The macro theory says that, in effect, though carpenters wages are down, the natives who would have been carpenters are better off now that they have a new career in real estate or supervision of these immigrant carpenters (for instance).
This wasn’t a bad theory 1980-2000, overall, as both labor force participation and median incomes were rising most of the time.
Or, perhaps,the truth was hiding in the collinear data.
It’s much harder to make this argument for 2007-2015.
The macro theory is a bunch of crap. I don’t know one carpenter who has a new career.
That just doesn't happen in reality. For one, the skill set and temperament to be a foreman (supervisor of carpenters) is different that that of a carpenter. Some start out as carpenters and rise through gaining experience and skills on the job, but many do not, and actually can not.
The situation for real estate agents is similar. Vastly different skill set. Now there are carpenters who work for real estate professionals -- the ones who flip houses. But the real criterion here is solid work at a low cost.
I almost all cases, a low-wage migrant will drive down the wages of a native worker who competes in the same area. The truth on there ground is that there are many low-skill, low education native-born workers in this country. The illegals coming in are going to displace them for two reasons: (1) lower wages and (2) higher skills and work ethics. I know, I have been there and done that in construction. For many years I remodeled real estate as a sideline. I tried hard to use American labor -- college kids, etc. None of them understood what made a good worker. They all wanted to quit well before the end of the day, and they all just dropped their tools (actually the tools I supplied them with) and walked off when it was quitting time.
Then I hired some day labor from the Home Depot parking lot. They worked steadily until about 15 minutes before quitting time and then cleaned up the site and brought the tools they had been using back to the shed. They made sure they were in good order, locked up and secured before leaving. They knew there would be no work the next day if there were no tools to work with.
The language barrier was a problem, but one that was much lower than then the work ethics problem of the American kids.