For low-income families, a home in places with these characteristics is often a financial stretch. Rachelle Hawkins, a 32-year-old single mother in California, rented an apartment in Contra Costa late last year with help from a Contra Costa nonprofit called Shelter, Inc., which paid her first month’s rent. She moved from a gritty neighborhood near Oakland and was homeless for a time. She makes about $29,000 as a customer-service agent in online banking and faces an annual rent bill of almost $17,000.

But she thinks the burden is worth it for her children, who are 4 and 6. “I don’t think my kids are going to remember what we went through,” Ms. Hawkins said. “They are absolutely better off, just because of the environment.”

In addition to studying the outcomes of more than five million children who moved, Mr. Chetty and Mr. Hendren also revisited the subjects of the Moving to Opportunity experiment. Working with Lawrence Katz, one of the original researchers to study the program, they analyzed more recent, richer data — and concluded that children who moved before they were teenagers did indeed benefit economically. (The original study had found health benefits for both younger and older children.)

In both studies, the younger children were when they moved, the better they did. Children were less likely to become single parents when they grew up, were more likely to go to college and to earn more. The original research had not been able to follow the economic outcomes of younger children, because not enough time had passed, Mr. Katz said.

Still, the more extensive nationwide data on moving found that older children were also affected by their neighborhood. The effect was what statisticians call linear: Each additional year in a different place had roughly the same average effect on a child’s adult earnings. A teenager’s year in a better neighborhood mattered as much as a 9-year-old’s year — but 9-year olds still had their teenage years in front of them.

Some economists who have seen the new study say that it argues for a new approach to housing policy. Current policy often forces the parents of young children onto waiting lists for housing vouchers. It also gives tax incentives to developers who build in poor neighborhoods, rather than rewarding those who build affordable housing in areas that seem to offer better environments.