“Our findings show that parents are indeed concerned about privacy and online safety issues, but they also show that they may not understand the risks that children face or how their data are used,” that paper concluded.

Facebook has long said that it is difficult to ferret out every deceptive teenager and points to its extra precautions for minors. For children ages 13 to 18, only their Facebook friends can see their posts, including photos.

That system, though, is compromised if a child lies about her age when she signs up for Facebook – and thus becomes an adult much sooner on the social network than in real life, according to the experiment by N.Y.U. researchers.

The key to the experiment, explained Keith W. Ross, a computer science professor at N.Y.U. and one of the authors of the study, was to first find known current students at a particular high school. A child could be found, for instance, if she was 10 years old and said she was 13 to sign up for Facebook. Five years later, that same child would show up as 18 years old – an adult, in the eyes of Facebook — when in fact she was only 15. At that point, a stranger could also see a list of her friends.

The researchers conducted their experiment at three high schools. They were able to construct the Facebook identities of most of the schools’ current students, including their names, genders and profile pictures.

The researchers identified neither the schools nor any of the students. Their paper is awaiting publication.

Using a publicly available database of registered voters, someone could also match the children’s last names with their parents’ — and potentially, their home addresses, Professor Ross pointed out.

The Coppa law, he argued, seemed to serve as an incentive for children to lie, but made it no less difficult to verify their real age.

“In a Coppa-less world, most kids would be honest about their age when creating accounts. They would then be treated as minors until they’re actually 18,” he said. “We show that in a Coppa-less world, the attacker finds far fewer students, and for the students he finds, the profiles have very little information.”

How children behave online is one of the most vexing issues for parents, to say nothing of regulators and lawmakers who say they wish to protect children from the data they scatter online.

Independent surveys suggest that parents are worried about how their children’s social network posts can harm them in the future. A Pew Internet Center study released this month showed that most parents were not just concerned, but many were actively trying to help their children manage the privacy of their digital data. Over half of all parents said they had talked to their children about something they posted.

Teenagers seem to be vigilant, in their own way, about controlling who sees what on the pages of Facebook.

A separate study by the Family Online Safety Institute that was released in November found that four out of five teenagers had adjusted privacy settings on their social networking accounts, including Facebook, while two-thirds had placed restrictions on who could see which of their posts.

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