Almost four decades after the federal education law called Title IX opened the door for girls to participate in high school and college athletics, a crucial question has remained unanswered: Do sports make a long-term difference in a woman’s life?

A large body of research shows that sports are associated with all sorts of benefits, like lower teenage pregnancy rates, better grades and higher self-esteem. But until now, no one has determined whether those improvements are a direct result of athletic participation. It may be that the type of girl who is attracted to sports already has the social, personal and physical qualities — like ambition, strength and supportive parents — that will help her succeed in life.

Now, separate studies from two economists offer some answers, providing the strongest evidence yet that team sports can result in lifelong improvements to educational, work and health prospects.

Using a complex analysis, Dr. Stevenson showed that increasing girls’ sports participation had a direct effect on women’s education and employment. She found that the changes set in motion by Title IX explained about 20 percent of the increase in women’s education and about 40 percent of the rise in employment for 25-to-34-year-old women.

“It’s not just that the people who are going to do well in life play sports, but that sports help people do better in life,” she said, adding, “While I only show this for girls, it’s reasonable to believe it’s true for boys as well.”