Public debt: What makes it bearable, or not

French public debt is above one hundred and ten per cent of GDP. The figure is scary. But on its own, it doesn't say much.

Japan lives with a much heavier debt. Other countries, far less indebted, have still defaulted. Why?

Because a debt is sustainable or not depending on two numbers: the interest rate paid, and the growth of the economy.

Economists call them r and g. r is the cost of the debt. g is the growth of national income, inflation included.

Take an imaginary country, with a debt equal to its GDP. Its budget, excluding interest, is balanced.

If the debt costs three per cent and the economy grows two, the debt grows faster than income.

After ten years, it goes from one hundred to one hundred and ten per cent of GDP. With no new deficit at all, just interest.

Swap the two numbers: two per cent interest, three growth. After ten years, the debt falls back to ninety-one per cent.

The twist: the same debt can melt or swell on its own. It all depends on the gap between r and g.

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When r exceeds g, you need a surplus before interest to stabilize it. Here, almost one point of GDP every year.

During the years of very low rates, r was often below g. Since rates rose again, the gap has narrowed. The debate is back.

Second question: who holds this debt? Savers and banks in the country, foreign investors, and the central bank.

In France, about half is held by non-residents. It is a sign of trust, but also a dependence.

A debt held by its own residents is renegotiated among themselves. A debt held abroad can leave faster.

Central banks also bought a lot of it during the crisis years. They have become very big creditors.

Third question: how have states got out of it in the past? There are four main ways.

Growth, first. After the Second World War, the United Kingdom owed more than twice its GDP. Decades of growth brought it down.

Inflation, next. It inflates income in euros, not the debt already issued. But savers pay the price.

Austerity: spend less, tax more. Sometimes effective, always painful, and risky if it breaks growth.

Default, finally. In twenty twelve, Greece had its private creditors write off more than half the value of their bonds.

None of these exits is free. Each one chooses who pays: taxpayers, savers, or creditors.

To judge a debt, then, look at three things: the gap between r and g, who holds it, and the budget before interest.

The level matters. But a debt is judged mostly by its path. And that path is decided every year.