The findings come amid a political push by the Obama administration for government-funded preschool for 4-year-olds. But a growing number of experts, Professor Heckman among them, say they believe that more effective public programs would start far earlier — in infancy, for example, because that is when many of the skills needed to take control of one’s life and become a successful adult are acquired.

The study in Science drew its data from the Carolina Abecedarian Project, in which about 100 infants from low-income families in North Carolina were followed from early infancy to their mid-30s. The project is well known in the world of social science because of its design: The infants were randomly assigned to one group or the other, allowing researchers to isolate the effects of the program. Such designs are the gold standard in medical research, but are rarely used in investigations that influence domestic social policy.

The researchers had already answered their original question about cognitive development: whether the treated children would, for example, be less likely to fail in school. The answer was yes. Over all, the participants’ abilities as infants were about the same, but by age 3 they had diverged. By age 30, those in the group given special care were four times as likely to have graduated from college.

“Forty years ago, it was all about cognition,” Professor Heckman said. “But it turned out that when you expand these capabilities — not only cognitive but social and emotional — one of the effects is better health. Nobody thought about that at the time.”

Frances Campbell, a senior scientist at the Frank Porter Graham Child Development Institute at the University of North Carolina at Chapel Hill, who started work on the project in the 1970s, said of the health improvements, “I would not say to you that we were expecting to see much of a difference at all.”