As a result, the number of people under 21 with a credit card has dropped by 18 percent, the report found. That might appear to be a good thing, but this study suggests it may not be, as early access to a credit card is related to lower risk of negative financial consequences, a strong credit history and home ownership at an earlier age.
(Read more: Paying cash costs Americans $200 billion a year)
"We found that credit cards can be dangerous for anybody," Ghent said. "Lots of people get into trouble with their credit cards, but there's never been a law proposed to ban everyone from having a credit card."
The authors point out that their findings differ from the widely held view that young people who apply for a credit card do so in response to aggressive marketing. They believe the kids who get cards are often more financially literate and want to start building a credit history. Their parents may even encourage them.
"I don't want every 19-year-old to go get a card, because a lot of young people do get into trouble with them," Ghent said. "But parents don't need to be overly worried about it—depending on their kid, of course."
What's a parent to do?
It's important to teach your kids how to use credit wisely. Personal finance experts say the best time to do this is while they are still living at home.
John Ulzheimer, consumer credit expert at CreditSesame.com, advises parents to make a child "an authorized user" on one of their credit card accounts when he or she is between 15 and 17. He calls it "a credit card with training wheels."
Your child gets a different card number, but it's linked to your account. You are still in control because their charges show up on your monthly statement.
(Read more: Employers can't force debit cards on their workers)
"This way, your child can understand how to use the card and what happens when they do, as well as learn the drawbacks if they misuse it," Ulzheimer said. "As an authorized user, they're building a credit history at a young age."
In this arrangement, primary account holders (parents) see all charges from the authorized user listed on the their monthly statement. If the child abuses the privilege, the card can be canceled at any time.
Remember, debit cards (whether prepaid or the traditional type linked to a checking account) are not credit products, so they do not help your child build credit.
Gerri Detweiler, director of consumer education at Credit.com, agrees that it makes sense for young people to establish credit before they graduate from college, so long as they manage it well.
"The problem is that even one 'minor delinquency,' such as a single late payment, can stay on your credit reports for seven years," she said. "When you also have a slim, newly established credit history and then you pay late, the impact to your credit scores can be significant. For that reason, someone in this age group should try to stay squeaky clean and make sure everything is paid on time."
—By CNBC contributor Herb Weisbaum. Follow him on Facebook and Twitter @TheConsumerman or visit The ConsumerMan website.