The world’s public finances look increasingly precarious. In the year to July America’s federal government borrowed $2.3trn, or 8.6% of GDP—the sort of deficit usually seen during economic catastrophes. By 2025 five of the G7 group of big rich countries will have a net-debt-to-GDP ratio of more than 100%, according to forecasts by the imf. Such debts may have been sustainable in the low-interest-rate era of the 2010s. But those days are long gone. This month the ten-year Treasury yield briefly hit 4.3%, its highest since before the global financial crisis of 2007-09.

How will governments shed these burdens? Economists are increasingly gripped by the question. A recent paper by Serkan Arslanalp of the imf and Barry Eichengreen of the University of California, Berkeley, presented at America’s annual monetary-policy jamboree in Jackson Hole, Wyoming, on August 26th, sets out a menu of options. It is not exactly an appetising one.

Big economies have had big debts before. Broadly speaking, they have dealt with them by employing one of two strategies. Call them the austere and the arithmetic. The austere method is to run primary surpluses (ie, surpluses before debt-interest payments). In the 1820s, after the Napoleonic wars, Britain’s debts reached almost 200% of GDP; the Franco-Prussian war left France owing nearly 100% of GDP in the 1870s. Previously Mr Eichengreen and co-authors found that between 1822 and 1913 Britain ran primary surpluses sufficient to reduce the debt-to-GDP ratio by more than 180 percentage points; France did enough to reduce its ratio by 100 percentage points in just 17 years after 1896.

Messrs Arslanalp and Eichengreen are pessimistic about the prospect of democracies repeating the trick today. In the 19th century welfare states were minimal. British politicians followed the Victorian philosophy of “sound finance”; the French sought to reduce debts so as to be ready for their next war. In contrast, modern welfare states are weighed down by ageing populations, and the need for more defence spending and green investment means the size of the state is growing. Politicians could raise taxes. But other research by the IMF finds that in advanced economies, from 1979 to 2021, fiscal consolidations were less likely to succeed in cutting debts if they were driven by tax increases instead of spending cuts, perhaps because raising taxes harms economic growth.

What about the arithmetic approach? This was the path many countries followed after the second world war, when America’s debts peaked at 106% of GDP (a level they could soon surpass). It involved the rate of economic growth exceeding the inflation-adjusted rate of interest, such that legacy debts shrank relative to GDP over time, with small primary surpluses chipping in. It is possible to argue that recent high rates of inflation have started the world economy on the arithmetic debt-reduction route. Indeed, advanced-economy net debts have fallen by about four percentage points after shooting up in 2020 when covid-19 struck.

Yet inflation only reduces debt when it is unexpected. If bondholders anticipate fast-rising prices, they will demand higher returns, pushing up the government’s interest bill. Persistent inflation helped after the second world war only because policymakers held down nominal bond yields in a policy known as financial repression. Until 1951 the Federal Reserve capped long-term rates by creating money to buy bonds. Later a ban on paying interest on bank deposits would redirect savings to the bond market.

The resulting low real interest rates were paired with rapid post-war growth. Between 1945 and 1975, this reduced the debt-to-GDP ratio by a weighted average of 80 percentage points across the rich world. Both sides of the equation were important. Everyone can agree growth is desirable—it is the “painless way of solving debt problems”, write Messrs Arslanalp and Eichengreen, and it averaged an annual 4.5% across the rich world in this period. But high growth typically raises real interest rates. Another working paper, by Julien Acalin and Laurence Ball, both of Johns Hopkins University, finds that with undistorted real interest rates and a balanced primary budget, America’s debt-to-GDP ratio would have declined to only 74% in 1974, rather than the actual figure of 23%.

Unless artificial intelligence or another technological breakthrough unleashes a step change in productivity growth, today’s ageing economies have no chance of matching post-war rates of expansion. America’s GDP is expected to rise at an annual pace of just 2% over the next decade. That immediately limits the arithmetic strategy by putting the onus on real interest rates. There are good reasons to expect rates to be “naturally” low, such as more saving as societies age. But investors seem to be having doubts, as the recent rise in long-term bond yields demonstrates. Financial repression and high inflation to bring down real rates would require sweeping changes, such as central banks abandoning their inflation targets, as well as a reversal of much of the financial liberalisation that took place towards the end of the 20th century.

Best of the worst

What, then, will happen? “Governments are going to have to live with high inherited debts,” reckon Messrs Arslanalp and Eichengreen. The best politicians can do is not to make a bad situation worse. Yet the ongoing accumulation of debt suggests it is unlikely that politicians will follow this advice. On its current path America will match its post-war record of spending 3.2% of GDP on interest in 2030. Two decades later this will pass 6%. The bill could be higher if another pandemic or major war arrives in the meantime.

However unlikely it seems that voters and politicians will be willing to tolerate primary surpluses, sustained inflation or financial repression, they will probably reach a point where they are equally unwilling to put up with handing over a large chunk of tax revenues to bondholders. At such a time political constraints will ease—and the danger of a bond-market crisis will rise. The debt-reduction menu will then not look quite so unpalatable.

Read more from Free exchange, our column on economics:
Which animals should a modern-day Noah put in his ark? (Aug 24th)
Democracy and the price of a vote (Aug 17th)
Elon Musk’s plans could hinder Twitternomics (Aug 7th)

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