“What’s exciting about this is how good the outcome variables that they can look at,” said Janet Currie, a professor of economics and public affairs at Princeton. A few studies have tracked the health outcomes of children who were eligible for Medicaid over time, including one Ms. Currie wrote, but the study’s measures of economic outcomes are new.

The new paper was made possible by a series of policy changes throughout the 1980s and 1990s that slowly expanded Medicaid to cover more and more American children. The changes essentially happened in two phases: First, the federal government allowed the program to include older children, and then individual states approved expansion to those groups. The slow, state-by-state spread of the policy enabled the researchers to compare children who were eligible for Medicaid with a control group of similar children of the same age and family income level who were not eligible for the program. The study looked at children who were eligible for Medicaid, even though not every eligible child actually signed up.

Expanded eligibility had two other important effects closely related to the earnings statistics: Children who were eligible for coverage were less likely to die before reaching 28, and they were more likely to attend college. Those are outcomes that, Ms. Kowalski points out, the government may value even if the program doesn’t return any money to the Treasury.

The study can’t entirely explain how access to childhood health insurance helped low-income children earn more later in life. But Ms. Kowalski has a few theories. One is that it may have helped the girls, in particular, by offering them a way to get contraception (which Medicaid covers to varying degrees in all states) and avoid unplanned pregnancies. The earnings effect was much more pronounced for girls than it was for boys.

The difference may also come from the way that public health insurance changed the budgets of the children’s families, she said. By taking care of health care bills, Medicaid may have freed the parents to make other investments in their children’s development that paid off.

Ms. Currie said that earlier studies of children’s health outcomes also suggest that children with serious illnesses often go on to be sick as adults as well — meaning they are more likely to miss work or have limited career options. Medicaid supports and funds a lot of important preventive health care for very young children. She said the lesson could be that “an ounce of prevention is worth a pound of cure.”

Now that the earlier expansions have had a chance to spread, nearly every low-income child in the country is eligible for Medicaid, and more than a third of all American children are currently enrolled in either Medicaid or a closely related federal-state program, called the Children’s Health Insurance Program.

“If this is right, then we’re going to be seeing a lot more impact for the kids that are born now and in the future,” said Judy Solomon, a vice president for health policy at the left-leaning Center on Budget and Policy Priorities.