No, at least not in the short run. Rambo gets the bad guys off the streets. And for a while they even seem to calm down:
What is the short-run impact of media violence on crime? Laboratory experiments in psychology find that exposure to media violence increases aggression. In this paper, we provide field evidence on this question. We exploit variation in violence of blockbuster movies between 1995 and 2002, and study the effect on same-day assaults. We find that violent crime decreases on days with higher theater audiences for violent movies. The effect is mostly driven by incapacitation: between 6PM and 12AM, an increase of one million in the audience for violent movies reduces violent crime by 1.5 to 2 percent. After the exposure to the movie, between 12AM and 6AM, crime is still reduced but the effect is smaller and less robust. We obtain similar, but noisier, results using data on DVD and VHS rentals. Overall, we find no evidence of a temporary surge in violent crime due to exposure to movie violence. Rather, our estimates suggest that in the short-run violent movies deter over 200 assaults daily. We discuss the endogeneity of releases. Potential interpretations for our results include a cathartic effect of movies, displacement of crime, and decrease in alcohol consumption. The differences with the experimental results may be due to experimental procedures, or to sorting into violent movies. Our design does not allow us to estimate long-run effects.
Here is the full paper.