I looked at the 2010 – 2014 population trends in the counties of these old industrial cities: Cleveland, Detroit, Milwaukee, Pittsburgh and Toledo. Each experienced net out-migration of native-born Americans, partially (and for Milwaukee completely) compensated by natural growth (births less deaths). All combined, they lost the equivalent of about 2% of the combined 2015 population over these four years these ways.
Foreign-born in-migration (combined, five cities) in 2010 – 2014 was equivalent to 1% of 2015 population. Thus foreign in-migration made up about half the loss from native-born exits and births/deaths, and about one third of the loss by exiting native-born exits.
What’s not shown in these summary figures is the likelihood that the exiting native-born persons were tilted towards working age (15 – 64) and that the immigrants moving in were more likely of prime working age and more engaged in the workforce. Thus, the workforce impact of these migrations was probably larger.
Summary: continued incremental shifting of the workforce toward immigrants in old industrial cities. An annual average shift from native to foreign-born workers of perhaps… .0.3 – 0.5 percent?