If your output variable is “#cancer in large population”, yes, an increase in tobacco use rate causes it to go up. I don’t think that’s true of crime, though. Not every recession causes a jump in crimes rates.

But I was talking about the output variable “Does person X commit a crime?” For that, most of the time poverty will not cause crime. There must be many other factors involved such as community relationships, opportunity, values, likelihood of going to prison, etc.