In all, 26 percent of the children said they had been bullied and 9.5 percent said they had bullied others or were both bullies and victims, the researchers found.
Years later, when those in the study were young adults, the researchers interviewed more than 1,200 of them to ask about their psychological health.
They found that both those who had been bullied as kids and those who had been both bullies and bullied had a higher risk for psychological problems than those who weren't bullied.
Those problems included depressive disorders, anxiety disorders, generalized anxiety, panic disorder and agoraphobia, which is anxiety about feeling trapped in a place.
Those who were both bullies and victims of bullying had, in addition to being at risk for anxiety and depression, the highest levels of suicidal thoughts.
Bullies were also at risk for antisocial personality disorder, which the U.S. National Library of Medicine defines as an ongoing pattern of "manipulating, exploiting or violating the rights of others."
To be sure their findings were confined to bullying, the researchers accounted for other factors such as poverty, abuse and an unstable or dysfunctional home life, which might have contributed to psychological problems.
One expert said that in many cases bullies and their victims have preexisting mental health problems that continue into adulthood.
"That shouldn't shock us, because most mental health problems have their beginning in adolescence or childhood," said Dr. Victor Fornari, director of the division of child/adolescent psychiatry at North Shore-LIJ Health System in New Hyde Park, N.Y.
"That's all the more reason why early intervention is important, to try to change the course of the difficulties," he said.
Ignoring the problem is not the way to go, Fornari said, and parents need to take these problems seriously.
"Parents who become aware that their child is either a bully or
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