SEATTLE — Jackie Rath says she was sexually assaulted by four different men, including a stepfather and a stepbrother, by the time she was 16. That is also when her mom went to prison for murdering a boyfriend’s lover.

Rath, now 38, was the third generation in her family to endure a traumatized childhood that led to poverty, and now she is a single mom with six children of her own who might also be at risk. But she is part of an experiment unfolding in and around Seattle that shows immense promise in breaking cycles of poverty so that her youngest daughter, Amina, 2, can have the wind at her back.

For all those who think that poverty is hopeless, that nothing can change — read on! The experiment is deceptively simple and cheap: It helps families move to neighborhoods with a proven record of helping kids do better. A major research study about the experiment, co-written by Prof. Raj Chetty of Harvard, has just been published by Opportunity Insights of Harvard.

Early word of the results has provoked a nationwide stir among Democrats and Republicans alike, and 21 cities across America are already working to start similar programs. Anti-poverty work is sometimes seen as bleak, but these findings are thrilling.

One insight of the study is that although the United States spends $44 billion a year on affordable housing, that money perversely concentrates poverty in blighted neighborhoods. The counterproductive result is that children are sentenced to grow up in areas rife with crime, teenage pregnancy and educational failure.

In contrast, with small tweaks, it turns out to be possible to administer housing vouchers so that families like Rath’s move to neighborhoods that aren’t more expensive but are where children stand a much better chance of thriving.

In Rath’s new “high-opportunity neighborhood” in Renton, a suburb, a low-income 2-year-old like Amina will on average earn $260,000 more over a lifetime than growing up in her old neighborhood, Chetty calculates. Such a girl will also be 8 percent less likely to have a baby as a teenager.

The Seattle program is an outgrowth of a national initiative called Moving to Opportunity, which in the 1990s provided vouchers for low-income families to move to better neighborhoods. Early evaluations suggested it had failed: Adults who received the vouchers didn’t earn more money.

Then in 2015, a follow-up study shook the policy world. While the moves hadn’t helped the adults, those who moved as toddlers were more likely to go to college, to marry, to earn more money and to pay more taxes — enough to pay for the program with interest.

Subsequent research has backed this finding: Neighborhood matters enormously, for young children. That’s the reason for the focus on Amina: Older siblings will also benefit, but the impact is greatest on those who move young and grow up entirely in a high-opportunity neighborhood.

Chetty has developed an online “Opportunity Atlas” that shows how some neighborhoods around the country, without being more expensive, consistently help children get ahead. It’s still unclear what the secret sauce is, although it apparently has something to do with decent schools, less poverty, lots of dads present in families and positive social norms.

The problem has been that even when families get housing vouchers, they often move only from one troubled neighborhood to another. Is it that struggling families don’t want to move to better neighborhoods or can’t? Or is it that small barriers block them?

Seattle’s experiment, called Creating Moves to Opportunity, answered that question. It provides a “housing navigator” who helps low-income families receiving vouchers find homes in better neighborhoods, while also negotiating with landlords and helping to pay security deposits.

This assistance costs an average of only $2,600 per household but has had a stunning effect: Families were almost four times as likely to use their vouchers to move to a high-opportunity area.

Because these are inexpensive tweaks to our existing housing voucher program, amounting to just 2.2 percent of the cost of the underlying voucher, we could easily incorporate these elements and make vouchers far more effective at breaking cycles of poverty.

“Economic segregation in America is not a consequence of deep-rooted preferences but rather is driven by small barriers in housing search that we can easily address through policy,” Chetty said. “This is a much more optimistic view of the world.”

This research underscores that the common American view that nothing works to address poverty is a fallacy. There are no silver bullets, but there is silver buckshot, and moving kids to better neighborhoods is one of those pellets.

We also need early childhood education, job training and much more. But moving from a low- to high-opportunity neighborhood can, by Chetty’s calculation, close almost one-quarter of the gap in lifetime earnings between disadvantaged kids and those who are better off.

As for Rath, she told me that she was determined to break the cycle of poverty that enmeshed her grandmother, her mother and herself. And she thinks her move to a new neighborhood with a history of good outcomes will make all the difference for Amina and her other children.

“Lots of people need a footstool to get ahead,” she said. “That’s what this program is.”

The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips. And here’s our email: letters@nytimes.com.– Nicholas Kristof has been a columnist for The New York Times since 2001.

Nicholas Kristof has been a columnist for The New York Times since 2001.