Does immigration help to sustain welfare in rich European countries? There is a lot of discussions about immigration and its effect on economies lately in Europe, so I'd like to ask a question. Is it true that immigration helps to sustain welfare in rich European countries? For example, in the case of pensions, since life expectation is increasing and natality rates are decreasing in the richest European countries, the ratio of people receiving a pension to that of active workers (who pay those pensions with their taxes) is increasing. Since immigrants usually have a higher natality rate, they should help counteract this effect.

However, often people counter this argument by saying that immigrants receive much more money from welfare, than they return through taxes, for various reasons:


unemployment is much higher among immigrants than among natives
there are many irregular immigrants who still receive healthcare (if they go to an emergency room), but who don't pay taxes
etc.


Especially (but not only) in Denmark, this constant grievance has reached incredible levels. It seems to me baseless racism, but I'm not an economist, so I'd like to know:  are there studies which prove that the contribution to welfare from immigrants is a net positive? Are there studies that indicate that by blocking immigration, rich European countries would risk not being able to pay pensions in the future?
Here is a chart from the OECD, which shows the net fiscal impact of migrants on their recipient country (i.e. by how much to they contribute or withdraw from the welfare state, albeit excluding in-kind benefits such as healthcare). For most Western countries, Denmark included, migrants are modest net positive contributors ("they pay in more than they take out").

This is because migrants tend to be disproportionately working age, whereas the native population contains many retired or young people. Thus, migrants tend to pay a lot of income tax relative to the average native. Luxembourg and Switzerland stand out because both are small economies that attract many high-wage knowledge workers.

On the vertical axis of this chart is the net contribution to the fiscal budget. So a value of 1% means $(\$\text{tax paid}-\$\text{welfare received})/\$\text{GDP}=0.01$. Note that this is different to (and less than) migrants' overall contribution to GDP because, for example, migrants keep much of their contribution to GDP in the form of after-tax wages.



I took the chart from Oxford's migration observatory, which has more information specific to the case of the UK.