In the face of a potential Brexit, the UK debates whether the economic impacts in terms of wages, employment and public services due to migration are beneficial or detrimental to the country. Those pushing for Brexit argue that it is European labour migration organized by Brussels that causes British workers to lose jobs, earn lower wages and lead to higher payments for the welfare state. This view is at odds with the European project suggesting that free markets including free labour mobility will lead to a more efficient allocation of resources in the long term and hence to greater welfare.
Is this all a mistake? The empirical evidence globally, but also for the UK, shows that in spite of all fears, labour migration does not come with relevant harmful effects for jobs and earnings. If anything, it does come with more equality. The effects on the public coffers depend on selection, but European labour migration typically leads to net benefits. Skilled people are better protected against adjustments, but this is independent of migration. Yes, leaving the EU would lead to a loss of labour migrants but cause economic harm including a raise in taxes to balance the British budget.
Recent European migration provides insights: EU enlargement has not caused Europe a problem, to the contrary it was beneficial. See:
Kahanec, Martin, and Zimmermann, Klaus F. (Eds.), Labor Migration, EU Enlargement, and the Great Recession, Springer 2016.
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Klaus F. Zimmermann talking about European migration, the EU enlargement book and Brexit in Wroclaw, Poland on June 20, 2016.