How many British families have 17 children?

In the wake of recent welfare reforms in the UK, the UK Chancellor George Osborne decided to score cheap political points by connecting welfare and the tabloid frenzy surrounding the Philpott family. Well, perhaps that is not surprising coming from a Conservative politician. Osborne’s opposite number, Ed Balls, criticised him - correctly in my view - for this ‘calculated decision to use the shocking and vile crimes of Mick Philpott to advance a political argument’. Which is pretty much how you would expect a Labor politician to react.

So I was astounded to hear the following exchange on the Andrew Marr Show this morning, between host Eddie Mair and Labour MP (Shadow Deputy PM, no less) Harriet Harman:

MAIR: Should people on benefits be allowed to have as many children as they want?

HARMAN: Well, I- you know, it’s absolutely understandable when people limit their families… [and she goes on]

The correct answer to Mair’s deliberately provocative question, obviously, was a simple “Yes.” Because we don’t punish children for the choices their parents have made, and nor do we ‘allow’ or ‘disallow’ people from having children. But that’s not all.

Later in the interview comes this exchange.

MAIR: So 17 children is fine? The state will continue to cough up for that?

HARMAN: I don’t think it’s fine. I don’t think anybody thinks what was going on in that family [the Phillpots] was acceptable—

MAIR: No I’m not talking about just this family.

This got me wondering, if Mair’s not talking about the Phillpots, who is he talking about? How many families in the UK actually are there with 17 children?

Andrew Dilnot has written and spoken on the similar tabloid favourite, of ‘gymslip mums’ (single parents on benefits under 18). It turns out there are far fewer than most people think. It must, surely, be the same with very very large families.

Finding data is not straightforward. I couldn’t find benefits statistics, so I’m using standard ONS household data, which includes everyone, those receiving benefits and those not. In general, ONS groups together all families with “3 or more” children, which doesn’t get us very far. But even that group is only 14% of families with children, or 1 million out of 7 million total families with dependents (see figure 4 of this). This gives us a good starting indication.

ONS does provide slightly more disaggregated data on household size. Household size is an imperfect reflection of family size, because households include adults living together (like me and my three adult housemates). So households should give us an overestimate. A family with 17 children must have at least 18 people (including, conservatively, one parent/guardian), so we could use the number of 18 person households as an upper bound on the number of 17 child families . Here again, ONS data doesn’t help much: they group together households with six or more people. But in 2012, there were about 507,000 such households, out of about 26 million total, or around 2% of households.

We can make a guess at how many 18 person households there are by making an assumption about how the “Six or more people” category is distributed. A simple and reasonable assumption is that for each single-person increase in household size, the number of households of that size falls by some fixed fraction (there are more complex assumptions we might make, but little would be gained here by using them). Based on that idea, I estimate that for each extra person in a household over four, the number of households falls by 70%. That is, there will be around one-third as many six person households as there are five-person households. That seems pretty reasonable, and you can see that fits the fall from four to five person households fairly well. Using this model, the graph now looks like this:

Notice the change of scale, and that I’ve left out the households with 1-5 people. But the message is clear: households with 10 or more people are pretty much non-existent. The exact estimates are (note these are no longer in thousands, but in units):

Household  Number of 
  Size     households
   10        3,144
   11          967
   12          298
   13           92
   14           28
   15            9
   16            3
   17            1
   18            0

In other words, an 18 person household, and therefore a 17 child family, is a statistical anomaly. I wouldn’t be surprised if there were no other families in the UK with 17 children.

But, wait, you say, Mair’s question was hyperbole, like when he called Boris Johnson a ‘nasty piece of work’. What he really meant was not ‘17 children’ per se, but just large families in general. And there must be lots of of those, right? Well compared with very very large families, yes. But compared with all families, not so much.

First we have to decide what a large family is. I have two siblings, and I think that wasn’t too unusual. I don’t experience shock if I hear someone has four children. Perhaps five children is the point that first starts to seem ‘large’ to me. How many families in the UK have five or more children? Well, again, conservatively, let’s instead count households with six or more people - and that number, you will recall, was 507,000, or 2% of all households. Practically negligible. But we should be fair, because it is people in households, and not households, that receive benefits. By my model, the 6+ households would include around 3.2 million people, or around 5% of the UK population. Bigger, but still pretty small.

Finally, remember, all these numbers are for the total number of households of a certain size in the population, and many of these will likely be receiving no state benefits. Some very large families are actually quite well off.

In short, Eddie Mair should ask better questions.