The reason why it matters is not that they are “immigrants”, it is that there is usually a reasonably high level of cash outflow from the ocuntry in remittances to support family in another country.
search.worldbank.org/data?qterm= … anguage=EN
siteresources.worldbank.org/INTP … reland.pdf
That ammounted to US$2.7billion that flowed out of Ireland (US$1.2billion is non-compensation) at the peak in 2008, offset by US$600million (US$0.01billion in non compensation) that was received. These are the official numbers, very difficult to count and likely underestimated. Compensation remittances need to be removed as they reflect professionals on assignment overseas, may include directors renumeration for some private companies, etc.)
The impact is less money in the country to be spent in the local economy and the impact is large. Allot of studies exist of the impact of remittances on the receiving country, like Mexico where more than US$20billion per year is received or the 2nd largest source of income after oil. Interestingly, the average remittance is around US$250.00 per month and most of the money received is spent very locally on basics so the influence on local economy is massive.
On the oppsite side, there is precious little study but US$1.2billion outflow is not a small matter in a country like Ireland. If, in addition, some of these funds are coming from welfare payments, child support, etc. and there is additional cost to house and maintain health in the host country the numbers can add up pretty quick.
I am an emmigrant/immigrant myself and support open immigration policy, however, the welfare supports in Europe add a hefty cost to the host related to remittances and supporting unemployed immigrants and it certainly should be considered in any economic and policy analysis.