Deficit maths: Krugman slips up.

I was delighted to see this phrase in a recent article by Paul Krugman: “If we think that normal times involve 2 percent growth and 2 percent inflation, a deficit of 4 percent of GDP would be consistent with a stable debt/GDP ratio..”.

The significance of that phrase will be lost on the UK’s finance minister, George Osborne. It will also be lost on many others who write about the debt and who have no grasp of the basic and very simple maths involved: e.g. Kenneth Rogoff, Niall Ferguson, etc.

Anyway, the significance is thus.

As I explained here some time ago, if the inflation target is X% and that target is being met (or at least if inflation over several years AVERAGES X%), then the value of the national debt in real terms (i.e. inflation adjusted terms) will fall at X%pa, all else equal.

Ergo if the if debt is to be maintained at a constant percentage of GDP (and that constant percentage actually is maintained over the very long term – a century or so) then the national debt has to be topped up. And that can only be done via a deficit.

Moreover, the same point applies to the monetary base.

And if the economy grows in real terms at say Y%pa, then even more “topping up” will be required to keep “base plus debt” constant relative to GDP.

To summarise, if “base plus debt” is to be maintained at Z% of GDP then the deficit will have to be (X+Y)%xZ% of GDP. Or taking the 2% growth and 2% inflation assumed by Krugman, then a deficit that is 4% of GDP would maintain “debt plus base” at a constant 100% of GDP.

But note that Krugman said nothing about exactly what the debt:GDP ratio is. That’s his slip up.

Put another way, suppose there is no debt or base at all and that inflation is 2% and growth is also 2%, then if the state runs a 4% deficit, “debt plus base” will eventually stabilise at 100% of GDP. Or if the deficit is 2%, then eventual stabilisation will be at 50% of GDP.

So far Krugman is the only economist I’m come across who is aware of the above simple mathematical reltionships. And just confirms that most of those writing on this subject are clueless.