29 September 2009

Debt or Depression

The Tories seem to think that debt is worse than depression. Here is one more reason why they are wrong.

Government debt is manageable in a growing economy. Get the economy moving and a little bit of growth and a little bit of inflation will deal with the debt. Even with inflation kept to its 2% target, growth at the UK average of 2.5% is enough .

In thinking about government debt and deficits, I find this little equation helpful:
where d is the government deficit (as % of GDP), D is government debt as (% of GDP) and y is the nominal growth rate.

This is the equilibrium debt-deficit equation. If the government consistently ran a deficit of d% then its debt would converge to D%, given a growth rate of y%.

What does this mean for the UK today? Let's take 4.5% as the nominal growth rate (ie growth rate before inflation is stripped out):

This year the deficit is 13% of GDP. If it stayed at that level then debt would stabilise at 289% of GDP. If we felt comfortable with debt almost 3 times national income then a 13% deficit would be sustainable. We don't feel comfortable and the people lending the money wouldn't either.

If debt of 80% feels better then, government needs to bring the deficit to d= 4.5% x 80% = 3.6%.

The good news is that to stabilise debt, government doesn't need to run a surplus. It doesn't even need to balance the budget; it only has to hold the deficit to 3.6% for a (longish) period of time. (Compare that with the Maastricht Treaty rule that deficits should be below 3%).

If we want to get back to the old debt rule of 40% GDP, then the deficit needs to fall to 1.8% and the magic of a little bit of growth and a little bit of inflation will do the rest. (In practice the government would not keep the deficit constant; it should make the deficit smaller when growth is good and larger when growth is low.)

So far I have taken y= 4.5%. (You could work on 5% to make the calculations easier, but 4.5% is consistent with 2% inflation and 2.5% real growth.) What happens if nominal growth is say -1%? That could happen with low growth and deflation, the Japanese scenario.
d= -1%xD
Say the debt is at 70%:
d= -1% x 70% = -0.7%

So the government would need to run a surplus of 0.7% of GDP just to avoid adding to the debt ratio.

Even with slightly positive growth, say 0.5%, the figures are bad. To bring the debt level down from 70% , the Tories would need to cut the deficit below d= 0.5% x 70% = 0.35% of GDP, almost a balanced buget.

The conclusion is obvious: fix the economy first and then a little bit of growth and a little bit of inflation will make fixing the debt a whole lot easier.

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