How government debt grows or shrinks
Governments rarely pay their debts back. What matters is whether debt grows faster or slower than the economy that carries it. That comes down to three numbers: the interest rate the government pays, how fast the economy grows, and the budget balance before interest. This page explains how they fit together, with this year’s figures for ten countries.
The terms you need
Each definition is followed by a real example from the latest data.
- Debt-to-GDP ratio
- A government’s total debt divided by the economy’s annual output. It shows how heavy the debt is relative to the country’s ability to pay. The EU’s reference value is 60%.
- Budget deficit
- The amount by which a government’s spending exceeds its revenue in a year, usually shown as a share of GDP. The government covers the gap by borrowing, mostly by selling bonds.
- Primary balance
- A government’s budget balance before interest payments: revenue minus all spending except interest. It shows whether the government covers its day-to-day costs, setting aside the cost of past debt.
- Nominal GDP growth
- How fast an economy grows measured in money, before removing inflation: roughly real growth plus inflation. It is the growth rate that matters for debt, because debt and taxes are in money too.
- Interest rate minus growth (r − g)
- The gap between the average interest rate a government pays on its debt (r) and nominal growth (g). When r is below g, the debt ratio shrinks on its own; when r is above g, it grows on its own, before counting any new borrowing.
- Government bond
- A loan to a government. The buyer pays a price today, receives a fixed interest payment (the coupon) every year, and gets the face value back when the bond matures.
- Credit rating
- A grade from an agency such as S&P, Moody’s or Fitch on how likely a borrower is to repay. A downgrade can force some investors, whose rules limit how much lower-rated debt they hold, to sell.
What moves the debt ratio
The debt ratio is debt divided by GDP. Anything that changes the top or the bottom of that fraction moves it.
- 1 →The budget before interestIf the government spends more than it collects, not counting interest, it borrows the difference. A primary deficit adds to debt; a primary surplus pays some off.
- 2 →Interest on existing debtEvery year the government owes interest on everything it has borrowed. If it doesn’t pay that from a surplus, it borrows more to pay it, and debt grows at the interest rate.
- 3 →The economy growsGDP rises with real growth and with inflation. Both make the same debt smaller relative to the economy, and to the tax revenue that services it.
- 4 →Interest versus growthIf the interest rate is below nominal growth, the debt ratio falls on its own. If it is above, the debt ratio rises on its own, even with a balanced primary budget.
- 5Investors judge the pathIf the ratio looks set to keep rising, investors demand higher yields, which raises the interest rate and makes the arithmetic worse. That is how debt worries become self-reinforcing.
r is the average interest rate on the debt, g is nominal growth. With debt at 100% of GDP, r at 3% and g at 4%, the ratio falls by 1 point a year on its own. A primary deficit of 3% of GDP would still push it up by 2.
Most debt was issued years ago at fixed rates. As bonds mature and are refinanced, the average rate drifts towards today’s market yields. In most rich countries the average maturity is five to nine years (the UK, at about 14, is an exception), so a jump in yields takes years to show fully in the interest bill.
A burst of unexpected inflation raises GDP in money terms while old fixed-rate debt stays put, so the ratio falls. The relief fades as bonds are refinanced at higher yields, because investors then demand compensation for inflation.
UK government debt peaked at about 250% of GDP after the Second World War and fell below 50% by the mid-1970s. There was no default: steady primary surpluses, growth, inflation and interest rates held below inflation shrank it over three decades.
Greece’s economy shrank by about a quarter between 2008 and 2013, so g was sharply negative. Despite deep spending cuts, its debt ratio rose from about 150% of GDP in 2010 to about 180% in 2014: the bottom of the fraction was falling faster than the top.
This year’s debt arithmetic
In 2026, the average interest rate governments pay on their debt is below their economy’s nominal growth in United States, Germany, France, Italy, United Kingdom, Japan, China and India, but above it in Brazil. Where interest is below growth, the debt ratio shrinks on its own unless the government runs a primary deficit, which most of them do. Today’s 10-year market yields are already above nominal growth in France, United Kingdom and Japan: as old debt is refinanced at those rates, the interest bill will keep rising.
| Country | Debt% of GDP, 2025 | rinterest rate paid | gnominal growth | Rate vs growtheffect on debt, points | Primary budgeteffect on debt, points | Expected changesum of the two | IMF estimateactual change |
|---|---|---|---|---|---|---|---|
| United States | 124% | 2.9% | 6.0% | −3.6 | +4.9 | +1.3 | +2.4 |
| Germany | 63% | 1.5% | 4.0% | −1.5 | +3.4 | +1.8 | +1.9 |
| France | 116% | 2.1% | 2.8% | −0.8 | +2.9 | +2.1 | +3.0 |
| Italy | 137% | 2.9% | 4.1% | −1.7 | −1.0 | −2.7 | +0.8 |
| United Kingdom | 102% | 2.6% | 4.6% | −2.0 | +1.1 | −0.9 | −0.1 |
| Japan | 205% | 0.1% | 2.7% | −5.1 | +1.2 | −4.0 | −5.4 |
| China | 99% | 1.1% | 5.5% | −4.1 | +6.9 | +2.8 | +5.8 |
| India | 84% | 6.3% | 12.4% | −4.5 | +2.2 | −2.3 | −1.2 |
| Brazil | 93% | 8.3% | 6.7% | +1.4 | +0.3 | +1.8 | +3.7 |
IMF estimates for 2026. r is net interest paid divided by last year’s debt; g is real growth plus consumer-price inflation, an approximation. A plus sign means the effect raises the debt ratio, a minus sign that it lowers it. The two effects don’t add up exactly to the IMF figure: exchange-rate moves, privatisations, loans and accounting changes also move debt.
What stands out today
- Growth still beats the average interest rate almost everywhere, a legacy of a decade of very low rates. Debt is rising mainly because of primary deficits.
- But market yields have moved up. France borrows for ten years at about 4.85%, well above the 2.8% its economy is expected to grow in money terms this year.
Why it matters
As cheap old debt is replaced, r will move towards today’s yields. Where those exceed growth, governments will need smaller primary deficits just to keep debt stable, which means tax rises or spending cuts. That is the arithmetic behind the budget fights in France, the UK and the US.
This mechanic in the news
Recent stories that show this mechanism at work, newest first.
Sources and notes
- Debt, balances, growth and inflation: IMF World Economic Outlook and Fiscal Monitor (via the IMF DataMapper); this year’s figures are IMF estimates.
- The equation is an approximation. It leaves out exchange-rate effects on foreign-currency debt, privatisation receipts, loans the government makes, and changes in its cash holdings.
- History: UK debt from the Office for Budget Responsibility’s historical series; Greece from Eurostat.
- 10-year yields: OECD (via FRED), monthly averages.