Economic myths: Negative equity [Square law of negative equity]

Yes, being in negative equity is horrible, whether that resulted from greed, recklessness, gullibility or sheer bad luck. So let's assume it would be a good idea to "help" people out of negative equity.

There are of course two ways of doing this in the short term*:
a) by pumping up house prices or
b) by writing off the element of any mortgage which is in excess of the potential selling price of the house (unsecured).

Let's look at the relative "costs" of doing this, and see what would happen if we went for option (c), allow house prices to fall and then write off all unsecured elements. We can illustrate this in diagrams.

As it happens, the distribution of mortgages by loan-to-value is almost a straight line (and even if it isn't, it makes the maths a lot simpler). In other words, one per cent of mortgages are almost paid off and represent only one per cent of the original principal/purchase price; one per cent of mortgages represent two per cent of the original principal/purchase price and so on. We also know that there are about 12 million outstanding mortgages with a total principal of £1,200 billion and about 12 million privately-owned homes which are owned outright.

To get the ball rolling, let's assume that a tenth of mortgages are in nequity (the official figure is half this, because of Funding for Lending and Help to Buy subsidies, but let's keep the maths simple). As things stand, there are 1.2 million mortgages with average unsecured principal of £10,000, that's total nequity of £12 billion (shaded red), which equals one per cent of total outstanding mortgages of £1,200 billion (0.1 x 0.1 = 0.01).


Under option a) we introduce a subsidy worth £20,000 per home/mortgage and eliminate nequity entirely (in the short term: this merely increases the risk that people will get into nequity in future). The total cost of the subsidy (shaded blue) required is twelve million homes x £20,000 = £240 billion - and we can double that for the twelve million homes which are mortgage-free = £480 billion. Which seems like a high price to pay for eliminating £12 billion of nequity. That means basically that future purchaser and taxpayers will end up net £468 billion worse off:


Under option b) the total cost of simply writing off all unsecured principal is a one-off cost of £12 billion.

What about option (c)? Let's withdraw some existing subsidies to land ownership and allow prices to fall by twenty per cent. The amount of nequity which now has to be written off is now 3 million mortgages x average £25,000 = £75 billion. This sounds like a lot, but in relative terms it isn't. £75 billion is only about one per cent of what UK bankers claim are their total/gross assets/liabilities (which are said to be five times UK GDP = £7,500 billion). This is 6.25% of total mortgage principal (0.25 x 0.25 = 0.0625).

And there is an even bigger saving to future purchasers and taxpayers: the total principal value of the subsidy withdrawn is 24 million x £30,000 = £720 billion. So there is still a net gain to them of £645 billion (and that's even assuming that they would bear the cost of the initial mortgage write off):

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All of this leads us to Wadsworth's Square Law of Negative Equity - when you multiply numbers less than one, you end up with a smaller number than you started with.

Even allowing house prices to fall by fifty per cent and writing off all the unsecured amounts would only "cost" 0.5 x 0.5 = 0.25 x £1,200 billion = £300 billion. The reduction in the cost of the subsidy would be £80,0000 x 24 million = £1,920 billion, which is an overall saving to future purchasers of £1,620 billion.

If you take it to extremes and withdraw the subsidy to land values entirely and allow house prices to fall to £zero, the "cost" is £1,200 billion and the saving is £200,000 x 24 million = £4,800 billion, an overall saving of £3,600 billion.
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* The mainstream view is that a) is far better, as pumping up house prices creates or at least preserves "wealth" and that b) would lead to the banking system somehow "imploding" or that it leads to moral hazard. Method a) does not create or preserve "wealth", it merely preserves "privilege" (i.e. the flow of wealth from the productive economy and non-landowners to large land owners and bankers) and on closer inspection, b) does no such thing.

The longer term (and ultimately only sensible) way is to get the economy going again by e.g. reducing the tax burden on people with large mortgages relative to income. These will be largely recent younger purchasers who own, relative to their earned income, lower value houses, so shifting taxes from earnings to the rental value of land will benefit them particularly. But let's gloss over this for now.