Have Public Finances in the OECD Area Been Sustainable?

Abstract The aim of this article is to test, from an empirical standpoint, the existence of sustainable public finances in the Organisation for Economic Co-operation and Development (OECD) area as a whole, over the most recent period of the world economy, 1973-2016. The research methods include not only standard stationarity tests, but also tests, which allow for a structural break. The relevant results of this research are a stationary public budget balance expressed as a percentage of GDP and a debt to GDP ratio that is stationary in first differences. According to the literature, this means that a “necessary and sufficient” condition is fulfilled for proving the existence of a strong sustainability. We hope this research can make a valuable contribution to the debate regarding public finances in the world economy. To obtain other relevant conclusions, additional tests will need to be performed in the future in order to assess which members are contributing to the fiscal sustainability of the OECD aggregate.


INTRODUCTION
In the theoretical literature, it is possible to find a number of similar definitions for sustainable public finances / fiscal policy sustainability. These definitions are founded on the premise of the government's solvency.
According to Blanchard et al. (1990), a sustainable fiscal policy can be defined as a policy that makes the ratio of debt eventually converge back to its initial level. On the other hand, as pointed out by Chalk and Hemming (2000), it requires that today's debt should be matched by an excess of future primary surpluses over primary deficits at current values. Adopting a similar position, the European Central Bank (2011) defined fiscal sustainability as the government's capacity to service its debt obligations in the long term, which means that a government that has outstanding debt therefore has to produce primary surpluses in the future, and these have to be large enough to accommodate the cost of servicing the government's debt obligations.
European Commission (2016) also stated that the sustainability of public finances, sometimes referred to as fiscal sustainability, is the ability of a government to sustain its policies in the long run without threatening the _______________________________________________________________ 2018 / 32 37 government's solvency or without defaulting. Therefore, a fiscal policy can be considered as unsustainable if, over time, it leads the government away from solvency.
Based on this concept of sustainability -associated with the government's solvencysome academic studies have been conducted with the aim of testing the sustainability of public finances / sustainability of fiscal policy in many different countries. However, it was not possible to identify any study that so far has analysed the sustainability of finances in the Organisation for Economic Cooperation and Development (OECD) area as a whole; meaning all the thirty-five member countries assessed as if they were one body.
Assessing the sustainability of this economic aggregate is an interesting issue, since it is composed of many different realities presented in more than one continent, which have been subjected to various shocks over the last decades. Taking this into account, the main aim of this article is to test the existence of sustainable public finances in the OECD over the most recent period of the world economy 1 ; starting in 1973, and ending in 2016. This is a relatively broad time horizonslightly over four decadesfor which comparable data relating to the public finances are available.
After the present introduction, Section 1.1 provides a brief analysis of the data. This is followed by Section 1.2, in which a framework for the empirical approach is presented. In Section 2, the sustainability of the OECD economy is tested and the results are analysed. Finally, the conclusions are documented.

The Public Finances Data: Brief Analysis
Official statistics of public finances for a relatively long time horizon, and for different nations and economic aggregates (for example, the OECD area or the euro area), is available in the OECD databases. Based on those statistics, it is possible, first of all, to analyse the evolution of the OECD area public revenue and expenditure as a percentage of GDP.
Thus, through a close observation of Figure 1, it is possible to highlight some relevant facts with regard to the behaviour of these two variables during the most recent period in the world economy, 1973-2016. First of all, it can be seen that, despite various oscillations, public revenue and expenditure (% of GDP) as a whole showed a slight tendency to increase in the period under analysis.
Secondly, it can be seen that there were sharp increases in public expenditure in the following sub-periods: 1974-1975, 1980-1982, 1991-1992 and 2008-2009, which were not accompanied by increases in revenue of a similar size. As far as the first two sub-periods of increases are concerned, in Table 1, we present the value of public expenditure (% of GDP) in a sample of some OECD countries for the years 1973, 1976, 1979 and 1982. In table 1, it can be seen that there were significant increases; in some of the countries, there were increases of more than 10 percentage points (pp). These years correspond to the disturbances related to high oil prices / oil shocks (BP, 2016).
The 1970s and the early 1980s are in fact considered in the relevant literature as turbulent times characterised by economic adversity (Llewellyn, 1983;Black, 1985).
On the other hand, in the third sub-period (1991)(1992), most of the OECD countries that are considered in Table 1 displayed a more moderate increase in public expenditure (% of GDP) 2 . However, Finland and Sweden were exceptions. In these two countries, the public expenditure ratio rose from 47.9 and 56.5 of GDP in 1990 to 61.7 and 66.9, respectively, in 1992. Such changes represent significant increases in a relatively short time.
The beginning of the 1990s is in fact connoted, in the international context, with economic depression in the so-called "economic twins". Between 1990 and 1993, Finland and Sweden's GDP fell in real terms by 3.4 % and 1.5 % per year, respectively (the author's own calculations, using the data taken from the World Bank, 2017). Some authors attribute this crisis to the financial deregulation that occurred in the mid-1980s (Jonung, Kiander & Vartia, 2008;Chabert & Clavel, 2012) Finally, the last most obvious increase in the OECD area public expenditure was in 2008-2009 (see Figure 1). These were the years that marked the intensification of the global financial crisis (European Commission, 2009) and to avoid a more prolonged recession, one of the main remedies adopted was expansionary measures (European Commission, 2008).
In Table 2, we present a new sample of public expenditure in the OECD countries, where it can be seen that in this short period of time, there were significant increases. It is also important to stress that for the entire period of 1973-2016, the OECD area public revenue was always lower than expenditure (see again Figure 1). Consequently, there was not a single positive balance in its public accounts during the entire time horizon. However, it should be noted that the sub-period 2008-2012 stands out because of the higher deficits recorded as a percentage of GDP, as shown in Figure 2. Note 1: the OECD public deficits (% of GDP) were obtained from the difference between the public revenue (% of GDP) and the public expenditure (% of GDP) presented in OECD (2017). Note 2: the OECD public debt (% of GDP) was calculated by the author, using the data from AMECO (2017) and IMF (2017). For more details, see Table A1 in the Appendix.
Consequently, this meant a sharp rise in the debt ratio in those same years 3 , a period which covers the time of the global financial crisis and the euro area sovereign debt crisis (one of the effects produced by the 2008 crisis).
In general, it is also possible to conclude that, despite several oscillations, the OECD area public debt ratio showed a clear tendency to increase when one considers the period as a whole. This trend meant an increase of forty-five percentage points (pp) when comparing the value recorded in 1973 with the one recorded in 2016.
_______________________________________________________________ 2018 / 32 41 But does this evolution mean that the OECD area public finances were unsustainable during the most recent period of the world economy, 1973-2016? How can we obtain an answer to this question based on the data that we have just briefly analysed?

Empirical Approach: Public Finances Sustainability
It is possible to present the concept of sustainable public financesbased on the idea of the government's solvencyfrom an algebraic standpoint. To do so, we need to resort to the government's budget constraint, which can be displayed in real terms, as follows 4 : where 5 the primary expenditure (expenditure without interest) at time t; the revenue at time t; the real interest rate in period t paid to public debt holders; and −1the public debt in period t and in period t -1. The above equation can also be expressed as follows: By making a set of algebraic transformations, it is possible to deduce the government's budget constraint for successive periods, resulting in the so-called intertemporal budget constraint. Assuming that the real interest rate is stationary (r), and making some changes, we will have: Considering as the primary expenditure in period t plus the real interest payments (with interest rates around r), we have: From the last equation, and proceeding to a set of successive recursive substitutions, we can obtain the designated intertemporal budget constraint: A sustainable fiscal policy would therefore require the following condition: Thus, a sustainable fiscal policy should ensure that the value of the public debt tends towards zero. In other words, the public debt cannot continue to grow indefinitely at a higher rate than the real interest rate.
In addition, this means that the government must have future real primary balances that have a value equal to the real debt stock in the initial period: There are some empirical procedures that make it possible to validate these conditions. One of these procedures is associated with Trehan and Walsh (1991). This procedure requires that the stationarity of public debt should be tested: if the public debt is a stationary series in levels, I(0), or, in first differences, I(1), then the condition given by equation (7) will be respected. The latter case is conceptually equivalent to having a stationary public budget balance.
Thus, Trehan and Walsh (1991) considered that, in a context in which the expected real rate of interest is constant, the stationarity of the public budget balance, I(0), is a necessary and sufficient condition for a sustainable fiscal policy when the public debt is I(1).
Another procedure is attributed to Hakkio and Rush (1991) and involves testing public revenue and expenditure. Given that the intertemporal budget constraint can also be written for the variables in first differences, we have: Considering that = -, after applying the no-Ponzi scheme, we will have the alternative equation (10): Assuming that R and E are non-stationary variables, but that their first differences are stationary, the left side of the equation will also have to be stationary. Thus, the procedure proposed by Hakkio and Rush (1991) assumes that GG and R are both I(1) and involves testing the cointegration between them. This means testing the regression, = α + β · + , with the following two options: 1) the null hypothesis, and , both integrated of order 1, I(1), are not cointegrated, and 2) the alternative hypothesis, and , both integrated of order _______________________________________________________________ 2018 / 32 43 1, I(1), are cointegrated. Note that these authors considered it more appropriate to use ratios for growing economies when testing the variables. According to Hakkio and Rush (1991), it is a necessary condition for the sustainability of fiscal policy that GG and R should be cointegrated. This is also conceptually equivalent to having a stationary public budget balance.
In summary, according to the literature quoted here, the "necessary and sufficient" conditions for sustainable public finances / sustainable fiscal policy requires a stationary public debt (or a first difference stationary public debt) and also a stationary public budget balance (or a cointegration between revenue and expenditure). In this context, and following Quintos (1995), we can also talk about "strong sustainability".

EMPIRICAL RESULTS
In order to empirically test the sustainability of the OECD area public finances in the period 1973-2016, the following variables were chosen (expressed in the form of annual time series data): debt to GDP ratio ( ), public expenditure as a percentage of GDP ( ), revenue as a percentage of GDP (ρ ) and the public budget balance as a percentage of GDP ( ).
Before performing the tests, it is customary to analyse the behaviour of the variables graphically. Taking into account Figures 1 and 2 presented in Section 1.1, we may suspect that with the most probable exclusion of the public debt (as a percentage of GDP), there is the possibility of the remaining variables being stationary in levels, I(0).
To confirm this perception, the most commonly used unit root and stationary tests are chosen: the ADF (Dickey & Fuller, 1979) and the PP (Phillips & Perron, 1988), which take as their null hypothesis (ℎ 0 ) that there is a unit root. Also, the KPSS test (Kwiatkowski et al., 1992) is selected, which takes as its null hypothesis (ℎ 0 ) that there is stationarity.
The conclusions of tests for all the variables under consideration are presented in Table 3.
The intersection of the results allows us to conclude that the debt ratio as a percentage of GDP is stationary in first differences, I(1); only the KPSS test showed a different result. On the other hand, the combination of the results of tests on the expenditure and revenue ratio tells us that both variables are stationary in levels, I(0) 6 ; in the case of revenue, only the ADF tests showed another result. As far as the public budget balance is concerned, all the tests present I(0) as their result.

Table 3. Conclusions of the stationary tests
According to the literature, these results allow us to conclude that the necessary and sufficient condition for sustainability is met. This means that, when evaluating the OECD economy as a whole, its public finances were strongly sustainable over the 1973-2016 period.
In addition to the standard unit root tests, it is also possible to perform tests allowing for a structural break 7 . These are modified ADF tests and present as their null hypothesis (ℎ 0 ) the presence of a unit root with a possible break. The breakpoint is determined by finding the minimum value for the DF statistic in the residuals. However, there are different tests that can be performed, based on four alternative models: 1) Non-trending data with intercept break (Model 0)tests a random walk against a stationary model with intercept break; 2) Trending data with intercept break (Model 1)tests a random walk with drift against a trend stationary model with intercept break; 3) Trending data with intercept break and trend break (Model 2)tests a random walk with drift against a trend stationary model with intercept and trend break; 4) Trending data with trend break (Model 3)tests a random walk with drift against a trend stationary model with trend break.
These tests can also be performed in a sequential manner (by starting with Model 0 and stopping at the model that presents evidence of stationarity). The conclusions of this process in relation to our variables are presented in Table 4. Note: For more details about these results, see Table A5 in the Appendix. 6 If revenues and expenditure are I(0), this means sustainability. For obvious reasons, it does not make sense to perform cointegration tests. 7 Perron (1989) pointed out that, in certain cases, a trend-stationary process with a break could be almost observationally equivalent to unit root processes. In such cases, the standard tests may lead to the conclusion of the presence of a "false" unit root when there is, in fact, a trend-stationary process with a structural break.
_______________________________________________________________ 2018 / 32 45 Comparing these conclusions with the ones that were obtained with the standard stationary tests, it can be seen that there is a divergence with respect to which now appears to be I(1), i.e. with a different order of integration to ρ , which, in turn, is now trend-stationary in the presence of a structural break. On the other hand, as remains as I(0) and as I(1) in the presence of a structural break in the year 2007, there is enough evidence to confirm that the necessary (stationary public budget balance) and sufficient (stationary public debt ratio) conditions continue to be met (despite the unfavourable results regarding revenue and expenditure).
Therefore, in the presence of a structural break, we may also conclude that the public finances of the OECD area were sustainable over the 1973-2016 period 8 .

CONCLUSION
The public finances in the OECD area as a whole were strongly sustainable during the most recent period of the world economy, 1973-2016.
This empirical statement is based on the results obtained with different stationarity tests. Firstly, the ADF, PP and KPSS tests showed a stationary public budget balance as a percentage of GDP, a stationary public revenue and expenditure as a percentage of GDP, and also a debt to GDP ratio that was stationary in first differences. This set of results represents a "necessary and sufficient" condition for "strong sustainability". Secondly, the stationarity tests, which allow for a structural break, also showed a stationary public budget balance as a percentage of GDP and a debt to GDP ratio that was similarly stationary in first differences. This means that the "necessary and sufficient" conditions for fiscal sustainability are also robust in the presence of a structural break in data.
The conclusion on the strong sustainable public finances over the period 1973-2016 is especially interesting if we take into account the problems in the world economy that marked this period and seriously affected the OECD countries, such as two oil shocks, and an international financial crisis already in the present century (the most severe since the Great Depression).
We hope that this research may make an important contribution to the debate regarding public finances in the world economy. The results presented do not, however, signify that there has been individual sustainability in all of the OECD member countries. Thus, it is our intention to perform additional tests (namely stationarity tests) in the near future, in order to assess which members are contributing to the fiscal sustainability of the OECD aggregate and which ones are not.  Source: Own calculations using Eviews (2017). Note 1: *, ** and *** denote rejection of the null hypothesis (h0) of a unit root at the 10 %, 5 % and 1 % levels. Note 2: the maximum lag was chosen using the rule provided by Schwert (1989). The actual lag was obtained automatically by Eviews (2017) using the Schwarz Info Criterion (SIC). Source: Own calculations using Eviews (2017). Note 1: *, ** and *** denote rejection of the null hypothesis (h0) of a unit root at the 10 %, 5 % and 1 % levels. Note 2: the actual lag was obtained automatically by Eviews (2017) (2017). Note 1: *, ** and *** denote rejection of the null hypothesis (h0) of stationarity at the 10 %, 5 % and 1 % levels. Note 2: the actual lag was obtained automatically by Eviews (2017) using the New-West automatic selection of bandwidth. 2009 -6.31*** Stationary Source: Own calculations using Eviews (2017). Note 1: *, ** and *** denote rejection of the null hypothesis (h0) of a unit root at the 10 %, 5 % and 1 % levels. Note 2: the maximum lag was chosen using the rule provided by Schwert (1989). The actual lag was obtained automatically by Eviews (2016) based on the Schwarz Info Criterion (SIC).