_{1}

This paper aims to investigate the sustainability of the general Greek government net borrowing, applying novel techniques for both to determine the order of integration of a difference stationary series and to specify the final form of the co-integration equation . Co-integration analysis was applied, and robust rules of thumb are suggested taking into account the individuality of the case un der consideration. The empirical application revealed that the Greek debt is not sustainable. Fur ther, we introduce consi stent planning methods to obtain optimal time paths for both government revenue and spending , so as sustainability of the debt to become a feasible task under certain as sumptions. Finally, we suggest a policy making approach on macrolevel combining co-integration with optimal contro l.

For the budget deficit to be sustainable, the government must run further budget surpluses (expressed in present value terms) equal to the current value of its liabilities. Although policy makers are concerned about the aggravation of budget deficit, economists look at the deficit issue from a different point of view. Instead of emphasizing the size of the deficit at any particular time-instant, they are more concern with the intertemporal budget constrain, which in turn focuses on the long-run path of expenditures and revenues. According to Hakkio [

In this context and considering some research works for countries where Greece included, Fountas and Wu [

Greece jointed the European Union (EU) in 1981 and adopted the euro in 2001 since it has achieved fiscal adjustments over the period 1993-1999, regarding the reduction of the general government deficit, the decrease in inflation and interest rates, together with the gradual increase of the primary surplus and GDP. Hence it was expected that Greece would accelerate its real economic growth and the social convergence with the other European countries. In the following years, the Greek economy exhibited an upwards trend, till the US financial crisis of 2008 that hit the world economy and severely affected the most European countries, given that some large financial institutions collapsed, and banks were bailed out by government aid. Although noticeable economic growth characterized Greece over the period 2000-2007, it was fatal that a policy which could not ensure sustainable progress has been adopted. In particular, the growth was based on domestic demand, mainly underpinned by private consumption due to the rising incomes. Besides, low mortgage rates led to the increase in residential investment and consumer credit expansion, resulting in high levels of borrowing both for the public and private sector. It is noted that in contrary to exports of goods and services, imports had an upwards trend contributing thus to the increase of current account deficit and the growth of the Greek general government deficit, in conjunction with the increased levels of public spending and the parallel decrease in revenues (Bank of Greece [

In 2009, Eurostat revised the data referred to the Greek budget deficit resulting to a considerable upwards reform revealing thus that the Greek fiscal problem was unexpectedly wider than it was estimated till then (Kouretas and Vlamis [

Under this economic pressure, Greece requested support from its European partners, as to restore sustainable growth. In this context, the European Commission (EC), European Central Bank (ECB) and International Monetary Fund (IMF) provided bailout loan rescue packages in order to help the government to pay its creditors and to straightly cover its operational needs. In return, Greek government signed for each loan a Memorandum of Understanding specifying the required policy measures to achieve a sustainable recovery regarding fiscal and financial sustainability, growth, competitiveness, investment and needed reforms in the public administration. The measures imposed mainly referred to immediate actions, including the decrease of public expenditure and the increase of public revenue via indirect taxes, taxes on luxury goods, firms’ profits and the reduce of tax evasion. Also measures regarding the freeze and cutback of wages and pensions, suspension in recruitment of public sector, abolishment of the 13th and 14th annual salary, privatizations as well as introduction of reforms regarding the benefit system and health care sector, in order to satisfy all requirements for achieving growth, competitiveness, and economic development. Although the imposed program aimed to stabilize the Greek economy, it had a devastating effect on Greece’s already weak economic recovery mainly due to the decrease in demand for goods and services, the enormous high rate of unemployment, the inefficient public sector, the reduced level of investments, the existing bureaucracy, the political and economic corruption and the hesitation of the government to undertake decisive reforms due to the political cost incurred. All the above leaded the Greek economy to a more severe recession including capital controls.

It is worthy to mention that some politicians and many rioting Greeks favor country’s default and return to the drachma (previous national currency), due to the Greece’s economic situation. However, the most efficient initial reaction is to realize the actual cause of this unfavorable situation that makes the future of Greece uncertain. Regarding expenditures mentioned above, it is true that some major public projects have been undertaken, such as the Venizelos International Airport, the Athens metro, the northwest highway known as Egnatia highway, the Rio-Antirio Bridge and other, due to 2004 Olympic Games. It should also be noted that the Olympic Games cost together with improvement infrastructure came up to 15 bill dollars (about 8% of GDP), although the initially estimated cost was about 6 bill dollars (Lynn [

In 2004, the Greek government faced a financial audit and the debt crisis begun in 2009. Greece was in debt over the entire time-period considered, with a rapid increase starting from 2002, as it is verified from ^{1}. During the period preceding EU entry (1981), the net borrowing gap reduced considerable as Greece attempted to meet up EU entry requirements as mentioned earlier. After that, the borrowing gap followed a smooth increase before rapidly growing in 2008-2009.

Apart from the complicated procedures to trace possible structural breaks of this form which are unknown a priory, a simple rule of thumb is to compute

where T denotes the number of observation points. When ^{2} to

This paper aims to investigate the sustainability of the general Greek government net borrowing. Novel techniques have been applied for both to determine the order of integration of a difference stationary series (DSS)

and to analytically specify the final form of the co-integration equation. Finally a proper policy planning is suggested by combining co-integration analysis and optimal control.

In section 2 we graphically present our data and in section 3 we investigate whether the government net borrowing is sustainable with an analytical discussion of the robust procedures adopted both, for determining the order of integration of the time-series considered, together with the relevant co-integration tests. Results together with some further considerations and additional remarks are presented in sections 4, 5 and 6 respectively, whereas conclusions are cited in section 7.

Following Hakkio and Rush [

that can be viewed as a possible co-integrating relation. In (2)

If the series

It should be recalled at this point that if the order of integration of a DSS series, say

is m < d. It should be emphasized that co-integration ensures long run equilibrium. In general, considering that the two time series are both I (d), then in case that the series

From

Our results are derived by properly applying co-integration analysis, taking into account the individuality of the case under consideration. Besides, instead of employing too complicated techniques (see for instance Camarero, Carrion-i-Silvestre and Tamarit [

both to determine the order of integration of a difference stationary series and to specify the final form of the co-integration equation.

The fairly new and robust approach proposed by Lazaridis ( [

Starting with n = 1 we estimate the following equation applying OLS.

It is clear that the model in (4) is a re-parametrized AR (q) with intercept, where a trend (

It is noted that for n = 1 its value is omitted from (4) and that

Next we proceed to test the hypothesis

To compare the computed F statistic we have to concern in this case the Dickey-Fuller F-distribution. In

Note that in order to reject (5), F statistic should be much greater than the corresponding critical values seen in

In our case for n = 1 and s = 3 we found

Since the lagged dependent variable is among the explanatory variables list, we have to consider statistic h, which can’t be computed in this case. Note however that the value of DW d is 2.05. The rule of thumb suggested, for being able to say that no autocorrelation exists, is to estimate the autocorrelation function of the residuals ^{th} column of

A practical way to trace heteroscedasticity is to detect the explanatory variable which yields the smallest p-value for the corresponding Spearman’s correlation coefficient

Sample size | α = 0.01 | α = 0.05 | α = 0.10 |
---|---|---|---|

25 | 10.61 | 7.24 | 5.91 |

50 | 9.31 | 6.73 | 5.61 |

100 | 8.73 | 6.49 | 5.47 |

250 | 8.43 | 6.34 | 5.39 |

500 | 8.34 | 6.30 | 5.36 |

>500 | 8.27 | 6.25 | 5.34 |

where T denotes the actual sample size considered during estimation.

In model (6), such a variable is

Considering the p-value we can accept the null (homoscedastic disturbances). As already mentioned, for large samples the statistic

Additionally, considering the Jarque-Bera statistic (0.298) and particularly the corresponding p-value (0.86), we accept the null (normal residuals, Jarque and Bera [

Thus with s = 3 (approximately

Hence, we increase the value of n (n = 2) and repeat the same steps considering the model

With s = 2, we found that according to the tests described above, the noises are white Gaussian. The value of F-statistic is: 3.35. Thus, the null seeing in (5) is accepted, and we increase once more the value of n (n = 3). Now the model to be estimated has the following form.

Values of k | AC | PAC | Q_Stat. (L-B) | p-values | Q_Stat. (B-P) | p-values |
---|---|---|---|---|---|---|

1 | −0.04014 | −0.04014 | 0.05333 | 0.81737 | 0.04833 | 0.82600 |

2 | −0.13103 | −0.13286 | 0.64200 | 0.72542 | 0.56341 | 0.75450 |

3 | 0.03393 | 0.02308 | 0.68292 | 0.87721 | 0.59794 | 0.89690 |

4 | −0.00437 | −0.01967 | 0.68363 | 0.95333 | 0.59852 | 0.96323 |

5 | 0.29652 | 0.30925 | 4.05999 | 0.54081 | 3.23630 | 0.66361 |

6 | −0.24257 | −0.25186 | 6.41369 | 0.37848 | 5.00157 | 0.54361 |

7 | −0.06193 | 0.02611 | 6.57376 | 0.47456 | 5.11663 | 0.64573 |

8 | 0.05781 | −0.05110 | 6.71957 | 0.56717 | 5.21687 | 0.73417 |

9 | −0.26808 | −0.28044 | 10.00491 | 0.35009 | 7.37288 | 0.59836 |

10 | −0.01144 | −0.11261 | 10.01119 | 0.43951 | 7.37680 | 0.68946 |

11 | −0.21148 | −0.19415 | 12.27093 | 0.34363 | 8.71852 | 0.64786 |

12 | 0.05717 | 0.03045 | 12.44524 | 0.41062 | 8.81657 | 0.71851 |

13 | 0.01587 | −0.08659 | 12.45945 | 0.49038 | 8.82412 | 0.78609 |

14 | −0.22149 | −0.04492 | 15.40285 | 0.35118 | 10.29582 | 0.74025 |

Indication: | r_{s} coefficient | Stand. error | t-statistic | df | p-value | |
---|---|---|---|---|---|---|

Value: | 3174.0 | 0.2939 | 0.1806 | 1.627 | 28 | 0.1149 |

Value of Z^{*} statistic to test the significance of Spearmans’ corr. coefficient r_{s} is: 1.583 |

With s = 2 we found that the noises are white Gaussian since the p-value of the J-B statistic is 0.099 and the autocorrelation function is analogous to the one presented in

We observe that the value of F (10.318) is greater than the corresponding critical values of

Regarding both series ^{3}, it is noticeable that we reached the same result even applying the rule of thumb mentioned earlier. Further, we computed at each stage together with the F-statistic, the Hansen’s statistics as well as the Cumulative Sums (CUSUM) and Cumulative Sums Squared (CUSUMSQ) statistics to trace any coefficients instability related to a possible shift. None of these tests revealed such instability. For better understanding the latter point we present in

According to Hansen [

Applying the same steps we found that

Since both series

COLLECTIVE SIGNIFICANCE TEST OF 2 COEFFICIENTS. The value of F (2, 24) statistic is 10.318 (p = 0.0006) | |
---|---|

Variables | Coefficient No. |

2 | |

t | 3 |

Variables | Estimated coefs. | Hansen statistics |
---|---|---|

0.016944 | 0.057857 | |

−2.284834 | 0.040101 | |

0.651961 | 0.081702 | |

0.176969 | 0.078151 | |

Intercept | −0.337598 | 0.065566 |

General Hansen statistic for all coefficients | 0.540877 |

estimating (2) we have a strong indication of coefficients instability as it is verified from the corresponding graph seen in

Thus, we have an indication for a possible regime shift as can be verified from the Hansen’s statistics presented next. The simplest way to trace the starting point (period) is to combine the indications provided by the two graphs presented in

As already mentioned, the coefficients instability can be analytically traced from the Hansen’s statistics presented in

Given that the critical value for α = 0.05 to test the coefficients individually is 0.47, and to test them collectively is 0.749, we can conclude that the coefficients instability detected may be due to a possible regime shift. The easiest way to face it is the introduction of a dummy variable (

- The coefficient of the newly introduced dummy is significant.

- The CUSUMSQ test together with the values of Hansen’s statistics don’t reveal any instability problem, and the value of J-B statistic favors the null (normality).

For the finally specified model all these are satisfied as can be verified from

It is noted that in many cases CUSUMSQ statistic is more sensitive than the corresponding CUSUM, and this is the reason for considering the first one.

With all these in mind, the dummy we finally introduced in (2), has the value of 1 for the years 1994 up to 2013 and the value of zero elsewhere. The estimation results are presented next.

Variables | Estimated coefs. | Hansen statistics |
---|---|---|

0.905046 | 0.483212 | |

Intercept | −3.821562 | 0.527181 |

General Hansen statistic for all coefficients | 0.899867 |

The CUSUMSQ statistic and the J-B and Hansen’s statistics are showed in

Since the critical value for α = 0.05 to test all coefficients stability collectively is 1.010, it is evident from

It is constructive to mention at this point, that in some cases more than one dummy variable must be introduced to the initial regression (2) following the same steps as described above. In any case, it is worthy to emphasize that according to the procedure analytically presented here, it is not necessary to divide the initial sample into sub-samples (see for instance Bajo-Rubio, Díaz-Roldán and Esteve [

Model (9) has been estimated applying OLS and then we obtained the series

Applying all conventional tests, we found that the order of integration of the series

Further, we have to perform some significance tests. Regarding the residuals presented in

From the estimation results seeing in (9), it is clear that the coefficient of

Variables | Estimated coefs | Hansen statistics |
---|---|---|

8.593422 | 0.161131 | |

0.339396 | 0.132500 | |

Intercept | 15.35933 | 0.143715 |

General Hansen statistic for all coefficients | 0.754934 | |

Jarque-Bera statistic | 2.615378 | |

p-value | 0.270444 |

1 | 0.509661 | 13 | 0.634294 | 25 | −1.305775 |

2 | −2.013371 | 14 | 1.023527 | 26 | −0.126511 |

3 | 0.274069 | 15 | −5.457256 | 27 | −0.205329 |

4 | 0.672840 | 16 | −2.798439 | 28 | 0.619239 |

5 | 0.812143 | 17 | −1.477005 | 29 | −0.4592285 |

6 | −0.160461 | 18 | −0.208771 | 30 | −3.939049 |

7 | 0.563721 | 19 | 1.507164 | 31 | −1.651150 |

8 | 1.369938 | 20 | 2.324970 | 32 | 0.683041 |

9 | −0.552626 | 21 | 3.186874 | 33 | 2.810177 |

10 | −2.450771 | 22 | 1.570400 | 34 | 4.059738 |

11 | −1.177298 | 23 | 0.979912 | ||

12 | 0.494329 | 24 | −0.113010 |

testing the hypothesis

where the second part of the inequality is the critical value of t-statistic for certain level of significance α and 31 degrees of freedom (df). For

The most crucial step is to test the hypothesis

Since

It should be emphasized that all these tests refer to coefficient b and not to its estimate

Finally, due to (11) we can say that the debt is not sustainable but we have the weak form of deficit sustainability as defined by Quintos [

It was mentioned earlier that Fountas and Wu [

Applying the procedure analytically presented here, we found that the empirical findings do not satisfy the strong form of deficit sustainability defined by Quintos [

According to our empirical findings it is evident and very encouraging that EU entry did not substantially contribute to the Greek crisis, neither the fact that Greece joined the euro area in 2001. Instead, we can say that the general elections of 1996 contributed to an increase in Greek government spending since the government started from 1994 to increase any provisions, benefits and allowances mainly to its voters, something that is a common practice for almost all governments in Greece. Further the finance of large public infrastructure projects, already mentioned, contributed to the unsustainable Greek deficit. Also, military expenditures (as percent of GDP) begun to rise again from 1994 with a pick at 2000 (about 3.6%), having a proportional contribution to the government’s deficit.

It is recalled that in the co-integrating equation,

Observing

It may be constructive to recall at this point that the QUSUM and QUSUMSQ statistics are computed from the recursive residual. The number of these residuals is equal to the number of the observation points minus (m + q), where m denotes the model coefficients and q (≥0) is the number of possible singular bases detected and thus the observations to be skipped in the computational process (see the numerical example in Lazaridis [

Using the levels of

regarding revenue, where r multiplied by 100 denotes the mean annual rate mentioned above.

After many experiments aiming to obtain a feasible solution assuring sustainability of the debt and avoiding at the same time any radical distortion of the observed mean annual rates we end up to the following issue: Increasing the annual mean rate of

Since 2.55 > −1.69552 we accept the null i.e.

We strongly believe that this is the basic rule to face the problem of debt sustainability. In this context, the decision makers have to first define the optimal trajectories of both ^{4}). Obviously, some reforms may be required, and these should be considered as the major topics for bargaining

and negotiation with the EU and IMF authorities. In this context, optimal control can be applied to provide detailed numerical indications regarding the measurements required to retain these trajectories for ^{5}. In brief, the most efficient planning over a predefined planning horizon for say N years is summarized in what follows.

- Determine the average annual rates of increase for both revenue and expenses so that the series

- Solve the optimal control problem to obtain analytical indications for every time-period regarding the measures required to attain the desired paths mentioned above in the closest possible way.

- In case that the measures required can be afforded, then the problem of making the debt sustainable has been solved.

- If the measures required to make feasible the optimal paths are unattainable, and a possible haircut or debt restructuring cannot be considered, then it is inevitable for the government to default on its debt.

Going through the relevant works on this subject, one gets the impression that a ready-made standardized formula has been adopted in many cases. In other words, in most of the works known to the author, a conventional style of co-integration analysis is adopted, that is the variables in the co-integration equation are all I (1), and applying the Dickey-Fuller [

In this context we mention that Shin [

This paper aims to examine as to whether general Greek government net borrowing is sustainable, applying novel, simple and easy to understand techniques for both to determine the order of integration of a difference stationary series and to specify the final form of the co-integration equation. We have analytically presented the case where the series considered are not I (1) as assumed in most relevant studies and analyzed the methodology to find the answer as to whether the Greek debt is sustainable by applying co-integration analysis in conjunction with suggested robust rules of thumb. According to our findings, we can conclude that the Greek government debt is not strongly sustainable, since we face the weak form of sustainability.

In addition, some propositions are clearly stated as to whether this debt can be finally turned up to become sustainable under certain assumptions. In this sense, we introduce consistent planning methods to obtain optimal time paths for both government revenue and spending, so as sustainability of the debt to become a feasible task. Finally, we suggest a policy making approach on macrolevel combining co-integration with optimal control.

The only limitation of this study refers to the moderate size of the available sample. The period 1980-2013 however, is characterized by some significant macroeconomic, political and social reforms leading to a more open, integrated and hence more globalized Greek economy. With this in mind, our intention was to propose an efficient method we haven’t met in the relevant literature, based on a reliable sample obtained from IMF [

Anna Maria Mouza, (2016) Sustainability of the Greek Government Net Borrowing: An Analytical and Comprehensive Exposition. Theoretical Economics Letters,06,768-782. doi: 10.4236/tel.2016.64081