Tara Watson has a paper that sounds interesting, based on the abstract.
American metropolitan areas have experienced rising residential segregation by income since 1970. One potential explanation for this change is growing income inequality. However, measures of residential sorting are typically mechanically related to the income distribution, making it difficult to identify the impact of inequality on residential choice. This paper presents a measure of residential segregation by income, the Centile Gap Index (CGI) which is based on income percentiles. Using the CGI, I find that a one standard deviation increase in income inequality raises residential segregation by income by 0.4-0.9 standard deviations. Inequality at the top of the distribution is associated with more segregation of the rich, while inequality at the bottom and declines in labor demand for less-skilled men are associated with residential isolation of the poor. Inequality can fully explain the rise in income segregation between 1970 and 2000.
I have a succinct description of inequality in Montgomery County, Maryland, where I live. I point out that there is a 300 point gradient in SAT scores (using the old two-test metric) between our local high school and the best-scoring high schools in Potomac. That is, we are at about 900 and the better-scoring schools are at about 1200.
Whenever I give this description, everyone immediately understands that this is a measure if differential affluence. You could believe that the causal factor is differences in school quality, with rich parents choosing the better schools. Alternatively, you could view this as a segregation equilibrium, in which rich people pay a premium to live near other rich people, rich people tend to have better cognitive abilities, and they pass on their abilities to their kids. I suspect that it is primarily the latter.