Prostitution and the pitfalls of precision and estimation

In 2009, there were an estimated 60,879 female prostitutes in the UK.

At five significant figures that is remarkably precise, even more so as it’s an estimate. The UK’s Office for National Statistics (ONS) came up with the figure in tackling the challenge of calculating the contribution of prostitution to the country’s economy.

So how did the ONS arrive at this number? The numbers of prostitutes aren’t something that are routinely collected. Well, not any more. In the nineteenth century things were different. For example, the Journal of the Royal Statistical Society, volume 30 (1867) has a table at page 389.

In the twenty-first century, ONS had to do things by estimation. First, it found an estimate for the number of female prostitutes in London for 2004. It adjusted this in proportion to the growth in the population of men aged 16 or more and came up with its 60,879 estimate for 2009.

You’d think that the figure ONS found for 2004 must have been similarly precise. It wasn’t. It was a nice, round 58,000. And that came from scaling up from figures for London presented in an Eaves Poppy Project report (pdf, opens in new window).

ONS then estimates the numbers of client per prostitute per week based on looking at Dutch practice. It researched a figure for the average price per client visit in 2004 – £55 – and inflated this to a 2009 price of £67.16. Presumably £55 was an estimate, so perhaps that 2009 price is also too precisely stated. Multiplying numbers of prostitutes, numbers of clients, numbers of weeks a year worked (all 52), and the average price of a visit, ONS arrives at an estimated average annual contribution to the UK economy of £5,314,000,000 … over five billion pounds. This, and the figure for illegal drugs, has not been calculated and reported previously to the EU. Because each country’s ‘membership fee’ of the EU is based on its economic performance this means the EU wants roughly £1,600,000,000 in back payments.

If that wasn’t big enough to make you think twice – especially if you’re the UK Prime Minister – there are lots of reasons to be wary of the ONS estimate on which it’s based.

Professor David Spiegelhalter, whose day job includes work on the public understanding of uncertainty, has blogged in detail sense-checking the figures.

Another sense-check can be added to that by looking at other countries. Germany, for example, has included the contribution of prostitution to its economy in its national accounts for some years. According to the web site of Deutsche Welle, Germany’s international broadcaster, the gross added value is a little over seven billion euros – a little under six billion pounds. There are roughly 35 million adult German men. The figure for the UK is around 25 million. If UK men use prostitutes as much as German men, all other things being equal, we would find a contribution of around four billion pounds to the UK economy (quite a bit less than the ONS estimate). Estimates of the numbers of German prostitutes range from 200,000 to 400,000, and this includes both men and women. The ONS figure is an estimate only for women and some argue that the figure may be closer to 100,000 once male prostitutes are included.

So a bill of over £1.5 billion pounds has been based on estimates arising from a modest amount of data with a great deal of uncertainty.

Meanwhile, the improbably precise estimate of 60,879 UK-based female prostitutes has got a life of its own. It has spread beyond the economic debate. It crops up in the Daily Telegraph in “Are we doing enough to protect male sex workers?”  And the BBC uses it in its online article “Paying for sex ‘should be illegal’, campaigners say“, though at least they acknowledge its status as an estimate even if they still use the precise figure.

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