The tale took on new relevance recently, when Mr. Guyer downsized to a small house from a more luxurious one. He was worried that his children, a daughter, 15, and twins, 22, would be upset. To his surprise, they weren't. Instead, their reaction echoed their great-grandfather's. "What they care about," Mr. Guyer says his children told him, "is how warm are the people in the house, how much of their heart is accessible."

As parents cut budgets, many are finding family stories have surprising power to help children through hard times. Storytelling experts say the phenomenon reflects a growing national interest in telling tales, evidenced by a rise in storytelling events and festivals. New research bears out the value of family stories, linking teens' knowledge of them to better behavior and mental health.

An Emory University study of 65 families with children ages 14 to 16 found kids' ability to retell parents' stories was linked to a lower rate of depression and anxiety and less acting-out of frustration or anger, says Robyn Fivush, a psychology professor. Knowing family stories "helps children put their own experience in perspective," Dr. Fivush says.

The trick is telling the stories in a way children can hear. We're not talking here about the kind of story that begins, "When I was a kid, I walked to school every day uphill both ways, barefoot in the snow." Instead, choose a story suited to your child's needs, and make eye contact to create "a personal experience," says Sherry Norfolk, chairman of the National Storytelling Network, a Jonesborough, Tenn., nonprofit. "You don't have to tell children what they should take from the story," she says. "They can intuitively understand what the moral is."

When Carla Freeman's daughter became anxious a few years ago about having to change schools, the Atlanta mother related her own childhood stories of switching to another school in her community. Her old friends dropped her and, at her new school, "I was kind of an oddball" at first, she told her daughter. But Ms. Freeman bounced back and made new friends. She credits the stories with helping her daughter, now 12, develop resiliency and the ability to "hold herself together" against challenges.

A to uch of humor helps. At Scott Prengle's Dallas home, his son Bobby, 17, has heard tales about his grandfather growing up in times so hard that his hungry schoolmates would devour apple cores left over from his lunch. As Bobby tapped a nearly empty salad-dressing bottle over his salad at dinner one evening, Scott laughed and invited him to do as his grandfather did: Put water in the bottle and shake it up, to use every last drop. Scott says his father's frugal habits "drove us crazy, but the idea was that nothing went to waste."

While Bobby declined to water down his dressing, he says of his grandfather that "I follow in his footsteps" in other ways, saving paper clips and rubber bands. And when Scott recently trimmed the family budget, he thought he saw an echo of his late father in Bobby, in the way he calmly accepted the loss of his oft-used gym membership.

Even when you think your children aren't listening to your stories, Dr. Fivush says, they probably are. Thomas Pontes thought his children, 12, 14 and 16, shrugged off tales of his grandfather, an immigrant farmhand who worked his way up from living in a barn to owning a home. To Mr. Pontes, of Providence, R.I., the story shows "the kind of optimism you need to pick yourself up from a field somewhere tending cattle" to cross the Atlantic, fueled solely by hope.

But when I asked his daughter Katie, 16, about the stories, she not only remembered them, but said they've "helped me become more appreciative of my life and how easy things are for me." Even if kids don't seem to appreciate family stories, she says, in time they'll "realize just how important they are."