So argues a new paper (pdf) by Ekrame Boubtane, Dramane Coulibaly, and Christophe Rault, the abstract is here:
This paper examines the causality relationship between immigration, unemployment and economic growth of the host country. We employ the panel Granger causality testing approach of Konya (2006) that is based on SUR systems and Wald tests with country specific bootstrap critical values. This approach allows to test for Granger-causality on each individual panel member separately by taking into account the contemporaneous correlation across countries. Using annual data over the 1980-2005 period for 22 OECD countries, we find that, only in Portugal, unemployment negatively causes immigration, while in any country, immigration does not cause unemployment. On the other hand, our results show that, in four countries (France, Iceland, Norway and the United Kingdom), growth positively causes immigration, whereas in any country, immigration does not cause growth.
This result reflects two broader lessons. First, at the margin the major benefits from migration are to the migrants. Second, again at the margin, most policy changes matter less than you think they will.
Hat tip goes to Ben Southwood.