As long as I'm on the subject of immigration, a complex matter, I always find Ludwig von Mises always quotable, providing clarity in such complex matters (I've previously cited him on labor more generally). As he notes in the essay "The Freedom to Move as an International Problem" (1935):
If the European workers are prevented from emigrating and thus have to stay at home, this does not mean they will remain idle as a result. They will continue to work in their old homeland under less favorable conditions. And because of the less advantageous conditions of production there, they will be compensated in lower wages. They will then compete on the world market, as well as on the home market of the industry producing under more favorable conditions. These countries may then very likely strike out with tariffs and import embargoes against what they call the "unfair" competition of cheap labor. By doing this, they will be forfeiting the advantages which the higher division of labor brings. They will suffer because production opportunities which are more favorable, i.e. which bring a higher return with the same expenditure than do the production opportunities which must be used in other lands, are not being used in their own countries.Of course, Europe is much better off today than at the time Mises wrote these words, but his insight applies to any two countries facing different economic conditions. Finally, I couldn't help but think of the current wave of anti-Americanism sweeping through parts of the world, especially immigrant-rich Latin America, reading the following passage:
[I]f the freedom of migration is not reestablished, the lower wages in those lands will attract capital and entrepreneurial effort. Then, in place of the hot-house industries, artificially fostered by governmental measures and unviable still in spite of these measures, industries with lower wages and lower living standards for the masses will develop there, industries which will be viable in view of the location. These people will certainly still have just as much cause to complain as before—not over the unequal distribution of raw materials, but over the erection of migration barriers around the lands with more favorable conditions of production. And it may be that one day they will reach the conclusion that only weapons can change this unsatisfactory situation. Thus, we may face a great coalition of the lands of would-be emigrants standing in opposition to the lands that erect barricades to shut out would-be immigrants.