Reuters: Sovereign debt maths show risk of vicious circle — Hugo Dixon

Sovereign debt maths show risk of vicious circle — Hugo Dixon

APRIL 10 — How can a country support debt of over 100 per cent of Gross Domestic Product (GDP) for many years and then suddenly start spiralling towards insolvency? That question of sovereign debt maths is not merely academic. It is highly relevant to the likes of Greece and Italy.

The answer is that size of the sovereign debt burden is not everything when it comes to keeping up with interest payments. No matter how high the ratio of debt to GDP may be, it does not need to increase as long as the government has two factors going its way: the “primary” budget balance — the balance before interest payments — and the growth rate of nominal GDP.

To see how these play out, consider two countries. One has a moderate debt load, 50 per cent of GDP, which carries a four per cent average interest rate. If the budget is in primary balance, the government will still run a deficit of two per cent of GDP, which is four per cent (the interest rate) of 50 per cent (the debt). As long as nominal GDP grows by four per cent, the ratio of debt to GDP stays the same.

The other country is highly indebted, with a debt/GDP ratio of 100 per cent. Assume it also pays an interest rate of four per cent. With a primary budget balance, its fiscal deficit is four per cent of GDP. However, as long as nominal GDP keeps growing at four per cent a year, the ratio of debt to GDP stays the same — 100 per cent.

In effect, the highly-indebted government doesn’t pay a penalty for its profligacy, as long as growth
keeps up and interest rates stay low. Greece and other heavily indebted countries benefited from such a happy environment for years.

But the equilibrium is fragile. It can be disturbed in three ways: nominal GDP growth can decline, interest rates can go up or the country can start running a primary deficit. The pain is much worse for highly indebted countries like Greece, which has managed all three at once.

Start with growth. Imagine nominal GDP growth drops to zero. If nothing is done, the debt/GDP ratio will rise by two percentage points in the moderately indebted country, but by four percentage points in the highly indebted one.

Countries can keep that key ratio from increasing, by running compensating primary surpluses. That means moving from balance to a surplus of two per cent of GDP for the moderately indebted and from zero to four per cent for the heavily indebted. The higher the debt level, the more the government’s belt will have to be tightened.

But such budgetary squeezes tend to put further downward pressure on GDP — making the debt burden even heavier. Imagine that actual GDP falls by a quarter of a percentage point for every budget surplus increase of one percentage point of GDP. The four per cent fiscal squeeze would then knock GDP by one per cent in the profligate country, while the modestly indebted country’s GDP would fall half a per cent.

Next, interest rates. Investors jack up interest rates to compensate for the risk that the population will not stomach a humungous budget squeeze. Foreign buyers are likely to be more demanding than patriotic domestic ones. As the proportion of expensive debt increases, the government’s interest bill rises, potentially starting a debt snowball.

Finally, the government’s budget. While the state would ideally be aiming for a budget surplus, recessions normally lead to higher deficits. As business activity drops off, tax revenue falls and more people qualify for government benefits. This is the worst moment for markets to turn hostile.

When all three factors — economic contraction, higher rates and rising deficits — come at once, they easily start fuelling one another in a vicious cycle. If the profligate country has to pay a six per cent interest rate instead of four per cent and recession and belt-tightening have cut nominal GDP by two per cent, a primary surplus of just over eight per cent is required just to keep the ratio of debt to GDP stable.

That is a huge move, and may be too much to bear politically for the sort of country which has historically run big deficits. Investors have good reason to fear some sort of debt work-out. They then don’t push up the interest rate they are prepared to lend at — they stop lending completely. — Reuters