Shortly after House Budget Committee Chairman Paul Ryan of Wisconsin unveiled his plan to convert federal Medicaid funding to a block grant — which has since passed the House — Maryland Gov. Martin O’Malley and 16 other governors issued a letter to congressional leaders to say they “strongly oppose” it.

Mr. Ryan, like most of his Republican comrades, hasn’t always been on the side of fiscal responsibility. He voted for the Troubled Asset Relief Program, various bailouts, and that unfunded Republican entitlement program, Medicare Part D. On Medicaid reform, however, Mr. Ryan has the better side of the argument.

Mr. O’Malley and the other governors wrote that block grants “would shift costs and risk to states.” In reality, the matching‐​grant system these governors seek to preserve is a massive cost‐​shifting scheme. Block grants would reduce this phenomenon.

For every additional dollar a high‐​income state spends on its Medicaid program, the federal government sends the state one matching dollar. Low‐​income states get as much as $4 from Washington for each additional dollar they spend.

Therefore, every time a governor expands his or her state’s Medicaid program, the federal government’s system of matching grants effectively shifts 50 percent to 80 percent of the expansion’s price tag to taxpayers in other states.

The same is true in reverse. If governors tolerate waste, fraud and abuse, the matching‐​grant system shifts 50 to 80 percent of the cost to taxpayers in other states.

Today’s system even shifts costs across generations. Matching grants are such a cash cow that states hatch all manner of schemes to “pull down” as much federal money as possible. (One common practice is for states to secure federal dollars by pretending to increase their Medicaid outlays, but then recapturing those outlays by taxing providers.) But each time they do so, states add to the federal deficit, which shifts the cost of current consumption to future taxpayers.

What’s really upsetting Mr. O’Malley and his colleagues is that block grants would reduce their ability to shift the cost of their Medicaid programs to other states.

Under a block‐​grant system, Washington would give each state a fixed amount of money that would neither rise nor fall with the amount the state spends. Governors would be free to expand their programs, but they would have to come up with 100 percent of the money for those expansions.

Mr. O’Malley and colleagues warn that having to choose “between increasing taxes, cutting other state programs, or cutting eligibility, benefits, or provider payments” would put them in an “untenable” position. What they mean is that they want to preserve the open‐​ended, perennial bailout that Medicaid has always offered.

But since there is no more money in Washington for bailouts or anything else, perhaps a second‐​best option would be to ask the nation’s governors to start taking responsibility for their Medicaid policy choices.

Finally, Mr. O’Malley and the other governors call for “federal policy that creates cost savings, not cost shifting.” As luck would have it, block grants would do just that, by encouraging states to reduce Medicaid fraud and abuse.

Fraudulent and other improper payments account for an estimated 10 percent of this $466 billion program according to the Government Accountability Office (with much higher estimates in specific jurisdictions — an inspector general cited 40 percent in New York City).

Medicaid and similar programs crowd out private coverage at rates as high as 60 percent. That suggests there are millions of people on the Medicaid rolls who could obtain coverage on their own and that states could reduce the cost of the program by targeting subsidies to the truly needy.

The matching‐​grant system that Mr. O’Malley defends actually encourages fraud and abuse.

Matching grants make combating fraud and abuse a low‐​return proposition for states. Providers inevitably chafe under the additional paperwork and investigations necessary to police fraud. Currently, if a state inflicts enough of this political pain to eliminate $1 of fraud, it only keeps 20 to 50 cents; the rest goes back to Washington. As a result, Mr. O’Malley and other governors have quite rationally made policing fraud and abuse too low a priority.

Under block grants, states would keep 100 percent of the savings from rooting out fraud and abuse. That would encourage states to spend their Medicaid dollars wisely, reduce the cost of the program, and enable states to do more with fewer resources.

It wasn’t their intention, but Mr. O’Malley and the other 16 governors inadvertently demonstrated why block grants are necessary.