Yes, Medicaid could still be playing a role, but as with all correlations, it’s important to consider both directions of causality. It’s possible that states experiencing larger growth in drug deaths might have been more eager to expand Medicaid programs. After all, Medicaid also provides financial support for drug abuse treatment. One study found that prescriptions for medications that treat opioid addiction increased by 43 percent in Medicaid expansion states, relative to states that did not expand their programs. When Gov. John Kasich, a Republican, talks about why he’s happy that Ohio expanded the Medicaid program, he often cites the opioid crisis in his state.

Craig Garthwaite, a Republican labor economist of Northwestern University’s Kellogg School of Management, said: “It’s not that there isn’t a single case of an individual insured by Medicaid developing an opioid habit or illicitly obtaining drugs. But the evidence to date doesn’t suggest that this is the net effect.”

Another way to test the Medicaid-opioid connection is to examine a dose response. States with higher levels of uninsurance saw greater coverage gains through Medicaid. If more Medicaid causes more opioid death, then states that added more Medicaid beneficiaries should see greater increases than states with smaller coverage expansions. But Mr. Goodman-Bacon and Ms. Sandoe show that the opposite holds. Counties in states with historically higher levels of uninsurance (and therefore greater subsequent growth in Medicaid) had lower growth in drug-related death rates from 2010 to 2015. This relationship holds within expansion and nonexpansion states separately.

Or course, drug-related deaths include those from prescription opioids as well as those from black-market drugs (like heroin and fentanyl). Medicaid directly enhances access only to the former. This makes it hard to identify the role of Medicaid in the opioid crisis definitively, which is all the more reason to be cautious about suggesting the program is fueling it.

“The really sad thing here is that these numerical arguments have the veneer of seriousness, and as a result, they can drive really bad policy,” Mr. Garthwaite said.

Providing health care through insurance means providing access to both its benefits and harms. No one seems concerned that the increased access to health care that private insurance provides might lead more people to take opioids — only that Medicaid could. It’s also interesting to note that no one makes assertions that increased coverage, even increased Medicaid coverage, probably leads to more deaths by medical errors.

We should not look at harms in isolation. Even if Medicaid does enhance access to prescription opioids, thereby playing a role in their misuse, that is far from the only thing the program does. Medicaid provides many other benefits, about which we’ve written, including increased access to substance use disorder treatment.

To use a theoretical Medicaid-opioid connection (for which the evidence is weak anyway) to justify scaling back Medicaid ignores the larger picture — that it is a crucial aspect of our safety net, providing access to health care and financial protection that many low-income Americans could not otherwise obtain.