Finland: Selected Issues and Analytical Notes

This Selected Issues and Analytical Note on Finland discusses the potential spillovers to Finland from various shocks associated with cross-country interlinkages. The note provides an overview of the trade and financial linkages, assesses the impact of global fiscal consolidation on Finland via trade links, quantifies dynamic contributions from external sources to growth, and uses these contributions to forecast the potential loss to Finnish GDP from a growth slowdown in other European countries; and analyzes the potential impact from the banking sector or sovereign stress.


This Selected Issues and Analytical Note on Finland discusses the potential spillovers to Finland from various shocks associated with cross-country interlinkages. The note provides an overview of the trade and financial linkages, assesses the impact of global fiscal consolidation on Finland via trade links, quantifies dynamic contributions from external sources to growth, and uses these contributions to forecast the potential loss to Finnish GDP from a growth slowdown in other European countries; and analyzes the potential impact from the banking sector or sovereign stress.

VI. Analytical Note 6: From Short-Term Vulnerabilities to Long-Term Sustainability1

With a rapidly aging population, Finland needs to address its long-term fiscal challenges. At the same time, the turmoil in the euro area sovereign debt markets has led to increased focus on debt sustainability and associated short-term vulnerabilities. First, this note will present Finland’s short-term fiscal position and challenges in an international context. Second, the note quantifies the long-term fiscal challenges by estimating the sustainability gap and examines the optimal pace of consolidation under quadratic preferences.

A. Finland’s Short- and Medium-Term Vulnerabilities in Perspective

1. Finland’s public deficit continued to narrow in 2011 but the turmoil in other euro area periphery countries put renewed focus on underlying vulnerabilities. After a strong rebound in 2010, growth remained buoyant in the first half of 2011. In addition, though Finland was subject to the Excessive Deficit Procedure, the 2010 general government deficit came in below the Stability and Growth Pact (SGP) ceiling at 2¾ percent of GDP, only marginally worse than in 2009. In 2011, the continued recovery in combination with fiscal adjustment measures facilitated a further narrowing of the deficit, which reached 0.8 percent of GDP. However, the escalating tensions in the euro area sovereign debt markets in 2011 led to contagion and growth spillovers throughout the region, and the turmoil spread to more sovereigns, which previously had been very liquid. Financial markets showed how underlying vulnerabilities quickly can increase financing pressures.

Assessing Short- and Medium-Term Vulnerabilities

2. Fiscal vulnerabilities should be monitored closely, but they are manageable in Finland. The euro area sovereign debt turmoil has shown how markets swiftly can put pressure on countries, and spreads and funding costs can increase rapidly. In turn, this quickly increases rollover risks, thereby aggravating the crisis. This section provides an overview of a few short- and medium-term fiscal vulnerability indicators for advanced countries, following Schaechter et al. (2012), which we then apply to Finland. We conclude that with the benefit of a generally conservative fiscal stance prior to the crisis and fiscal consolidation as the recovery resumed, Finland’s short- and medium-term vulnerabilities are comparatively low.


3. We assess fiscal vulnerabilities from several different angles and horizons including both public debt and financial market indicators. First, to assess the sovereign debt rollover risk we compute two indicators: (i) the governments’ gross funding needs (GFN) for 2012 as an indicator of short-term vulnerabilities; and (ii) the average amount of the end-2011 stock of debt that needs to be annually repaid and/or refinanced in the future. This provides an indicator of longer-horizon vulnerability. Second, we compute two government default risk indicators: (i) one based on sovereign Credit Default Swap (CDS) spreads; and (ii) one based on relative asset swap (RAS) spreads. Third, we evaluate fiscal vulnerabilities associated with growth and interest rate shocks through a simple partial equilibrium model. Last, we decompose the movements in Finnish 10-year government bond yields in order to identify the main drivers of changes in the yield. The appendix contains detailed information on the underlying assumptions and methodologies.

4. The level of gross funding needs in the current year is a measure of how vulnerable countries are to changes in market sentiment. With large fiscal deficits from the 2008–09 global crisis and the subsequent euro area crisis, many advanced countries will be issuing large amounts of net debt in 2012. In addition, a significant amount of maturing debt will need to be refinanced. With frazzled financial markets, this could be associated with increased financing and rollover risk. Rapid increases in funding costs can quickly put severe pressure on countries with high gross funding needs. Therefore, we compute the gross funding needs (GFNs) as the sum of the projected 2012 general government deficit and government debt maturing in 2012, both in percent of GDP. In addition, based on the ratio between the stock of end-2011 general government debt and the average debt maturity, we compute the average amount of debt that needs to be annually refinanced or repaid in the current and future years. A country is more exposed to financing pressures the higher the stock of debt and the lower the average maturity of debt.

5. Two high-frequency financial variables reflect investors’ concerns about fiscal sustainability and risk. Sovereign CDS spreads measure the direct cost of seeking insurance against sovereign default and are quoted as a percentage of the notional amount insured. Therefore, we create a CDS indicator, which is computed as the average of 5-year sovereign CDS spreads during April 19—May 2, 2012. Furthermore, Alper et al. (2012) consider the RAS spread indicator, which is the spread between 10-year government bond yields and the 10-year fixed interest rate arm in interest rate swap contracts. This indicator allows for a comparison of risk premia attached to various government bonds. In fact, as both rates are denoted in local currency, the RAS spread indicator abstracts from currency risk and is therefore comparable across countries also outside the euro area. We thus compute a RAS indicator as the average of daily RAS spreads during April 19—May 2, 2012. One note of caution is necessary, however, in the use of these types of indicators as recent experience has shown that spreads for countries with significant public finance problems can remain low well into the path to a crisis and then surge suddenly.

6. The sensitivity of general government debt to shocks captures how an adverse economic outlook would affect the debt to GDP ratio. First, we compute general government debt based on the debt accumulation equation, where debt is expressed as a function of debt in the previous period, the growth-adjusted interest rate, and the primary balance in the current period. Second, using the debt accumulation equation we project an alternative debt path under the assumption of either (i) a 1 percentage point lower real and nominal GDP growth rate or (ii) a 1 percentage point higher nominal interest rate. Both shocks are assumed to persist during 2012–17. Hence, we evaluate the effect on the debt-to-GDP ratio relative to the no-shock scenario in 2017—the end of the projection period.

7. A decomposition of changes in Finnish bond yields can help identify the main drivers of Finnish yields. To better understand the fluctuations in Finnish bond yields, we decompose the changes in the 10-year bond yield using a 16-country vector autoregression (VAR) on weekly data. Using several different VAR specifications, we then compute the average contribution to the change in the Finnish yield from movements in other countries’ bond yields.


8. Sovereign debt rollover risk in Finland is lower than in a number of other advanced countries. Gross funding needs (GFNs) are indeed substantial for some countries. However, owing to below average debt (in percent of GDP) maturing in 2012, Finland’s GFNs are below the advanced country sample average (Figure 6.1). And though the average number of years to maturity in Finland is below that of several of its peers, total public debt of around 50 percent of GDP places Finland below the median country in the sample with respect to the level of the estimated stock of end-2011 debt that needs to be annually repaid and/or refinanced.

Figure 6.1.
Figure 6.1.

Gross Funding Needs

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: Bloomberg, IMF World Economic Outlook (WEO) database, and IMF staff calculations.Note: Total debt from WEO differs from total debt in Bloomberg. The difference is assumed to have a maturity of longer than one year and not to affect the average debt maturity.

9. Market risks in Finland are also comparatively low. The CDS indicator puts Finland among the least vulnerable countries in the advanced country sample (Figure 6.2). However, recent fluctuations show that Finland is not immune to the escalating tensions in euro area debt markets, though spreads have remained below their September 2011 peak. Similarly, the RAS indicator places Finland in the low-spread group of advanced countries. Here, a negative RAS spread indicates that investors assess government paper as less risky than the flow of funds exchanged between big commercial banks as part of the interest rate swaps (Schaechter et al., 2012).

Figure 6.2.
Figure 6.2.

Market Perception of Sovereign Default Risk

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: Datastream and Fund staff calculations.Note: Daily data do not include weekends.1/ Average over April 19-May 2, 2012.

10. With a comparatively low baseline level, Finland’s gross debt is among the least affected by shocks. Staff projects baseline general government gross debt at around 50 percent of GDP in 2017. However, with the turmoil in the euro area sovereign debt markets, the economic outlook is subject to greater-than-usual uncertainty. The analysis suggests that if growth were to average just below 1 percent per year during 2012–17 instead of the current projection of 1¾ percent per year, public debt would increase by more than 10 percentage points of GDP by 2017. Recent turbulence has, however, increased the volatility of growth. Thus, a shock twice as large would raise debt above 70 percent of GDP by 2017. This would still place Finland well below the European average debt level, though it would breach the Maastricht debt criterion. The impact of a 100 basis point shock to the nominal interest rate would be smaller (Figures 6.36.4, Table 6.1).

Figure 6.3.
Figure 6.3.

Impact of Shocks

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: IMF World Economic Outlook and Fund staff calculations.
Figure 6.4.
Figure 6.4.

Public Debt Sustainability: Bound Tests 1/2/

(Public debt in percent of GDP)

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: International Monetary Fund country desk data, and Fund staff estimates.1/ Shaded areas represent actual data. Individual shocks are permanent one-half standard deviation shocks. Figures in the boxes represent average projections for the respective variables in the baseline and scenario being presented. Ten-year historical average for the variable is also shown.2/ For historical scenarios, the historical averages are calculated over the ten-year period, and the information is used to project debt dynamics five years ahead.3/ Permanent 1/4 standard deviation shocks applied to real interest rate, growth rate, and primary balance.4/ One-time real depreciation of 30 percent and 10 percent of GDP shock to contingent liabilities occur in 2012, with real depreciation defined as nominal depreciation (measured by percentage fall in dollar value of local currency) minus domestic inflation (based on GDP deflator).
Table 6.1

Finland: Public Sector Debt Sustainability Framework, 2007–17

(In percent of GDP, unless otherwise indicated)

article image
Sources: GlobalInsight, IMF World Economic Outlook, Statistics Finland, and Fund staff calculations and projections.

Indicate coverage of public sector, e.g., general government or nonfinancial public sector. Also whether net or gross debt is used.

Derived as [(r - π(1+g) - g + αε(1+r)]/(1+g+π+gπ)) times previous period debt ratio, with r = interest rate; π = growth rate of GDP deflator; g = real GDP growth rate; α = share of foreign-currency denominated debt; and ε = nominal exchange rate depreciation (measured by increase in local currency value of U.S. dollar).

The real interest rate contribution is derived from the denominator in footnote 2/ as r - π (1+g) and the real growth contribution as -g.

The exchange rate contribution is derived from the numerator in footnote 2/ as αε(1+r).

For projections, this line includes exchange rate changes.

Defined as public sector deficit, plus amortization of medium and long-term public sector debt, plus short-term debt at end of previous period.

The key variables include real GDP growth; real interest rate; and primary balance in percent of GDP.

Derived as nominal interest expenditure divided by previous period debt stock.

Assumes that key variables (real GDP growth, real interest rate, and other identified debt-creating flows) remain at the level of the last projection year.

11. The VAR analysis shows that movements in Finnish bond yields are driven largely by their German equivalents but points to vulnerabilities from other countries. The adjacent text chart shows the average contribution to the changes in the Finnish government bond yield, resulting from several different VAR specifications. Indeed, downward movements in Finnish yields are highly associated with downward changes in German and U.S. yields. However, the main determinants also point to sources of vulnerability from real-financial linkages and spillovers from other countries, as increases in yields in Greece, Ireland, and Portugal or Spain are associated with upward pressure on Finnish yields. Nonetheless, domestic factors in Finland continue to work in Finland’s favor.


Decomposing Finnish Government Bond Yield, 2007–12

(Contribution to changes in government bond yield, basis points)

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: Bloomberg and Fund staff calculations.

With Short-Term Vulnerabilities in Mind, What is the Appropriate Fiscal Stance?

12. With relatively low short- and medium-term fiscal vulnerabilities, short-term fiscal policy should pay due attention to the growth momentum. Euro area periphery countries with high vulnerabilities and immediate funding pressures have no choice but to continue fiscal consolidation in order to calm markets and restore prospects for fiscal sustainability. However, short-term fiscal consolidation should be limited where possible, while fiscal adjustment in the medium and long term remains on the agenda (IMF, 2012). Countries with credible medium-term fiscal consolidation plans should allow automatic stabilizers to work fully so as not to have strong negative spillovers on near-term growth and possibly consider some discretionary stimulus. As Finland falls in the second category, authorities should be careful to avoid too rapid a consolidation of public finances. With a rapidly aging population and an associated sustainability gap (see below), the speed of consolidation therefore involves a careful balancing act.


Finland: General Government Balances, 2007–17

(Percent of potential GDP)

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: DataInsight, Finland Ministry of Finance, Statistics Finland, and Fund staff calculations.1/ Adjusted for interest expenditure.

13. With a still negative output gap, fiscal consolidation should be carried out at cautious speed. With a general government deficit of -¾ percent of GDP in 2011 and 2011 output around 3 percent below potential as suggested by the production function approach, the general government structural balance is in a slight surplus and the structural primary surplus is just above 2 percent of GDP. However, this mainly reflects the 3 percent of GDP surplus in employment pension funds, while the central government balance is showing a structural deficit. Nonetheless, while fiscal adjustment is necessary, a level of output below potential underlines that Finland should pursue fiscal consolidation at a moderate pace.

B. Long-Term Sustainability

14. On the back of manageable short-term vulnerabilities, this section assesses long-term fiscal sustainability in Finland and examines the optimal pace of consolidation. The estimates of aging pressures from the European Commission’s (EC’s) Sustainability Report 2009 (EC, 2009), which are still the latest estimates from the EC, are incorporated in the analysis, as well as the implications of the recent movements in the fiscal position. The sustainability gap is evaluated from a starting point of 2012, and thus incorporates only those consolidation measures that were implemented through 2011. We conclude that the sustainability gap as of 2012 is significantly smaller than that estimated for 2010 in the 2010 Staff Report (IMF, 2010a), though still substantial. Measures to help erase the sustainability gap are briefly discussed. In addition, an inter-temporal model is calibrated to Finland and used to shed light on the optimal fiscal consolidation path given quadratic preferences over the sustainability and output gaps.

15. ECFIN’s baseline estimates of aging pressures for Finland are in the mid-range in comparison with other European countries. From 2007 to 2060, aging pressures are estimated to add 6.4 percent of GDP to fiscal expenditures in Finland, moderately above the median of 5.3 percent of GDP across the European Union. The increase for Finland is composed of increased pension expenditure of 3.3 percent of GDP, higher long-term care expenditure of 2.6 percent of GDP, higher health-care expenditure of one percent of GDP, and reduced education and unemployment-benefit expenditures of 0.3 and 0.2 percent of GDP, respectively.


Change in Expenditure Due to Aging, 2007–60

(Percent of GDP)

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: DG ECFIN: The 2009 Ageing Report, and Fund staff calculations.

Aging-Related Expenditure: Different Scenarios, 2008–60

(Percent of GDP)

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: DG ECFIN: The 2009 Ageing Report and Fund staff calculations.

16. These baseline estimates are sensitive to the underlying assumptions used. A variety of alternative scenarios run by ECFIN suggest that the increase in aging related expenditures could vary between 5.8 and 7.4 percentage points of GDP, with the worst case being one of zero immigration, while a scenario with higher employment rate is the best case. As long-run estimates are inherently subject to substantial error margins, our estimate of the sustainability gap should be interpreted as a baseline estimate subject to a sizeable confidence band.

Estimating the Fiscal Sustainability Gap

17. The sustainability indicator used is based on the general government intertemporal budget constraint. This is consistent with the S2 sustainability indicator used in the EC’s sustainability reports. The starting point for this analysis is the equation defining the evolution of public debt:


Where Bt, r, and Pt, represent the debt stock at the beginning of period t, the discount rate, and the primary surplus in period t, respectively. Dividing equation (1) by GDP gives the following equation:


Here, bt and pt represent the debt-to-GDP ratio at the beginning of period t and the primary surplus-to-GDP ratio in period t, respectively, and g represents the growth rate of GDP, assumed to be constant for algebraic simplicity. Solving equation (2) forward and imposing the no-Ponzi-scheme condition yields the government inter-temporal budget constraint:


For any given fiscal stance (e.g. the current structural primary fiscal balance) and given the outlook for growth and other expected exogenous changes such as demographic changes and depletion of natural resources, a “passive” path for the primary surplus over an infinite horizon can be estimated. On that basis, the sustainability gap in stock terms (which is the total inter-temporal debt in present value terms) is given by:


The sustainability gap in flow terms—hereafter simply called the sustainability gap—(which is defined as the constant change in the primary balance in percent of GDP such that the sustainability gap in stock terms is zero) is thus derived as:


18. Staff’s updated estimate of the sustainability gap is about 1¾ percent of GDP lower than that in the 2010 Staff Report. Stronger than anticipated fiscal performance in 2010 led to a broadly stable headline fiscal balance compared to 2009, whereas staff had anticipated a deterioration of around 1½ percent of GDP. This improvement reduced the buildup of public debt. Also, revisions to staff’s estimated output gap imply that the estimated level of the structural primary balance is higher than before. Taking these factors into account, as well as the structural tightening of one percent of GDP in 2011, we find that the estimate of the sustainability gap has declined to 4¼ percent of GDP, well below the previous estimate of 6 percent of GDP in the 2010 Staff Report. The sustainability gap could turn out to be smaller than estimated if the external current account balance deteriorates as a rising number of retirees draw down their accumulated pensions, raising consumption-based tax revenues over the long run as a share of output. However, we have not taken this into account in our calculations because the size of this effect is quite uncertain.

19. Absent corrective measures, net public debt is projected to rise to over 200 percent of GDP by 2060 in view of the still substantial sustainability gap. The primary balance is projected to decline by 4¾ percentage points of GDP to a deficit of 4¼ percent of GDP, while the overall fiscal deficit deteriorates by 15 percentage points of GDP to 14¾ percent of GDP as interest payments consume an ever-increasing share of fiscal expenditure. In contrast, immediate full adjustment implies that net debt remains on a gradually declining path through 2060.

20. While immediate full adjustment on the scale required is implausible, delaying adjustment requires a higher long-run primary surplus target to ensure sustainability. Staff estimates that phasing in the adjustment over a 10-year period, with uniform adjustment each year, requires structural measures totaling 4½ percent of GDP for sustainability. In comparison, delaying the onset of adjustment for 10 years would require structural measures totaling 4¾ percent of GDP for sustainability. In general, slower adjustment is associated with a higher public debt path.

21. Other commonly-used sustainability indicators generally show smaller gaps, but do not satisfy the intertemporal budget constraint. In particular, the European Commission defines another indicator, S1, as the constant change to the primary balance in percent of GDP such that the public gross debt to GDP ratio is 60 percent of GDP in 2060. The IMF’s Fiscal Affairs Department sometimes uses an indicator (which we will call S3 here for brevity) defined similarly as the constant change to the primary balance in percent of GDP such that the public gross debt to GDP ratio is 60 percent of GDP in 2030. S1 and S3, however, generally do not satisfy the intertemporal budget constraint as they do not address what happens beyond the respectively envisaged time horizons. For Finland, we estimate S1 and S3 to be 2½ percent of GDP and ½ percent of GDP, respectively. In both cases our estimates indicate that gross debt is on a strongly rising path beyond the respective time horizons used. Thus, we do not focus on these indicators beyond this point.

Measures to Achieve Sustainability

22. With an already high revenue ratio, there is little scope for further increases in the tax burden. Revenue measures should therefore focus on a broadening of the tax base and a shift from labor taxation to consumption and property-based taxation. Reduced labor taxation would help stimulate employment and output, while consumption and property taxes are generally less distortionary than income taxes. In this connection, recent reductions in income tax rates, the increase in VAT rates by one percentage point in mid-2010, and plans to raise energy taxes are steps in the right direction; but more should be done, including by reducing the number of items on reduced VAT rates. In addition, property tax rates are low in international comparison and higher rates would provide municipalities with a more stable source of income, creating scope for reducing municipalities’ reliance on highly cyclical corporate taxes.

23. Expenditure measures will need to account for the majority of adjustment. This reflects both the already high revenue ratio and the fact that international evidence generally indicates that expenditure–based consolidations have been more successful. In this regard, the focus will need to be on reducing the impact of aging on fiscal expenditures and on an overhaul of local government—where expenditures have been rising fastest in recent years. Some reduction of the generosity of the social and unemployment benefits system is likely to be needed as part of the fiscal consolidation package. Tuition fees and a reduction of student grants in favor of loans at the tertiary education level would also be helpful in generating expenditure savings and encourage faster graduation and entry into the work force.

24. Measures to directly contain the impact of aging on public finances should be a key plank of efforts to secure sustainability. In this regard, further pension reform is needed. The decomposition of the projected buildup in pension pressures indicates that the increase arises from a pronounced increase in the old-age dependency ratio, which is projected to be partly offset by tightening of eligibility rules. However, more could be done. The OECD (2010) notes that the average effective retirement age is about 60 and estimates that raising it to 67 would be sufficient to close the sustainability gap. Such a large increase would be very challenging to achieve, but movement in this direction should be a major focus of adjustment efforts. Other areas where there is scope for savings include lowering the accrual rate for pension benefits—particularly for periods of parental leave, unemployment, and education—and tightening access to early retirement via disability or unemployment. For example, the number of persons on disability pension is estimated at about 9 percent of the labor force, which appears excessive. The authorities do not dispute the need for such measures. Indeed, they have raised the effective retirement age in recent years and the latest agreement with social partners further increases it by four months, while further measures are to be implemented by 2017. Also, from 2010 onward new pensions are adjusted downward by a life expectancy coefficient, helping to reduce the impact of aging on pension expenditure.


Decomposing Pension Expenditure Projections, 2010–60

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: DG ECFIN: The 2009 Ageing Report and Fund staff calculations.

25. Eligibility, entitlements, and arrangements for old-age care could also be revisited as this is an area where aging pressures will be significant. The projected increase in long-term care spending for Finland is well above the median for the EU, suggesting that reforms drawing on lessons from other EU countries could yield substantial savings.

26. An overhaul of local government is also needed. Spending at the municipal level has grown faster than in other parts of general government (see AN 7). While some of these spending pressures may have been inevitable given that municipalities are responsible for education, social services, and health care, the OECD (2010) estimates that municipality productivity has declined by about 10 percent over 2000–08. Productivity declines have been most marked in social work and health. Alongside, municipal income tax rates have increased steadily, partially offsetting reductions in central government taxation in recent years. Soft budget constraints have helped encourage fiscal slippages, with buoyant (and highly cyclical) corporate taxation enabling strong expenditure growth in good times.

27. There is a need to harden municipal budget constraints and reduce the cyclicality of their revenues, thus strengthening incentives to generate expenditure savings. The reliance on corporate taxes at the municipal level should be reduced, and the reduction should be offset by higher property taxation or central government transfers. At the same time, a ceiling on municipality income tax rates and restraint in the growth of central government transfers would strengthen incentives for expenditure consolidation at the municipal level. Also, the scope for competitive bidding for the provision of services to municipalities should be broadened to generate cost savings. Finally, there is also scope for efficiency gains through mergers of municipalities as the median population of municipalities is less than 5,000 people.

28. Improving the rate of return on public financial assets would also help reduce the sustainability gap. Liquid financial assets totaled more than 100 percent of GDP in 2010, and substantial portions of these assets are low-yielding, reflecting a cautious investment approach. Given the large stock of assets, an asset management strategy that generates a modest increase in returns could make a significant contribution to closing the sustainability gap.

C. Optimal Fiscal Consolidation Paths

29. The pace of consolidation will reflect the balancing of the government’s twin stated objectives of reducing both the output gap and the fiscal sustainability gap. We construct a model to assess the optimal pace of consolidation as follows: the authorities are assumed to care about both the sustainability and output gaps and to prefer that both be zero. However, these objectives are conflicting in that action to close the sustainability gap (fiscal tightening) comes at the expense of widening the output gap, while on the other hand, action to close the output gap (fiscal loosening) increases the sustainability gap. Thus, over an infinite horizon, the authorities’ problem can be characterized as choosing a path for the fiscal stance that minimizes the following quadratic objective function:2


Here, Ot, α, γ, and β represent the output gap in percent of GDP in period, t the weight placed by the authorities on closing the output gap, the weight placed by the authorities on closing the sustainability gap, and the authorities’ rate of time preference, respectively, with β = 1/(1+r).

30. The output gap is assumed to evolve according to the following reduced form equation:


Here, ft, λ, and ξ represent, respectively, discretionary fiscal measures taken (in percent of GDP) in period, t an autoregressive parameter on the output gap, which determines how long it would take for the output gap to be eliminated through self-repair of the economy rather than fiscal action, and the fiscal multiplier.

31. Discretionary fiscal measures are assumed to have no effect on potential growth. In effect, discretionary measures only affect GDP growth temporarily, with corresponding changes to the output gap. The constant growth rate assumed in the derivation of the sustainability gap is best interpreted as the average of the annual growth rates over the infinite horizon. With the underlying potential growth path unchanged, temporary deviations of annual growth rates have a negligible impact on the average calculated over the infinite horizon. Moreover, since the output gap closes, temporarily low growth rates must be offset by temporarily higher growth rates. Thus, notwithstanding some variation in growth rates, equation 5 would still give a close approximation to the sustainability gap.

32. It is necessary to adjust the sustainability gap formula to reflect discretionary actions. If we adjust equation (5) to take account of discretionary fiscal measures taken in time t in addition to the “passive” evolution of the primary surplus, then we get:


Some algebraic manipulations then reveal that the sustainability gap evolves as follows:


33. Equation (9) confirms that in the normal case where the discount rate exceeds the GDP growth rate, delaying actions to ensure sustainability is costly. The magnitude of the sustainability gap increases over time absent discretionary measures to close it, since the discount rate (which governs the pace of debt accumulation) exceeds the GDP growth rate (which governs the burden of debt relative to GDP).

34. The authorities’ problem is to choose the size of fiscal measures in time t to minimize the objective function (6) subject to equations (7) and (9). Given the quadratic preferences and linear constraints, we know that the optimal fiscal tightening in any time period is a linear function. We therefore speculate that the fiscal consolidation pace is governed by the following equation:


Here, A > 0 and B > 0. Substituting equation (10) into the first-order condition of the authorities’ problem and solving for A and B yields:


35. Thus, the optimal path for fiscal consolidation depends on the starting values for a number of factors. Specifically, the optimal consolidation path depends on starting values for the output and sustainability gaps, the fiscal multiplier, the speed of self-correction of output gaps, the discount and GDP growth rates, and the authorities’ preferences. For Finland, starting in year 2012, the initial sustainability gap is, as mentioned, calculated at 4¼ percent of GDP, while it is estimated that the (negative) output gap in 2011 was around 3 percent of GDP. λ is calibrated to equal 0.5, implying that absent fiscal measures and ceteris paribus, an output gap of 2 percent of GDP is eliminated after six years via spillovers, confidence effects, monetary policy actions, self repair etc. The fiscal multiplier is taken to be 0.5, as estimated in IMF (2010b) for advanced European countries. The discount rate and GDP growth rate are taken to be 5 percent and 3.5 percent respectively, consistent with EC’s (2009) findings.

36. Given these estimates, the parameters governing the authorities’ preferences are pinned down by “revealed preference.” We renormalize the policy function, without loss of generality, by assuming that γ = 1-α, where O ≤ α ≤ 1. On this basis, the value of α is taken to be that which is consistent with the size of the announced change in the structural primary balance in 2012, given the initial values of the output and sustainability gaps. We focus on 2012 (rather than using the entire path of announced annual tightening over the medium term to pin it down) because measures for 2012 are fully fleshed out and passed by parliament in the 2012 budget. For subsequent years, plans are often less detailed and measures to support envisaged tightening may not be fully in place. On this basis we estimate that α = 0.9.

37. In general, the optimal consolidation path includes some front-loading of adjustment, but also envisages that full elimination of the sustainability gap takes place over a long horizon. Quadratic preferences mean that the pressure to act to reduce any of the two gaps under consideration increases in nonlinear fashion with the size of that gap. Thus, if the sustainability gap is large enough relative to the output gap, the optimal immediate fiscal tightening would be one that trades a substantial reduction in the sustainability gap for some increase in the output gap. Therefore (subject to the weights in the authorities’ preferences) the larger the sustainability gap, the more optimal it is to front-load adjustment. Also, the authorities have a very long horizon over which to consider and implement adjustment, and under quadratic preferences they would tend to select a path in which both the output and sustainability gaps trend toward zero, which then pushes back the timing for full sustainability to be achieved.

38. For Finland, the model predicts an optimal path with fiscal tightening of about one percent of GDP in 2013 and with the pace of adjustment tapering off over time. Under this scenario, the sustainability gap declines steadily, though the pace of decline drops over time, and it is eliminated in 2034. Because of the delay in achieving sustainability, the total amount of measures needed rises above the sustainability gap to about 4½ percent of GDP.

39. The preponderance of downside risks to the near-term macro forecast, however, suggests that a more uniform adjustment pace would be advisable. The model, being deterministic, does not explicitly take forecast risks or shocks into account. With downside risks dominating, and uncertainties unusually large over the near term, this argues for lower adjustment in the near term. A uniform adjustment path, also depicted as the plausible adjustment scenario in Figure 6.5, with a view to close the sustainability gap in 10 years, could be considered plausible, and would require total measures of about 4½ percent of GDP.

Figure 6.5.
Figure 6.5.

Fiscal Sustainability, 2011–60

(Percent of GDP)

Citation: IMF Staff Country Reports 2012, 254; 10.5089/9781475506013.002.A006

Sources: ECFIN: The 2009 Ageing Report and Fund staff calculations.1/ The plausible adjustment scenario is that of uniform adjustment over a 10-year period.2/ Net debt is defined as gross debt minus liquid financial assets.

D. References

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  • Kanda, Daniel, 2011, “Modeling Optimal Fiscal Consolidation Paths in a Selection of European Countries,” IMF Working Paper 11/164, Washington: International Monetary Fund.

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Appendix 6.1. Methodology for Short- and Medium-Term Vulnerability Indicators

(i) Sovereign Debt Rollover Risks: Gross Funding Needs

Methodology: The Gross Funding Needs is the sum of the projected general government deficit for 2012 and of government debt maturing in 2012, both in percent of GDP.

Data: General government deficit projections and nominal GDP is from the World Economic Outlook (WEO) database, while data on maturing debt in 2012 are from Bloomberg as of end-2011. One caveat of the data involves the difference in debt levels between Bloomberg and WEO data. As the coverage of total public debt from Bloomberg differs from that in the WEO database, data on maturing debt likely do not have the same coverage either. Hence, the results can only be considered approximate.

(ii) Sovereign Debt Rollover Risks: Average Repayment and/or Refinancing Needs

Methodology: The annual average amount of end-2011 debt that needs to be repaid and/or refinanced in the future is computed as the ratio between the end-2011 general government debt in percent of GDP and the average maturity of the government debt.

Data: Data on the general government debt and GDP are from WEO, while the average debt maturity in years is from Bloomberg.

(iii) Market Perception of Default Risk: Sovereign Credit Default Swap (CDS) spreads

Methodology: We compute the CDS spread indicator as the average of daily CDS spreads during April 19–May 2, 2012.

Data: Daily 5-year sovereign CDS spreads are from Datastream.

(iv) Market Perception of Default Risk: Relative Asset Swap (RAS) Spreads

Methodology: We compute the RAS spread indicator as the average of daily data according to the following formula: RASi = Ri - RSWi where Ri is the yield of 10-year government bonds issued by country i, and RSWi is the 10-year fixed rate on interest rate swaps in the currency of country i.

Data: Input data are from Datastream.

(v) Fiscal Vulnerabilities to Shocks

Methodology: First we compute the general government debt level as follows:


Here, dt is the general government debt in percent of GDP, it is the nominal interest rate, γt is the nominal GDP growth rate, and pbt is the primary balance at time t. In turn, the nominal interest rate is compute as the ratio between period t interest payments and period t-1 general government debt.

Due to country-specific factors, this debt accumulation equation may lead to a debt projection that differs from the baseline debt projection from WEO. Hence, we compute an adjustment factor as the difference between the WEO debt projection and the projection from the debt accumulation equation in the no-shock scenario.

The first shock assumes that annual real and nominal GDP growth is 1 percentage point lower than in the baseline projection during 2012–17. As this is a partial equilibrium analysis, the GDP deflator and potential output are assumed unaffected by the shock. The primary balance in the shock scenario is then computed as


where pbtWEO is the baseline primary balance from WEO, ε is the semi-elasticity of the budget balance with respect to the output gap, and Δogt is the change in the output gap from the baseline to the shock scenario.

To compute the debt under the shock scenario, the debt accumulation equation is then rerun, using the shock-modified primary balance and nominal GDP data, while the nominal interest rate, i, is assumed unchanged. Finally, the debt adjustment factor from above is added for consistency with the baseline debt-to-GDP ratio.

The second shock assumes the nominal interest rate is 100 basis points higher than in the baseline during 2012–17. Real and nominal GDP, the output gap, and the primary balance are assumed unaffected relative to the WEO baseline. Debt under the shock scenario is then computed as above and compared to the WEO baseline.

Data: The underlying data on debt, nominal and real GDP, the primary balance, and interest payments are from the WEO database in local currency units. The semi-elasticity of the budget balance with respect to the output gap is from Girouard and Andre (2005).

(vi) Decomposition of Changes in the Government Bond Spread

Methodology: We estimate a vector autoregression (VAR) with weekly data on 10-year government bond yields for 16 countries. The decomposition of the changes in the Finnish bond yield is computed based on the average impulse response and structural errors from 48 different Choleski orderings of the data in the VAR.

Data: The weekly data on 10-year government bond yields are from Bloomberg. The data cover 16 countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Portugal, Spain, Sweden, Switzerland, United States of America, and United Kingdom.


Prepared by Lone Christiansen, Daniel Kanda, and Sebastian Weber.


See Kanda (2011) for full details of the model.

Finland: Selected Issues and Analytical Notes
Author: International Monetary Fund