NEW YORK — The Affordable Care Act has provided health insurance to 20 million people. Are they any better off?

This has been the central question as the complex and expensive health law unfurls. Information about whether it’s protecting people from debt or helping them be more healthy has been slow to emerge.

Recent studies suggest people have become less likely to have medical debt or to postpone care because of cost. They are also more likely to have a regular doctor and to be getting preventive health services like vaccines and cancer screenings.

A study published Monday in JAMA Internal Medicine offers another way of looking at the issue. Low-income people in Arkansas and Kentucky, which expanded Medicaid insurance to everyone below a certain income, appear to be healthier than their peers in Texas, which did not expand.

The study took advantage of what Dr. Benjamin Sommers, an author of the paper and an assistant professor of health policy and economics at Harvard, called “a huge natural experiment.’’

In 2012, the Supreme Court made the health law’s Medicaid expansion optional for states. The resulting variations make it much easier to compare what happened in different states and draw conclusions about what effects health insurance coverage might have on finances and health.

The researchers did a large survey of low-income residents of the three states. They asked the same questions three times: in 2013, before the law’s Medicaid expansion; at the end of 2014, after it had been in place for a year; and at the end of last year. Then they compared what happened over time, using Texas as a kind of control group.

The survey found people in Arkansas and Kentucky were nearly 5 percent more likely than the Texans to say they were in excellent health in 2015. The difference was bigger than it was the year before.

No two states are exactly the same; there are many differences between Texas, Arkansas and Kentucky, besides their decisions on this part of the Affordable Care Act. The authors cautioned that their results can’t prove Medicaid expansion caused people to be healthier.

There are differences between Arkansas and Kentucky, as well. Kentucky expanded Medicaid in a more conventional way, while Arkansas tried an innovative expansion, offering its low-income residents private insurance. But the study found only small differences between the two approaches.

That finding may be of interest to states that have not expanded Medicaid but are considering it. Louisiana this summer became the 31st state to expand its program.

It might sound simple to measure whether people are healthier than they used to be, but it’s actually tough. While tests can tell you whether someone has high cholesterol or high blood pressure, a single test may not tell the whole story. It turns out, however, that if you ask people how healthy they are, they do a good job of telling you. Research shows that people who say they are in poor health really are much more likely to die than those who describe their health as good.

On financial measures, the study was in line with some previous studies, finding that people in Kentucky and Arkansas were less likely to postpone care or avoid taking prescribed drugs because of the cost.

Amy Finkelstein, an MIT economist, described the three-state survey as “entrepreneurial,’’ because it gives us an early glimpse at important questions.