For one thing I don’t see how you can define areas where everyone is poor. Even looking at a place like North Korea, the top government officials are very well off compared to the average person.
In general, poorer countries are much less safe than richer ones. Poorer neighborhoods are much less safe than richer ones. I can see the point that even in those cases it’s often related to inequality, e.g. theres gang related violence because gang leaders are much richer than the average person in the area. But that’s a tautology, because there’s nowhere that has absolutely no inequality.
If you look at the graph on page 8, you can see obvious clustering of poor countries vs other countries. This study does not compare the overall wealth of the countries against crime.
The reason that is important, is that in a rich country, even poor people have many options. In a poor country like Venezuela, they don't. As a result, even if they had the same Gini coefficient, the crime would look much different.
So when you take that into account (which is what I tried to do in my statement, but probably could have worded better), then being in a "rich but unequal" society is much better than a poor country of either high or low inequality. I think the high clustering of OECD countries demonstrates this.
That's not true. Violence is caused by inequality. Areas where everyone's equally poor are about as peaceful as areas where everyone's equally rich. It's dramatic inequality that causes violence. This is true no matter whether you look at neighborhood level, city level, national level etc.