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Studies have long shown that violence in PG-13 movies has been steadily rising, leading some parents to wonder: Is it time to consider adding a PG-15 rating?

The suggestion comes from a study conducted by the Annenberg Public Policy Center at the University of Pennsylvania.

“The findings suggest that parents may want a new rating — that the film industry is taking inappropriate advantage of the PG-13 system,” said Daniel Romer, lead author of the study. “These movies often get a PG-13 rating by omitting the consequences, such as blood and suffering, and by making the use of gun violence seem justified. But parents of teenagers say that even scenes of justified violence are more appropriate for teens who are at least 15.”

The Motion Picture Association of America, which runs the voluntary domestic film ratings system, declined to comment.

Researchers showed 90-second clips to a national sample of 610 parents who had at least one child between ages 6 and 17. The footage was taken from six movies that received PG-13 ratings, including “Skyfall,” the James Bond thriller from 2012, and “Terminator Salvation” from 2009. Romer said his team also used scenes from two R-rated films, “Sicario” (2015) and “Training Day” (2001), editing the clips to remove blood and suffering to “mimic the effect of PG-13 movies.”

Participating parents were asked to report their perceived justification for the violence and their emotional reaction when viewing it. They were also asked the minimum age they would consider to be appropriate for watching the entire film.

The finding: Justified gun violence was judged suitable for 15-year-olds; unjustified but bloodless gun violence was deemed appropriate at age 16.

There was one exception. The smattering of parents who described themselves as frequent moviegoers — seeing at least one movie a month — were more permissive, saying that films with unjustified violence were suitable for 13-year-olds.

“There seems to be a numbing or desensitization effect for parents who see these movies all the time,” Romer said.

The MPAA introduced the PG-13 classification in 1984 after parents complained that “Indiana Jones and the Temple of Doom” and “Gremlins” were too intense for their PG ratings. It is a suggestion, not a restriction. The movie association defines PG-13 as meaning that parents should exercise “strong caution” because some material may be inappropriate for children 12 and younger.

R-rated films are restricted for those younger than 17 unless the child is accompanied by an adult, although enforcement varies.

Researchers and advocacy groups concerned about the potential effect of various on-screen content — guns, foul language, sex, tobacco use — have long attacked the ratings system, which was introduced nearly 50 years ago. The critics point out that countries like Britain, Japan and Australia have ratings that limit certain content to 15-year-old viewers.

The MPAA has vigorously defended its system. Ratings are assigned by a panel of about a dozen parents who watch films in their entirety and base their judgment on what “the majority of American parents” are likely to believe is currently appropriate, according to the association’s website. In other words, as societal standards change, so do the classifications.