Tuesday, 30 November 2010

Sex and happiness

Despite Chris's warning, I went to Tim Worstall's book launch today. I even bought a copy which I will review on here when I have read it (on the bus tomorrow).

But before that, I learned something nice from his answer to an audience question.

Apparently, there's a clear relationship between GDP per head and population growth. We already know that people in poorer countries have more children, and the population of those countries grows faster. It seems that there's a measurable cut-off point: at $16,000 per head of GDP, fertility drops to around replacement rate (just over two children per mother) and the population stabilises.

Which reminded me of another statistic I read recently: national happiness grows with GDP until a certain point, at which it levels off and people stop getting happier. That level? $17,000 per head*.

Now perhaps there's something important in that $1,000 difference, but the two figures are within the margin of error for cross-country macroeconomic data series. Surely this can't be a coincidence: perhaps there is a common cause behind both effects?

If so, then surely the only conclusion is: People stop getting happier when they stop having unprotected sex.

Well, maybe not the only conclusion. Let's say you think the $1,000 difference is significant and in fact the fertility and happiness effects happen at different times. What is the typical growth rate of an economy at the $16,000/head level? Lithuania and Libya are the closest to this level (in PPP terms), and their growth (pre-recession) was about 8% in both cases. On this measure, how long does it take to grow per-capita GDP from $16,000 to $17,000? Nine months. So now our explanation is different. People start using contraceptives (or stop having sex) when their income reaches $16,000. Nine months later, children stop being born - and people stop getting happier. On this theory, people stop getting happier when they stop giving birth.

So it could be children that make people happy, or it could be bareback sex. We don't know, but surely it's one or the other?

Maybe not. Let's look at the statistics a third way.

Maybe people are having less unprotected sex and fewer children all the way up the income graph. So impoverished people in Burundi have lots of sex, many children - and are really miserable. The richer they get, the less sex and the fewer children they have, and the happier they become. Until we reach $16,000 - where the fertility rate levels off at 2.1 children per mother. And then people stop getting happier.

This means that both sex and children make people unhappy. The less they have, the happier they get - until they can't get away with reducing it any further, lest the population die out. At this point, they reluctantly force themselves to have sufficient sex and children to keep the grandparents happy (and provide enough workforce to pay their pension) and this is why the happiness effect levels off.

So David Cameron doesn't need the ONS to do a complicated survey to measure happiness. He can just count the new people born every year - which we already do - invert it, and there's our happiness measure.

It's no coincidence that the word "gay" also means "happy", you know.

* a more nuanced argument is here but let's not let that spoil our story


Niklas said...

Your post has some very tempting (and amusing!) reasoning, but unfortunately you're wrong about happiness not being increased by higher GDP per head after $17,000.

The mistake you (and a lot of other people) have made is graphing absolute GDP per capita against a happiness indicator. If you graph logarithmic GDP per capita against a happiness indicator you find a trend all the way: http://www.economist.com/node/17578888

In other words, people's happiness increases by the same amount when you double their income, regardless of whether they were starting out at a dollar a day or £500 a week. A lot of economic relationships work on a log scale rather than an absolute one. And after all, we always talk of GDP growth as a percentage rather than an absolute amount (so many billion pounds).

Leigh Caldwell said...

Hi Niklas

You are quite right - this was the "more nuanced argument" I referred to in the footnote. Of course this does invalidate all three of my inferences, which is why I didn't want to spoil things by including it.

But as you hint, the quality of statistical reasoning here is not much worse than in many published economics papers and better than in most economics journalism.