> If they do, it's just like a non-migrant worker.
It isn't quite. Imagine dollars leave the US, get sent to Nigeria, and eventually return to the US to buy some music.
Compare that to the case where the dollars do not get sent to Nigeria, but remain in the US.
In the latter case, the Nigerian person wanting their music needs to find another source for the dollars to buy their music. That in turn makes the dollar more valuable, and reduces Nigerias buying power for US products and services.
Imagine dollars leave the US, get sent to Nigeria, and eventually return to the US to buy some music.
I'm definitely on board with the idea that if those dollars never return to the US, then the US effectively got free labour (which is why a trade deficit, I often suggest, isn't automatically a bad thing - it's free stuff, at least until the dollars all come back!), which is quite a win for the US, and given that of all dollars sent overseas, some will never come back, the US has a steady supply of free labour purely because migrant workers are sending dollars overseas (which sure feels like a win for the US).
So the only "downside" for the US is if those dollars sent overseas do eventually make their way back and buy something; at that point the US is handing over goods and services in exchange for that original work done by the migrant worker. Not so much a downside as a delayed fair exchange.
Let me just think out loud for a moment; sending the US dollars to our Nigerian chum, and him returning them to the US in exchange for something, is the same (barring people skiming off the top and postage etc.) as our migrant worker just buying something and posting that to the Nigerian chum. So I think I agree with what you say, but I hypothesise it's not making the US any worse off than the money not making that round trip and just being spent on goods/services in the US by the migrant worker (barring postage etc).
NOT sending the US dollars to our Nigerian chum, and him needing to source US dollars from somewhere else, does make the US dollar a tiny bit more valuable as there is a tiny increased demand for it. Whether that's a good or bad thing for the US, I couldn't say, but if the US dollar becomes too expensive, US exports go down. At this point I guess we're heading into second-order effects of what happens when US exports become too expensive, and I wouldn't like to run into that right now.
It isn't quite. Imagine dollars leave the US, get sent to Nigeria, and eventually return to the US to buy some music.
Compare that to the case where the dollars do not get sent to Nigeria, but remain in the US.
In the latter case, the Nigerian person wanting their music needs to find another source for the dollars to buy their music. That in turn makes the dollar more valuable, and reduces Nigerias buying power for US products and services.