ASSESSING THE FISCAL SUSTAINABILITY OF GOVERNMENT FINANCES IN EUROPEAN COUNTRIES

This paper analyses the fiscal sustainability of government finances in the 27 EU countries and Norway using an empirical, statistical approach and ADF tests for a unit root in the time series of the differences between the GDP growth rate and the long-term interest rate, and the primary balance.


Introduction
The fiscal sustainability of government finances has become a critical issue for many countries around the world after the financial crisis of 2008, especially in the Eurozone that has been hit hard.These countries faced downfalls in key macroeconomic indicators such as GDP growth rates and government revenue, simultaneously with increasing government expenditures and debt stock.Greece, Spain, Portugal and Ireland are the examples of countries with debt and solvency problems.
This article analyses the fiscal sustainability of government finances using an empirical approach and statistical tests.

Sustainability framework
A government finances a budget deficit through the issuance of debt when that country's expenditure exceeds revenue [4]: Deficit financing = Net issuance of debt + Seigniorage (1) or expressed in mathematical notation as: where t -time, t G -government expenditure, t T -government revenue, t B -quantity of public debt at the end of period t, t M -monetary base at the end of period t.
If we subtract interest payments (I t ) from both sides of equation ( 2) we get: . (3) Since [ ] is the primary balance, we obtain: where t X is the primary balance in time t.
The identity (4) is the government budget constraint and the central concept of fiscal sustainability analysis.

Assessing the Fiscal Sustainability of Government Finances in European Countries
Another key indicator is the inter-temporal budget constraint, which states that the government finances its initial debt by the present value of future primary surpluses:

Empirical and statistical analysis in assessing fiscal sustainability
There are four important variables in assessing fiscal sustainability: Primary balance to GDP, Public Debt to GDP, Long-term interest rate and GDP growth rate.We are going to investigate the effect of these variables on the fiscal sustainability of government finances.
The budget is said to be balanced if government revenue equals its expenditure.We believe that countries tend to have a balanced budget process in the long-run (eventually all revenues and expenditures must equal).We cannot say that about the short-run or medium-run and this is the task of fiscal sustainability analysis.
Let's look at the box plot for the sample of the primary balance to GDP ratio in percentages for 28 countries from 1997-2012 in figure 1, on the left (the list of the countries includes the 27 EU countries and Norway).As we can see, the shape of the data is quite symmetric (a little bit right-skewed with extreme observations) and centered approximately around zero.Although this dataset has some very extreme observations from -27.67% of primary deficit to 20.25% primary surplus, we would like to concentrate on most of the observable data and treat negative extreme observations as the ones when country definitely has fiscal problems.On the other hand, positive extreme observations may tell us that the government generates high surpluses in order to reduce its debt burden faster.We can eliminate outliers in our sample from both ends and try to get robust estimation for the mean in order to test a country's ability to repay its debt.
Table 1 shows summary statistics for two datasets: with and without outliers respectively.We can see that the mean, median, first quartile and third quartile haven't changed much after removing outliers.
Figure 2 shows Quantile-Quantile plots for the sample with (on the left) and without (on the right) outliers.As we see, the distribution of the sample without outliers approximately normal.We can also observe this in figure 3, which shows the same distribution.
As we mentioned above, the budget process should be balanced in the long-run because in the end all revenues must equal expenditures.Now let's test the hypothesis that the average ratio of the primary balance to GDP equals zero using the sample of primary balance to GDP ratios without outliers.
One Sample t-test: H 0 : µ = 0 (the average ratio of the primary balance to GDP equals zero).H A : µ ≠ 0 (the average ratio of the primary balance to GDP does not equal zero).t = 1.729, df = 426, p-value = 0.08454 95% confidence interval: (-0.0377, 0.5896) The p-value = 0.08454 > 0.05, so we fail to reject the null hypothesis that the average ratio of the primary balance to GDP is equal to zero.
Based on the results we obtained from our test, we can suggest that in the long-run countries have indeed a balanced budget process, so that revenues must equal expenditures.

Assessing the Fiscal Sustainability of Government Finances in European Countries
The distribution of the public debt to GDP ratios for the 28 countries from 1997 to 2012, shown in figure 4, has mean 51.7% (95% confidence interval: 48.97, 54.43) and standard deviation 29.39%.This distribution is right-skewed.Now let's look at figure 5, it shows the box plots of primary balances to GDP for all 28 countries from 1997 to 2012.The horizontal red line is the mean of the primary balance to GDP ratio which equals zero as we suggested above.The two dashed blue lines are the standard deviations for the sample without outliers (-3.30, 3.30).We can observe that 23 or 82% of the country medians are less than one standard deviation and none of them are less then one negative standard deviation.We also calculated that none of the country means is below the negative threshold of -3.3%.We would like to take that fact as an indicator for assessing fiscal sustainability, so if the country has primary balance (primary deficit) to GDP ratio less than -3.3% in a particular year then it has a risk of having unsustainable government finances.Figure 6 shows box plots of the public debt to GDP ratio for the 28 countries from 1997 to 2012.The horizontal red line is the mean of the public debt to GDP ratio (51.7%).The two dashed blue lines are the boundaries of one standard deviation from the mean of the public debt to GDP ratio (51.7% -29.39%, 51.7% + 29.39).We see that only three countries have medians which are more than the upper bound: Belgium, Greece and Italy.We would like to take that fact also as an indicator for assessing fiscal sustainability.If country has a ratio of public debt to GDP in a particular year of more than the upper bound (81.09%) than it has a risk of having unsustainable finances.Taking into account our indicators, we split the countries first by the critical value of the primary balance to GDP ratio of -3.3%, because having sufficient primary surpluses is crucial for sustainable government finances.The obtained sample we split again by the critical value of the public debt to GDP ratio of 81.09%.The result is presented in table 3.This table tells us that countries started to have risks of having unsustainable government finances after financial crisis in 2008.Greece is observed almost in every year, except 2011.For this country, the stock of debt is rising each year coupled with primary deficits, high interest rates and negative GDP growth rates.

Fig. 1 .
Fig. 1.A sample of 448 primary balances to GDP in percentages for 28 countries from 1997 to 2012Source: AMECO database -European Commission and author's calculations.

Fig. 2 .
Fig. 2. Quantile-Quantile plots for the sample of primary balances with and without outliers (left and right panel respectively)

Fig. 5 .
Fig. 5. Box plots of primary balance to GDP by country from 1997-2012 Source: AMECO database -European Commission and author's calculations.

Fig. 6 .
Fig. 6.Box plots of public debt to GDP by country from 1997-2012 Source: AMECO database -European Commission and author's calculations.

Table 1 .
Summary statistics for the samples of 448 primary balances to GDP

Table 2 .
Summary statistics for the samples of 448 public debts to GDP

Table 3 .
Countries with a potential risk of unsustainable government finances