## Tuesday 20 March 2012

### A nice bit of maths by David Miles

First, let's get the spin over with

The Home-Owner-Ist media were cock-a-hoop at a report brought out by David Miles, an external member of the Bank of England's Monetary Policy Committee:

The Telegraph ran the headline House prices to rise for years, says BoE's David Miles, the Mail went with New house price boom is on the way but the young will have to wait longer to buy, says Bank of England and the deeply schizophrenic City AM with BANK’S MILES SAYS HOUSE PRICES WILL RISE. Only The Guardian saw the obvious downside, and ran the headline Bank of England house prices paper is grim reading for first-time buyers.

Now let's look at the maths

I've printed out but not read the full report yet, but its a lengthier rehash of a presentation he gave in November 2011, which I have read in full. His cunning formula says that assuming a constant average house price (of four times earnings), the size of the deposit required before you can take out a mortgage affects the average age of first-time buyers ('FTBs'), and further that the average age of FTBs affects the proportion of owner-occupiers.

Formula number one assumes that houses cost four times one year's earnings, first-time buyers take four years to save up a 5% deposit (i.e. they save on average 5% of their gross income every year, which is quite a lot), and they start saving at age 28, so if banks are happy to dish out 95% mortgages, the average FTB will buy at age 32.

Formula number two says that an average housing career is from age 20 to age 80 (when you die), and that people spend the last 5 years of their lives in a care home. So if deposits are only 5%, the proportion of households who are owner-occupiers will tend (or trend?) towards 72% as follows:

(75 - 32) ÷ (80 - 60) = 43 ÷ 60 = 72%.

His Chart 8 shows that deposits of 5% were the norm between 1980 and 1997 and owner-occupation levels reached 68.6%* at the end of that period. Working backwards, average FTB age during that period must have been about 34 [check: (75 - 34) ÷ (80 - 60) = 41 ÷ 60 = 68%.] and people must have started saving at age 30 (34 - 4).

From 1997 to 2007, the average deposit was 10% and owner-occupation levels were 70.7%* in 2005 (the peak was 70.9% in 2003, but after that, stupid prices started choking things off again). So average FTB must have been 32.5 and people must have started saving at age 24.5 (32.5 - 8).

His chart shows that average deposits demanded shot up from 10% to 25% between 2007 and 2009, they now appear to be 20%. We don't know whether the age at which people start saving up for a deposit is more like 30 or 24.5, so let's pitch it at 28 (younger people are worse paid nowadays). Using formula number one, it will take them 16 years to save up a 20% deposit and average FTB age will tend towards 44. If we insert 44 that into formula number two, that means a long-run rate of owner-occupation of only 52%.

Is 52% plausible?

A rate of only 52% would push us back to 1972*, the first dawn of the Home-Owner-Ist era. Clearly, we're not going to have twelve years of there being absolutely no FTBs at all, as some young people can and will save much more than 5% of their income every year, or they will get help from BOMAD, but FTB numbers are down to about half of the number required, so the adjustment period will take twenty-four years, rather than twelve.

In the six years after 2005, owner-occupation rates fell from 71% to 67%, if this continued for eighteen years, we can deduct another three falls of 4% every six years and we are down to 53% (BOMAD will run out of money sooner or later), which is pretty close to 52%.

* I've taken those figures from the DCLG, not the report.

#### 12 comments:

Sarton Bander said...

The trouble is that in a bubble existing house "equity" is released to provide new deposits.

So it tends to favour those who have already bought until it runs out of steam and all the banks go bankrupt.

Anonymous said...

Very cunning but completely invalid.

First, "FTBs take four years to save up a 5% deposit". Do they? That would depend on the levels of wages, the levels of house prices, the proportion of couples where both work etc etc

"Banks demand deposits of 20%" - well maybe they do now, but a) once the government lets interest rates rise to more realistic levels, credit availability will rise and b) that assumes everybody will always grab the biggest mortgage they possibly can as opposed to thinking about how much they can afford.

Then, the analysis does not take account of buy-to-let buyers, who have very different financial profiles but compete with FTBs in the housing market.

And finally, the analysis makes no allowance for regional variations.

And finally finally, the analysis assumes no change in current planning policy, which may not be a correct assumption.

Mark Wadsworth said...

SB, I said that BOMAD would run out of money sooner or later.

AC, not so hasty!

1. Yes of course different people save up at different rates. There must be an average though, and he guesstimates that average at 1.25%.

2. I wouldn't be so sure about interest rates rising, or what impact they will have. His charts and everything cover from early 1970s to know, when we've had very high and very low rates, the deposit requirement has stayed very stable for long periods despite that.

3. Of course it takes into account BTL, if somebody hasn't bought a house yet they are a tenant and so the balance of houses coming onto the market will be bought by BTLs. The natural tendency of land ownership, in the absence of a sensible tax on it, is to become more concentrated over time.

4. Regional variations, see point 2.

5. He covers rampant NIMBYism in the other report, although we can tell whose side he's on because he says that "The UK is a densely populated island" which is a big f-ing lie.

But this is also self-correcting - if more than half the voters are owner-occupiers, new construction gets choked off; if more than half are tenants and a lot of these would like to buy, there's a lot of new construction. Click the link "the first dawn".

Finally finally, I take it you didn't read his presentation and secondly, it's not a complete coincidence that his calculations actually fit the facts, is it?

Bayard said...

"The UK is a densely populated island" which is a big f-ing lie."

No it isn't. It depends what you mean by "densely populated". It is certainly more densely populated than almost any other island in the world, apart from places like Singapore, Hong Kong or Manhattan, all of which are a lot smaller. It is also one of the most densely populated countries. It's just that the denseness of the population of densely populated countries (or islands) isn't very dense. It's like saying something is very quick in geological time.

"if more than half the voters are owner-occupiers, new construction gets choked off; if more than half are tenants and a lot of these would like to buy, there's a lot of new construction."

I'd disagree. That depends on the theory that owner- occupiers are against new construction, which is not proven. Some are, but the majority of those are NIMBYs, who only oppose construction in their back yard (the B and the Y of NIMBY). Rarely are they interested in what goes on over the horizon. NIMBYs are almost always people who have moved into an area, usually rural, usually from a town. Thus, except in a few "hotspots" close to our major cities, they form a strident minority. So the number of o-o's who are against new construction anywhere (the BANANAs) are a minority of this minority. All of which suggests that a majority of o-os are indifferent to new construction, if not actually supportive of it.
Also, if there is plenty of new construction, what is to prevent it all being snapped up by BTLs? There has to be an adjustment in interest rates and house prices, which, as we know from places like Ireland and Spain, are almost completely unaffected by new construction.

Mark Wadsworth said...

B, yes it is a f-ing lie. If you whizz round the world in an aeroplane, you notice that most people live in very densely populated towns and cities, and there are big gaps between them. So a town or city dweller in the USA (very sparsely populated) perceives things no differently to somebody living in a town or city in the South East of England (densely populated).

And it is not just perception, it is reality. It's just that your US city dweller has a six hour drive to the next city, and the English city dweller has a half hour drive.

As to the 50% cut-off, just click the link "the first dawn", is it a coincidence that new builds plummeted in the 1970s, shortly after o-o passed the magic 50% level?

Or that London, despite being 'densely populated' has in relative terms the most new construction of anywhere in the UK? It's because tenants are a very high proportion of the London population.

Bayard said...

Coincidence is not causality. Remember, there were no nuclear weapons before women got the vote.

London could well have the most new construction of anywhere in the UK simply because that's where the property rental and sales prices are highest and where demand for residential and office space is greatest. No-one is going to build any new housing in Pembroke, not because it's an ancient town stuffed with owner-occupier NIMBYs, but because it's an ancient town stuffed with empty houses, many of them built just a few years ago and never occupied.

And you completely ignored my point about the meaning of "densely populated". By island and country standards, Britain is densely populated. That doesn't mean the whole country looks like Wimbledon. It means the whole country looks like it does, with cities, towns and villages separated by countryside. I'd say that a half-hour drive to the next city is pretty damn densely populated. It's not wrong to say the the UK is densely populated, it's wrong to say that the UK is densely populated, therefore there is no space to build new housing.

Mark Wadsworth said...

B, coincidence is not causality.

But the electoral power of NIMBYism is a direct function of the percentage of owner-occupiers*, that is
a) basic logic and
b) observable in real life.

* And o-o levels and new construction are not just negatively correlated, it's a binary thing. More than 50% O-O = no new construction, less than 50% O-O = lots of new construction.

I fully accept your other points, but Pembroke is a red herring. The question is, why are huge blocks of flats being built well within London instead of nice semi-detached houses a few miles further out? Of course land values play a large part, but O-O levels play a large part as well.

Bayard said...

"His cunning formula says that assuming a constant average house price (of four times earnings).."

Isn't this a bit high? ISTR that the average house-price-to-earnings ratio over the last hundred years or so was lower, around 2.5?

Mark Wadsworth said...

B, his formula is a simplification to illustrate a point. His report includes charts showing ratio of house prices to income, yes, it varies between 3 and 6 but the long run average is about 4.

Bayard said...

"The question is, why are huge blocks of flats being built well within London instead of nice semi-detached houses a few miles further out?"

One possible answer: There is a lot less objection to new building in central London because, unless you live on the edge of a park, your view is, at best, other houses and could easily be a railway yard, a major road or an industrial estate, so more houses or flats in your view might even be a good thing. If you live in the Green Belt, your view is usually greenery of one kind or another and so swapping that for houses is usually a bad thing. It really makes no difference if you are a owner-occupier or a tenant, you are still going to object if you think you are going to lose your view. It's a bloody sight easier to try and stop something being built than it is to move home (the third most stressful thing in peoples' lives after death and divorce, I believe).

Old BE said...

Wait, the average size of a deposit doubled to 10% after 1997? And the market bubbled?

Mark Wadsworth said...

B, there might be some correlation with that, but taking the country as a whole, the biggest dampener on new builds is the level of o-o.

BE, that's what the report says, using CML figures. The rate of increase of o-o definitely slowed after 1997, and came to a halt in 2005-ish.