Suppose that by the mid-2000s, immigration from the EU (and the potential for additional immigration) had led to an important shift in the UK labour market. The possibility of bringing labour from overseas meant that old relationships between the tightness of labour market and wage increases no longer held.
You might think that was bad for workers, but that is not so. It would mean what economists call the natural rate of unemployment (or NAIRU) has fallen. Unemployment can be lower without leading to wage increases that threaten the inflation target, because workers fear that the employer can resort to finding much cheaper overseas labour. It reduces the power of workers in the labour market, but also leads to overall benefits. (This is just an example of the standard result that reducing monopoly power is socially beneficial.)
But it is only good news if the Bank of England recognises the change. If they do not, we get stagnant wage growth and unemployment higher than it need be. The obvious response is that the Bank will know there has been a change because wages will start falling faster than they would expect based on previous relationships. However that effect may be masked by the well documented employee and employer reluctance to actually cut nominal wages. Add in the shock of the financial crisis, and this change in the way the labour market works might well be missed.
Here is the big leap. Suppose the above had happened, and the Bank of England did not miss the change. Monetary policy would have been much more expansionary, bringing unemployment well below the 5% mark. Nominal wage growth would have been stronger, and a buoyant labour market would have generated a feel good factor among workers. With more vacancies and less unemployment, concerns about immigration would have begun to fade. The Brexit vote would still have been close, but would have gone the other way.
You may say how could monetary policy be more expansionary given how close we are to the Zero Lower Bound? If that was the case the Bank should have said they were out of ammunition, and placed responsibility with the government and austerity. But for the last two years at least, the Bank could have cut interest rates and has not. You could blame the relentless expectation in the media and financial sector that rates would increase, but the Bank should be able to rise above that.
Of course the Brexit blame game is easy to play when the vote was so tight. The most speculative aspect of this chain of thought is the initial premise about a shift in the NAIRU created by immigration potential. While the possibility makes sense, whether the data backs it up is much less clear. Yet there is some evidence of a structural shift in the UK labour market in the mid-2000s, as Paul Gregg and Steve Machin report.