Immigration and wages: getting the numbers right

Is immigration from the EU pushing down the wages of British workers, especially the low paid? This has become a central theme for the Leave campaign. The Sun reported:

Open-door immigration knocks 10% of UK wages, claims Iain Duncan Smith...He quoted a Bank of England report that found wages fall by 2% for every 10% increase in immigration.  Calling for voters to back Leave on June 23, Mr Duncan Smith said: “We have seen a 50% rise in immigration, which means around a 10% fall in wages.”

Boris Johnson and Gisela Stuart, not coincidentally, repeated this claim in their ITV debate

There is a 10% growth in #immigration and a 2% reduction in wages and that bears thinking about"

The problem is that Mr Duncan Smith’s arithmetic is simply wrong, by a factor of at perhaps 25. It’s true that net migration has risen by about 50% over the last two years. But that’s not the right number to look at. The Bank of England paper he quotes is talking not about the immigration rate, but the number of immigrants as a proportion of the workforce – percentage points, not %. [Unsure about the difference? See note at end].

And how much has that risen over the same period? Not by 50 percentage points.  Or even 10 percentage points. But by about 2 percentage points. The implied impact on wages, then, wouldn’t be a fall of 10%, but rather of about 0.4%. Actually, it would be considerably lower than this, since the numbers from the Bank report refer only to wages in one sector (semi/low skilled service workers),  not for all workers. 

In fact, when the paper came out, I looked at it in some detail and did a very similar calculation to the one Iain Duncan Smith did, only using the correct data.  The bottom line:

We can calculate that the new paper implies that the impact of migration on the wages of the UK-born [in the semi-skilled service sector] since 2004 has been about 1 percent, over a period of 8 years. With average wages in this sector of about £8 an hour, that amounts to a reduction in annual pay rises of about a penny an hour.

Let me emphasise that Mr Duncan Smith and Vote Leave have made an honest mistake here – the paper could have been more clearly drafted on this point. But they should now have the honesty to admit this error, and to accept what I said then:

The idea that immigration is the main or even a moderately important driver of low pay is simply not supported by the available evidence. Politicians who claim the contrary are either so obsessed with immigration that they are blind to more important issues - or they are merely trying to divert attention from their failure to propose policy measures that would actually make a meaningful difference to the low paid. 

*Note: percentages and percentage points.  Suppose there are 100 workers in a particular sector. Over time, the number of migrants increases from 10 to 15, that is from 10% to 15%. This represents an increase of 50% - but only of 5 percentage points. And it is this latter statistics that the Bank of England paper is referring to "a 10 percentage point rise in the proportion of immigrants working in semi/unskilled services -  that is, in care homes, bars, shops, restaurants, cleaning, for example - leads to a 1.88 percent reduction in pay."  Hence, in calculating the implied impact on wages, Iain Duncan Smith's reference to a "50% increase in immigration" is irrelevant; the number to look at is the far smaller increase in the migrant share of the labour force.  

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