1. Government debt and deficits: why there is no magic number for too much debt

Macro 5: Debt, credit and crises

Few macro questions are answered worse in public than this one: how much government debt is too much. The usual answer is a percentage, normally 90% or 100% of GDP, delivered with the confidence of someone reciting a physical constant. No such constant exists. Some countries have spent decades above 200% while paying rates close to zero; others panicked at half that ratio.

The ratio compares a stock with a flow

The debt-to-GDP ratio divides two things of a different nature. The numerator is a stock: everything a state owes, accumulated since it began borrowing. The denominator is a flow: what it produces in one year. A ratio of 120% does not mean the country would take 1.2 years to pay off its debt, any more than a mortgage worth three times your salary is repaid in three years.

What decides whether that debt is sustainable is not the level but the ability to service it: paying the interest and rolling over the principal as it matures. Interest spending as a share of GDP is in fact far more informative, because it measures what the state actually hands over each year.

The only equation that matters: interest rate against growth

The whole of debt sustainability fits into a comparison between two numbers:

• The average nominal interest rate the state pays on its debt, usually written *r*.
• The nominal growth of the economy, which is real growth plus inflation, written *g*.

If nominal growth exceeds the average rate paid, the denominator of the ratio grows faster than the numerator and the debt dilutes itself, even if the state never repays a penny. If the opposite holds, the ratio drifts upwards on its own and can only be stabilized by running a primary surplus, that is, taking in more than it spends before interest is counted. That is the heart of the matter: for much of the past decade advanced economies paid an average rate below their nominal growth, which is why they could borrow without the ratio running away from them. When that difference flips sign, the very same fiscal policy turns explosive without anyone having changed their mind about anything.

Why two countries with the same ratio do not run the same risk

Four features separate a comfortable issuer from a fragile one with the same ratio on paper:

• The currency of issuance. A borrower in its own currency cannot be forced into an involuntary default: it can always create the units it pays in. The cost of doing so is inflation and depreciation, not default. Borrow in a foreign currency and that exit does not exist, which is why Argentina is playing a different game from Japan.
• The average maturity of the debt. With an average maturity of one year, the state is back in the market constantly and a rise in rates feeds through almost immediately. With ten years or more, as in the British case, that rise takes a decade to show up in the full bill.
• Who holds the paper. Debt in the hands of domestic savers, domestic pension funds and the central bank itself behaves very differently from debt held by foreign banks, which can run for the exit and do not vote in that country.
• The liabilities you cannot see. The official ratio excludes guarantees, backstops and the likely cost of rescuing the banking system. Ireland went into 2007 with government debt of around 25% of GDP, one of the best figures in Europe, and came out of the crisis above 120% after absorbing the hole in its banks. Spain went from roughly 35% to close to 100%. The debt that kills you is almost never the debt that was on the spreadsheet.

The 90% threshold and the spreadsheet

In 2010 Carmen Reinhart and Kenneth Rogoff, authors of the influential historical study of financial crises *This Time Is Different*, published a paper that was read as proof that crossing 90% debt to GDP sank growth. The figure was quoted in entire parliaments to justify austerity programs.

In 2013 three researchers at the University of Massachusetts reproduced the calculation and found a spreadsheet error that left several countries out, the exclusion of available years, and a weighting that gave one country the same weight as entire decades of another. With the data corrected, average growth above 90% was still clearly positive and the sharp drop disappeared. What remained was a mild correlation with no clear direction: it is at least as plausible that low growth produces high debt as the other way round.

Japan above 250% against Italy at 120%

The most useful contrast there is. Japan has carried the highest gross government debt in the developed world since the 1990s, well above 250% of GDP, and between 2012 and 2023 its ten-year bond paid less than 1%. Betting against that debt earned the nickname of the widowmaker trade, for the number of managers ruined waiting for the collapse. Japan issues in yen, its holders are almost all domestic, and the Bank of Japan has come to own more than half the paper in circulation.

Italy, in 2011, had a ratio close to 120%, half the Japanese figure, and its ten-year bond went above 7%. Greece, with a lower ratio than Japan, ended up restructuring. The difference was not the level: neither of those countries issued in a currency it controlled, and their central bank had not yet taken on the role of buyer of last resort. The market does not punish a number; it punishes the combination of somebody else's currency, short maturities and holders who can walk away.