We often talk about the first-order benefits of health care, the wounds treated or diseases caught when families and children have the luxury of visiting a doctor. Many of the second- and third-order benefits are harder to see, whether they take the form of money not spent treating illness, or lifestyles that are possible when people aren't sick.

Give people access to health care, in short, and a lot of other things become possible, too. For instance: Children are better able to learn.

Education policymakers and teachers regularly argue this. But researchers at Cornell and Harvard have found particularly convincing evidence that it's true. In a National Bureau of Economic Research working paper, Sarah Cohodes, Samuel Kleiner, Michael F. Lovenheim and Daniel Grossman found that the expansion of public health care to many more children in the 1980s and 1990s produced long-term educational benefits.

Evidence across states that rolled out more generous programs at different times suggests that expanded access to public health care led to lower high school dropout rates, increased college attendance and more bachelor's degrees. The effects were large and consistent across the country. And they bolster both the underlying idea that health is an important input to education, and the policy argument that investments in public health care yield cascading benefits.

Specifically, the researchers found that a 10 percentage point increase in Medicaid eligibility among children in a state translated into a 5.2 percent decline in high school dropouts (among all students), a 1.1 percent increase in college attendance, and a 3.2 percent increase in students completing bachelor's degrees. Over the period of time the researchers studied, states increased their Medicaid eligibility by on average 24 percentage points (for example, from covering 5 percent of children in a state to 29 percent). That's the equivalent of reducing high-school dropouts in the long run by 12.5 percent and increasing college enrollment by 2.6 percent.

Because Medicaid and the Children's Health Insurance Program are designed to cover the low-income, it's likely that most of these gains were concentrated among poor children who also tend to have lower educational attainment. This implies that health-care access may also have implications for narrowing the achievement gap.

"Our estimates suggest that the long-run returns to providing health insurance access to children are larger than just the short-run gains in health status," the authors write, "and that part of the return to these expansions is a potential reduction in inequality and higher economic growth that stems from the creation of a more skilled workforce."

The study used data from the American Community Survey and Current Population Survey on adults, 22 to 29 years old at the time of the research, who were born between 1980 and 1990. Over that decade and the next, states dramatically ramped up access to public health care, expanding eligibility to cover children in two-parent households, as well as children living in households with higher incomes.

States adapted their programs, though, at different times, and with different levels of generosity, enabling the researchers to exploit those differences to identify the effects of expanded access on education. Their findings are the first to link the two.

As for what exactly may be going on here, two explanations in particular are plausible. Other studies suggest that children who are healthier do better in school. They're less likely to miss class. They face fewer distractions when they're there. Cohodes and her co-authors found evidence supporting the theory: Medicaid expansion was linked to tangible health benefits for teens, leading to less risky sexual activity, lowered likelihood of obesity and fewer reported mental health problems.

The other potential explanation lies with their families. Parents may have more resources to spend on their children -- and less stress to contend with themselves -- when they're not spending a disproportionate share of their income on health care.

These findings also suggest that we may not yet have seen all of the benefits of public investments in health insurance during the 1980s and 1990s (to say nothing of the more recent expansion). These same educational outcomes may further translate into higher incomes or more stable employment for children who once benefited from these programs. In turn, those benefits could influence the life outcomes of their children, too.

All of these interrelated benefits, though, also mean that states might blunt some of the impact of investments in health care if that money comes at the expense of spending on education.