In its continuing campaign to get more Americans covered by Medicaid, the federal government used two simple and time-honored strategies this week: one carrot and one stick. It will need to use more of both, but especially the stick.

To appreciate why, it’s first worth repeating why making more people eligible for Medicaid is a good idea. The Affordable Care Act expanded the program to cover anyone earning as much as 138 percent of the federal poverty level, with the federal government paying 100 percent of the cost at first, gradually reducing to 90 percent by 2020, with states paying the rest. Sixteen million people were expected to gain health coverage as a result.

The U.S. Supreme Court disrupted that expectation by giving states the option not to expand their programs. Today 25 states, 22 with Republican governors, have exercised that choice, leaving 5.2 million Americans without health insurance on the spurious argument that enlarging Medicaid would cost too much and leave states vulnerable to a future drop in federal funding. (In fact, the federal contribution to Medicaid has been remarkably steady over the program’s four-decade history.)

The resistance to Medicaid’s expansion is political, not economic. Hence, the need for carrots and sticks.

The administration of President Barack Obama, and in particular the Centers for Medicare and Medicaid Services, is proving quite good at the former. On Tuesday, CMS approved Iowa’s request to expand Medicaid in a way the state’s Republican leadership can brand as friendly to conservative principles: Those newly eligible will get private coverage through the state’s insurance exchange, and some will pay premiums for that coverage.

CMS allowed Arkansas to take a similar approach, and it may yet approve versions of that model for Pennsylvania and Tennessee. The compromise isn’t ideal, because traditional Medicaid is more cost-efficient than private coverage, but CMS is right to offer it when the alternative is no expansion at all.

Other states, however, will need more than technical concessions to change their minds. They’ll need pressure. That’s what makes this week’s other initiative interesting. On Monday, the administration released a report showing how Medicaid expansion can ease racial inequality in health coverage.

Blacks are disproportionately likely to be uninsured, the report noted; two-thirds of blacks eligible for help under Obamacare live in states that aren’t expanding Medicaid; and the states with the greatest number of eligible uninsured blacks are Florida, Georgia and Texas -- three states that have so far refused to budge on Medicaid.

Enough with the data. The takeaway here is that a politician’s decision to expand Medicaid is not only about politics -- that is, helping make the Obama administration’s signature law a success. It is also economics, helping his or her state improve its balance sheet. And it is about morality as well: helping the most vulnerable stay healthy.

There may be other ways to expand coverage to those who need it. But at the moment, this is what’s available. And it costs states a pittance compared with the financial and social benefits they’ll receive. Denying your constituents a chance to get health insurance out of political pique comes perilously close to governmental malpractice.

This is a truth that bears repeating, but especially in states that are denying their residents the benefits of expanded Medicaid coverage. Expanding Medicaid is good economics, but it’s also about fairness.

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