The benefits and perceived costs of immigration

This article discussing migration to Britain, the benefits it brings and British reaction to it, was recently on the front page of the FT. Some key points:

Britain’s willingness to absorb migrants … have brought “undoubted economic benefits”, John Reid, home secretary, said last year. By helping to fill skills shortages and keeping a lid on wage inflation, immigrants have helped produce stronger economic growth.

[However,] 47 per cent of Britons believe migration by workers within the EU has been negative for the economy and only 19 per cent think it has been good. Asked whether there should be stricter controls to prevent workers from central and eastern Europe entering the country, 76 per cent of Britons agreed.

A friend of mine questioned whether these two sentences from the article were contradictory:

The Bank of England believes that the large influx of migrant workers has contributed to lower inflation by helping to contain wage growth. David Blanchflower, a member of the Bank’s monetary policy committee, said last month there was little evidence that immigrants from eastern Europe had depressed the wages or employment chances of British workers.

They’re not – they’re saying that migrants have caused wage growth to fall (first sentence) but it has remained positive (second sentence), meaning that wages themselves are not falling – but it does raise a key point in understanding why people feel economically cheated in an environment of high immigration.

Suppose that Price Inflation tomorrow is equal to Wage Growth today minus a bit related to “real” growth in the economy (which is plausible), but when considering their Wage Growth today, workers compare it to Price Inflation today. Then we might have (all figures are percentages):

Inflation today: 2

Without immigrants
Wage Growth today: 3
Perceived benefit: 3-2 = 1
Inflation tomorrow: (3-n)
Actual benefit: 3 – (3-n) = n

With immigrants
Wage Growth today: 1
Perceived benefit: 1-2 = -1 (!)
Inflation tomorrow: (1-n*)
Actual benefit: 1 – (1-n*) = n*

If you also suppose, as the BoE clearly believes, that the ‘n’ actually increases with immigration (n* > n), then people are unambiguously better off with immigrants coming in, but believe that they are worse off.