Yesterday the ONS published a report showing average disposable incomes at their lowest level since 2003. This is difficult news for ministers: as Isabel pointed out, concerns about the cost of living – stagnant wages and rising prices – are one of the main reasons given by voters in recent polls for turning away from the Conservatives.

Imagine, then, how pleased ministers must have been when they saw that the ONS had thrown them a lifeline: the chance to blame it all on immigration. The ONS report discusses the effects of wages and prices, and then adds that ‘finally, sustained population growth led to incomes being spread across a greater number of people, and therefore further reduced the growth of actual income per head over the period’. Quick as a flash, the Immigration Minister Damian Green put out a statement saying that ONS have today confirmed that the population growth caused by Labour’s uncontrolled immigration has reduced incomes’.

Let us leave on one side Green’s substitution of ‘reduced the growth of incomes’ with ‘reduced incomes’, and his conflation of population growth with immigration (on which see here). The bigger problem is with the ONS’ claim that ‘population growth… reduced the growth of income per head’. There appears to be no evidence for this claim in the report, nor can I think of any evidence in anything the ONS has published previously. In the absence of any evidence, we can only conclude that the ONS has committed the elementary statistical fallacy of conflating ‘X rose and Y fell’ with ‘X caused Y to fall’.

What the data actually tells us, is that if we compare 2012 with 2003, the population is higher, and income per head is lower. This is consistent with population growth having reduced income per head; but it is also consistent with the opposite, that population growth increased income per head – but was outweighed by other factors.

Perhaps our statistician friends were confused by the rather different idea that, in a hypothetical scenario, if we assume a fixed level of national income, then increasing the population will reduce income per head. This is a claim which does not require any evidence: it is a matter of definition. But it is not the same thing, at all, as the empirical claim that the real world phenomenon of population growth – an actual phenomenon involving real factors like immigration, increased fertility, and increased longevity – has caused the real world phenomenon of falling real incomes. That is a claim which very definitely does require evidence.

Some readers will find this so obvious as to be hardly worth saying. But it seems that participants in the immigration debate do need continually reminding that to show that ‘X caused Y’ – that immigration caused youth unemployment, for example – you must first show that the two variables are genuinely rather than accidentally correlated (which involves testing the relationship, controlling for other variables, etc) and second, provide a plausible causal relationship to explain the correlation.

Consider one of the other elements of population growth in the last decade, namely, longevity. Studies have found a genuine correlation between longevity and income per head, over many decades and many countries: not the negative correlation you might expect if you spent too much time listening to the modern-day Malthusians (whose reaction to the Census seemed to imply that people living longer was an intolerable burden on society), but a positive one. Of course, only a fool would conclude from this that ‘rising longevity increased income per head’: it is far more plausible that the causation – if there is any – is the other way around.

In the case of immigration and income per head, various studies have attempted to establish a genuine correlation. For what it is worth, the most recent major international study suggests that there is a correlation: again, it is positive rather than negative. Various hypotheses have been put forward about a possible causal relationship. The opponents of immigration may find this study, and these hypotheses, unconvincing: they are entitled to that position. But they must accept that it is not enough simply to say that immigration rose and incomes fell over the same period, and therefore immigration reduced incomes. This is the kind of shoddy methodology I’d expect from pressure groups like MigrationWatch, but I would expect rather more of the Office for National Statistics – and indeed of a Minister of the Crown.

UPDATE, 16.00, 2 August: The ONS has published a correction to the stats here. I’ve raised it as an issue with Damian Green, asking him to withdraw the claim.

Matt Cavanagh is a visiting fellow at IPPR.

Tags: Immigration, UK politics