This 2013 Article IV Consultation examines the performance of Sweden’s fiscal policies to counter effects of global financial crisis. Economic growth in Sweden has been moderate since global financial crisis of 2008–2009. The IMF report posits that with potential growth moderately weaker and the natural rate of unemployment to remain elevated, policies should focus on growth-enhancing reforms, especially in the labor market. It suggests that good policies that secure the soundness of Swedish international banking groups are expected to benefit borrowers not only in Sweden but across the region.

Abstract

This 2013 Article IV Consultation examines the performance of Sweden’s fiscal policies to counter effects of global financial crisis. Economic growth in Sweden has been moderate since global financial crisis of 2008–2009. The IMF report posits that with potential growth moderately weaker and the natural rate of unemployment to remain elevated, policies should focus on growth-enhancing reforms, especially in the labor market. It suggests that good policies that secure the soundness of Swedish international banking groups are expected to benefit borrowers not only in Sweden but across the region.

V. Contingent Liabilities for The Swedish Government and Optimal Size of Fiscal Buffers1

Government contingent liabilities arising from a potential need to support the Swedish banking system could be large, ranging from just below 20 percent of GDP to about 90 percent of GDP depending on the magnitude of the crisis. However, there is considerable uncertainty around such estimates, including from the scope of the potential government intervention, changing reliance on wholesale funding, and potential losses on the balance sheets. A small, stylized model of the Swedish economy suggests that the optimal size of fiscal buffers needed to prepare for such losses is roughly in the range of the contingent liabilities. But the results suggest a gradual build-up to smooth the impact on government spending and GDP.

A. Estimating Government Contingent Liabilities

The Scope of Liabilities—Overview

1. When one or more banks fail in a country, the central government may have to come to the rescue. Whether a government is obligated by law or simply forced by circumstances to provide public financing to cover such contingencies, the realization of such contingent liabilities can lead to large increases in public debt. As recent episodes have indicated, the scope of the government bailout of the banking sector may only cover insured depositors, or may additionally extend to uninsured depositors, and even unsecured creditors (as in Ireland in 2008). Such uncertainty about the extent of the government bailout makes estimating the size of contingent liabilities very difficult. In Sweden, a discussion has begun on how to ensure the framework’s countercyclicality as well as the absence of an explicit long-term anchor to take into account potentially large contingent liabilities from the financial sector.2

2. To shed light on the scope of liabilities a government might face, this note estimates contingent liabilities of the government under different bailout scenarios. The methodology—the balance sheet method—allows for estimation of government contingent liabilities arising from insured and uninsured deposits.

  • This approach assumes that when a bank fails, the assets of the bank are placed in a bankruptcy estate, while the depositors are paid out by the government through the depositor insurance fund.

  • The net loss of the government arising from bailing out depositors is then derived by estimating the liquidation value of the bankruptcy estate and taking the priority ranking of the government against the bankruptcy estate. This net loss is taken as the contingent liability of the government from bailing out depositors.

  • Three different scenarios with varying degrees of government support are considered: in the first scenario insured depositors are bailed out; in the second scenario, in addition, the uninsured depositors are kept whole; and in the third scenario senior unsecured creditors are also held without loss.

3. Combining the estimates from different scenarios gives an estimate of the sum of contingent liabilities facing the government from different claimants on bank assets (Figure 1). The next sections discuss the approach in detail.

Figure 1.
Figure 1.

Bank Liabilities by Seniority and Methodology for Estimating Government Contingent Liability

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

Balance Sheet Method

4. The analysis focuses on the largest six Nordic banks (“Nordic-6”), four of which are headquartered in Sweden. Table 1 provides details about the size of these six banks and Figure 2 demonstrates the cross-border operations of these six banks. The second panel of Figure 2 illustrates that some Swedish households and firms deposit money in non-Swedish banks such as Danske Bank, while simultaneously, Swedish banks operate in other countries (mostly Nordic) and accept deposits from non-Swedish households and firms.

Table 1.

Largest Nordic Banks

(EUR billions, most recent quarter)

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Figure 2.
Figure 2.

Exposure of Nordic-6, by Geography 2012

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

Sources: 2012 Annual Reports and Fund staff calculations.

5. The cross-border nature of banking in the Nordic region implies that any fiscal consequences of government support is highly dependent on the burden sharing rule, which determines how the cost of a bank failure will be shared between the countries involved. To capture this issue, the analysis considers two different burden sharing rules: a deposit base approach, determining each country’s burden based on the share of depositors residing in the respective countries; and a location-of-parent approach, which determines each country’s burden based on the headquarter location of each of the Nordic-6 banks.

6. In addition, the analysis varies the treatment of unsecured depositors by considering three bailout scenarios. In Scenario A, all uninsured depositors are bailed in (implying a haircut of 100 percent), whereas in Scenario B the uninsured depositors are also bailed out completely. Lastly, in Scenario C, there is an additional bailout for the senior unsecured creditors of the banks (with all other assumptions being identical to Scenario B). Note that in all three scenarios, the insured depositors are kept whole.

7. To complete the analysis, additional assumptions about the liquidation value of the bankruptcy estate are needed. Table 2 summarizes all relevant assumptions and Table 3 lists the timeline of the analysis.

Table 2.

Assumptions and Inputs

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In Scenario B the recovery prospect for the Deposit Insurance Fund is lower since for simplicity it is assumed that the initial payout to uninsured depositors is also serviced by the DIF.

Table 3:

Timeline of Scenario Analysis

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Source: Fund staff calculations.

8. In the event that any one of the six banks fails, it is expected that the insured depositors will be bailed out with certainty due to the explicit coverage by deposit insurance. Therefore, the losses under Scenario A should be interpreted as the lower bound of government contingent liabilities arising from the Nordic-6. That is, the expected loss calculations under Scenario A should be interpreted as the minimum losses to the government arising in a tail event when the banking system as a whole requires a bailout. It is, however, likely that in such an event, the uninsured depositors may also get a partial bailout. Scenario B is constructed to factor such additional liabilities into the calculation of possible losses. Similarly, in order to contain systemic risks the authorities may, in principle, also consider extending the bailout to senior unsecured creditors, and Scenario C considers this case.

9. Table 4 summarizes the result of this analysis. As anticipated, the expected losses—that is, the contingent liabilities stemming from the treatment of depositors—to the Swedish government are very sensitive to the burden sharing rule, whereby the losses vary from 17–60 percent of GDP under a deposit base approach to burden sharing to 26–90 percent of GDP under a country of location-of-parent approach. This is because four out of the six largest Nordic banks are headquartered in Sweden (Nordea Bank, Swedbank, SEB, and Handelsbanken). Correspondingly, if the Swedish government ends up having to bear the losses emanating from the cross-border operations of these banks then the size of contingent liabilities ends up becoming quite large.

Table 4:

Estimated Fiscal Costs from the Failure of Big 6 Banks under Different Scenarios

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Source: Fund staff calculations.

Summing Up

10. The balance sheet method suggests that the Swedish government’s contingent liabilities arising from the possible need to support the depositors of the six largest Nordic banks range from just below 20 percent of GDP to 90 percent of GDP. This estimate crucially depends on whether the government will bail out the uninsured depositors and the senior unsecured creditors, and also on the burden sharing rule between the Nordic countries (Figure 3).

Figure 3.
Figure 3.

Potential Fiscal Costs to Sweden of Bailing Out the Six Largest Nordic Banks 1/

(Percent of GDP)

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

Sources: SNL Financial and Fund staff calculations.1/ Bailout costs cover different types of creditors and depositors under alternative burden sharing rules across the Nordic countries involved.

11. Taking a mid-range of the contingent liabilities arising from both burden sharing rules suggests overall contingent liabilities amounting to 30–45 percent of GDP. There is considerable uncertainty around such numbers. One reason is that the government’s approach to unsecured depositors and bond holders could be different than assumed. For example, the estimate would drop to between 20 and 30 percent were the government only to support insured depositors. Another source of considerable uncertainty is the level of bank losses on the balance sheets, which might be higher or lower than those implied by the end-2012 numbers used in the calculations above. Overall, these estimates are very large relative to the ex-post cost of the 1990s bailout of Swedish banks, estimated at less than 5 percent of GDP. The difference can be explained mostly by the much larger size of the banking system, increased asset encumbrance due to heavy reliance on collateralized debt, and complications for the resolution strategy associated with cross-border operations.

B. Optimal Fiscal Buffer and Speed of Accumulation

12. What kind of fiscal buffer should Sweden consider in light of its large contingent liability arising from the financial sector? While the first response is certainly further progress in strengthening the banks themselves, reducing risks from household credit growth, and improving internal and Nordic macroprudential coordination, it also seems prudent to secure fiscal buffers that allow the government to absorb the fiscal burden should the need arise. In principle, such fiscal buffers can be created, for example, by limiting gross debt levels such that contingent liabilities could be covered by issuing new debt if necessary, or by building up sufficiently liquid reserves in a dedicated fund that is deployed when such contingencies materialize.3 In what follows, we explore the conceptual issue of how the government should go about building such a buffer if no such buffer existed at the outset.4

Setup

13. In order to determine the optimal size of a fiscal buffer given contingent liabilities and the speed of accumulation, we rely on a simple optimization problem of the government (see the Appendix). In the model, the government’s sole objective is to smooth government spending subject to its dynamic budget constraint. Each period the government raises a fixed quantity of tax revenue and has to decide on the optimal spending plan. The only source of risk the government faces is that in each period, there is a constant probability of the contingent liability being realized, thereby wiping out a fraction of government wealth (or, equivalently, leading to a spike in the gross debt position of the government). Once the risk is realized, the government faces no further risks.

14. In setting up the model this way, the analysis abstracts from other sources of fiscal risk—such as longevity risk, cyclical fluctuations, etc.—and focuses on the problem of contingent liabilities arising from the financial sector. One interpretation of this approach is that it pertains to the permanent component of the government budget that abstracts from both longer-term trends and cyclical factors.

Results

15. Two key results emerge:

  • The long run fiscal buffer target should approximately match the size of the contingent liability: In the long run (over several decades) the government should target building a fiscal buffer that is almost as large as the size of the contingent liability.

  • The speed of accumulation of the fiscal buffer gradually declines over time: The model suggests that the government front-loads the accumulation of the buffer, with the speed of accumulation gradually declining over time until the optimal fiscal buffer target is reached.

Size of Target Fiscal Buffer

16. The model’s solution suggests that the government’s long-run fiscal buffer target is approximately the size of the contingent liability. The intuition stems from the assumption that the government faces a constant probability of a banking sector crisis (i.e., that the contingent liability is being realized in each period): the longer the time horizon, the more likely it is that a crisis will actually occur; ultimately, as the time horizon becomes very long, the crisis probability converges to one. Therefore, from a long run perspective, the contingent liability can be viewed approximately as a real liability, and consequently, the government will find it optimal to create a buffer at least as large as the size of the liability over a period of a few decades.

17. An interesting subtlety of the optimal solution is that it requires the government to slightly ‘over-buffer’ by creating a target fiscal buffer somewhat larger than the size of the contingent liability (Figure 4). The intuition is that since the government aims at smoothing government spending between periods, it wants to ensure that spending does not increase by a large amount as the contingent liability is realized. Spending in each period depends on the level of debt, since it determines the interest payments the government has to make. This implies that since the government knows that the spending levels will increase after the contingent liabilities are realized due to the increased debt levels, ex-ante they will find it optimal to keep the debt levels low by over-buffering.

Figure 4.
Figure 4.

Target Fiscal Buffer as a Function of Contingent Liability

(Percent of potential GDP)

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

The Optimal Path to Accumulate a Fiscal Buffer

18. How to build the fiscal buffer? The same analytical model used to calculate the size of the buffer also suggests an optimal path for its accumulation along with the implied best time path for government spending. For illustrative purposes, assume that government contingent liabilities amount to 30 percent of GDP. Then for a given set of parameters, the model implies that the target fiscal buffer is roughly 34 percent of GDP. Suppose, in addition, that the government believes that the maximum acceptable level of gross debt is 60 percent of GDP (after the contingent liabilities are realized). Then the model implies that the ex-ante target gross debt level should be around 26 percent of GDP and that this target debt level should be reached gradually. Figure 5 plots the optimal debt path as well as alternative paths for different-sized contingent liabilities.

Figure 5.
Figure 5.

Model-based Transition Path for Government Debt to Build Optimal Fiscal Buffers against Contingent Liability 1/

(Sovereign debt, percent of GDP; years on horizontal axis)

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

Source: Fund staff calculations.1/ Debt threshold, defined as the level of debt the government views as acceptable after the contingent liabilities are realized, is taken to be 60 percent.

19. The figure confirms that, no matter the targeted debt level, building the fiscal buffer should happen over several years. Moreover, the speed of accumulation under the optimal path is high in the first few years, but then tapers off as the size of the fiscal buffer approaches the target fiscal buffer. In the model solution, by front-loading the accumulation, the government ensures that it is at least partially insured if the contingent liabilities materialize immediately.

C. Conclusions

20. This note suggests that the Swedish government could be facing contingent liabilities arising from the financial sector in the range of just below 20 to 90 percent of GDP, with large uncertainties around these estimates. For example, any such number crucially depends on the underlying estimates of bank losses as well as on whether the government decides to bail out unsecured depositors and unsecured bond holders (in addition to insured depositors), and on the burden-sharing rules between countries and the exposure of bank assets to euro area risks.

21. These findings add emphasis to the need for fast progress on financial reforms. Measures to further cool household credit growth and strengthen banks’ liquidity and capital positions (see the Policy Agenda section of the 2013 staff report for Sweden) will help to reduce systemic banking risk help limit the size of the contingent liability.

Appendix. Methodology

This model writes down an optimal spending problem of the government when they are faced with a one-time risk of contingent liabilities being realized. This analysis therefore strips away other sources of risks, and focuses on the problem of contingent liabilities arising from the financial sector. Since, other risks arising from longevity, short-term business cycle fluctuations are assumed away, the analysis here should be understood as one pertaining to the permanent (or detrended) component of government spending.

Environment

Consider the problem of a benevolent government that has to choose an expenditure path to maximize household utility. Household’s lifetime utility additively depends on private consumption (Ct) and government expenditure (Gt) in each period t, and is given by

Ut=EtΣj=0βj[u(Ct+j)+v(Gt+j)](0)

with the discount factor β ∊ (0,1).

The government faces a deterministic gross rate of return (R), and an exogenous deterministic income stream from taxes (T). Define Mt as resources available to the government (wealth plus current income) at time t, At as the end-of-period assets after the government has made its expenditure decisions, and Bt as balance before receipt of current income. Then the budget constraint of the government can be decomposed as:

At=MtGtBt+1=RAt(2)Mt+1=Bt+1+Tξt+1Z

Here the only risk arises from a one-time cost arising from an adverse event (for e.g. expenses related to the bailout of the banking sector, natural disaster, etc.). Therefore, Z > 0 is the contingent liability of the government, and ξt+1 is a dummy variable indicating whether the liability is realized for the government in period t.

The government faces a constant risk ϕ of the shock realizing. That is, in each period ξt = 1 with probability ϕ, and ξt = 0 with probability 1 – ϕ. In this setup, the liability is a one-time only risk, and therefore once the risk is realized there is no chance of any such events in the future. Therefore, if ξt = 1, then ξt+j = 0 ∀ j > 0.

In addition, the government is subject to a no-Ponzi condition of the form

limjEtDt+jΠx=1jRt+x=0(3)

The Problem of the Government after Risk has been Realized

Once the risk has been realized, the problem becomes deterministic, since there is no future risk of any additional shocks. This makes the problem tractable. The government chooses a path {Gt+j}j=0 to maximize (1) subject to (2) and (3).

Let’s assume that v(·) exhibits constant relative risk aversion (CRRA), and is given by

v(Gt)=11ρ(Gt)1ρ(4)

Then the solution to this problem is given by the first order condition, which is the government’s Euler equation:

v(Gt)=Rt+1βEt[v(Gt+1)](5)

Let’s use the superscript a for the period after which the risk has been realized, and b for the period before the shock. The solution to the government’s optimization problem after the shock has been realized with the utility function given in (4) is a standard result, and is simply:

Gta=κBt(6)

where Κ is the marginal propensity to spend out of total assets. The marginal propensity to spend is a function of the gross rate of return and the discount factor

κ=1R1(Rβ)1/ρ(7)

For the purposes of this analysis we impose the condition that Κ > 0 (Assumption 1). This condition essentially guarantees that the present discounted value of government spending remains finite.

The Problem of the Government before Risk has been Realized

In this case the consumer’s preferences are the same; however the government’s exposure to risk is different.

Consider the case of the government in period t when they have not experienced a shock in the current period. If they still do not experience a shock in the next period, i.e.ξt+1 = 0, then government resources in the next period can be represented as

Mt+1b=R(MtbGtb)+T(8)

We once again obtain the standard Euler equation. Using i ∊ {b,a} to indicate the two possible states (before and after), we get

v(Gt)=RβEt[v(Gt+1i)]or 1=RβEt[(Gt+1iGtb)ρ](9)

We can rewrite the government’s Euler equation as:

1=Rβ[(1φ)(Gt+1bGtb)ρ+(φ)(Gt+1aGtb)ρ](10)

This representation shows that the right-hand side is a probability-weighted average of the growth rates of marginal utility—the first term is the case before the risk is realized, whereas the second term is associated with the case after the risk is realized.

Steady State

First, let’s rewrite (10) as

Gt+1bGtb=(Rβ)1/ρ[1+φ{(Gt+1bGt+1a)ρ1}]1/ρ(11)

To find the steady we must find the loci at which ΔGt+1b=0 and ΔBt+1b=0.. Let’s consider the case when the government experiences the shock in period t. Then from (2) we get that

Bt+1a=R(Btb+TGtbZ)(12)

Substituting Gt+1a=κBt+1a into (11) and using (12) we get

1=(Rβ)1/ρ[1+φ{(Gt+1bκBt+1a)ρ1}]1/ρGt+1bκR(Btb+TGtbZ)=((Rβ)1(1φ)φ)1/ρπ(13)

By setting Gt+1b=Gtb we get

Gtb=(πκR1+πκR)(Btb+TZ)(14)

To ensure that steady state consumption is positive, from (13), we know that we want π > 0. This condition essentially requires that (Assumption 2):

(Rβ)1<1φ(15)

This ensures that the consumer is sufficiently impatient, and the steady state consumption is positive. Now we turn to characterizing the second equation of the system.

The second equation for steady state comes from the budget constraint in (2) after we set Bt+1b=Btb:

Gtb=(R1R)Btb+T(16)

Equations (14) and (16) together form a system of two equations and two unknowns. Solving them simultaneously yields the steady state target wealth in the before period:

Btb=(R1+πκRR)[T+(πκR)Z](17)

And for steady state government expenditure in the before period we get:

Gtb=(R11+πκRR)[T+(πκR)Z]+T(18)

Figure A1 plots the phase diagram given by the two equations (14) and (16), and the solution in (17) and (18) corresponds to the intersection of the two curves, and represents the target wealth, and government spending in steady state. Here, the stable arm of the phase diagram also represents the government spending function as a function of government assets. This illustrates that the government spending function is concave: the marginal propensity to spend is higher at low levels of assets because the intensity of the precautionary motive increases as resources decline. That is, the marginal propensity to spend is higher at lower levels of assets (Bte) because the relaxation in the intensity of the precautionary motive induced a small increase in Bte is relatively larger for the government which starts with less than for a government which starts with more resources.

Figure A1.
Figure A1.

Phase Diagram

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

Size of Spending Risk

The second graph (Figure A2) represents the size of spending risk, i.e. (Gt+1b/Gt+1a) as a function of the probability of the shock being realized in any given period. This graph shows that when the likelihood of the shock is higher, the drop in government spending after the shock is lower. This is because the precautionary incentive motive is much stronger in this case (because the shock is more likely), and therefore in the before period the government engages in much bigger buffer stock saving.

Figure A2.
Figure A2.

Size of Spending Ratio Risk as a Function of Probability of Contingent Liability Being Realized

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

This intuition is indeed confirmed when one examines the derivative d(dBb/dZ)dφ in equation (17).

This derivative measures the how the sensitivity of buffer wealth to size of contingent liability changes when we increase the likelihood of the shock. It can be shown that derivative is positive, confirming the intuition that when ϕ increases the buffer saving motive becomes stronger.

Size of Target Buffer Wealth

Here the concept of target buffer wealth is defined as the amount of wealth the government should target due to the contingent liability arising from the financial sector. That is, it is the second term in equation (17). Figure 4 in the main text shows that the target asset as a function of the size of contingent liability. The slope of this is given by the derivative dBb / dZ in (17), which under our assumptions is greater than one. This is a counterintuitive result, since it implies that an increase in the size of contingent liability by one unit, should lead to an increase of greater than one unit in the target buffer wealth. The idea behind this result is that the government spending is financed by both tax revenues and interest payments from the buffer wealth. When the contingent liability gets realized, the size of buffer wealth jumps down by amount Z. This reduces the interest payment the government receives in the post-period, thereby reducing a source of financing government spending in the post-period. Thus, in order to smooth the spending ratio risk (i.e. difference between pre-period government spending and post-period government spending, Ga / Gb), the government will find it optimal to target a buffer wealth slightly higher than Z.

Transition Path

To find a solution for the transition path, we get two transition equations. First, from the budget constraint in (2) we get

Bt=R(Bt1+TGt1)(19)

The second equation is obtained by rewriting (10) and substituting Gt+1a=κBt+1a, which yields:

Gbt+1={(11φ)Rβ1(Gtb)ρ(φ1φ)[κR(Btb+TGtbZ)]ρ}1ρ(20)

Equations (19) and (20) form a system of difference equations which together pin down the transition path of the government’s problem under study. However, no closed-form solution exists for this problem and we rely on numerical methods to obtain the transition path for a given set of parameters (see Table A1).

Table A1.

Parameters

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Optimal Government Spending Growth

The next graph (Figure A3) shows government spending growth as a function of total assets on the transition path. When the asset level tends to zero, the precautionary motive becomes arbitrarily large. That is, as assets decline, expected spending growth approaches infinity.

Figure A3.
Figure A3.

Government Spending Growth as a Function of Total Assets

Citation: IMF Staff Country Reports 2013, 277; 10.5089/9781484382554.002.A005

1

Prepared by Ruchir Agarwal (EUR).

2

A newly appointed government committee—the Inquiry on Swedish Government Debt Management—is tasked with exploring issues of long-term debt targets.

3

A potential downside to having a dedicated fund is that it exacerbates potential moral hazard by pre-committing to deploy funds in the event of a banking crisis. On the other hand, a benefit of having a fund is that it allows Sweden to have a sufficiently active and liquid market for sovereign debt by not limiting the size of debt levels.

4

A different question is whether the existing debt level or funds accumulated in the Swedish Stability Fund do already provide the required buffer.

Sweden: Selected Issues
Author: International Monetary Fund. European Dept.
  • View in gallery

    Bank Liabilities by Seniority and Methodology for Estimating Government Contingent Liability

  • View in gallery

    Exposure of Nordic-6, by Geography 2012

  • View in gallery

    Potential Fiscal Costs to Sweden of Bailing Out the Six Largest Nordic Banks 1/

    (Percent of GDP)

  • View in gallery

    Target Fiscal Buffer as a Function of Contingent Liability

    (Percent of potential GDP)

  • View in gallery

    Model-based Transition Path for Government Debt to Build Optimal Fiscal Buffers against Contingent Liability 1/

    (Sovereign debt, percent of GDP; years on horizontal axis)

  • View in gallery

    Phase Diagram

  • View in gallery

    Size of Spending Ratio Risk as a Function of Probability of Contingent Liability Being Realized

  • View in gallery

    Government Spending Growth as a Function of Total Assets