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Can a government keep growing its debt forever?

No country can sustain infinite debt growth. But the right question is not whether debt should be zero—it shouldn't—but whether a country's debt is on a sustainable trajectory. A government with debt equal to 50% of GDP but no plan to stabilize it faces eventual crisis. A government with debt at 100% of GDP but a credible path to stabilization may be sustainable. Debt sustainability is the cornerstone of long-term fiscal health, and understanding it requires grasping the dynamics that determine whether debt grows faster or slower than the economy. This is not about politics or ideology; it is arithmetic. Get the equation right, and you can assess any country's fiscal future.

Quick definition: Debt sustainability is the condition that a government's debt-to-GDP ratio remains stable or declines over time, such that the government can continue servicing its obligations without eventually defaulting.

Key takeaways​

  • The primary debt dynamic depends on the primary balance (surplus/deficit excluding interest), the debt-to-GDP ratio, the real interest rate, and the real growth rate of the economy.
  • The debt sustainability condition is that the primary surplus (or deficit) must offset the interest burden to prevent debt from growing faster than the economy.
  • If real growth exceeds the real interest rate, debt can grow in absolute terms while declining as a share of GDP—the "growth solution."
  • Debt becomes unsustainable when the primary deficit is large, real growth is weak, interest rates are high, and the debt ratio is already high—a "bad equilibrium."
  • Credibility and inflation expectations affect the real interest rate, so fiscal policy and monetary policy interact to determine sustainability.

The debt dynamics equation​

The foundation of debt sustainability analysis is the debt dynamics equation, a simple but powerful relationship that shows how debt evolves over time. The equation relates the change in the debt-to-GDP ratio to four key variables:

Change in debt-to-GDP = (interest rate - growth rate) × current debt ratio + primary deficit.

To illustrate, suppose a country has debt equal to 60% of GDP (d = 0.60), faces a real interest rate of 3% (r = 0.03), real growth of 2% (g = 0.02), and runs a primary deficit of 3% of GDP (pb = −0.03). The change in the debt ratio is:

Δd = (0.03 - 0.02) × 0.60 + (−0.03) = 0.006 - 0.03 = −0.024.

This means the debt ratio falls by 2.4 percentage points annually, from 60% to 57.6%. Even though the country runs a primary deficit (spending exceeds tax revenue), debt declines as a share of GDP because growth is strong enough to offset the deficit burden.

Now suppose the interest rate rises to 5% and growth slows to 1%:

Δd = (0.05 - 0.01) × 0.60 + (−0.03) = 0.024 - 0.03 = −0.006.

Debt still falls, but slowly. The debt ratio declines by only 0.6 percentage points. The adverse interest-growth gap (r − g = 0.04) is now working against consolidation, requiring a larger primary surplus to stabilize debt.

This simple equation reveals the key insight: a country's fiscal sustainability depends not just on current deficits, but on the interplay between interest rates, growth, and the existing debt burden.

The sustainable debt level​

For a given primary deficit and interest-growth gap, there is a sustainable level of debt toward which the economy gravitates. This equilibrium is found by setting the change in debt equal to zero and solving:

Sustainable debt-to-GDP = primary surplus / (growth rate - interest rate).

Or equivalently:

Sustainable debt-to-GDP = −primary deficit / (interest rate - growth rate).

If a country runs a primary deficit of 2% of GDP, faces an interest rate of 4%, and grows at 2%, then:

Sustainable debt = −0.02 / (0.04 - 0.02) = 0.02 / 0.02 = 100%.

This country can sustain debt at 100% of GDP indefinitely without the debt ratio rising further. If current debt is only 60%, the debt ratio will gradually rise toward the 100% equilibrium. If current debt is 110%, the ratio will eventually fall.

This "stable debt" concept is crucial for policymakers. A country cannot simply freeze the debt-to-GDP ratio at its current level; it must move toward the sustainable level implied by current policies. Ignoring this dynamic has led many countries (and many analyses) astray. A government that believes it can run a primary deficit forever without the debt ratio rising is misunderstanding the arithmetic.

The growth solution and the interest-growth gap​

One of the most important insights in debt dynamics is that growth can solve debt problems without austerity. If the real growth rate exceeds the real interest rate (g > r), then the denominator (r − g) is negative, and the sustainable debt level is negative—meaning any positive debt ratio is unsustainable and will fall as a share of GDP over time.

This is the "growth solution." A country with 90% debt-to-GDP, running a small primary deficit, can stabilize its debt if growth is high enough. The U.S. experienced this in the 1950s–1960s: debt left over from World War II (exceeding 100% of GDP) declined to under 40% over two decades, largely because real growth (3–4% annually) exceeded real interest rates (near zero, sometimes negative), while the primary budget was roughly balanced.

Conversely, when r > g (real interest rates exceed real growth), every unit of outstanding debt creates a growing burden, and the primary deficit must be large enough to prevent the debt ratio from exploding. This is the situation many developed economies face in the 2020s, as real growth is modest (1–2%) and real interest rates (even with inflation) are positive. In this regime, growth alone cannot solve debt problems; primary surpluses (or at least much smaller deficits) are necessary.

The role of inflation​

Inflation complicates debt dynamics because nominal and real values diverge. The debt dynamics equation should properly use nominal variables: the nominal interest rate on government debt, the nominal growth rate of GDP, and nominal debt figures.

Change in debt-to-GDP (nominal terms) = (i - (g + π)) × d + pb,

where i is the nominal interest rate, g is real growth, π is inflation, and (g + π) is nominal growth.

For a given nominal interest rate and real growth, higher inflation reduces the real burden of debt. If a country owes $1 trillion and inflation is 5% annually, the real value of that debt declines by 5% per year. This is sometimes called "financial repression"—the implicit tax on creditors through inflation.

A government facing an unsustainable debt trajectory can resolve it through three channels: (1) primary consolidation (raise taxes or cut spending), (2) growth acceleration, or (3) inflation/debasement of the currency. Many countries use a combination. The U.S. and other developed economies used inflation in the 1970s and 1980s to erode the real value of debt (though this came at the cost of inflation volatility and central bank credibility). Japan and Eurozone countries, committed to low inflation, must rely on primary consolidation and growth.

Debt spirals and bad equilibria​

Debt dynamics can exhibit multiple equilibria—some stable, others not. A country with high debt, high interest rates, and primary deficits can enter a debt spiral: rising debt requires higher taxes or spending cuts to sustain, which dampens growth; slower growth makes the interest-growth gap worse; the worse gap requires larger primary surpluses; larger surpluses further dampen growth. The vicious cycle continues until the country either consolidates sharply, defaults, or inflates away the debt.

Assessing a country's fiscal position​

This dynamic explains why debt crises often happen suddenly. A country may have high debt for years, with yields stable. Sentiment shifts slightly—perhaps due to electoral uncertainty, a banking crisis, or contagion from another country's fiscal stress—and risk premiums rise. Higher interest rates worsen the fiscal position and trigger faster debt growth. If markets believe the government cannot consolidate or grow fast enough to stabilize debt, they stop lending, forcing default.

The classic example is the Eurozone crisis of 2010–2012. Greece, Ireland, and Portugal faced high debt, weak growth, and elevated borrowing costs. Higher interest rates worsened fiscal positions, requiring more austerity, which further dampened growth. Only when the European Central Bank committed to "whatever it takes" to prevent default did the crisis stabilize. The commitment to support sovereign bond markets lowered interest rates, breaking the debt spiral.

Conversely, countries with credible fiscal frameworks and central bank independence can sustain higher debt ratios because interest rates remain low. The U.S. has debt above 120% of GDP in 2024 yet faces borrowing costs only slightly above global risk-free rates because the dollar is the world's reserve currency and the U.S. has never defaulted. Japan has debt above 250% of GDP yet low interest rates because the Bank of Japan is committed to monetary stability and the debt is mostly held by domestic savers. These countries face high debt sustainably because credibility keeps interest rates low relative to growth.

Assessing a country's fiscal position​

To evaluate whether a country's debt is sustainable, analysts examine several metrics:

Debt-to-GDP ratio: Is it rising or falling? Is it above or below historical norms? High debt (above 80–90% in most developed countries) constrains future fiscal space and raises crisis risk.

Primary balance: Is the country running a primary surplus or deficit? Countries with primary surpluses can sustain higher debt because interest is being paid from current tax revenue rather than by borrowing. Countries with primary deficits are running the race in reverse.

Interest-growth gap (r − g): How adverse is the spread between interest rates and growth? In favorable conditions (r < g), debt declines naturally. In adverse conditions (r > g), consolidation is necessary.

Interest payments as a share of revenue: How much of government revenue goes to servicing debt? If interest is above 10–15% of revenue, consolidation becomes urgent. If above 20%, default risk rises sharply.

Maturity structure of debt: Does the government face a large refinancing need soon? Short-maturity debt is cheaper to issue but riskier (vulnerable to rolling-over crisis). Long-maturity debt is more expensive but safer.

Ownership of debt: Is it mostly held domestically or externally? Domestic debt is less vulnerable to sudden capital flight. External debt, especially in foreign currency, is riskier.

Inflation and exchange rate expectations: Are markets expecting currency debasement? If so, interest rates on nominal debt will be high. Credible inflation targets reduce this risk premium.

Fiscal consolidation: how to achieve sustainability​

When debt is unsustainable, consolidation is necessary. The options are:

  1. Raise taxes or cut spending (primary surplus): This directly reduces deficits and increases the primary balance. The trade-off is that austerity can depress growth in the near term, partially offsetting the deficit reduction (a phenomenon called the "expansionary austerity" debate—some economists believe austerity can boost growth by improving fiscal credibility, while others believe it worsens recessions). The IMF has published extensive research on the fiscal multiplier and consolidation dynamics.

  2. Accelerate growth: If real growth can be raised—through investment in education, infrastructure, research and development, or pro-business reforms—the interest-growth gap narrows or reverses, and debt becomes sustainable at a higher current ratio. This is sometimes called the "growth strategy," but it requires structural reforms and often takes years to bear fruit.

  3. Reduce interest rates through credibility: If a government commits to price stability, fiscal discipline, and transparent institutions, creditors lower risk premiums, reducing borrowing costs. Central bank independence is key here; markets care whether the central bank can resist pressure to monetize the deficit. The Federal Reserve provides resources on inflation targeting and monetary policy credibility.

  4. Inflate or debase the currency: Higher inflation erodes the real value of debt, but at the cost of price instability and erosion of central bank credibility. This is a last resort.

Credible consolidation plans typically combine elements of all four. A country commits to a multi-year adjustment path (primary balance improvement), pairs it with structural reforms to boost growth, ensures central bank independence, and sometimes includes debt restructuring (negotiating lower interest rates or extended maturity with creditors) to reduce near-term refinancing risks.

Real-world examples: Greece vs. Germany vs. Japan​

Greece (2010–2015): Had debt above 100% of GDP, ran a large primary deficit, faced high interest rates (10%+ on new borrowing), and had weak growth. The unsustainable equilibrium implied debt would spiral. The troika (IMF, ECB, EU) imposed harsh austerity—raising taxes and cutting spending to achieve a primary surplus. Austerity was contractionary; unemployment spiked to 27%. Only when reforms began bearing fruit and markets stabilized (partly due to ECB support) did the debt trajectory stabilize. The experience illustrates the pain of correcting unsustainable positions.

Germany (2000–2007): Had debt below 60% of GDP and ran small primary deficits. Growth was steady at 2–3% annually. The interest-growth gap was narrow. Debt remained stable as a share of GDP. But after 2008, the financial crisis temporarily raised debt. The government then tightened fiscal policy (austerity), running primary surpluses. Combined with low interest rates and modest growth, debt declined from 80% of GDP in 2010 to below 60% by 2019. Germany's consolidation was relatively painless because it started from a stronger position and had room for primary surpluses without severe austerity.

Japan (1990–2024): Has had debt above 100% of GDP since the 1990s, rising to over 250% by the 2020s. Yet debt is sustainable because of several factors: (1) most debt is held domestically by stable savers (insurance companies, pension funds) and the central bank; (2) the Bank of Japan caps long-term interest rates through purchases; (3) inflation is moderate and stable; (4) the interest-growth gap is close to zero (low rates offset low growth). Japan demonstrates that very high debt can be sustainable if credibility is strong and growth is predictable, even if consolidation is deferred.

Common mistakes​

Mistake 1: Confusing a high debt-to-GDP ratio with unsustainability. A country with 100% debt can be sustainable if growth is strong, interest rates are low, and the primary balance is favorable. Conversely, a country with 50% debt but a large primary deficit may be on an unsustainable trajectory. The ratio alone is insufficient; the dynamics matter.

Mistake 2: Assuming debt must be reduced to zero or near-zero. This is neither necessary nor achievable. Developed economies have sustained debt at 40–80% of GDP for decades. Very low debt may actually be suboptimal because it limits fiscal flexibility for recessions or crises. The goal is stability, not elimination.

Mistake 3: Ignoring the interest-growth gap. Analysts sometimes focus only on the primary deficit without considering whether r > g or r < g. But this gap determines whether debt is on a stable trajectory even with no primary surplus. In low-interest, high-growth environments, modest deficits are sustainable indefinitely.

Mistake 4: Treating inflation as the easy solution. Some politicians advocate inflation to erode debt. But unexpected inflation erodes central bank credibility, raising future interest rates and harming growth. Using inflation for debt relief is a one-time gain with long-term costs. It is rarely the optimal strategy except as a last resort.

Mistake 5: Assuming austerity is always contractionary. In some contexts, credible austerity can boost growth by improving fiscal confidence and lowering interest rates (so-called expansionary contraction). But in recessions with slack resources, austerity tends to deepen downturns. The context matters enormously.

FAQ​

Is the United States' debt unsustainable? As of 2024, the U.S. has debt above 120% of GDP and runs a primary deficit of roughly 5% of GDP. The interest-growth gap is widening as real interest rates rise. By the debt dynamics equation, this trajectory is unsustainable without adjustment. However, the U.S. benefits from the dollar's reserve status, strong institutions, and credibility, keeping interest rates low. A crash is not imminent, but consolidation is necessary within 15–20 years to prevent a debt crisis in subsequent decades.

Can the Fed solve the debt problem by printing money? The Fed can purchase government bonds (monetization), lowering short-term interest rates and removing debt from private circulation. However, persistent monetization leads to inflation, eroding the real value of debt and credibility. The Fed's current policy is to avoid permanent monetization and instead let deficit reduction and growth address sustainability. Excessive monetization would be self-defeating.

Why don't all countries just run primary surpluses to eliminate debt? Primary surpluses require raising taxes or cutting spending, which is politically unpopular and economically contractionary in the short term. Cutting spending during recessions can deepen downturns. Raising taxes can distort incentives and lower growth. Hence, many governments favor gradual consolidation, paired with growth. Additionally, some debt is economically beneficial (e.g., borrowing for productive infrastructure), so eliminating all debt is not optimal.

How do demographics affect debt sustainability? Aging populations reduce growth (fewer workers) and raise spending (more retirees on social security and healthcare). Both worsen the debt dynamics. Japan and Europe face this challenge acutely. The U.S., with higher immigration and relatively younger demographics than Europe or Japan, faces a less severe demographic headwind. Countries with deteriorating demographics must consolidate sooner or risk unsustainable debt trajectories.

What happens if a country reaches an unsustainable debt level? Options include: (1) default (refusing to pay creditors), (2) restructuring (negotiating lower interest rates or extended maturity), (3) sharp consolidation or growth acceleration, (4) inflation/debasement, or (5) international support (IMF loans in exchange for austerity commitments). All are costly. Early consolidation is preferable to waiting for crisis.

Is debt sustainability just an accounting exercise, or does it matter for real outcomes? It matters for real outcomes. Unsustainable debt leads to either costly consolidation (austerity), default (destruction of wealth and credit), or inflation (price instability). All reduce growth and welfare. Maintaining a sustainable debt trajectory is essential for long-term prosperity.

Summary​

Debt sustainability is determined by a simple but powerful equation: whether the primary deficit, the interest rate, the growth rate, and the current debt burden imply a rising or stable debt-to-GDP ratio. A country with high debt but favorable growth, low interest rates, and a primary surplus is sustainable; a country with low debt but large deficits and weak growth may not be. Growth above real interest rates ("g > r") allows debt to stabilize or decline naturally, while growth below interest rates ("r > g") requires primary surpluses to prevent debt explosion. Countries with strong institutions, credible central banks, and stable inflation can sustain higher debt because interest rates stay low. Those facing doubts about credibility face debt spirals where rising rates worsen sustainability, forcing sharp consolidation. Long-term fiscal health requires that countries maintain a sustainable debt trajectory through some combination of primary balance adjustment, growth acceleration, and credible monetary frameworks. Ignoring debt dynamics is a recipe for future crises.

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