A New Approach on Country Risk Monitoring

Abstract

Most of indexes regarding Credit Rating of the national debt bonds are associated to Gross National Product, which involves the well-known Keynesian Multiplicator of the IS-LM Equilibrium. Specifically, a common way of Sovereign Debt evaluation is its percentage of the Gross National Product in terms of a spot value. Another index is the spot value of the percentage of the annual interest rate payments of the state to the owners of sovereign debt. These indexes provide an inefficient evaluation of the national debt and moreover they are sensitive in their calculative aspect. Hence, we propose another index of national debt evaluation, which is more realistic, since public debt is a part of the balance sheet of the state itself. Moreover, this index may be translated into growth variables of the national economy. Since Gross National Product relies on consumption of the Economy, more consumption implies an ’illusion’ about sovereign debt. On the other hand, this index has limits to its credibility because it depends on the size of the annual investments.

1. Introduction

1.1. Different Approaches of the Sovereign Debt Crises in Research

A sovereign debt crisis is a sudden stop paying the lenders of the state by the state itself. A reference for this ‘naive’ definition arises in seminal works about this topic, like Eaton et al. (1986). The meaning of the word ‘sudden’ implies that the nominal amount of the debt is too large, such that it cannot be separated into smaller payments for the state at the time of default. In Hatchondo and Martinez (2009) a stochastic consumption approach of the sovereign debt, where the utility of the state is obtained through the consumption factor for the state itself. In Hatchondo and Martinez (2009), the income of the sovereign bond owner is a time-series model, which is actually an AR(1) time series. This time-series assumes a prior probability distribution between two sequential time-periods t and $t+1$. This Markovian setting is also present in Soytaş and Volkan (2016). The authors in Soytaş and Volkan (2016) actually fit the above model. The importance of low tax collection inside the crises time period is essential in a more realistic approach of Public Debt Rating, is analysed as a low liquidation equilibrium problem of the private sector, in Arellano and Kocherlakota (2014). In Aitken (2020), the author is aware of that Gross National is not proper for the sovereign debt examination. In Tomz and Wright (2007), authors show that increasing Gross National Product is increasing at least before the exact time of sovereign debt’s default. Gross National Product may be increasing, even in the case of national debt crisis. This approach is also present in Aguiar and Gopinath (2006) and Amador and Phelan (2021).

This assumption implies that a nice contract form is the one which sovereign debt has a limited-time time of maturity. The approach appearing in Rampini (2005) refers to the properties of the state as a representative agent. In such a case, the total endowmet assures the debt repayment, while the repayment schedule implies that the maximization of the representative agent’s utility may be achieved. A constant absolute risk aversion is an assumption, which is supposed for the state’s behaviour. In practice, the common point in fiscal policy implied by these papers is practically the same one: The best fiscal policy such that the state is able to afford sovereign debt is a constant tax policy and a constant rate of gonverment’s income, which has to be combined by a high initial government’s income. This is exactly the best policy implied by the present paper, as well. The expectations for the receipt in the state balance sheet have to be ‘fulfilled’ in short-time intervals. This is exactly the policy implication of Eaton and Gersovitz (1981). A similar policy is also implied in Bulow and Rogoff (1989). Moral Hazard types of assymetric information is present in the case of countries, through he last sovereign debt crisis of 2008. Borrowing institutions were not willing to lend countries of lower rate of state’s income. The presence of moral hazard is unfortunately the essential cause for national debt crises. Information assymetries in sovereign debt were studied in Atkeson (1991); Cole and Kehoe (2000) and Reinhart and Rogoff (2011). The bad effects of tax policy if the governmment imposes a tax riot in order to avoid default, is entirely studied in Bassetto and Phelan (2008). Tax riot is actually a ‘sudden’ change in the tax policy, under which government expects to receive income in a short-time period. Authors prove that a tax riot does not achieve its aim, because households underreport their incomes, precisely because other households are expected to do so as well. In Atkeson (1991), the author also refers to the risk of repudiation, which is entirely applied in the countries of European Union. This is the exact topic of Diamond (1984). In Kocherlakota (2001), the author’s conclusion is that the best collateral investment is sovereign debt bonds. This conclusion implies that a private debt abnormal behaviour is a consequence of the public debt issue abnormal behaviour, since state bonds cannot insure the private endowments in this case. In Schneider and Tornell (2004), authors prove that since a bailout level of borrowing in a competitive firm is provided, a possibility of a bankruptcy is not prevented. The point of view of our paper is public debt is alike the current assets of a competitive firm. This point of view does not imply better policy, in order to prevent sovereign debt in a future time period. It is actually a way of better monitoring the sovereign debt. A significant paper on sovereign debt study, whose content is similar to the above is Medas et al. (2018).

A review of the research made in this direction, is written in Oetzel et al. (2001). We remind that the global financial crisis refers to the 2008 subprime crisis starting in the United States and having global consequences. Since the 2010 EU sovereign debt crisis had similar international consequences, the reent study Floros et al. (2024) obtained recently employed data only up to 2016, because they targeted only the examination of these financial crises.

1.2. Sustainability of National Debt

IMF is the abbreviation used about International Monetary Fund below. The present paper is devoted to the indexes being used by IMF for Public Debt Rating. We also emphasize on the role of private consumption in Public Debt Rating Models.

As it was indicated in (International Monetary Fund 2016a, p. 4) in the case of Greek National Debt evaluation, the change of the present stock regime of evaluation ${\displaystyle \frac{F_t}{GN{P}_t}}$, where $F_t$ is the total nominal debt and $GN{P}_t$ is the Gross National Product at the year t, to a flow regime of evaluation ${\displaystyle \frac{D_t}{GN{P}_t}}$, where $D_t$ denotes the total financial needs of Greece, and $GN{P}_t$ is the Gross National Product at the year t. Hence, by this IMF report concerning Greek National Debt evaluation regime, we may quote in general on the weakness of every evaluation regime relying on GNP, either this index is a stock index, or a flow index. The opinion of IMF on the use of each index is relative to the National Debt situation. For example, we may notice that in the case of Iceland, where the macroeconomic situation is better than Greece, in (International Monetary Fund 2016b, p. 5) of IMF Report’s on Ireland, the flow index of current deficit of Iceland as a percentage of $GN{P}_t$. In the case of Portugal, the recent IMF Report (International Monetary Fund 2017, p. 11) evaluates either net National Debt, or the value of National Debt plus the interest payable on it, as a percentage of the current $GN{P}_t$ of Portugal. The use of these indexes on Greece, Iceland and Portugal by IMF is interesting, because they were among the countries affected in a more severe way by the recent financial crisis. Below, we explain why we are against the use of consumption metrics in the area of public debt rating. We would like to emphasize on the model being developed in Aguiar and Gopinath (2006), since the ‘current account’ or else the directly liquid assets of the state budget is the main cash flow, which is important for the debt rating of a country. In recent literature, the authors in Dvorkin et al. (2021) develop a model of endogenous debt restructuring that captures key facts of sovereign debt and restructuring episodes; they report three factors which are important in overcoming the effects of dilution and generating maturity extensions upon restructurings: income recovery after default, credit exclusion after restructuring, and regulatory costs of book value haircuts. The model presented in Amador and Phelan (2021) is a continuous-time model of sovereign debt. For a recent review on sovereign debt and sovereign risk, see in Sun et al. (2024). A recent paper on the same topic is Reis (2022), where the author shows that one of the factors impacting the limit of the Debt/GNP ratio might be a debt revenue term associated with the income generated when the debt itself is issued. Authors in Anand et al. (2023) notie that “understanding how the drivers of sovereign credit risk have evolved beyond economic and fiscal issues, as well as the importance of additional drivers in sovereign credit risk assessment, is critical”. They argue that sovereign credit risk is a function of the macroeconomic environment of a country as well as sustainability risk factors. In Nakatani (2024), the author argues that countries should be cautious about the risks associated with fiscal devolution. In particular, he reports that fiscal crises include sovereign debt crises, episodes in which the country receives exceptionally large official financing from the International Monetary Fund or the European Union, implicit domestic public debt default and episodes associated with extreme market pressures. Finally, in Badia et al. (2022) the authors identify fiscal crises if any of the following four criteria is met: credit events, exceptionally large official financing, implicit domestic public debt default, loss of market confidence.

We notice that most of the research in this topic is related to a microeconomic percertion of the sovereign debt as a problem between the owners of the debt and the state. We do believe that the main point in the study of sovereign debt crises is the structure of the national economy itself. Facing and handling this structure is going to prevent from future crises. This is the reason for proposing another way of national debt evaluation and mention its advantages and its ‘limits’. Its limits are related to the taxes which may reduce net investments and increase the national debt in a near future time.

1.3. Stock and Flow Method of National Debt Rating

The evaluation of National Debt relies on some indexes being used for Credit Rating of the countries by IMF and other institutions. In most cases, the denominator of these indexes is the $GN{P}_t$ or in a more general sense the equilibrium income of the IS-LM equations $Y_t$, which is related to $GN{P}_t$. Since $GN{P}_t=Y_t+X_t-I{m}_t$, where $X_t-I{m}_t$ is the difference between Exports minus Imports at the year t, we may suppose that $X_t-I{m}_t={\delta }_t{Y}_t$, hence

$$\begin{array}{c}\hfill GN{P}_t=(1+{\delta }_t)Y_t.\end{array}$$

Definition 1.

The nominal debt method of National Debt Rating Evaluation is the fraction ${\displaystyle \frac{E_t}{GN{P}_t}}$, where $E_t$ denotes the annual financial needs of the specific country or the annual total nominal national debt payment of it at the year t.

Definition 2.

The spot debt method of National Debt Rating Evaluation is the fraction ${\displaystyle \frac{F_t}{GN{P}_t}}$, where $F_t$ denotes the annual total spot national debt payment at the year t.

The above Definitions are obtained from the Reviews of International Monetary Fund about the Sovereign Debt Sustainability, like International Monetary Fund (2016a, 2016b, 2017).

2. A Framework of Studying Sovereign Debt

The main points of the Study and Policy on Sovereign Debt presented in this paper may be summarized in the following points:

• We show that consupmption-based models have to be abandoned, because they imply a sensitivity of the related calculations.
• We show that the use of GNP as a way of Sovereign Debt Scaling may imply that a state is well-evaluated, while it may be near a National Debt Crisis,
• We propose an index of Sovereign Debt Evaluation which relies on the Surplus of the State,
• We calculate this index for the European Union Countries inside the period of its own countries’ National Debt Crisis, before Brexit and inside the period of the global finance crisis. This is the time-period 2005–2015.
• We imply that this kind of evaluation is related to the State’s Tax policy and its use is not a number which shows that ‘everything goes well’.

3. Instability of the Use of GNP in the Flow and the Stock Method

By $D_t$ we denote the total annual public debt payment at the year t, while by

$$Z_t=c_0^t+c_1^t(Y_t-T_t)+I_t+G_t=Y_t,$$

is the annual IS-equilibrium equation, which leads to the Equilibrium Income

$$Y_t={\displaystyle \frac{1}{1-c_1^t}}(c_1^t{T}_t-G_t-I_t-c_0^t),$$

(1)

In order to make things simple, we call

$$U_t=c_1^t{T}_t-G_t-I_t-c_0^t.$$

$c_0^t$ denotes the annual standard consumption, $c_1^t$ denotes the marginal rate of consumption, $T_t$ denotes the total annual taxes of the state, $G_t$ denotes the total annual state expenses, and $I_t$ denotes the total annual income from investments. Hence, if the Keynesian Multiplicator is

$${\lambda }_t={\displaystyle \frac{1}{1-c_1^t}},$$

then

$$\begin{array}{c}\hfill Y_t={\lambda }_t{U}_t,GN{P}_t=(1+{\delta }_t)Y_t,GN{P}_t=(1+{\delta }_t){\lambda }_t{U}_t.\end{array}$$

The value of the index ${\displaystyle \frac{D_t}{GN{P}_t}}$ is equal to

$${\displaystyle \frac{D_t}{(1+{\delta }_t){\lambda }_t{U}_t}}={\displaystyle \frac{D_t(1-c_1^t)}{(1+{\delta }_t)U_t}}.$$

The above calculations may be obtained by Blanchlard and Fisher (1989).

Proposition 1.

If the marginal rate of consumption changes and the other variables remain the same, (for example $c_1^{t+h}=c_1^t+\epsilon ,$ where ε is a small non-zero number, either positive or negative), then if the value of the index $w_t={\displaystyle \frac{D_t}{GN{P}_t}}$, the new value is

$$w_{t+h}=w_t-{\displaystyle \frac{D_t\epsilon }{U_t(1+{\delta }_t)}}.$$

Proof. 

$w_{t+h}={\displaystyle \frac{D_{t+h}}{GN{P}_{t+h}}}={\displaystyle \frac{D_{t+h}(1-c_1^{t+h})}{(1+{\delta }_{t+h})U_{t+h}}}={\displaystyle \frac{D_t(1-c_1^t-\epsilon )}{(1+{\delta }_t)U_t}}=w_t-{\displaystyle \frac{D_t\epsilon }{U_t(1+{\delta }_t)}}.$ □

Proposition 2.

If the marginal rate of consumption changes and the other variables remain the same, (for example $c_1^{t+h}=\epsilon c_1^t,$ where ε is a small non-zero positive number), then if the value of the index $w_t={\displaystyle \frac{D_t}{GN{P}_t}}$, the new value is

$$w_{t+h}=\epsilon w_t+{\displaystyle \frac{D_t(1-\epsilon )}{U_t(1+{\delta }_t)}}.$$

Proof. 

$$w_{t+h}={\displaystyle \frac{D_{t+h}}{GN{P}_{t+h}}}={\displaystyle \frac{D_{t+h}(1-c_1^{t+h})}{(1+{\delta }_{t+h})U_{t+h}}}={\displaystyle \frac{D_t(1-\epsilon ·c_1^t)}{(1+{\delta }_t)U_t}}={\displaystyle \frac{D_t((1-\epsilon )+\epsilon (1-c_1^t))}{(1+{\delta }_t)U_t}}$$

$$=\epsilon w_t+{\displaystyle \frac{D_t(1-\epsilon )}{U_t(1+{\delta }_t)}}.$$

□

The above Propositions imply a sensitivity of the above evaluation method of National Debt in terms of small changes of marginal rate of consumption.

The equivalent index relying on the total nominal amount of national debt $F_t$ is equal to

$${\displaystyle \frac{F_t}{(1+{\delta }_t)Y_t}}={\displaystyle \frac{F_t·{\lambda }_t}{(c_1^t{T}_t-G_t-I_t-c_0^t)(1+{\delta }_t)}},$$

according to the Equation (1), hence it is related to the Keynesian Multiplicator ${\lambda }_t$, as well. Also, if the state balance sheet has no deficit, namely $c_1^t{T}_t=G_t$, the factor of the Keynesian Multiplicator ${\lambda }_t$ may lead to the following value

$${\displaystyle \frac{F_t}{GN{P}_t}}=-{\displaystyle \frac{F_t·{\lambda }_t}{(I_t+c_0^t)(1+{\delta }_t)}}.$$

The value of the index ${\displaystyle \frac{F_t}{GN{P}_t}}$ is equal to

$${\displaystyle \frac{F_t}{(1+{\delta }_t){\lambda }_t{U}_t}}={\displaystyle \frac{F_t(1-c_1^t)}{(1+{\delta }_t)U_t}}.$$

Proposition 3.

If the marginal rate of consumption changes and the other variables remain the same, (for example $c_1^{t+h}=c_1^t+\epsilon ,$ where ε is a small non-zero number, either positive or negative), then if the value of the index $e_t={\displaystyle \frac{D_t}{GN{P}_t}}$, the new value is

$$e_{t+h}=e_t-{\displaystyle \frac{D_t\epsilon }{U_t(1+{\delta }_t)}}.$$

Proof. 

$$e_{t+h}={\displaystyle \frac{F_{t+h}}{GN{P}_{t+h}}}={\displaystyle \frac{F_{t+h}(1-c_1^{t+h})}{(1+{\delta }_{t+h})U_{t+h}}}={\displaystyle \frac{F_t(1-c_1^t-\epsilon )}{(1+{\delta }_t)U_t}}=e_t-{\displaystyle \frac{D_t\epsilon }{U_t(1+{\delta }_t)}}.$$

□

Proposition 4.

If the marginal rate of consumption changes and the other variables remain the same, (for example $c_1^{t+h}=\epsilon c_1^t,$ where ε is a small positive non-zero number), then if the value of the index $e_t={\displaystyle \frac{F_t}{GN{P}_t}}$, the new value is

$$e_{t+h}=\epsilon e_t+{\displaystyle \frac{F_t(1-\epsilon )}{U_t(1+{\delta }_t)}}.$$

Proof. 

$$e_{t+h}={\displaystyle \frac{F_{t+h}}{GN{P}_{t+h}}}={\displaystyle \frac{F_{t+h}(1-c_1^{t+h})}{(1+{\delta }_{t+h})U_{t+h}}}={\displaystyle \frac{F_t(1-\epsilon ·c_1^t)}{(1+{\delta }_t)U_t}}={\displaystyle \frac{F_t((1-\epsilon )+\epsilon (1-c_1^t))}{(1+{\delta }_t)U_t}}$$

$$=\epsilon e_t+{\displaystyle \frac{F_t(1-\epsilon )}{U_t(1+{\delta }_t)}}.$$

□

The above Propositions do indicate a sensitivity of this evaluation method of National Debt in terms of small changes of marginal rate of consumption, as well.

4. Some Further Quotes Against the Use of GNP in Public Debt Rating

Due to the sensitivity of the stock and the flow indicators, which involve GNP, to the possible errors that may arise in rate of consumption metrics, we do formulate another index, which does not involve GNP, and hence the Keynesian Multiplicator, which is a “famous” question of talking about public rating influence in IMF. Except sensitivity of the stock and flow indicators, which involve GNP and in general consumption metrics, we doubt whether the use of consumption is ‘rational’ in public debt rating, in any form. Two countries, which have equal total nominal debt, or equal annual debt at the time-period t, but different $GN{P}_t$, are classified according to the principle of the “lower risk utility” $U_t(GN{P}_t,I_t)$, according to their $GN{P}_t$. As we show above, since the consumption metrics play an important role in the calculation of $GN{P}_t$, the problem of default arises as a problem of consumption (or non-consumption). This is also the approach in the papers Eaton and Gersovitz (1981); Hatchondo and Martinez (2009); Soytaş and Volkan (2016). The question of tax income (and the rate of it), which arises from investments and not from the consumption factor (and moreover consumption exists, if only if investment is a present factor). Hence, the utility function of a national economy $U_t(GN{P}_t,I_t)$ has to be an increasing function with respect to the investments.

5. Towards a New Way of ND Rating?

By $D_t$ we denote the total annual public debt payment at the year t. The annual surplus of the state at the year t is equal to $S_t=T_t-G_t$. This implies a flow index of National Debt Rating on total state income $S_t=a_t{T}_t$, where $a_t$ expresses this income as a percentage of the annual taxes, as follows:

$${\displaystyle \frac{D_t}{S_t}}={\displaystyle \frac{D_t}{a_t{T}_t}}.$$

This implies $a_t{T}_t=T_t-G_t$, which indicates that $G_t=(1-a_t)T_t$. If the annual balance sheet of the state has no deficit, then $G_t=c_1^t{T}_t$, and consequently $c_1^t=1-a_t$, hence $a_t$ (which takes values in $(0,1)$) denotes the annual marginal savings’ rate. Here, we may quote on the role of the $I_t$, because a rational equation regarding the taxes is the following one:

$$T_t=(1-b_t)T_t+b_t{I}_t,$$

where $b_t$ is called ‘factor of separation’, because it separates the taxes from investments. The above equation indicates that the efficiency of a tax-system relying only on consumption is limited. This is true because the factor $b_t$ taking values in $(0,1)$, is the one which determines the sharing of the taxes between the consumption (or the taxes coming from the household income) $(1-b_t)T_t$ and the taxes coming from the investments’ revenue $b_t{I}_t$. Hence, the relation between the annual payment of debt and the annual income of a national economy from growth, may be expressed by the same index:

$${\theta }_t={\displaystyle \frac{(1+b_t)D_t}{a_t{b}_t{I}_t}}.$$

The last form of $\theta$ implies that its use has limited credibility because it depends on the size of the annual investments.

6. Some Policy Implications

Some policy implications arising in a more clear way via the expression of ${\theta }_t$, appearing above. Specifically, policy implications arise from actions, which decrease ${\theta }_t$. If we would like to summarize the above notifications we have to mention the following main actions:

• Increase private tax factor $a_t$, under a promise to decrease it in the future,
• Do not increase $b_t$, since this action may decrease investments’ spot value $I_t$.
• $b_t$ should remain constant for some time-periods.

The above policy implications are similar to the ones proposed in Elgin and Uras (2013). Tax costs in formal evonomy, which appear as a ‘consumption’ has not to be very high, because a part of capital flows lying in the informal economy remain in such an informal regime. In this paper, authors argue that the informal sector-(the so-called ‘shadow economy’) of a national economy is a significant variable, highly correlated to the probability of sovereign default. Specifically, a greater annual capital flow of exchange in the informal economy, implies a higher interest rate of the sovereign bonds.

7. Caclulation of the $\mathit{\theta }$-Index in European Union Countries and Related Remarks

By the definition

$${\theta }_t={\displaystyle \frac{D_t}{S_t}},$$

of the $\theta$-index, we may understand the meaning of the numbers of the following Table. The meaning for a specific value a of ${\theta }_t$ for any t is that sovereign debt owners’ payments at the end of the year t (which is equal to $D_t$), is atually an amount of money ${\theta }_t$ multiplyied by the total surplus of the state $S_t$ at the end of the same year. It may be understood that a higher value of ${\theta }_t$ implies a higher country risk exposure.

We obtained the numbers arising below-about the time period 2005–2015, because it used to be the period of the last great sovereign debt crisis. Some values of the $\theta$-index appear in the

Table 1. Values of $\theta$.

	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015
Belgium	1.93	1.89	1.80	1.88	2.04	2.02	2.03	2.35	2.00	2.05	2.06
Bulgaria	0.70	0.59	0.42	0.33	0.39	0.46	0.48	0.49	0.45	0.73	0.67
Czech Rep.	0.72	0.72	0.71	0.75	0.89	0.99	0.98	1.09	1.08	0.97	0.97
Denmark	0.67	0.57	0.50	0.62	0.75	0.79	0.85	0.83	0.82	0.79	0.76
Germany	1.57	1.55	1.48	1.50	1.64	1.88	1.80	1.80	1.74	1.68	1.59
Estonia	0.13	0.12	0.10	0.12	0.16	0.16	0.15	0.25	0.25	0.27	0.25
Ireland	0.75	0.64	0.66	1.21	1.85	2.60	3.29	3.54	3.50	3.09	2.85
Greece	2.73	2.64	2.55	2.69	3.26	3.53	3.91	3.43	3.61	3.83	3.67
Spain	1.07	0.96	0.87	1.07	1.51	1.66	1.91	2.28	2.47	2.58	2.59
France	1.35	1.28	1.29	1.36	1.59	1.64	1.68	1.72	1.74	1.79	1.81
Croatia	0.99	0.93	0.89	0.94	1.18	1.41	1.59	1.69	1.93	2.00	1.92
Italy	2.37	2.33	2.20	2.27	2.45	2.53	2.54	2.58	2.68	2.75	2.77
Cyprus	1.70	1.57	1.32	1.14	1.47	1.51	1.79	2.20	2.80	2.70	2.74
Latvia	0.34	0.28	0.25	0.56	1.06	1.31	1.20	1.13	1.08	1.13	1.01
Lithuania	0.52	0.50	0.46	0.42	0.78	1.02	1.11	1.20	1.17	1.19	1.22
Luxemburg	0.17	0.19	0.18	0.35	0.35	0.45	0.43	0.49	0.53	0.52	0.52
Hungary	1.45	1.53	1.46	1.59	1.69	1.79	1.82	1.69	1.64	1.61	1.54
Malta	1.77	1.62	1.60	1.63	1.76	1.78	1.80	1.73	1.74	1.70	1.60
Netherlands	1.17	1.04	1.00	1.25	1.33	1.37	1.44	1.54	1.54	1.55	1.50
Austria	1.40	1.40	1.35	1.41	1.63	1.70	1.70	1.67	1.63	1.69	1.69
Poland	1.15	1.14	1.07	1.14	1.31	1.38	1.38	1.37	1.44	1.29	1.31
Portugal	1.66	1.69	1.65	1.72	2.07	2.37	2.61	2.94	2.86	2.92	2.93
Romania	0.49	0.37	0.36	0.40	0.74	0.91	1.01	1.11	1.13	1.18	1.08
Slovenia	0.60	0.60	0.54	0.52	0.82	0.88	1.07	1.21	1.57	1.81	1.84
Slovakia	0.92	0.88	0.87	0.82	1.00	1.18	1.19	1.44	1.41	1.36	1.22
Sweden	0.77	0.73	0.66	0.62	0.80	0.90	0.90	1.00	1.02	1.10	1.17
Finland	0.90	0.82	0.74	0.71	0.79	0.75	0.74	0.74	0.79	0.90	0.87
UK	1.04	1.07	1.09	1.26	1.70	1.97	2.10	2.23	2.20	2.31	2.31

. The calculations appearing in the Table 1, rely on quarterly spot payments’ data expressed in Euros, regarding the years 2005–2015 for the EU countries: Belgium, Bulgraria, Czech Republic, Denmark, Germany, Estonia, Ireland, Greece, Spain, France, Croatia, Italy, Cyprus, Latvia, Lithuania, Luxemburg, Hungary, Malta, Netherlands, Austria, Poland, Portugal, Romania, Slovenia, Slovakia, Sweden, Finland, United Kingdom. The data are obtained from EUROSTAT (for annual debt and annual state revenue data see the official site, https://ec.europa.eu/eurostat, accessed on 10 July 2024).

Some remarks on the above table’s values, which are important are the following ones:

(i)

The Tables’ values indicate the countries having the greater country risk exposure: Greece, Italy, Spain, Ireland, Cyrpus, Portugal, Belgium (which was also a candidate for a public debt crash).

(ii)

Another country having a high level of country risk exposure according to this indicator, is Great Britain.

(iii)

Germany’s country risk exposure according to this indicator, is not negligible.

(iv)

The values of the variables involved in the above calculations rely on their spot values.

(v)

The values of the table which are relatively lower, such as Bulgaria or Estonia may be related to the lower inter-temporal net rates of investment. The lower value of $\theta$ does not imply that these countries are out of a possible debt crisis.

(vi)

A case which is related to the above remark is the case of Greece. The values of $\theta$ in the above table are relatively high. However, Greece’s net investements are not high in these years.

(vii)

The values of the index in the case of United Kingdom between the years 2005–2015 are high. This fact may be discussed further, related to ’Brexit’.

In the Appendix A of the present paper, we may see the time-series plots corresponding to the above Table. The time period 1 is the year 2005, the time period 2 is the year 2006, the time period 3 is the year 2007, the time period 4 is the year 2008, the time period 5 is the year 2009, and so on. The time period 6 is the year 2010, the time period 7 is the year 2011, the time period 8 is the year 2012, the time period 9 is the year 2013. Finally, the time period 10 is the year 2014 and the time period 11 is the year 2015. The values of $\theta$ appearing in the order of the Table as they also appear in the time-series graphs are the following:

C3 stands for Belgium, C4 for Bulgaria, C5 for Czech Republic, C6 for Denmark, C7 for Germany, C8 for Estonia, C9 for Ireland, C10 for Greece, C11 for Spain, Also, C12 stands for France, C14 for Croatia, C15 for Italy, C16 for Cyprus, C17 for Latvia, C18 for Lithuania, C19 for Luxemburg, C20 for Hungary, C21 for Malta, C22 for Netherlands, C23 for Austria and C25 for Poland. Finally, C26 stands for Portugal, C27 for Romania, C28 for Slovenia, C29 for Slovakia, C30 for Sweden, C31 for Finland and C32 for United Kingdom. We may notice that Memoranda applied in Greece and Brexit in United Kingdom are relatd to not a high trend of $\theta$.

8. Conclusions

8.1. Summary and Directions

Modeling country risk for EU countries under various macroeconomic factors that influence their financial and fiscal stability is still an important issue because European economy saw several challenges which affected its growth before and after GFC, e.g., sovereign debt. Risk modeling with European data for the period from 2005 to 2015, can help understand how EU countries impacted from the GFC (2007–2008) as well as the EU debt crisis (2010–2012). In addition, this examined period is particularly important because it shows how recovery and austerity measures influenced debt sustainability, economic growth, and financial stability in Europe. Further, by considering this period of uncertainty, we are able to examine whether risk models can be used to predict future sustainability of public finances. Hence, we selected this time period because it used to be the period of the last great sovereign debt crisis. When building a country risk model, several macroeconomic variables and financial indicators are typically considered. The presence of GNP either in the stock, or in the flow method of public debt rating indexes implies the acceptance of some consumption–based model for the country risk. The consumption-based models argue that consumption is essentianl role on the evaluation of the evaluation of national debt. We argue that due to the essential role of the investments’ volume in any national economy, the consumption-based models are not so effective. A great net volume of investments implies less national debt issue. This is ignored by consumption-based models. We also show that consumption-based models are sensitive in small changes of consumption. A wrong estimation of total consumption may imply a false evaluation of any consumption-index evalution of any public debt. As a matter of fact, we propose an index $\theta$ which relies on the state income from the taxes. The index $\theta$ is directly associated to the annual spot value of investments. The main policy implication is to increase taxes on households. We also obtained real data from EUROSTAT and we confirmed some real situations about country risk exposure, by the annual evolution of $\theta$ between 2005–2015.

8.2. Future Work

These results may be compared to the COVID-19-pandemic crisis and its influence to the values of $\theta$. This is an immediate future work proposal, since COVID-19-pandemic crisis was a time-period of lower tax incomes. Another future work may be devoted to the time-correlations of the index $\theta$. As we mentioned above $\theta$ has limited credibility because it depends on the size of the annual investments. Hence, countries having lower annual net investments may have a low value of $\theta$, due to their imter-temporal lower growth, and sovereign debt crisis may arise as well in the next time. This is a subject of further study.