Anatoly Karlin, who is making himself the go-to guy on analyzing the investment implications of international school test scores (a potentially lucrative niche), has a long, fascinating write-up of PISA scores adjusted by immigration status:
One thing that immediately leaps out from above is that just as US scores leap upwards (from 496 to about 525, in line with Australia and Canada) once only whites are considered, so do scores in many European states when only natives are considered (e.g. Germany from 510 to 533; Switzerland from 517 to 542; the Netherlands from 519 to 533). In fact, the Germanic nations equalize with Japan’s 529, Taiwan’s 534, and South Korea’s 541 (the natives of these developed East Asian societies also score a lot higher than their immigrants, but the overall effect on the national average is modest because migrant children are such a small percentage of their school-age populations). In other words, in the worst affected European countries, immigrants are lowering the mean national IQ (converted from PISA scores) by as much as 3 points.
This might not seem like much, but it is highly significant when bearing in mind the extremely close correlation between national IQ and prosperity. Furthermore, since immigrant population tend to be highly variant – for instance, Britain has a lot of Poles, who are essentially equal to the natives in cognitive capacity (maybe even superior, once you adjust for the fact that it is better-educated Poles who tend to emigrate), and a lot of Pakistanis, who are far below them. This is a good explanation for the general sense of dereliction one sees (and the crime one is likely to experience) when entering Pakistani ghettos in the UK.
Also note from the graph that there is typically a very high degree of overlap between 1st and 2nd generation immigrant children. The 2nd generation children DO typically perform better, presumably because 1st generation immigrants may frequently have language difficulties and problems with adjusting to a new culture. But the degree of convergence of 2nd generation children to the native mean is modest, despite their transferal to typically far more advanced educational environments. Convergence is almost inconsequential in most European countries like Germany, France, Benelux, Norway, and actually negative in the US (i.e. American 2nd generation immigrant children do worse than the 1st generation).