Housing prices are barely correlated with incomes in a meaningful way across cities, let alone caused by them. See [1]. The #1 determinant of housing prices is supply, which is usually an issue of regulation, not of local ability to pay rent/mortgage. There's not much consensus on this topic among economists since there are so many confounding factors - the best paper I've seen so far is [2] which finds that income increases via minimum wage hikes might increase rents anywhere from a quarter to a half of the wage increase, absent other factors.

[1] https://www.cnbc.com/2019/03/07/heres-the-share-of-income-th...

[2] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3282661

https://news.ycombinator.com/item?id=23857621 gets at what I was thinking but was too lazy to articulate.