I couldn't find a paper with a quick google, but i did hear in a recent podcast that it is exactly income inequality (as measured by the Gini coefficient) rather than absolute poverty that is the biggest predictor in criminality.
Here is a clip that mentions it; if I can find a paper to reference i'll edit this comment when I get home:
I don't have a good answer for that observation, I was just repeating what I had recently heard. It's not clear how localized the measured effect is, ie. how proximate the inequality must be. It's possible that since the top 1% is getting so much more disproportionately wealthy, it might in fact be making the rest of America more equal to each other. Maybe (wild guess on my part) there is less average difference between the poor in a neighborhood, and the middle class in the same area. The wealth inequality is hidden in statistics and is not so much in our faces.
Here is a clip that mentions it; if I can find a paper to reference i'll edit this comment when I get home:
https://podverse.fm/clips/BJE2hv7gZ
Edit: The connection was made specifically with violent crimes. Here is an article about it that has links to some research papers:
https://www.theatlantic.com/business/archive/2014/10/does-in...