (3). If we are not able to reject the hypothesis about equality, we cannot conclude about fiscal sustainability. According to our approach we confirm fiscal sustainability if the indicator of fiscal sustainability is significantly above zero, i.e. if the coefficient α2 is positive and larger than r * þ 2βd  g. Such a result is obtained only for 8 countries in our sample, including Belgium, the Czech Republic, Denmark, Germany, Poland, Slovakia, Sweden and UK. Therefore, our results are less optimistic than in many previous studies on fiscal sustainability in Europe cited above showing that in general fiscal policy in European countries was sustainable. It is worth noting, however, that in the case of two countries in the sample – Romania and Slovenia – we obtained positive fiscal sustainability indicator, but its value is not statistically different from zero. For these countries we cannot state with certainty either lack of sustainability or its existence, basing solely on these results.

countries from our sample), we use in addition the fiscal sustainability indicator S1 published by the European Commission (EC)13 that is estimated for all the countries we analyzed, with exception of Greece, and may be treated as a proxy for the fiscal space. Our sample covers 14 countries analyzed in Ghosh et al. (2013): Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden and UK. For these countries correlation between the FSI and the fiscal space calculated by Ghosh et al. (2013) amounts to 0.66. It means that for the group of advanced economies our measure is broadly consistent with the concept of fiscal space of Ghosh et al. (2013). For the whole sample of 27 EU countries correlation with the alternative indicator of the fiscal space published by EC is much lower, although statistically significant, and amounts to 0.21.14 However, for the group of advanced economies this correlation is higher and equals to 0.63. For comparison, correlation of the same indicator with the Ghosh et al. (2013) fiscal space is equal to 0.83. The fact that the correlation of the FSI with EC indicator of fiscal space is stronger for the advanced economies than all 27 EU economies is not surprising. Our findings suggest that the real interest rates paid on the government debt in advanced economies do not depend very much on

4.2. Comparison with other indicators of fiscal sustainability

13

European Commission compiles three fiscal sustainability indicators: shortterm S0, medium-term S1 and long-term S2. Most closely related to our study is indicator S1 because it takes into account the necessary adjustment in the primary balance needed to achieve specific debt target (set at 60% of GDP) over 15 years. The short-term indicator S0 does not refer to the intertemporal government budget constraint whereas the long-term indicator S2 relies heavily on the predicted costs of population aging that are not taken into account in our study. The source of data is European Commission (2018), Debt Sustainability Monitor 2017. 14 In contradiction to fiscal space, whose higher values indicate lower risk, higher values of S1 indicator denote higher risk. Therefore in the former case the negative correlation of S1 and our measure of fiscal sustainability is consistent with intuition.

As explained in the theoretical section our test refers to the fiscal sustainability concept of Ghosh et al. (2013), who calculated fiscal space as a measure of fiscal policy sustainability. Hence, it seems self-imposed to compare the measure proposed in our study, i.e. the fiscal sustainability indicator, with the fiscal policy space. As the latter one was calculated by Ghosh et al. (2013) only for advanced economies (14

12 For Germany we do not estimate equation (9). The limit (value in column III) is calculated as the difference between mean long-term interest rate in Germany (treated as the risk-free rate) and mean growth of GDP.

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increase of fiscal sustainability since 2015, while rolling-regression approach suggests that the fiscal policy has becoming less and less prudent since 2009. As far as fiscal sustainability in Cyprus is concerned, both methods suggests that recently fiscal policy has been unsustainable, while conclusions concerning the former period differ from each other, with TVP estimation suggesting lack of fiscal prudence and rolling regression estimates indicating sustainable policy. These findings generally confirm our results obtained for the whole sample period, although there are few differences in the classification of countries. In the case of 6 out of 8 countries whose fiscal policy we classified as sustainable, we find fiscal prudency during the whole period or only short-term violation of the sustainability condition (Czech Republic, Denmark, Germany, Poland, Slovakia and Sweden). In the case of remaining countries from this group, i.e. Belgium and UK, our assessment based on models capturing time variation of estimated coefficients, differs from whole sample results. We can observe that in Belgium our condition of fiscal sustainability was violated either since the European debt crisis (rolling regressions) or even before (TVC estimation). As far as fiscal policy in the UK is considered, both rolling-regression and TVC estimates show that in a dominant part of the sample period the response of primary balance to public debt was negative, however, at the end of the sample period, i.e. in 2017, it has become positive and significantly above the limit. It is why the whole sample estimates suggest responsible fiscal policy in this economy. However, taking into account historical developments, this conclusion should be treated cautiously. On the other hand, in the case of two countries, i.e. the Netherlands and Ireland, fiscal policy prudency assessed with rolling-regression and TVC models proves to be better than assessed with whole sample estimates. It seems that the fiscal sustainability condition in the Netherlands was fulfilled during most of the analyzed period, while in Ireland positive results can be noted in the most recent period. The regressions with coefficients evolving over time add some explanatory power in the case of two countries – Romania and Slovenia – for which whole sample estimates do not state fiscal sustainability unequivocally. The developments in these two countries were opposite to each other: while in Slovenia fiscal policy making violets the principles of sustainability, Romania has improved fiscal prudency, however only TVC estimates suggest fiscal sustainability in the most recent period. It is worth emphasizing that the results of the rolling-window and time-varying-coefficient regressions demonstrate that in many economies the picture of the fiscal policy sustainability is volatile. Therefore, it is important to monitor the situation constantly. In this sense, the proposed test may be used not only as a tool of assessing past fiscal policy behavior but also to signal potential threats, as it allows to analyse the fiscal performance in a dynamic manner.

fiscal policy performance. Hence, our approach does not differ significantly from the conventional method to studying fiscal sustainability in the case of these economies. Lower correlation for the group of all 27 countries indicates that adding the factor of changing risk premium significantly affects the results. This finding supports our approach suggesting that financial market pricing of public debt should be taken into account while assessing fiscal sustainability, in particular in the case of less developed economies.15 4.3. Evolution of fiscal sustainability over time We check stability of the results presented in Table 1 by performing rolling-window estimations and time-varying-coefficient (TVC) estimations. The results of the calculations are presented in Fig. 2, including the evolution of coefficient α2 in equation (8), i.e. the response of primary balance to public debt, and the limit for this coefficient, below which fiscal policy becomes unsustainable. The latter variable is defined as: r * þ 2βd  g, where β is the rolling-window or time-varying-coefficient estimate of parameter β1 in equation (9), r* is the average of German longterm real interest rate (in a given estimation window in the rollingregression approach and cumulative in the TVC approach), d is the average of public debt and g is the average of the GDP growth.16 The results from both approaches with which we analyse changes in the conduct of fiscal policy have different features. Coefficients estimated in the rolling-regression approach are by construction more volatile than their counterparts based on time-varying-coefficient estimation. In addition, the former ones usually display larger confidence bands than the latter ones. The above differences reflect mainly short windows of observations used in the rolling-regression approach. As a result, changes in the coefficients based on this approach can contain a sizeable sampling error. Leaving aside these differences, the assessment of changes in fiscal sustainability in analysed economies is rather robust with respect to the analytical approach applied. We can broadly classify European economies into three categories. The largest group of countries are the economies, whose fiscal policy seems unsustainable, independently of the time period under consideration. This group includes Bulgaria, Greece, Austria, France, Croatia, Italy, Lithuania, Luxembourg, Hungary and Slovenia. In addition, in this group are classified countries with a history of imprudent fiscal policy performance that display minor signs of improvements in this respect at the end of the sample period, i.e. Ireland, Netherlands, Portugal and Romania. Belgium, Spain, Latvia, Finland and UK belong to the second group comprises, which used to fulfill the requirements of fiscal sustainability in the past, but since the beginning either of the global financial crisis or the European debt crisis have worsened substantially their fiscal policy performance. The third group comprises economies, whose fiscal policy seems prudent independently of the time period under consideration or countries, in which exceptions from responsible fiscal policy were short-lived – the Czech Republic, Denmark, Germany, Poland, Slovakia and Sweden. In the case of Malta and Cyprus our conclusions based on rollingregression estimation and time-varying-coefficient estimation are not robust. TVP estimation suggests that fiscal response to public debt in Malta was rather stable and close to the limit over the time, with the

5. Conclusions Increasing public debts in many economies, including European ones, pose a question on sustainability of fiscal policy. The analytical framework for testing fiscal policy sustainability has evolved from simple verification of statistical properties of public debt to estimating fiscal reaction functions. Empirical results for European economies reported in the literature have been in general reassuring, indicating responsible fiscal policy and limited risks in this respect. Our present paper contributes to this literature, both in terms of proposing an extended theoretical framework for testing fiscal policy sustainability and a synthetic fiscal sustainability indicator as well as in terms of presenting the new evidence on sustainability of fiscal policy in EU economies and on its evolution over time. We develop the concept of fiscal sustainability proposed by Ghosh et al. (2013) by endogenizing the long-term sovereign bond yields and assuming that the default risk is increasing with the level of debt. This extension can be substantial for emerging/transition economies or economies with high level of public indebtedness, whose long-term sovereign bond yields can significantly react to fiscal policy

15

It is worth noting that fiscal space may be viewed as a multidimensional concept and may be analysed with a range of various indicators, as described in details in IMF (2016) and Kose et al. (2017). 16 Differences in the limits estimated in rolling-window and time-varyingcoefficient approaches reflect only differences in the estimated impact of fiscal variables on yields on government bonds. All the remaining determinants of the limit are the same in both analytical approaches. In the case of Germany the second element of the formula is omitted, so the limit is defined as r* – g. 141

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Fig. 2. Results of the rolling window (RR) and time-varying parameter (TVP) regressions. Source: own calculations.

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Fig. 2. (continued).

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Fig. 2. (continued).

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Fig. 2. (continued).

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Fig. 2. (continued).

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Fig. 2. (continued).

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Fig. 2. (continued).

with the use of dynamic estimation method, shows however, that in many of analysed economies there were significant changes in the degree of fiscal sustainability over time. It suggests that fiscal sustainability should be carefully monitored on frequent basis. Interestingly, considering the group of developed European economies, our measure of fiscal sustainability seems highly correlated with the estimates of fiscal space based on Ghosh et al. (2013) as well as with the fiscal sustainability indicator S1 published by the EC. For the group of all 27 EU countries the correlation with the S1 indicator is lower, which, in our view, supports the need of including the changing risk premia in

performance, in particular to public debt. We show that after capturing this effect the existing notion of fiscal sustainability seems excessively loose and that actual requirements for fiscal policy being sustainable can be more demanding. Our empirical results, based on data from 27 European economies, clearly confirm the above hypothesis. Only in the case of six countries in our sample, i.e. the Czech Republic, Denmark, Germany, Poland, Slovakia and Sweden, fiscal policy can be classified as sustainable. In the remaining economies the response of primary balance to public debt is either insignificant or excessively small. In depth analysis, conducted

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fiscal policy performance in different economies. This assessment can be more reliable due to the fact that it considers an important factor conditioning prudent fiscal policy, i.e. the role of fiscal variables in the market pricing of risk.

the analysis, in particular in the case of countries where the response of financial markets to the increase in public debt is stronger. It seems that the extended concept of fiscal sustainability presented in this paper can constitute a useful and policy-relevant tool for analysing

Appendix

Table A.1 Unit-root test results. Debt

Belgium Bulgaria Czech Rep. Denmark Germany Ireland Greece Spain France Croatia Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Romania Slovenia Slovakia Finland Sweden UK

Primary balance

Real interest rate

ADF

PP

ADF

PP

ADF

PP

2.73* 3.96*** 2.06 1.88 0.47 2.25 0.16 1.09 0.04 0.18 0.48 0.45 0.99 1.00 0.58 1.66 1.13 0.88 1.11 1.72 0.97 1.38 0.13 0.91 0.38 2.28 1.11

2.55 3.25** 1.99 2.02 0.19 0.98 0.05 0.15 0.28 0.30 0.44 0.07 0.96 0.64 0.49 1.75 1.60 1.15 1.09 1.88 0.01 0.59 0.52 0.85 0.02 2.12 0.05

1.45 6.11*** 3.10** 1.60 1.42 1.88 2.92** 1.37 1.83 2.04 2.51 7.22*** 2.20 2.24 2.09 2.33 1.80 2.05 3.24** 2.62* 3.36** 6.60*** 8.16*** 3.22** 2.46 2.75* 1.60

3.11** 6.13*** 5.14*** 1.85 1.76 4.66*** 4.27*** 1.80 2.62* 4.16*** 3.62*** 7.37*** 3.63*** 5.38*** 2.54 6.01*** 8.98*** 2.02 6.85*** 4.36*** 6.39*** 10.51*** 8.55*** 3.15** 1.93 2.87* 3.03***

1.03 3.38** 2.81* 2.57 1.27 2.33 2.32 3.72*** 2.50 3.47** 4.07*** 2.33 4.09*** 4.13*** 3.06** 4.58*** 3.44** 2.08 1.83 2.37 2.46 2.65* 3.11** 3.64*** 2.17 1.60 1.65

1.63 2.50 2.43 1.87 0.99 1.85 1.82 2.54 1.73 2.26 2.95** 2.60* 2.50 2.76* 2.10 3.23** 3.23** 2.35 1.19 2.05 2.11 3.11** 2.47 2.55 2.02 1.60 1.32

Source: own calculations.

Table A.2 Estimation results for the remaining coefficients in equations (8) and (9) (not presented in Table 1). Equation (8)

Belgium Bulgaria Czech Rep. Denmark Germany Ireland Greece Spain France Croatia Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Romania Slovenia Slovakia

Equation (9)

Lagged primary balance

Output gap

Exp gap

Adj. R2

Real interest rate in Germany

GDP growth

Adj. R2

0.56*** (0.06) 0.18** (0.09) 0.14 (0.09) 0.63*** (0.07) 0.37*** (0.06) 0.40*** (0.07) 0.28*** (0.09) 0.80*** (0.06) 0.43*** (0.07) 0.15 (0.12) 0.22** (0.09) 0.03 (0.09) 0.31*** (0.10) 0.38*** (0.08) 0.09 (0.07) 0.38*** (0.08) 0.27** (0.11) 0.39*** (0.07) 0.21*** (0.07) 0.39*** (0.11) 0.27*** (0.09) 0.34*** (0.08) 0.43*** (0.11) 0.29*** (0.07)

1.20** (0.49) 0.58***(0.22) 0.50*** (0.13) 0.44 (0.32) 0.18 (0.11) 0.00 (0.27) 0.05 (0.19) 0.66** (0.26) 0.34 (0.38) 0.39** (0.16) 0.20 (0.14) 1.29*** (0.46) 0.09 (0.08) 0.14 (0.09) 0.14 (0.14) 0.05 (0.19) 0.09 (0.33) 0.05 (0.18) 0.15 (0.14) 0.73*** (0.24) 0.57* (0.31) 0.12 (0.15) 0.28** (0.12) 0.002*(0.001)

0.76 (0.72) 0.74*** (0.10) 0.38*** (0.08) 1.22*** (0.30) 0.73*** (0.11) 1.17*** (0.11) 0.96*** (0.11) 1.39*** (0.24) 0.80* (0.44) 0.58** (0.26) 0.56*** (0.19) 0.82*** (0.09) 0.86*** (0.12) 1.11*** (0.11) 0.92*** (0.16) 0.89*** (0.11) 1.05*** (0.14) 1.25*** (0.23) 1.02*** (0.10) 0.60*** (0.22) 0.92*** (0.12) 0.87*** (0.10) 0.18*** (0.06) 0.52*** (0.10)

0.80 0.60 0.54 0.72 0.82 0.76 0.56 0.78 0.70 0.52 0.32 0.11 0.63 0.74 0.65 0.64 0.52 0.65 0.69 0.35 0.57 0.70 0.42 0.64

0.90*** (0.06) 0.31 (0.26) 1.61*** (0.14) 0.78*** (0.06) – 0.43* (0.24) 0.70 (0.53) 0.80*** (0.12) 0.73*** (0.78) 1.08** (0.43) 0.37*** (0.07) 0.58** (0.27) 4.03*** (0.61) 3.19*** (0.47) 1.26*** (0.17) 0.34 (0.27) 0.67*** (0.13) 0.51*** (0.15) 0.96*** (0.04) 0.42*** (0.10) 0.11 (0.10) 0.99* (0.50) 0.18 (0.23) 0.03 (0.19)

0.11** (0.05) 1.05*** (0.12) 0.01 (0.04) 0.06 (0.04) – 0.20*** (0.04) 0.51*** (0.10) 0.40*** (0.05) 0.07* (0.04) 0.23*** (0.07) 0.13*** (0.03) 0.28*** (0.05) 0.07 (0.08) 0.19*** (0.04) 0.08 (0.07) 0.04 (0.19) 0.03 (0.07) 0.16* (0.09) 0.06 (0.04) 0.06 (0.07) 0.56*** (0.08) 0.03 (0.10) 0.24*** (0.05) 0.16** (0.07)

0.80 0.59 0.75 0.74 – 0.38 0.68 0.70 0.83 0.51 0.32 0.52 0.79 0.78 0.65 0.26 0.42 0.50 0.95 0.18 0.56 0.30 0.43 0.03

(continued on next column)

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Table A.2 (continued ) Equation (8)

Finland Sweden UK

Equation (9)

Lagged primary balance

Output gap

Exp gap

Adj. R2

Real interest rate in Germany

GDP growth

Adj. R2

0.76*** (0.05) 0.40*** (0.06) 0.64*** (0.08)

1.20** (0.49) 0.22* (0.12) 0.81** (0.35)

0.76 (0.72) 0.49*** (0.18) 0.12 (0.34)

0.80 0.79 0.65

0.82*** (0.08) 0.58*** (0.15) 0.81*** (0.15)

0.10*** (0.03) 0.05 (0.04) 0.31*** (0.04)

0.75 0.76 0.80

Standard errors in parenthesis. *** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level. Source: own calculations.

Table A.3 Estimates of parameter α2 for different specifications of equation (8) and two estimation methods (2SLS, GMM)

Belgium Bulgaria Czech Rep. Denmark Germany Ireland Greece Spain France Croatia Italy Cyprus Latvia Lithuania Luxembourg Hungary Malta Netherlands Austria Poland Portugal Romania Slovenia Slovakia Finland Sweden UK

I 2SLS, output gap

II 2SLS, output gap, government expenditures gap, inflation, trade openness

III GMM, output gap, government expenditures gap

IV GMM, output gap, government expenditures gap, inflation, trade openness

0.09*** (0.02) 0.08*** (0.03) 0.21*** (0.03) 0.10*** (0.03) 0.08*** (0.02) 0.05 (0.03) 0.04** (0.02) 0.05*** (0.01) 0.01 (0.01) 0.06*** (0.01) 0.01 (0.01) 0.08** (0.04) 0.07*** (0.02) 0.10** (0.04) 0.02 (0.03) 0.11*** (0.03) 0.14 (0.11) 0.01 (0.03) 0.004 (0.03) 0.14*** (0.05) 0.04*** (0.01) 0.11** (0.04) 0.03** (0.01) 0.13*** (0.02) 0.01 (0.03) 0.10*** (0.01) 0.03** (0.01)

0.09*** (0.03)

0.08*** (0.01)

0.09*** (0.02)

0.10*** (0.03)

0.08*** (0.02)

0.09*** (0.03)

0.19*** (0.03)

0.20*** (0.03)

0.19*** (0.03)

0.11*** (0.03)

0.10*** (0.04)

0.08** (0.03)

0.08*** (0.02)

0.08*** (0.02)

0.08*** (0.02)

0.05 (0.03) 0.06*** (0.02) 0.05*** (0.01)

0.02 (0.03) 0.04 (0.02) 0.01 (0.02)

0.03 (0.04) 0.06** (0.03) 0.04** (0.02)

0.01*** (0.003) 0.04*** (0.01)

0.01*** (0.003) 0.06*** (0.01)

0.01** (0.003) 0.04*** (0.01)

0.01*** (0.002) 0.05 (0.04) 0.04** (0.02)

0.01*** (0.002) 0.07** (0.03) 0.04** (0.02)

0.01*** (0.002) 0.06* (0.04) 0.04*** (0.01)

0.05** (0.02) 0.03 (0.02) 0.14*** (0.03)

0.07** (0.03) 0.0003 (0.01) 0.10*** (0.03)

0.05* (0.03) 0.02 (0.02) 0.14*** (0.04)

0.01 (0.01) 0.001 (0.005) 0.003 (0.02)

0.01 (0.004) 0.0005 (0.004) 0.002 (0.02)

0.01* (0.01) 0.001 (0.01) 0.003 (0.02)

0.16** (0.07)

0.14** (0.05)

0.16*** (0.06)

0.05*** (0.01)

0.03*** (0.01)

0.05*** (0.01)

0.13*** (0.03) 0.05*** (0.01) 0.11*** (0.02)

0.08** (0.04) 0.03** (0.01) 0.10*** (0.02)

0.11** (0.04) 0.04** (0.02) 0.11*** (0.02)

0.03 (0.03) 0.12*** (0.03)

0.01 (0.004) 0.10*** (0.01)

0.03 (0.03) 0.12*** (0.04)

0.03 (0.02)

0.02 (0.02)

0.03 (0.02)

Note: Headings of the columns indicate estimation method and controls used. Standard errors in parenthesis. *** denotes significance at the 1% level, ** at the 5% level, and * at the 10% level. Source: own calculations

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