# Average age of first-time house buyers

One of my favourite radio programmes is More or Less, presented by the excellent Tim Harford. If you are even remotely interested in statistics, then you should listen to it. It does a splendid job of unpicking some of the dodgy numbers we hear in the news.

In their most recent episode, one of the dodgy numbers they tackled was a claim by the former housing minister, Grant Shapps, that the average age of first time house buyers had been steadily climbing, and is now 37. That figure, as you might expect from a statistic quoted by a politician, is nonsense. It came from a rather specific analysis which excluded everyone under the age of 30, so it's not going to tell you anything about the average age of all first time buyers. Listen to the programme to find out more.

However, unusually for More or Less, I think the figure they presented as being the correct figure is also problematic. They gave a median age of 29, which comes from statistics compiled by the Council of Mortgage Lenders. Despite Shapps's claim that the average age of first time buyers has been rising, this statistic has stayed remarkably constant in recent years.

One problem in interpreting this figure is that it's not always clear when someone taking out a mortgage is actually a "first time" buyer, but this was discussed at length in the programme.

However, there is another big problem with the number which wasn't addressed on More or Less. The problem is that the statistics, as far as I can tell, are calculated only from completed mortgages. In statistical terms, calculating age at buying your first time is a survival problem. Some people may never buy a home, and this will affect the median age. Including only those people who actually buy a home will distort the statistics.

Let's illustrate this with an example. Suppose that our population consists of just 5 people. Three of them buy their homes at ages 28, 29, and 40. The other 2 never buy their own home, despite living to some age greater than 40. If we consider the three completed mortgages at 28, 29, and 40, then the median age would be 29. However, if we include all 5 people, then are data are 28, 29, 40, >40, and >40. The median age now is 40.

To look at this another way, to consider how "difficult" it is to buy a home (which is the point that Shapps was trying to make when he quoted his statistic), then we need to look at not only the age at which people buy a home, but also whether they do so at all. Looking only at the age of those who are lucky enough to complete their mortgage gives only part of the picture.

According to figures available in the spreadsheet from the Council of Mortgage Lenders on this page, the total volume of mortgage lending has more than halved since the financial crisis began, so clearly the number of mortgages matters greatly.

I discussed these statistics with my colleague Michael Grayer, and he pointed out that there is a very similar problem when you look at average age at death of a population as distinct from life expectancy, a subject about which he has written a helpful blogpost. While it might be tempting to think that "average age at death" and "life expectancy" are the same thing, they can in fact be hugely different. I think we have the same problem here: what we are actually measuring is "average age at first-time mortgage", but the statistic I think we are really interested in is "first-time mortgage expectancy".

So is life getting harder for first-time buyers or not? The bottom line is we really can't know from the statistics I've discussed here. But just because the median age at taking out a first mortgage has remained reasonably constant, it is certainly not safe to conclude that there is no change in the difficulty of getting onto the property ladder.