During the 2001 recession, 2008 financial crisis there were dire predictions that violent crime would go up. Misc property crime went up a bit and violent crime didn't. Violent crime perpetrated by young urban males continued to decline as well. In the face of high rates of unemployment.
Personally I think cultural normalization of violence and quality of policing plays a role in the level of violence. But socio-economic factors really don't.
Presumably, desperate circumstances will make it manifest as violent/property crime. But there are probably other manifestations that slide under the criminal justice radar too, like domestic violence and general aggression/bullying among communities in less desperate circumstances.