Alex is right. David Cameron's speech on the deficit yesterday consisted of "intellectually lazy lies". This, in particular, is dubious:

The choice is clear: staying on the road to recovery – or choosing the path to ruin. Competence or chaos.

To see what's wrong with this, remember the basic maths of government debt dynamics. This tells us that the primary deficit (that is, the deficit excluding interest payments) necessary to stabilize the debt-GDP ratio is:

d * [(r-g)/ (1+g) ]

where d is the debt-GDP ratio, r the real interest rate and g the real GDP growth rate.

d is currently 0.804: debt is 80.4% of GDP. Real long-term interest rates are around minus 1%, and the OBR estimates potential output growth over the next five years to be 2.2%. Plugging these numbers into our equation gives us minus 2.5%. In other words, we can stabilize the debt-GDP ratio with a primary deficit of 2.5% of GDP. This is a slightly higher deficit than the OBR expects next year, and much higher than the surplus of 3.2% the government plans by 2019-20.

In other words, more borrowing than the government plans would be quite consistent with stabilizing the debt-GDP ratio at around 80%.

What's more, if the government can borrow at less than four per cent - and nominal ten year gilt yields are now only 1.6% - then debt interest payments would be under 3.2% of GDP. That means we'd spend less as a share of GDP on debt interest (pdf) than we did in the Thatcher years.

This is not chaos. We can achieve debt stabilization with much less austerity than Cameron plans.

Of course, things will be different if borrowing costs rise sharply. If they do, though, it would come as a big surprise to the gilt market. The real yield curve is quite flat, which implies that the market is pricing in negative yields for a long time. It's odd that a Conservative government should be basing policy upon the idea that the Man in Whitehall knows better than the markets.

Now, this does not necessarily mean that there's no case for fiscal tightening. You could argue that a debt-GDP ratio of 80%, even if stable, is an unfair burden on future generations - though it's odd that a government which charges £27,000 for a university place and which presides over huge house price inflation should worry so much about intergenerational justice. And you could argue that such a ratio gives us less room to relax fiscal policy when the next downturn comes.

It's not clear, though, that these arguments are a case for a lot of austerity soon. As Frances says: