By "move-to", not sure if you mean Chicago overall, or the north side in particular, but if the former Chicago is growing slower than the national average. 2% last decade (vs 8% nationally) https://chicago.suntimes.com/2021/8/12/22622062/chicago-cens...
I had the impression Chicago was actually losing people, but that info was old, from the previous decade where it lost 7%.