The debt snowball in numbers
Systemic risk Crises Policy
In The next crisis I use the government debt identity to see where today's worries end up. This post has the numbers behind it, for nine countries.
The government debt-to-GDP ratio evolves according to
$$ \Delta d_t \approx (r_t - g_t) d_{t-1} - pb_t + \text{other}_t $$
where \(d_t\) is the debt ratio, \(r_t\) the effective real interest rate on the debt, \(g_t\) real GDP growth and \(pb_t\) the primary balance, revenues minus non-interest spending, relative to GDP. Interest makes the debt ratio grow, while growth and primary surpluses shrink it. The last term, \(\text{other}_t\) , is what changes the debt without passing through the deficit, such as government lending, asset sales or spending recorded in one year and borrowed for in another.
The term \((r_t - g_t) d_{t-1}\) is the snowball, how much the debt ratio grows by itself.
Today
So what do the numbers look like today? The table shows debt relative to GDP in 2025 and how it changed over the year, split into the primary balance, the snowball and the rest.
A negative snowball brings the debt ratio down, and so does a positive primary balance. Those are in green, and what pushes the debt up is in red.
| Debt | Primary balance | Snowball | Other | Change in debt | |
|---|---|---|---|---|---|
| United States | 123.9% | −3.2% | −2.2% | +0.6% | +1.6% |
| United Kingdom | 102.3% | −2.8% | −2.3% | +1.9% | +2.4% |
| France | 115.6% | −2.9% | 0.0% | +0.1% | +2.9% |
| Italy | 137.1% | +0.8% | +0.5% | +2.6% | +2.4% |
| Germany | 63.5% | −1.6% | −0.9% | +0.6% | +1.3% |
| Greece | 146.1% | +4.9% | −4.1% | +0.9% | −8.0% |
| Japan | 206.5% | −0.9% | −9.3% | +0.5% | −8.0% |
| Korea | 52.3% | −1.5% | −2.0% | +3.1% | +2.6% |
| South Africa | 78.6% | −0.3% | +2.6% | −0.2% | +2.7% |
For now, the snowball works for most of the governments.
The rich countries still pay an interest rate of about 3% or less on their debt. That is well below what the market asks now, and in most cases less than the economy grows.
In the US and the UK the snowball takes more than 2% of GDP a year off the debt ratio. In Japan it takes over 9%, which is why a debt of more than 200% of GDP is falling. It is close to zero in France and already positive in Italy and South Africa.
In the US, the UK, France and Germany, the debt is growing because of the deficits.
What comes next
The problem is what comes next. The interest rate in the debt identity is what the whole stock of debt pays. Higher market rates only feed into it as the debt matures and is refinanced.
The second table runs 2025 again, with the whole debt paying what it costs to borrow for ten years now. It shows the interest bill, as a share of GDP, and the change in debt, as they were and as they would have been. Japan and Korea are left out, for the reason given in the technical details.
| Interest bill now | Ten-year yield | Interest bill at that yield | Change in debt now | Change in debt at that yield | |
|---|---|---|---|---|---|
| United States | 3.7% | 5.0% | 5.8% | +1.6% | +3.8% |
| United Kingdom | 2.6% | 5.0% | 4.7% | +2.4% | +4.5% |
| France | 2.2% | 4.0% | 4.4% | +2.9% | +5.1% |
| Italy | 3.9% | 4.0% | 5.2% | +2.4% | +3.7% |
| Germany | 1.1% | 3.2% | 1.9% | +1.3% | +2.1% |
| Greece | 3.2% | 3.9% | 5.7% | −8.0% | −5.5% |
| South Africa | 5.4% | 8.8% | 6.4% | +2.7% | +3.6% |
The chart shows the last two columns of the table. Greece is left out, since its falling debt ratio would squeeze the scale.
For the US the interest bill goes from 3.7% of GDP a year to 5.8%. The debt ratio rises by 3.8 points a year, not 1.6.
The UK and France see a similar rise in the interest bill, between 2% and 2.5% of GDP. French debt would grow by more than 5 points a year. That comes on top of the deficits they already run.
And France now pays the same as Italy to borrow for ten years, and more than Greece.
How fast the higher interest bill arrives depends on the maturity of the debt. It is just under six years on average in the US and over thirteen in the UK, as the chart in The next crisis shows.
As a rough guide, a government with an average maturity of six years refinances about a sixth of its debt every year. So if yields stay where they are, the US interest bill rises by about 0.4% of GDP every year, and half of the rise in the second table arrives within three years. France gets about 0.3% a year, the UK less than 0.2% and Germany about 0.1%.
Technical details
For France, Italy, Germany and Greece, debt, the balance, interest paid and GDP in 2025 are the official figures Eurostat published in April 2026. They differ a little from the IMF estimates in the chart in The next crisis, which came out before them.
For the other countries, debt, the primary balance and the overall balance are from the IMF Fiscal Monitor and nominal GDP is from the World Bank. Their interest bill is the primary balance minus the overall balance, which is net of the interest the government earns. That understates what is paid on the debt, most of all in Japan and Korea, where the government holds large financial assets.
The interest bill divided by the debt a year earlier, with both in money terms, gives the effective rate, 3.1% for the US, 2.7% for the UK, 2.0% for France, 2.9% for Italy, 1.8% for Germany and 2.1% for Greece. The snowball is the effective rate minus the growth of nominal GDP, times the debt ratio a year earlier, divided by one plus growth. Nominal rates and nominal growth give the same snowball as real rates and real growth.
The change in debt is the change in the debt ratio from 2024 to 2025. Other is what is left after the primary balance and the snowball, mostly stock-flow adjustments. For the four euro area countries it matches the stock-flow adjustment Eurostat publishes to within 0.1. It is large for Italy, where building tax credits add to debt years after they were recorded in the deficit, and also for Korea. Rows may not add up because of rounding.
Ten-year yields are August 2026 averages, from the ECB for France, Italy, Germany and Greece and from FRED for the UK and South Africa, and the 16 September 2026 close for the US.
In the second table, the interest bill at that yield is the ten-year yield times the debt ratio a year earlier, divided by one plus growth. So it is 2025 with only the interest rate changed. The change in debt at that yield is the actual change plus the extra interest. It is what would happen if all the debt were refinanced at today's yield. That happens only as the debt matures, and most slowly in Greece, where most of the debt is long official loans.
The pace at which the higher interest bill arrives is the extra interest in the second table divided by the average maturity of the debt, 5.9 years for the US, 8.5 for France, 13.5 for the UK and 7.6 for Germany. It assumes that one over the average maturity is refinanced every year and that yields stay where they are. The maturities are for central government marketable debt, from the OECD Global Debt Report 2026.
Japan and Korea are left out of the second table because their net interest bill is close to zero, so the calculation would overstate the rise. Even on that overstated basis, Japan's debt ratio would still fall, by about 2% of GDP, because nominal GDP grew by 4.7%.