As far as Illegal Immgration goes, I would think that if one considered the initial act of entering the country, then getting a job, giving false information to authorities to continue employment, etc., then crime rates would actually increase.
That would not be violent however. But consider that if you are willing to commit several crimes to be here and live here, then how far is it to commit others? How difficult is it to see a crime industry preying on those who illegally immigrate and that crime being violent?
Taken several ways, illegal immigration could be a gateway crime.
I think the study is somewhat misleading on the illegal immigration issue.