NewScientist (9 April 2016, paywall) goes after the subject of migrant economic impact for the UK, as reported by Debora MacKenzie:
[Migrants] who do end up in wealthier countries are not the burden people sometimes assume. The Organisation for Economic Co-operation and Development, which represents 34 of the world’s wealthiest nations, calculates that its immigrants on average pay as much in taxes as they take in benefits. Recent research shows that EU workers in the UK take less from the benefits system than native Brits do, mostly because they are younger on average. Moreover, they bring in education paid for by their native countries, and many return to their homeland before they need social security. Based on recent numbers, Britain should conservatively expect 140,000 net immigrants a year for the next 50 years. The Office for Budget Responsibility, the UK’s fiscal watchdog, calculates that if that number doubled, it would cut UK government debt by almost a third – while stopping immigration would up the debt by almost 50 per cent.
Illegal migrants make a surprising extra contribution, says Goldin. While many work “informally” without declaring income for taxes, those in formal work often have taxes automatically deducted from their pay cheques, but rarely claim benefits for fear of discovery. Social security paid by employers on behalf of such migrants, but never claimed by them, netted the US $20 billion between 1990 and 1998, says Goldin. That, plus social security contributions by young legal migrants who will not need benefits for decades, is now keeping US social security afloat, he says.
While the UK and the United States are not directly comparable, this work is based on broader work on 1st world countries accepting immigrants, and their impact, which basically boils down to an initial extra strain as the newbies settle in, and then they begin working, often with great enthusiasm.