Fiscal Sustainability: A Primer

“[T]he principle of spending money to be paid by posterity, under the name of funding, is but swindling futurity on a large scale….” Thomas Jefferson, Letter to John Taylor, 1816

Nobody likes taxes, but the objections to debt-financed government spending usually are less forceful than Jefferson’s was. Consequently, public spending frequently exceeds revenues, leading governments to borrow (remember Jefferson’s Louisiana Purchase?). These budget deficits are a flow that add to the stock of debt.

Since the Great Financial Crisis of 2007-2009, public debt in a number of advanced economies has surged (see chart). In the United States. the Congressional Budget Office (CBO) recently projected that―in the absence of policy changes―federal debt held by the public is headed for record highs (as a ratio to GDP) in coming decades.

General government gross debt ratios (percent of GDP) and long-term average market risk premia, 2000 and 2017 (debt ratios) and 1980-2015 (market risk premia)

Note: The bars show BIS-reporting countries ranked by their 2017 debt ratios (left scale). The market risk premia (blue diamonds, right scale) are the average gap between the safe rate of return on government debt and the economic growth rate between 1980 and 2015. Sources: BIS credit to the government sector (nominal value) for government debt and Jordà et al (Tables 11 and 12) for the components of the market risk premia.

Importantly, however, there is a real (inflation-adjusted) limit to how much public debt a government can issue (see Sargent and Wallace). Beyond that limit, the consequences are outright default or, if the debt is in domestic currency bonds that the central bank acquires, inflation that erodes its real value leading to a partial default.

History is replete with sovereign defaults, with some countries repeat offenders. The famously uncreditworthy Kings of Spain defaulted on average once every 10 years between 1557 and 1696. Reinhart and Rogoff identify more than 150 episodes of default on external sovereign debt since 1800 (see here), with the 10 countries that default most frequently doing so at least 8 times (see here). They virtually define an “advanced” economy as one that no longer defaults on its debt (see This Time is Different), suggesting that it takes 50 years of tranquility for a country to gain trust. For a much larger, more recent sample of 93 countries starting in 1975, Uribe and Schmitt-Grohé estimate an annual default probability of 4.0%, with an average default episode lasting 8 years (Table 13.2 here).

Sovereign defaults usually are significant events for a country. Even if the direct loss of wealth is limited to foreigners, defaulting countries typically lose access to financial markets, compelling them to restore fiscal and current account balances simultaneously. At least in recent decades, such “sudden stops” typically trigger wrenching fiscal and economic adjustments, including plunging incomes and surging unemployment. Moreover, sovereign debt crises are frequently associated with other types of welfare-damaging disruptions: in a sample of 67 sovereign debt crises between 1970 and 2011, Laeven and Valencia find that 31 also involve a banking crisis (2), a currency crisis (19), or both (10). (See also the discussion here.)

There is considerable debate about whether a particular debt threshold is associated with a deterioration of economic growth prospects (see, for example, here and here). However, the broader link between persistent increases in debt and slower long-run growth prospects is far less controversial (see, for example, Chudik et al). One reason is that rising public debt crowds out private borrowing by raising the equilibrium real interest rate. Another is that persistent debt increases create concern about debt sustainability—the willingness and ability of a government to pay its debt—leading to a rising risk premium on the debt to compensate investors for default risk.

Ultimately, debt sustainability requires that a country’s ratio of public debt to GDP stabilize. Otherwise, debt eventually will rise above the real limit and trigger default or inflation. In the appendix to this note, we show how to use a government’s standard budget constraint to derive the following debt-sustainability condition. The condition states that the government's primary surplus―the excess of government revenues over noninterest spending—must be at least as large as the stock of outstanding sovereign debt times the difference between the nominal interest rate the government has to pay and the rate of growth of nominal GDP. If it is not, then the ratio of debt to GDP will explode.

That is:

where s is the primary budget surplus (relative to GDP), i is the market interest rate on the government’s debt, g denotes the real GDP growth rate, π is inflation, and b is the stock of outstanding debt (relative to GDP).

A useful way to interpret this expression it that the right-hand-side coefficient is a risk premium on the outstanding debt. Sustainability requires that the budget surplus be sufficient to cover this risk premium times the level of debt. So, the larger the risk premium, the greater the primary surplus must be for a given stock of debt. And, the larger the debt, the larger the necessary primary surplus.

The idea is that the fiscal authorities have to adjust tax revenues and non-interest spending to achieve a sufficiently large primary surplus. If the government chooses a larger surplus, the debt relative to GDP will decline over time. However, a smaller surplus would cause the debt to rise, eventually leading to default. To avoid default, investors must think that they will be repaid―something that only happens when they believe the present discounted value of all the expected future primary surpluses is sufficiently large (for a more detailed explanation, see Chapter 17 here). According to the CBO (Figure 12 on page 28), the U.S. government would need to shrink its annual overall deficit by 1.9% of GDP to stabilize the ratio of federal debt to GDP.

Thinking about sustainability leads us to focus on the market interest rate investors demand to hold the government debt and the resulting risk premium (the expression [i - (g + π)] in the previous inequality). In a sample of 16 advanced economies, Jordà et al estimate that the risk premium since 1980 averaged 1.6% (see Tables 11 and 12 here). In practice, market risk premia appear only loosely related to debt ratios (the diamonds in the chart at the beginning of this post). To see the point, note that Japan has the highest gross and net debt ratios but the lowest market risk premium among the advanced economies since 1980.

That said, a persistently rising level of debt relative to GDP, or a loss of investor confidence regarding repayment, can lead to a sudden change in investor sentiment, raising the compensation they require for default risk. At the peak of the euro-area crisis in 2011-2012, interest rates on the debt of the peripheral countries surged even as their nominal GDP growth slowed or declined, sharply boosting the market risk premium.

The table below highlights the impact of the debt ratio (columns) and the market risk premium (rows) on sustainable fiscal policy. The number in each cell is the minimum steady-state primary surplus as a percent of GDP that a country needs to meet the sustainability condition. For example, a country with a government debt ratio of 120% of GDP would require a primary surplus of at least 2.4% of GDP if the market risk premium were 2%. Should the risk premium to jump to 7%, the primary surplus needed to prevent a debt explosion would climb to 8.4% of GDP.

Steady-state primary surplus (percent of GDP) associated with different debt ratios and market risk premia

Note: The number in each cell corresponds to the minimum primary surplus-to-GDP ratio sufficient to stabilize the debt-to-GDP ratio at each combination of the debt-to-GDP ratio (column) and market risk premium (row). Source: Authors’ calculations based on steady-state fiscal condition provided in text.

A five-percentage-point jump in the market risk premium is large, but not without precedent. This is exactly what happened in Italy several years ago. As the doubts about the viability of the euro grew in the period from 2010 to 2012, the interest rate on Italian sovereign debt rose by about 1½ percentage points to 5½%, while the growth rate of nominal GDP plunged from roughly 2% to -1½%. (So [i − (g + π)] rose by 5 percentage points.) Any short-run attempt to tighten fiscal policy sufficiently to offset such a rise in the risk premium would mean a staggering 6-percentage-point rise in the primary surplus ratio. Even attempting this would almost surely create a far deeper economic downturn, making the needed adjustment even larger.

Furthermore, any resulting doubts about the Italian government’s fiscal commitment could have added to the market risk premium, rather than diminish it. The point is that changes in confidence about the ability and willingness of a government to repay its debt make high-debt countries fiscally fragile. This is especially true when a country’s debt is of short maturity, potentially requiring speedy refinancing at elevated interest rates. (Italy’s long average debt duration means that a jump in the market risk premium would have to persist for 7 years to raise the minimum steady-state surplus ratio as much as the table shows.) We highlighted the fiscal fragility of high-debt sovereigns in a post on the recent turbulence in Italian bond markets.

Italy is far from alone, but like other peripheral economies in the euro area, it faces a greater risk of outright default than do countries with similar debt dynamics and their own central bank. The reason is simple: central banks that issue their own national currencies can choose to erode the real domestic-currency debt through inflation. When the government compels the central bank to do this, we call it fiscal dominance. But members of the Eurosystem, with its common monetary policy objective of price stability, have no such option.

We close by highlighting what we see as a frequently underappreciated issue that is key for assessing fiscal sustainability in many economies: the existence of implicit, in addition to explicit, obligations. Governments today face a range of long-run commitments that do not affect their current deficit or debt. These come in different forms: for example, governments may encounter rainy-day obligations to recapitalize their banking systems in a crisis or to cover the losses of government-sponsored enterprises in a deep recession.

Perhaps the most widespread and costly examples of implicit obligations are government promises to provide pensions and health care to their people. If underfunded, as they frequently are, these obligations eventually will lead to some combination of future tax hikes, entitlement reductions, and increased borrowing. To give an example, in the United States, the current federal debt held by the public is $15.4 trillion, compared to a nominal GDP of $20.0 trillion. However, the trustees of the Social Security and Medicare trust funds estimate that the present discounted value of the unfunded liabilities of these programs over the next 75 years totals $53.7 trillion (see Table V.F2. here). Unless Congress acts to change the nation’s fiscal course, this shortfall eventually would boost the stock of debt sharply.

That would surely affect the sustainability arithmetic.

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APPENDIX: Government Debt Dynamics*

*The presentation of budget dynamics in this appendix largely follows that in Chapter 17 of The Global Economy, published by NYU Stern’s Center for Global Economy and Business.