Fiscal Sustainability Risk Assessment with Macroeconomic Factors Ábel István – Kóbor Ádám1
Fiscal sustainability conditions for the Maastricht gross nominal consolidated public debt are analyzed using Hungarian data. The components of debt dynamics are grouped following the commonly used debts sustainability approach while the factors and their contributions to the changes of the debt are analyzed using a VAR model. The stochastic properties (variance) of macro variables used in the VAR model help to asses risks to fiscal sustainability. This approach offers a way to determine the effect of possible macroeconomic shocks on debt dynamics. Using stochastic simulation, we can estimate a confidence interval around the expected debt ratio path at pre-specified probability levels. The path of the public debt may reflect complex changes in the macro variables and their interrelationships. When the level of public debt surpasses certain limits, sustainability may become an issue. When debt sustainability is in doubt, it imposes a strong constraint altering the behavior of macro variables and their interrelationships. Debt dynamics influences future potential performance and changes the economic outlook. This paper examines the sustainability of fiscal policy under uncertainty in the Hungarian economy for the period of 1995-2010. First we analyze the evolution of the nominal debt-toGDP ratio following the commonly used decomposition of the changes in the debt-to-GDP ratio. For Hungary a similar decomposition is published in Deli and Mosolygó [2009] and in the publication of the Hungarian Debt Management Agency (ÁKK) [2010] titled A magyar államadósság növekedésének tényezői a 2001-2009-es időszakban (Components of the increase in the Hungarian public debt in the period of 2001-2009). We extend this method with a probabilistic approach to analyze public debt sustainability inspired by Garcia and Rigobon [2004] and Tanner and Samake [2008]. Our approach is based on a simple macroeconomic VAR model like the one used in Tanner and Samake [2008], but we take this method a step further by combining the VAR model with the method of the decomposition of the factors contributing to the increase in the debt-to-GDP ratio. 1
István Ábel, Senior Advisor, International Monetary Fund, his email address is
[email protected]. Ádám Kóbor, World Bank, his email address is
[email protected] . The authors are grateful to Zsuzsa Mosolygó (ÁKK) and to Béla Simon (MNB) for help. The views expressed in the paper do not necessarily reflect the official position of the IMF or the World Bank.
1 Electronic copy available at: http://ssrn.com/abstract=1868543
A number of factors may change the debt-to-GDP ratio on the short run, but several of them have only a transitory effect. Debt sustainability is a long term concept of which we can derive certain limits on debt dynamics. These limits or thresholds, however, are not static. Debt tolerance may change abruptly with changes in the external economic conditions and/or the weakening of economic policy and financial soundness. This paper does not deal with these external or internal factors of debt tolerance. Reinhart and Rogoff [2009] gives a detailed and robust analysis of historical changes in debt tolerance. Instead, we focus on the effects of the changes in the main macroeconomic variables, like the exchange rate, growth rate, inflation rate, interest rate, and the primary fiscal balance. We use a simple metrics to attribute changes in the debt-to-GDP ratio to the changes in these macroeconomic factors. The analysis of this decomposition itself reveals interesting historical tendencies of debt dynamics. This decomposition also offers a way to channel in information from a simple VAR model based on these and other macroeconomic variables to allow a probabilistic assessment of debt dynamics and debt sustainability. Debt Dynamics The term debt dynamics refers to the study of the evolution of the measured debt-to-GDP ratio. It is useful to describe how the debt level has evolved in the past, as it may provide a distinctive perspective for future actions. It helps to identify which factors dominated the debt accumulation in the past and how could it be altered in the future by appropriate policy measures. Several simple and widely used methods are collected and their use is well demonstrated in Brunside [2005]. Such an analysis of debt dynamics may be helpful to illustrate risks to public finances. The analysis starts from a simple budget identity expressed in local currency units which states that the level of debt (D) today is the sum of the inherited debt plus interest (i) due on the debt stock augmented by the current primary fiscal deficit (P): . The economy 1 also grew, not just the debt, and nominal GDP (Y) had increased by the rate of growth (g) and 1 1 . The evolution of the debt-to-GDP ratio is given by (1): inflation (π): (1)
where, d: is the debt-to-GDP ratio p: is the primary fiscal deficit to GDP ratio (P/Y) g: is the real GDP growth rate π: is the inflation rate i: is the effective interest rate on the debt
2 Electronic copy available at: http://ssrn.com/abstract=1868543
The debt stock has a domestic and a foreign component and we denote the share of foreign debt in total debt by the parameter w. The foreign currency debt carries a foreign interest rate if, and is exposed to exchange rate risks. Introducing these distinctions in the formula (1) we arrive at formula (2):
(2)
where w: is the share of foreign denominated debt in total debt f: is the measure of depreciation of the domestic currency (in percentage) if: is the interest rate on the foreign component of the debt id: is the domestic interest rate. Formula (2) summarizes the main macroeconomic factors that influence the debt dynamics, but there are many other things that may change the debt volume. These other factors may include temporary or one off factors, like privatization revenues used for debt repayment. Valuation or accounting changes, like mark-to-market valuation, which reflects changes in market sentiments and other changes, may also alter the value of the debt. We can find a useful and quite extensive list of such other factors on several places in Brunside [2005]. We will show the effect of these other factors under the heading of “others” as a residuum in the attribution exercise and will not go into further details concerning them. To separate the effects of the macroeconomic variables we can rewrite the formula (2) as follows: (3)
There might be many other possible ways to break the formula into components, but we prefer to use this particular form in the empirical attribution exercise. The first part on the right hand side of equation (3) reflects the impact of interest rates, both domestic and foreign interest rates, on debt dynamics (interest rate effect). The second part is the exchange rate effect, with the simplification that we apply the same exchange rate to the stock of the foreign debt and the interest payment due on it. The third part gives the reduction of the debt-to-GDP ratio caused by the increase in GDP (growth effect). The next is the formula for the inflation effect, which covers the reduction in the debt-to-GDP ratio caused by the inflationary increase in GDP, combining both the direct inflationary effect and the cross effect of the real growth and inflation. The last 3
part denotes the effect of the increase in the primary deficit-to-GDP ratio on the debt-to-GDP ratio (primary deficit effect). Debt dynamics in the past 15 years Fiscal deficit and public debt are close relatives but their relationship is often complicated by other macroeconomic factors. In this part we will try to give a bird’s-eye view of the main tendencies in these relationships. For the fiscal deficit we use the data of the general government net financing requirement as published by the National Bank of Hungary. This variable is depicted in Figure 1. From this deficit figure we deduct the interest payments to arrive at the primary fiscal deficit (P) used in the analysis. Figure 1 General government net financing requirement (Seasonally adjusted) 12 10
GDP %
8 6 4 2
Net financing requirement
3/1/2010
5/1/2009
7/1/2008
9/1/2007
11/1/2006
1/1/2006
3/1/2005
5/1/2004
7/1/2003
9/1/2002
11/1/2001
1/1/2001
3/1/2000
5/1/1999
7/1/1998
9/1/1997
11/1/1996
1/1/1996
3/1/1995
0
Source: National Bank of Hungary
The historical evolution of the consolidated public debt of Hungary, both the gross and net debt, is depicted on Figure 2. Figure 2 Gross and net public debt 4
120 100 Gross debt
GDP %
80
Net debt
60 40 20
3/1/2010
5/1/2009
7/1/2008
9/1/2007
11/1/2006
1/1/2006
3/1/2005
5/1/2004
7/1/2003
9/1/2002
11/1/2001
1/1/2001
3/1/2000
5/1/1999
7/1/1998
9/1/1997
11/1/1996
1/1/1996
3/1/1995
0
Source: National Bank of Hungary There are several surprising divergences between the gross and net debt. In the second half of the 1990’s gross public sector debt had a tendency to fall. It fell from over 90 percent of GDP in 1995 to below 60 percent of GDP by 2001. The net debt, at the same time, almost continuously increased from below 20 percent of GDP to above 30 percent of GDP. Privatization revenues reduced gross debt. There was another particular factor, related to a change in the institutional framework and the accounting of the debt which altered the picture. Before 1997, public debt was financed in domestic currency. Even when the central bank raised foreign debt to finance fiscal debt or debt service, it transferred the financing in domestic currency while kept the foreign debt on its own books. Such intermediation carried a cost. When the domestic currency depreciated the central bank accumulated exchange rate losses on its foreign debt. The stock of the exchange rate losses due to the revaluation of the foreign debt was called “zero interest stock” in the balance sheet of the central bank (see MNB [2008] p. 52). In 1997 the foreign currency debt held by the central bank was swapped with the government. As a result of the debt swap between the central bank and the government the share of foreign denominated debt of the government jumped to 40 percent of total debt. After this date the effect of revaluation (exchange rate effect) affected directly the government held debt stock. There was another episode of a divergence between gross and net debt in 2008 and 2009. This is the period when Hungary drew on the EU-IMF stand-by arrangement of November 2008. The EU-IMF combined stand-by arrangement opened a credit line in scheduled tranches over a period of 18 months (later extended to 24 months), in total of euro 20 billion. Although actual drawings did not use the whole amount but in the last months of 2008 and the first half of 2009 significant amounts were drawn and this is reflected in the spike of the gross debt. Net debt at the same time shoved some moderation, but the reason for this was purely a consequence of accounting, namely the mark-tomarket valuation of government papers. Net debt is valued at market value, while gross debt is 5
accounted for in nominal terms. The crises suddenly had increased the yield on government papers and the stock of outstanding debt valued at market prices fell. Gross debt, however, valued in nominal terms was changed only by nominal transactions and not by market valuation. Part of the drawing from the stand-by arrangement was used to increase reserves which also helped to keep net debt stable while gross debt had increased. Now we apply the decomposition described in equation (3) to the evolution of the gross debt. The result is presented in Figure 3. Figure 3 The components of the increase in the gross debt (Result using equation (3) in the decomposition) 15.0 10.0 5.0
GDP %
0.0 ‐5.0 ‐10.0 ‐15.0 ‐20.0
Others
Exchange rate effect
Interest rate effect
Inflation effect
Growth effect
Primary deficit effect
Change in net debt
Financing requirement
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
‐25.0
Source: Authors’ calculation In this decomposition the changes in gross debt attributed to “Others” component not shown in equation (3) are typically negative, these factors normally reduced the level of debt. This effect was especially dominant in the years 1996 and 1997, possibly related to privatization revenues, valuation changes related to the debt swap between the central bank and the government, or other one-off factors. We have to admit that the method used for the decomposition also uses shortcuts and simplifications. The currency composition of foreign debt may easily change from one period to the other, but formula (3) assumes only one foreign currency and one exchange rate. Similarly, interest rates may also differ not just for different currencies but also for different maturities in the same currency, and different dates of the same maturity. All of these
6
simplifications help to keep the formula used for the attribution tidy, but at a cost of some errors. All of the deviations caused by these errors show up in the residuum called other factors. The change in debt attributed to the interest rate effect had increased the debt-to-GDP ratio significantly, although with some fluctuation. Taking the whole period, interest rates roughly followed a downward trend, which trend over time moderated the debt accumulation attributed to the interest rates. Prior to 2000 interest rate effect was accountable for about 6-7 percent of GDP increase in debt. But after 2000 the debt accumulation attributed to the interest rates fell to around 3-4 percent of GDP. The increase in the level of debt, however, led to an increase in the interest rate effect even with relatively stable or falling interest rates. After 2004 the interest rate effect has increased to over 4 percent of GDP and reached 4.6 percent in 2009, before falling to 3.2 percent of GDP in 2010. The exchange rate effect on debt dynamics was much less in size than the interest rate effect, which is not surprising. The exchange rate effect also fluctuated significantly. In most years it contributed to the increase in debt, but there were periods, like the years 2001, 2002, 2004, 2006, when the appreciation of the domestic currency reduced the debt-to-GDP ratio. In 2008 a reduction of 1.4 percent of GDP was a result of the appreciation of the Hungarian forint. In 2009 0.6 percent of GDP reduction, and in 2010 0.7 percent of GDP reduction in the debt was attributed to exchange rate appreciation. Almost every year about 3-4 percentage point reduction in the debt-to-GDP ratio is attributed to the nominal growth of GDP. This is the combined contribution of the growth effect and the inflation effect. The components of equation (3) handle these effects separately, and it would not be difficult to calculate these two effects accordingly, but at this level it would not add much detail to the picture, other than variance. When real growth was lower, inflation was normally higher, and vice versa, but the sum of these two factors deducted 3-4 percentage points from the debt-to-GDP ratio almost every year. Variance does matter though, and indeed, in the VAR model we will use both, the real GDP growth and inflation separately. There contribution to the macroeconomic risks is significant, as we will demonstrate in the second half of this paper. The primary deficit effect was debt reducing in the years 1996, 1997, 1999, 2000, and 2008, when the budget recorded a primary surplus. For the whole 15 years period, however, primary deficit was the most common occurrence with levels as high as 4-5 percentage of GDP, which increased the debt-to-GDP ratio with the same magnitude. The method based on equation (3) can be equally used for the decomposition of the net debt. The result is shown in Figure 4. Figure 4 The components of the increase in the net debt (Result using equation (3) in the decomposition)
7
12.0 10.0 8.0 6.0 GDP %
4.0 2.0 0.0 ‐2.0 ‐4.0 ‐6.0 ‐8.0
Others
Exchange rate effect
Interest rate effect
Inflation effect
Growth effect
Primary deficit effect
Change in net debt
Financing requirement
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
‐10.0
Source: Authors’ calculation
The primary deficit effect (denoted by p in equation (3)) is identical in both the gross and net debt-to-GDP ratios. The interest rate effect is slightly different, as the composition of foreign and domestic debt is also different in the case of gross and net debt. This difference in the interest rate effect, however, does not surpass 0.2 percent of GDP, and in most years it is significantly smaller. The exchange rate effect is markedly different (usually smaller) for the net debt-to-GDP ratio from the effect on the gross debt-to-GDP ratio. The exchange rate effect on the net debt-toGDP ratio is smaller than 0.3 percent of GDP in most years, except for 1998, when the depreciation of the domestic currency had increased this ratio by 0.6 percent of GDP.
Ex-ante scenarios for the public debt path in a VAR framework By using formula (3), we attributed historical debt ratio changes to a range of macroeconomic factors. In this section we take a step further by discussing ex-ante debt path scenarios based on various assumptions about the future development of these macroeconomic components. We pick the end of 2006 as the starting date for our ex-ante analyses, and calculate expected paths for the debt-to-GDP ratio in quarterly steps forward, based on the hypothetical scenarios set for the macroeconomic components. We chose the end of 2006 to be the inception point because thus we can compare our ex-ante scenarios to the realized debt path over the past 3 years, a period that was dominated by economic recession and hectic market movements. 8
We work with a VAR(1) model in order to build forward looking scenarios and conduct stochastic simualations. The VAR(1) model covers the following macroeconomic variables: domestic and foreign (euro) interest rates, real GDP growth, inflation, foreign exchange rate, and primary deficit. While the VAR(1) system does not directly involve the debt-to-GDP ratio, we can easily translate the simulated marcoeconomic variables to a corresponding debt path by using equation (2). A more detailed model description and the estimation results are shown in Annex 2. Note that in this section we use estimates based on years 1995-2006 in order to conduct the ex-ante simulations discussed bellow. As far as possible, the datasets used for the VAR model estimation and the ex-post attribution analysis are the same, but there are some differences as well. In the VAR model, we used both the domestic and the euro interest rates. For the interest rate on the euro denominated Hungarian debt the sum of the 3-year German bund yield and the Hungarian EMBI spread was used. On the other hand, in the ex-post attribution analysis we did not actually separate domestic and foreign interest rates, but instead simply took the reported interest rate expenditure to calculate the implicit (average) interest rate. This ex-ante simulation procedure has two building blocs. Our subjective scenarios are expressed by the deterministic component. We set scenarios by expressing long term expectations for the simulated macroeconomic factors. When our long term views are favorable, we classify the scenario as optimistic, whereas if we would like to analyze the impact of adverse long term values, we call the scenario pessimistic. We can set long term values by modifieng the constant vector of the VAR system as described in Annex 2. Still, the speed of convergence and the way the factors influence each other are determined by the VAR parameter estimates. The second component is the stochastic component. Taking the covariance matrix of the VAR(1) we run simulations around the deterministic component of the macroeconomic variables. For the long term outcome we chose two scenarios, one of which we call optimistic (or something reflecting the expectations at the starting date of 2006), while the other scenario is called pessimistic (or something that proved to be realistic in retrospect for 2008). First, we discuss the optimistic scenario. The assumptions about the target (model restriction) the economy is expected to reach in the future, starting from 2006, in the optimistic scenario are as follows. Long-run assumptions in the optimistic scenario: The share of foreign debt in gross debt: 30 percent Long-run interest rate on both the domestic and foreign debt: 5.0 percent Real GDP growth rate (annual): 4.0 percent Primary fiscal deficit: 0.0 percent of GDP
9
The change in the Hungarian forint exchange rate to the euro (long-run): 0 percent annual change (the forint is stable ) Inflation rate: 2.0 percent
The results of this analysis are shown in Figure 5. Besides the expected debt ratio path (“VAR projection”) and the 90% confidence interval (dashed gray lines), we also show the actual debt path (black line), as well as an ex-post estimation for the debt using the realized values of the macroeconomic factors in equation (2) (dashed black line). This ex-post estimation is the same as what we discussed in the previous section. Figure 5 Hypothetical debt path estimation, starting from the end of 2006 (historical path, ex-post path estimation by realized macroeconomic factors, and ex-ante path forecast based on optimistic macroeconomic assumptions) 90%
VAR projection (Gross debt) Gross debt 5% low 95% high Estimated gross debt
85% 80% 75% 70% 65% 60%
9/1/2010
6/1/2010
3/1/2010
12/1/2009
9/1/2009
6/1/2009
3/1/2009
12/1/2008
9/1/2008
6/1/2008
3/1/2008
12/1/2007
9/1/2007
6/1/2007
3/1/2007
12/1/2006
55%
Note: gross nominal debt, calculated according to the Maastricht criteria The ex-post estimated dashed line tracks the factual debt path fairly closely, indicating that oneoff factors did not divert the debt significantly in this period. The ex-ante simulated path of the macroeconomic variables is driven by the model and reflects the economic forces in the macroeconomic framework. Although the target values are somewhat arbitrary, the speed and the shape of their convergence to it are driven by the model. The simulation helps us to map the stochastic properties of the debt dynamics, in a sense that we can draw confidence intervals within which we can expect the outcome to be by 90 percent probability. This means that the probability of the debt path that would fall below the lower bound or would break the upper bound is only 5 percent on each side. 10
The speed of adjustment to the long-run expected values is not uniform for the variables but in about 8-10 quarters all of them get reasonably close to it. Substituting the calculated path of the variables into equation (2), where is the debt-to-GDP ratio at end-2006, we get the VAR projection for debt in Figure 5. This line depicts the gross debt-to-GDP ratio which is increasing with a slowing pace until about the time when the variables reach the values picked in the optimistic scenario. Going forward the ratio starts its slow but steady decline. The comparison of the actual debt path with these intervals indicate that the actual debt dynamics before 2008 was even better than what would have expected at 90 percent likelihood in the optimistic scenario. But even in this optimistic scenario an increasing (destabilizing) debt dynamics could not have been ruled out, as the upper side of the interval shows. The crisis in 2008 brought about a jump in the debt-to-GDP ratio, as the debt increased and GDP fell, but even this jump brought the debt line above the upper side of the interval only for a short period. It is interesting to note, that what happened in the debt-to-GDP ratio, was well within the realm of the Hungarian economy, which could not have been ruled out at 90 percent probability even in 2006. Such a gloomy possibility was not foreign even in a rather optimistic scenario for the coming two-three years. We assumed a balanced primary fiscal position in this calculation. The fact, that this assumption was breached in reality, should have raised doubt about the expected stabilization. The expectation expressed in this scenario might have been appealing in 2006, when it could have seen even as a realistic one, but it turned out to be an overly optimistic picture of the future. Let’s look at what would the model suggest if we pick a scenario closer to reality. Long-run assumptions in the pessimistic scenario: The share of foreign debt in gross debt: 30 percent Long-run interest rate on both the domestic and foreign debt: 7.5 percent Real GDP growth rate (annual): 2.5 percent Primary fiscal surplus: 0.5 percent of GDP The change in the Hungarian forint exchange rate to the euro (long-run): 2 percent annual depreciation of the forint Inflation rate: 3.0 percent The result of the simulation exercise for this scenario is summarized in Figure 6. The VAR projection and the actual debt path, as well as the estimated gross debt, which is the sum of the attributions based on the formula in equation (3), all got promisingly close in the period after 2009. This might be good news for the model, but it is rather worrisome for the observer, because this pessimistic scenario, which apparently proved to be realistic, depicts an explosive debt dynamics. The interval which covers 90 percent of all possible outcomes in the simulation would not rule out such a positive surprise that would bring the debt-to-GDP ratio on a stabilizing path, but the likelihood of such outcomes is pretty small. It is somewhat promising
11
that the VAR projection on Figure 6, although still is on an increasing trend, looks like it is approaching a plateau and could take a stabilizing turn afterwards. Figure 6. Hypothetical debt path estimation, starting from the end of 2006 (Historical path, ex-post path estimation by realized macroeconomic factors, and ex-ante path forecast based on pessimistic macroeconomic assumptions) 95%
VAR projection (Gross debt) Gross debt 5% low 95% high Estimated gross debt
90% 85% 80% 75% 70% 65% 60%
9/1/2010
6/1/2010
3/1/2010
12/1/2009
9/1/2009
6/1/2009
3/1/2009
12/1/2008
9/1/2008
6/1/2008
3/1/2008
12/1/2007
9/1/2007
6/1/2007
3/1/2007
12/1/2006
55%
Note: gross nominal debt, calculated according to the Maastricht criteria
On the stochastic properties (variance) of the debt-to-GDP ratio
The model simulation offers a way to explore the impact of the selected macroeconomic variables on the variation of the debt-to-GDP ratio. While the policymakers can directly influence some of the components of the debt-to-GDP ratio, they may have limited or no control over others, at least on the short run. Naively we could assume that policymakers can most directly influence the primary budget balance, although primary balance is a huge aggregate in itself, inherent with many uncertainties in its ingredients. The interest rate expenditure on the outstanding debt is a given factor, but the rate at which new debt can be issued largely depends on the prevailing market conditions. The prevailing government bond yield may reflect the general economic conditions, but also may depend on the sovereign credit risk premium required by the investors. The interest rate of the euro denominated debt is a combination of the Hungarian sovereign credit spread and the yield levels in the Euro zone. While the credit spreads 12
are closely linked to the expected credit risk of the issuer country, it is also influenced by the global investor sentiment that cannot be directly controlled. Similarly, the forint’s exchange rate may depend on many things, including the economic conditions and the relative yield levels. However, its short term variation is certainly influenced by several other factors also. Finally, while the inflation and real growth is considered to be the measure of success of the economic policy on the medium to long horizon, shocks in inflation and economic growth can occur that is hard to control on the very short horizon. All of these may have an impact on the debt-to-GDP ratio. When targeting a debt-to-GDP ratio, it is important to take the possible uncertainty into account. In case we want to impose a debt-to-GDP ratio ceiling, it is important to know to what extent this ratio can or cannot be directly controlled. There are several different ways to quantify the uncertainty around the debt-to-GDP ratio. In practice it may be actually wise to apply a couple of them jointly. One possible way is to use discrete scenarios. Calculating the debt-to-GDP ratios under the assumption of a fixed primary deficit level, but with a set of different exchange rates, inflation rates and real growth can highlight the possible range of the future debt-to-GDP ratio. Deli and Mosolygó [2009] presented a similar approach. This approach is fairly easy to follow, and leaves a lot of judgment to the analyst and the decision maker. This is the first method to use to discover how the macro factors may influence the changes in the debt-to-GDP ratio. Here, however, we discuss a different approach. The second approach is based on equation (3) which gives a decomposition of the changes in the debt-to-GDP ratio into 5 different factors. The covariance matrix of these components can be used to get a quantitative assessment of the contribution of these components to the overall variation of the debt-to-GDP ratio. The standard deviation of the debt-to-GDP ratio can be expressed as follows, where denotes the covariance matrix of the components, and is an nx1 vector as the change in the debt-to-GDP ratio is simply the sum of the n components (n is 5 in our case): √ ′ In this approach we follow the risk decomposition method widely used in the risk management practice. The marginal contribution of the components to the overall standard deviation is given by the vector
, while the relative weight in explaining the total variance of the debt-to-GDP
ratio is given by the vector
. We note that this is just an approximation to quantify the relative
importance of the selected components, as cross-effects are also in play. In addition, we excluded the “other” factors (temporary or one-off factors) from this analysis. We also merged the interest rate and primary deficit into a single deficit component. The reason for this is the following. In the ex-post analysis we estimated the primary deficit as the difference between the total deficit and the interest rate expenses. While we believe that this approach helped us to quantify the expost impact of the five components on the evolution of debt-to-GDP ratio reasonably well, the 13
correlation between the time series of the interest expenditures, and the difference between the overall balance and the interest expenditures (i.e. the primary balance) would be certainly biased. We summarize the estimation results in Table 1. The results are based on quarterly and yearly frequencies. We report the results based on the yearly differences for March-March (Q1-Q1), June-June (Q2-Q2), September-September (Q3-Q3), and December-December (Q4-Q4) cycles, because the results exhibit a significant variation. This variation can be explained by the relative shortness of our time series, but seasonality also plays some role. Table 1 summarizes the empirical variance of the debt-to-GDP ratio, and its decomposition. Table 1 Decomposition of the variance of the debt-to-GDP ratio
Gross, quarterly Gross, yearly Q1Q1 Gross, yearly Q2Q2 Gross, yearly 3Q3 Gross, yearly 4Q4
Percentage contribution to the variance of the debtto-GDP ratio Deficit Real growth Inflation Exchange effect effect effect rate effect 24% 15% 9% 52% 37% 17% 12% 34% 38%
19%
16%
27%
47%
20%
15%
19%
68%
12%
15%
6%
Standard deviation of the debt-toGDP ratio 1.2% 3.1% 3.3% 3.1% 2.5%
While our time series are quite short, our results suggest that the volatility of the market variables (exchange rate) dominate the variation in the debt-to-GDP ratio on a quarterly basis. Over a yearly horizon, on the other hand, the fiscal deficit becomes the most important contributor to the variance of the debt-to-GDP ratio. Real GDP growth and inflation exhibit a fairly consistent behavior: they each explain roughly 10-20% of the variance of the debt-to-GDP ratio.
Summary and conclusions The main factors driving the public debt-to-GDP ratio, including the interest rate, exchange rate, rate of growth, inflation and primary fiscal deficit, are policy dependent factors. We did not address the question how different policies may alter the path of these factors. The analysis focused on the issues how these variables derived the debt-to-GDP ratio in the past 15 years. First we took the actual values of these variables and calculated the change in the debt-to-GDP ratio attributed to the changes in the value of these variables. In the second part we used the main 14
macroeconomic variables, which had direct impact on the debt dynamics, and pooled the information in a VAR(1) model. The model estimates were then used to give a description of the main characteristics of the macroeconomic developments. Channeling this information into equations (2) or (3), we can get a picture of the debt dynamics. Simulations based on the model were used to analyze the stochastic properties of the debt dynamics. The scenario analysis, based on hypothetical expectations about the future path starting in 2006, indicated that the crisis that hit the Hungarian economy in late 2008 caused major changes in the path of the debt-to-GDP ratio. However, even these changes resided within a 90 percent confidence interval that could have been estimated back in 2006 under different assumptions. Starting in 2006, even with optimistic macroeconomic expectations, the unwelcome surprise in debt dynamics would have been within the 90 percent confidence interval determined by our VAR(1)-based stochastic simulation. Doing the same exercise, but working with more conservative macroeconomic expectations, which we may ex-ante call the pessimistic scenario, but which proved to be more-or-less the realized case ex-post, the crisis outcome of the debt-toGDP ratio looks like the most probable outcome. The actual debt ratio path fell very close to the central VAR projection. We have to add, though, that more benign debt dynamics with stabilizing characteristics could have not been completely ruled out under any of the two scenarios. Risks in debt dynamics are inherent, and assessing them is important. The stochastic characteristics of the main macroeconomic variables offer an approach to assessing macroeconomic risks. We believe that policy-makers should take these risks and uncertainties into consideration as well, beyond the central expectations.
15
References Államadósság Kezelő Központ (ÁKK) [2010]: A magyar államadósság növekedésének tényezői a 2001-2009-es időszakban (The components of the change in the Hungarian government debt, 2001-2009), mimeo Burnside, C [2005]: Fiscal Sustainability in Theory and Practice: A Handbook, The World Bank, 2005. Deli, Lajos - Zsuzsa Mosolygó [2009]: Hungarian Central Government Debt-to-GDP ratio May Decline After, http://www.akk.hu/object.F3D1A46F-3D7F-4F1C-B7C6-DADB89B4E41C.ivy Garcia, M., Rigobon, R. [2004]: A Risk Management Approach to Emerging Market’s Sovereign Debt Sustainability with an Application to Brazilian Data, NBER Working Paper Series, WP 10336 GKI: http://www.gki.hu/gazdasagpolitika/allamadossagrol-gki-hatter-elemzese KSH [2011]: A Kormányzati szektor adatai, 2010. III. negyedév, KSH Gyorstájékoztató, 2011. január 4. MNB [2008]: Magyarország pénzügyi számlái (Adatok, elemzések, módszertani leírások), http://www.mnb.hu/Root/Dokumentumtar/MNB/Sajtoszoba/online/mnbhu_pressnews/mnbhu_hi r_20070402/pszlakonyv_hu.pdf Mosolygó Zsuzsa [2008]: Eredendő bűnök - Magyarország és a pénzügyi válság, MNB http://www.akk.hu/object.8C3B64B6-1D3B-4D89-931B-2DFC2D93B74B.ivy, Pénzügyminisztérium [2005]: A gazdasági átalakulás számokban, 1994-2004, Pénzügyminisztérium, 2005. Szeptember. Reinhart, C. M., K. Rogoff [2009]: This Time is Different, Eight Centuries of Financial Folly, Princeton University Press, Princeton and Oxford, 2009 Tanner, E., Samake, I. [2008]: Probabilistic Sustainability of Public Debt: A Vector Autoregression Approach for Brazil, Mexico and Turkey, IMF Staff Papers, Vol. 55. No. 1.
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Annex 1: Sources of economic and market data Variable Net financing requirement of the general government, as percentage of GDP, seasonally adjusted
Period 1995-2010
Source National Bank of Hungary (Pénzügyi számlák adataiból készített grafikonok; www.mnb.hu „grafikonok.xls”)
Net financial position of the general government, as percentage of GDP
1995-2010
National Bank of Hungary (Pénzügyi számlák adataiból készített grafikonok; www.mnb.hu „grafikonok.xls”)
Gross liabilities of the general government, as percentage of GDP
1995-2010
National Bank of Hungary (Pénzügyi számlák adataiból készített grafikonok; www.mnb.hu „grafikonok.xls”)
Government debt, currency breakdown 1995-2010
Hungarian Debt Management Agency (Tables “A központi költségvetés bruttó adóssága”) http://akk.hu/object.c693e119-153c-49bcbc3d-71f805d83db1.ivy
Interest rate expenses of the central government
1995-2004
Ministry of Finance: “A gazdasági átalakulás számokban 1994-2004” http://www2.pm.hu/web%5C%5Chome.nsf/portalarticles /683EE0B231205DF3C1257097002D4072 /$File/Hossz%C3%BA%20id%C5%91sorteljes2004.pdf
2005-2010
Hungarian Central Statistical Office: A kormányzati szektor adatai, 2010. III. negyedév http://portal.ksh.hu/pls/ksh/docs/hun/xftp/g yor/krm/krm21009.pdf
Foreign currency reserves
1995-2010
National Bank of Hungary http://www.mnb.hu/Statisztika/statisztikaiadatok-informaciok/adatok-idosorok
Nominal GDP
1995-2010
Hungarian Central Statistical Office (Bloomberg: HUGQT Index)
Real GDP growth, seasonally adjusted
1995-2010
Hungarian Central Statistical Office (Bloomberg: HUGST Index)
Consumer pirce index
1995-2010
Hungarian Central Statistical Office (data
17
downloaded from the website of the NBH: http://www.mnb.hu/Statisztika/statisztikaiadatok-informaciok/adatok-idosorok) Exchange rates of the German mark and the euro
1995-2010
Bloomberg (Bloomberg: DEM/HUF illetve EUR/HUF Curncy)
Hungarian and Gerrnan government yields, 3-year maturity EMBI spread for the euro denominated Hungarian debt
1997-2010
Bloomberg
1998-2010
J.P. Morgan
18
Annex 2: Vectorautoregressive model specifications and estimation results The ex-ante scenario analysis is based on a vectorautoregressive (VAR) model. The VAR model covers the domestic and euro denominated Hungarian government debt yields (we use 3-year maturity yields as a proxy), the real GDP growth rate, the estimated primary fiscal balance (net financing need of the general government minus interest payments), the euro/forint exchange rate, and the consumer price index. Using formula (2), we can then easily estimate the debt-toGDP ratio as a function of the variables of the VAR model. The interest rates in our database are expressed in annual terms, whereas the change in the real growth, the primary fiscal balance, the exchange rate, and the consumer price index are expressed in quarterly frequencies. We present the unit root test results in Table F1. The results indicate that our time series, in general, are well behaved. Table F1: Unit root tests (1996-2010) 1 lag ADF statistics Domestic nominal interest rate (ID) -4,31 Nominal interest rate of the euro denominated -2,72 debt (IF) Real GDP growth (G) -2,35 Primary fiscal balance (P) -2,08 Euro exchange rate, change versus the forint -6,20 (F) Inflation (PI) -3,43
p-value 0,0011 0,0775 0,1596 0,2504 0,0000 0,0136
We choose using 1 lag for the VAR model, based on the information criteria summarized in Table F2. A VAR(1) model can be written as yt Ayt 1 u t , where
u t ~ N 0, .
The parameter estimates based on the full historical sample, as well as for the period 1996-2006 are summarized in Table F3 and F4 respectively. While our time series are fairly short, the results are robust enough to highlight some of the characteristics of the behavior of the variables: Except for the quarterly changes in the exchange rate, all other variables exhibit reasonably high degree of serial correlation, including the seasonally-adjusted primary fiscal balance; The real growth rate is negatively correlated with domestic and foreign interest rates in the same period, and reacts negatively to increasing rates after one quarter time lag; The domestic interest rate is positively correlated with the change in the euro vis-à-vis the forint in the same period, but the forint strengthens following hiking domestic interest 19
rates with one lag delay. Similarly, the forint reacts negatively to an increasing euro interest rate; While we see that domestic interest rates are positively correlated with inflation in the same period, we do not see the inflation dropping after domestic yield hiked; Finally, it is worth to mention that there is a relatively high correlation between the domestic interest rate and the primary fiscal balance.
The scenario-specific debt-to-GDP path forecast is calculated by adjusting the constant vector of the VAR model. In such a way the underlying variables converge to some pre-determined scenario-specific long term levels. Note, that the unconditional expectated value of VAR(1) can be expressed as Y I A 1
where the vector Y represents the long-term forecast for our variables of the VAR system. The value of the vector Y is obviously determined by our estimation results and depends on the selected historical sample. However, we would not like to tie the scenarios to pure historical data. We actually present two distinct scenarios in the paper: an optimistic and a realistic scenario for the variables of the VAR(1) model. Each scenario is detrermined in terms of setting subjective long term expectations for each economic and market variables in vector Y*. In order to have the variables to converge to our assumed optimistic or realistic levels of vector Y*, we need to replace vector ν with ν* so that
Y * I A *
In order to draw confidence intervals around the expected debt-to-GDP ratio path, we run stochastic simulations using the estimated covariance matrix of the VAR model. Table F2: Information criteria (1996-2010) Akaike Schwarz 1 lag -37,49 -35,99 2 lag -36,42 -33,62 3 lag -35,67 -31,55 4 lag -34,41 -28,94
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Table F3: VAR(1) estimation results, 1996-2010 ID IF G P 0.6235 -0.0021 -0.0127 -0.0431 (0.0981) (0.0855) (0.0454) (0.0822)
F -0.4706 (0.3683)
PI 0.0476 (0.0276)
IF (-1)
0.2576 (0.1652)
0.5730 (0.1440)
-0.1072 (0.0764)
0.0527 (0.1384)
0.7935 (0.6201)
0.0450 (0.0464)
G(-1)
0.4027 (0.2763)
-0.1975 (0.2408)
0.5945 (0.1277)
-0.2125 (0.2314)
0.2029 (1.0370)
0.1155 (0.0777)
P(-1)
-0.1222 (0.1113)
0.2127 (0.0970)
0.0123 (0.0514)
0.8174 (0.0932)
-0.5866 (0.4176)
0.0078 (0.0313)
F(-1)
0.0328 (0.0401)
0.0471 (0.0349)
0.0122 (0.0185)
0.0025 (0.0335)
-0.1202 (0.1503)
-0.0134 (0.0113)
PI(-1)
0.8830 (0.4269)
-0.1158 (0.3720)
0.1358 (0.1973)
0.4052 (0.3575)
2.5081 (1.6020)
0.6757 (0.1200)
C
0.0005 (0.0116)
0.0311 (0.0101)
0.0077 (0.0054)
-0.0076 (0.0097)
-0.0453 (0.0436)
-0.0028 (0.0033)
0.9211 0.9118
0.7037 0.6688
0.5990 0.5519
0.8730 0.8580
0.0751 -0.0337
0.9180 0.9084
ID(-1)
R-squared Adjusted Rsquared Covariance/correlation
ID
IF
P 0.000002 0.000007
F
PI
0.000320
0.000004 0.000005
ID
0.000140
0.000046
IF
0.38
0.000106
0.000011 0.000030
G
-0.17
-0.53
0.000030
0.000006
P
-0.02
-0.07
0.11
0.000098
0.000228 0.000066 0.000025
F PI
0.61 0.10
0.50 -0.15
-0.27 0.11
-0.06 0.40
0.001968 -0.20
21
G
0.000002 0.000013 0.000030 0.000011
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Table F4: VAR(1) estimation results, 1996-2006 ID IF G P 0.5938 0.0750 -0.0262 0.1506 (0.1160) (0.0623) (0.0325) (0.1043)
F -0.4075 (0.3636)
PI 0.0827 (0.0371)
IF (-1)
0.1219 (0.2033)
0.6969 (0.1093)
0.0441 (0.0570)
0.0381 (0.1828)
0.7278 (0.6374)
0.0349 (0.0650)
G(-1)
0.9708 (0.6008)
-0.1043 (0.3229)
-0.0607 (0.1684)
-0.6929 (0.5402)
2.5819 (1.8835)
0.1241 (0.1919)
P(-1)
-0.1890 (0.1225)
0.1481 (0.0658)
0.0283 (0.0343)
0.9650 (0.1102)
-0.8300 (0.3841)
0.0443 (0.0391)
F(-1)
-0.0103 (0.0552)
0.0378 (0.0297)
-0.0069 (0.0155)
0.0125 (0.0496)
-0.2052 (0.1729)
-0.0184 (0.0176)
PI(-1)
1.2612 (0.5191)
-0.3286 (0.2790)
-0.0040 (0.1455)
-0.5280 (0.4668)
2.9521 (1.6274)
0.4998 (0.1658)
C
-0.0028 (0.0134)
0.0171 (0.0072)
0.0116 (0.0038)
-0.0035 (0.0121)
-0.0841 (0.0421)
-0.0021 (0.0043)
0.9453 0.9362
0.8575 0.8337
0.1359 -0.0081
0.9091 0.8940
0.1847 0.0489
0.9297 0.9179
IF 0.000013 0.000032 0.12 0.04
G 0.000010 0.000002 0.000009 0.04
P 0.000004 0.000002 0.000001 0.000089
F 0.000150 0.000010 0.000024 0.000043
0.05 0.05
0.24 0.00
0.14 0.29
0.001085 -0.05
1996-2006 ID(-1)
R-squared Adjusted Rsquared
Covariance/correlation ID ID 0.000110 0.22 IF 0.32 G 0.04 P F PI
0.43 0.29
23
PI 0.000010 0.000001 0.000000 0.000009 0.000006 0.000011
