Some of these differences can be measured and are controlled for in statistical analyses, including the Virginia study. But many other unmeasured differences can skew results, even in studies with such statistical controls. The authors of the U.V.A. surgical study and of studies like it know this, and say as much right in their papers. They practically shout that the correlations they find are not evidence of causation.

That hasn’t stopped policy makers and others in the media from asserting otherwise.

Other approaches to studying Medicaid more credibly demonstrate the value of the program. The most straightforward way is a prospective randomized trial, which gets around the subtle biases that plague studies that use only statistical controls. There has been exactly one randomized study of Medicaid, focused on an expansion of the program in Oregon.

Because demand for the program exceeded what Oregon could fund, in 2008 the state introduced a lottery for Medicaid eligibility. A now famous analysis took advantage of this lottery’s randomness, finding that Medicaid increased rates of diabetes detection and management, reduced rates of depression and lowered financial strain. It did not detect improvements in mortality or measures of physical health, but it did not have enough sick patients or enough time to detect differences we might have expected to see. In other words, it was not powered to detect changes in mortality or physical health.

Saying that this study proves Medicaid doesn’t work ignores this limitation. Regardless, there was nothing to indicate that having Medicaid worsened health.

Another way to tease out the causal effect of Medicaid is to look at variations in Medicaid eligibility rules across states. With respect to health outcomes, these state decisions are effectively random, so they act like a natural experiment. Older studies based on this approach, using data from the 1980s and 1990s, have not found that Medicaid causes worse health.

Findings from more recent studies looking at expansions in enrollment, in the 2000s and then under the Affordable Care Act in 2014, are consistent with older ones. One can argue that Medicaid can be improved upon, but the credible evidence to date is that Medicaid improves health. It is better than being uninsured.

Here’s another telling way to test the idea that Medicaid is harmful. Some of the studies that associate Medicaid with worse health, as compared with private insurance, also find the same association with Medicare. No one argues that Medicare is making people sick.