Kill/sterilize all the criminals for a few centuries and see how much the crime rate falls by, and also look at the effects on other things (rates of drug addiction, gambling addiction, IQ, etc.)

Studies suggest that criminality is roughly 50% heritable and has a high rate of comorbidity with impulse control disorders and negatively correlates with IQ, so we would predict a significant negative trend in crime, lesser negative trends in other impulse control disorders, and a positive trend in IQ. However, it wouldn't surprise me if there were some weird side effects.