If I definitively knew the answer, I'd be a very wealthy economist. I'm an amateur in the field, so take anything I write on this topic with a grain of salt. My girlfriend works in this field (consultant, Master's degree, all her job experience is on poverty and effects), and most of what I've learned is from her. She's pretty good at explaining to me what falls under "her opinion" and what falls under "textbook-type consensus opinion", and I'm mostly trying to relay the latter.

One of the more popular measures of wealth disparity is the Gini index-- the math is slightly messy, but a zero Gini index would mean that everyone in your country has the same wealth, a 100 Gini index would mean one guy has all the money, and most industrialized nations fall between 20 and 60. In many high-anarchy countries, no one really knows where the wealth is, and the Gini index isn't known.

For some quick comparisons, the U.S. is at 45, Sweden is at 25 (very heavy tax burden forces it), and more laissez-faire capitalist countries (2001 Hong Kong at 52) or countries with corrupt or ineffective central governments (Columbia at 54) can run somewhat higher than the US. In practice, I'd have to say that free-market capitalism increases wealth disparity, or at the very least fails to decrease it. (Socialist systems decrease it very bluntly by direct redistribution of wealth.)

You can look up some raw numbers here:
https://www.cia.gov/library/publications/the-world-factbook/fields/2172.html

Now, when you get to causal links with poverty, the arguments seem to start because people point to things like unemployment, disrupted families, etc. All of those things correlate well with wealth disparity, and it's hard to isolate one variable, but (local) wealth disparity seems to be a popular choice. (Local, as in if you live in a poor farming village many miles away from the thriving metropolis, your opportunity and motivation to profit from crime isn't necessarily high, especially if it's impractical for you to even get there.)

The second problem is the definition of crime rates. One country might have a low crime rate just because they have no effective police force (therefore, nothing gets reported), and another might have a low crime rate because the police force has unlimited power (therefore, people avoid crime out of fear). Overall crime rates also vary by how many things a country considers a crime, so you often have to pick one crime (murder, theft of at least one day's wages at the poverty line, etc.) and hope that's meaningful.

The technical papers on causation of crime try to stress case studies-- for example, one city before and after an economic transition, etc. I'll ask the resident expert when she gets back from yoga if she can point me towards some useful examples.

valguarnera@carrionfields.com