In my little town in 1990 a good carpenter could get $15 per hour and there was not an illegal alien to be found. In 2000 this town was flooded with illegal aliens, mostly working construction, and a good carpenter would be lucky to get a job at $10 per hour.
That’s a pretty significant drop in wages if you ask me.
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.