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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.

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