shove, GDP and average wages have long been established as an unsatisfactory measure for calculating the effect of migration on the resident population:
www.gov.uk/government/uploads/system/uploads/attachment_data/file/257235/analysis-of-the-impacts.pdf
If you read that report I makes clear that it is an unsatisfactory measure because:
It is the immigrants themselves, rather than the extant residents, who are the main gainers.
It's also pretty well accepted that migration increases in average wages come from a positive effect on wages of the highest earners (who can pay themselves more when they pay their staff less), and that the effect on the wages of the very poorest is negative.
The effect on the poorest have been long term, and not corrected with economic up turns. Looking at figures in terms of average wages ignores other factors too, like deteriorating working conditions and terms.
It also ignores surrounding factors too. Saying 'Oh well there was a 0.1% increase in wages not only ignores the fact that those rises didn't go to the originally resident population, but also that knock on effects on things like the cost of housing effect the resident population making them poorer.
That leaves aside the fact that impact on wages in real terms are calculated in an appalling way for the least well off by assuming that they benefit from falls in things like the price of package holidays, brand new TVs and cars benefit the very poorest when they're largely irrelevant as they can't purchase them.
Anyway, it's all just more of the same. Remainers can wave studies until they're blue in the face. It makes absolutely no difference to people who work in industries such as construction (like my DH) who know that every time a new state ascends their pay packet will be lighter and they'll be working longer hours for less money. And who know that they kissed goodbye to the idea of anything like a permanent job, job security, sick pay, parental leave or staff training or development years ago when people starting queuing up to do their jobs for fuck all pay in rotten conditions.
They simply won't believe you.