A recent study published in the Journal of Communication by a researcher at Stetson University found that there were no associations between media violence consumption in society and societal violence.
Source: www.eurekalert.org
One study looks at violence in movies and societal violence between 1920 and 2005, another looks at violence in video games and societal violence between 1996 and 2011. Neither violence in movies nor video games found to be correlate (nor in a causal-relationship) with violence in society.