The federal government has now recouped much of the original cost of insuring those poor families, the research found, because their children have grown up to pay more in taxes and rely less on welfare and other public benefits. As an investment, Medicaid has returned at least 2 percent a year so far, according to the author of the paper, Vanderbilt University economist Andrew Goodman-Bacon -- excluding the benefits to patients themselves and focusing only on Uncle Sam's bottom line.
The research, part of an expanding effort among public-health experts to understand how Medicaid affects recipients, is timely as Republicans are contemplating major changes to the program.
Repealing the Affordable Care Act, as President-elect Donald Trump has pledged to do, would likely remove almost 13 million people from Medicaid's rolls, according to projections published Wednesday by the Health Policy Center at the nonpartisan Urban Institute. Beyond repeal, Republican lawmakers have talked about reforms to the structure of the program, such as charging recipients nominal premiums or deductibles to discourage them from seeking unnecessary medical treatment, or requiring them to work in order to receive insurance.
Already, however, Medicaid has helped further the GOP objectives of encouraging work and reducing dependence on public benefits, Goodman-Bacon said.
"It's providing benefits for people whose health really was poor," he said. "When it improves, they go off the program, and they start earning."
Before President Johnson created Medicaid in 1965, health insurance was rare among poor families, and medical treatment was prohibitively expensive. Goodman-Bacon cites surveys from 1963 showing that fewer than half of poor children had seen a doctor in the past year.
Families were automatically eligible for the new program if they were receiving cash through the old welfare system. The share of the population on welfare varied by state, however. Some states had less strict requirements for welfare beneficiaries, allowing more people to receive payments. In others, regardless of the rules on the books, the culture among case workers in public-assistance offices tended to be stingier.
As a result, children in some states were more likely to benefit from Medicaid than in others. This variation allowed Goodman-Bacon to estimate the effects of Medicaid on children by comparing mortality records compiled by the federal government for people born in different states.
This kind of comparison is not perfect, to be sure. It could be that other factors specific to the states with greater rates of welfare receipt prior to Medicaid also had an effect on children's health over the long term.
Yet Goodman-Bacon points out that, for children who came of age before Medicaid, there does not appear to have been any difference between these groups of states, suggesting that differences in the data later on result from Medicaid specifically. He estimates that between 1980 and 1999, Medicaid saved about 345,000 lives.
Using Census data through 2014, Goodman-Bacon also showed that access to Medicaid for children increased their earnings as adults, and reduced their reliance on disability insurance and other public assistance.
Among the white population, Goodman-Bacon estimates that 1.2 million fewer people are receiving disability payments through Social Security because they received Medicaid as children. He also calculated that an additional year of eligibility for Medicaid as a child under 10 increased their average earnings as adults by about $1,800, and reduced the public assistance they received by about $600.
Goodman-Bacon found only limited evidence that Medicaid had reduced disability among people of color. While this group enjoyed extraordinary improvements in longevity due to the program, it is possible that health insurance in childhood was not enough to surmount all of the factors that contribute to elevated non-white rates of disability.
The new study provides evidence of Medicaid's benefits that is consistent with other research on the subject. Another working paper published last year by the National Bureau of Economic Research also found that expansions of Medicaid under President Reagan had enduring benefits for children.
One puzzle, however, is that this research generally has not found that Medicaid has much of an immediate effect on recipients' health. It is not clear why public health insurance could help people decades later, and not while they are covered.
For instance, recent studies of Medicaid in Oregon suggest that although insurance through the program allows people to go to the doctor more frequently, they are not living longer or working more as a result. The program has not improved clinical measures of recipients' health, either, the data suggest.
"While the results are tantalizing, it’s not clear," said Robert Kaestner, an economist at the University of Illinois at Chicago and one of the authors of the study from last year. "There’s not a ton of evidence that insurance, either for children or adults, is effective," he added -- at least in the short term.
One possibility, Kaestner says, is that Medicaid helped these families not by providing them with better medical treatment specifically, but instead simply by offering them financial protection. For those households with enough money to send their children to the doctor even without insurance, the program would have allowed parents to use that money to improve their children's lives in other ways, such through better nutrition or education.
Other research on welfare in the early 20th century supports this theory. Economists found that boys whose parents received payments lived a year longer than boys whose parents applied for public assistance but were rejected.
Another explanation for the Medicaid puzzle is that children whose families are covered might learn to take care of themselves better when they are young. If those changes in behavior affect how much people smoke or use drugs or how people with mental illnesses manage those conditions, there would be real benefits only later in life.
"It might not be too surprising if you don’t see health problems turning up till they’re older," said Bruce Meyer, an economist at the University of Chicago and one of Kaestner's collaborators. "Kids are pretty healthy."
Correction: An earlier version of this item misstated the name of the group that estimated that 13 million people could become uninsured if the expansion of Medicaid were repealed. That figure comes from the Health Policy Center at the Urban Institute.