Ugh...sorry, here's a link to the study itself (I think, it's the same guy same year, but he studies a lot of this stuff). I'm having trouble copying and pasting the pdf, but you can read it yourself or just read the abstract.
SAGE Journals: Your gateway to world-class research journals
"
They find generally modest effects of wealth on these patterns of inter-neighborhood migration."
And...
"
The authors conclude that explanations for the racially stratified inter-neighborhood migration streams that underlie and reinforce black-Anglo residential segregation will need to look beyond the influence of wealth and other socioeconomic resources.
So income isn't the issue you think it is. I'm about 99% sure that's the same study.
There's other articles about why blacks don't move into white neighborhoods....but honestly, they contain such a large amount of racist stereotypes about whites that I don't really want to post them and give those racist ideas a platform.
The gist though is that being around whites is such a horribly negative experience for young black children that black parents don't want to put their kids through it...even if it means staying somewhere with worse schools or higher crime. You could imagine the outrage that the opposite of that article would cause....if whites were to stereotype entire black neighborhoods that way....their concerns would be immediately dismissed as racist.
That's part of the reason why this nation can't have a real conversation about race imo.