Debt dynamics and the snowball effect

Debt is measured not in euros, but as a share of GDP: it is this ratio that tells whether the burden is sustainable. Its change from one year to the next depends on two terms. The first is the gap between the average interest rate paid on the debt (call it r) and the economy's growth rate (call it g): if growth exceeds the rate, the economy "dilutes" the debt faster than it costs, and the ratio falls almost on its own. The second is the primary balance, that is, the budget excluding interest: a surplus cuts the debt, a deficit adds to it. The whole trajectory of a public debt reads in the interplay of these two forces.

The dangerous case is where r > g: the interest rate exceeds growth. The mere fact of paying interest then makes the debt grow faster than GDP, even without a new deficit. Interest is added to the principal, which in turn produces more interest: this is the "snowball" effect. Its practical consequence is harsh: as soon as r > g, stabilizing the debt is no longer enough to balance the current budget; a primary surplus is needed, all the larger the higher the debt already is. In other words, the more indebted you are, the greater the effort simply not to sink deeper. After a decade in which r stayed below g (a "free lunch"), the return of r above g reawakens this mechanics.

Cutting a deficit should lighten the debt. But the ratio is a fraction: debt on top, GDP below. Now a budget cut weighs on activity. If the fiscal multiplier exceeds 1 — that is, if one euro of saving destroys more than one euro of GDP, which happens above all in a weak economy — then the denominator falls faster than the numerator, and the debt-to-GDP ratio can rise instead of falling. This is "self-defeating" austerity, brought to light by the work of Olivier Blanchard and Daniel Leigh after the 2010 crisis. The virtuous effort then produces the opposite of its aim: you tighten the belt, and relative debt grows heavier.

The mechanism is no fate. Deleveraging works when well placed: in a strong economy, with a credible and spread-out consolidation, or when r stays below g. Nor is all debt equal: debt that funds a productive investment raises g and can repay itself, unlike pure operating debt. A state is not a household: it does not die, it refinances continuously, it borrows in its own currency when sovereign. Finally, r − g can turn favorable again: nothing freezes rates. One must therefore guard against both denial and catastrophism — Japan lives with a debt near 240% of GDP without a crisis. The real risk is not a sudden "wall," but slow suffocation by interest.