Why austerity's failing

Austerity isn't working. The public sector had a deficit on its current budget of £41.6bn in the three months to June, which is £6.5bn more than in the same period last year. Tax rises and spending restraint, then, have not reduced borrowing.

There's a simple reason for this. Net government borrowing is the counterpart of private sector net lending. Whilst the private sector is a big net lender, therefore, the government will remain a big borrower whatever its fiscal policy.

This is not a heterodox theory. It's simple maths. Let's recall the basic national accounts identities. GDP is the sum of consumer spending (C), investment (I), government spending (G) and net trade (X – M):

Y = C + I + G + (X – M)

Each pound of GDP is also either consumed (C ), saved (S) or paid in taxes (T), so:

Y = C + S + T

Some simple rearranging of these two gives us:

(T - G) = (I – S) + (X –M)

This tells us that if the government runs a deficit (T – G is negative), then one or both of (I –S) and (X – M) must also be negative. In other words, if the government is borrowing, either the domestic private sector is saving more than it is investing in capital and inventories, or foreigners are doing so: a UK balance of payments deficit is equal to the rest of the world having a surplus, and a balance of payments surplus is by definition equal to an excess of domestic saving over investment.

This tells us that government borrowing will fall (that is, T – G rise) if and only if I – S rises or X –M rises.

These are mere identities. They are consistent with any story you want to tell about deficit reduction. Advocates of expansionary fiscal contraction argued that cuts in public spending would reduce interest rates and increase business confidence, with the result that the effort to raise T – G would cause a rise in I – S, so much so that GDP would increase as the deficit fell. More conventionally, you can claim that efforts to raise T – G will partly reduce GDP, but also partly succeed in actually raising T – G, to the extent that I – S rises (if, say, workers laid off by the government eat into their savings) or if X – M rises (if the lower public spending reduces spending on imports).

However, the data tell us that neither of these happy stories has been true. Comparing Q2 with Q2 2011, T – G has fallen, which means that I – S and X – M, taken together, have fallen.

The obvious culprit here is the euro area's crisis. This is having the doubly nasty effect of hitting our exports to the region (thus reducing X – M) and depressing banks' willingness to lend and companies' willingness to borrow, thus reducing I – S. Brute arithmetic means this has reduced T – G.

Insofar as this is the case, our public finances will improve when and only when the euro area's crisis is resolved. UK government borrowing is determined more by Angela Merkel than by George Osborne.

However, this is not the whole story. Even without the euro crisis, banks have been loath to lend – a fact which has depressed I – S and hence T – G. In this sense, the funding for lending scheme aimed at getting banks lending again is a reasonable deficit reduction strategy; I doubt it'll work much, but that's a separate issue.

There is, though, a more awkward problem. Companies were investing less than they were saving long before the recession. This suggests that a negative I – S is not merely a temporary result of the recession, banking crisis and euro problem, but is instead a structural fact – a reflection of the lack of monetizable investment opportunities.

To the extent that this is the case, government borrowing might remain high for a very long time.

Now, I don't know how far the private sector's surplus – and hence government borrowing – is due to temporary factors and how much to near-permanent ones. What I do know is what I wrote two years ago: "As long as the private sector is in the mood to save, efforts to cut public borrowing will merely depress demand. It is only when firms and households regain the appetite and capacity to borrow that government can reduce its borrowing safely."

You're entitled to your own political opinion. You're not entitled to your own maths.

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