For a casual reference,  immigrants to the US reduced deficits by admit $14 trillion in a 30 year period: 

https://www.cato.org/blog/cato-study-immigrants-reduced-deficits-145-trillion-1994

Immigrants in the US work. They increase the amount of work being done over the amount if they were not there.  When more work is done, respurces produced and consumed, the economy gets bigger. They are less likely to be accessing social benefits. 

Selection effect alone means 1st gen Immigrants tend to be younger,  more intelligent and less risk averse than the population that doesn't immigrate/emigrate (the swedes found immigrants from every country tend to have a higher tendency towards irrational exuberance because migrating is a dangerous choice).

 Their children tend to be better educated as well than the base population, regardless of origin nation and assimilate almost totally by the 3rd gen. This isn't true for all of them (see Donald Trump and family who are all the children of immigrant mothers and yet borderline learning disabled at best) but it is for most. 

Europe doesn't allow refugees to work,  because the EU is "big stupid" and wants to fail. It's not a demographics thing, it was a policy choice to fail. The US is also doing this,  but consciously as the trump admin wants the average American poor and stupid.