"The Avengers," with Scarlett Johansson, left, and Jeremy Renner, was rated PG-13 because of sci-fi action and violence. Marvel/Walt Disney Co./Everett Collection

Today's PG-13 movies are more violent than R-rated ones, according to a new study, "Gun Violence Trends in Movies," (PDF) published Monday by the American Academy of Pediatrics.

The study, funded by the Annenberg Public Policy Center and the Robert Wood Johnson Foundation, looked at a sample of the top 30 films each year since 1950. It found that violence in films has doubled since 1950 and that gun violence in PG-13 movies has more than tripled since 1985, when the PG-13 rating took effect. Gun violence remained the same in R-rated movies and decreased in G and PG movies.

PG-13 movies took in $5.7 billion at the box office in 2012, according to Box Office Mojo — more than 50 percent of total box office revenue while accounting for only 18 percent of titles.

"The PG-13 rating is not really being used appropriately to tell people these films actually do show things that might be harmful," said Daniel Romer, one of the study's authors.

As for the harm done, Romer cites the weapons effect: that merely seeing guns increases the likelihood of aggressive responses, as some studies have concluded. The increasing presence of guns in popular movies, he said, can raise the weapons effect on both individuals and society.

"They're not being used in ways people who defend guns typically talk about — hunting, sport or target practice," he said. "They're used primarily to maim and kill people. So we think they create scripts that young people learn that's what a gun is for."

But some scholars argue that the weapons effect doesn't give a complete picture of the effects of gun violence in movies on society.

More than 200 academics signed an open letter sent to the American Psychiatric Association in September, saying that responsible scholars should "make good-faith arguments both that media violence may have some influence on aggression and other outcomes or that media violence may not have such effects." The letter said there is pressure to produce only "positive" findings that link media and societal violence.

Nevertheless, Romer said that the potential for such harm has increased dramatically as movies that would have earned an R rating in the past for depictions of violence now pass as PG-13 — meaning they can be seen by a larger, younger audience. He believes the trend is related to the increasing popularity of fantasy action movies like "The Avengers," "The Amazing Spider-Man" and "The Dark Knight Rises."

"They're human (actors), but they're based on comic-book stories, and the rating board seems to give them more leeway," he said.

According to Romer, there's another reason for the rise in PG-13 gun violence: It sells — even better than sex. "The Avengers," with its $1.5 billion haul in 2012, was last year's top-grossing film. Common Sense Media, an independent nonprofit that reviews and rates media for parents and their kids, deemed "The Avengers" inappropriate for children younger than 13 because of its massive explosions and numerous casualties. The parents and kids who posted reviews on the site believe the movie is suitable for ages 10 and up.

But Chris Ferguson, who studies media violence and is the chairman of the psychology department at Stetson University in Florida, doesn't buy Romer's arguments.

"The real question for me is, 'So what?'" Ferguson said.

He said the report offers no data that connects an increase in movie violence to an increase in real-world violence. Furthermore, while violence in movies has been growing, youth and gun violence in the United States has been declining. He believes the study distracts people from more probable causes of gun violence like poverty, educational disparities and mental health.

According to Ferguson, increasing movie violence reflects how community standards change over time — which isn't necessarily a bad thing. While movies of the 1950s were very tame, those of the 1920s were much more violent.

"We're certainly on a liberalizing trend," said Ferguson. "But I'm not sure people really want to go back to the 1950s with Lucy and Desi sleeping in separate beds."