At a glance, Medicare’s prescription drug program — also called Medicare Part D — looks like the perfect example of a successful public-private partnership.

Drug benefits are entirely provided by private insurance plans, with generous government subsidies. There are lots of plans to choose from. It’s a wildly popular voluntary program, with 73 percent of Medicare beneficiaries participating. Premiums have exhibited little to no growth since the program’s inception in 2006.

But the stability in the premiums belies much larger growth in the cost for taxpayers. In 2007, Part D cost taxpayers $46 billion. By 2016, the figure reached $79 billion, a 72 percent increase. It’s a surprising statistic for a program that is often praised for establishing a competitive insurance market that keeps costs low, and that is singled out as an example of the good that can come from strong competition in a private market.

Much of this increase is a result of growing enrollment — it has doubled in the past decade to 43 million — and higher drug prices. But there is also a subtle way in which the program’s structure promotes cost growth.

When enrollees’ drug costs are relatively low, plans pay a large share, typically about 75 percent. But when enrollees’ drug spending surpasses a certain catastrophic threshold — set at $5,000 in out-of-pocket spending in 2018 — 80 percent of drug costs shifts to a government program called reinsurance. This gives people in charge of private insurance plans an incentive to find ways to push enrollees into the catastrophic range, shifting the vast majority of drug costs off their books. For example, they could be less motivated to negotiate for lower drug prices for certain types of drugs if doing so would tend to keep more enrollees out of the catastrophic range.

Reinsurance spending, which is not reflected in premiums, has been rising rapidly.

“This harms the very competition that Part D was supposed to establish,” said Roger Feldman, an economist at the University of Minnesota. Consumers are naturally attracted to lower-premium plans, but choosing them increasingly shifts higher costs onto taxpayers if plans achieve those lower premiums in part by shifting more drug expenses onto the government’s books.

Documenting this is a recent study by Mr. Feldman and Jeah Jung of Penn State University that was published in Health Services Research. The study found that the disconnect between premiums and reinsurance costs has increased over time. Additionally, insurance company plans exhibiting less of an effort to manage the use of high-cost drugs had higher reinsurance costs. This is consistent with incentives to encourage enrollees into the catastrophic range of spending.

The Medicare Payment Advisory Commission has been warning about this problem for several years in its annual reports to Congress. According to MedPAC, between 2010 and 2015, the number of enrollees entering the catastrophic drug cost range grew 50 percent, from 2.4 million to 3.6 million, now accounting for 8 percent of enrollees.

“It’s ironic for a program supposedly built on market principles,” said Mark Miller, a former MedPAC director. “You wouldn’t see this kind of thing in the commercial market.” For commercial market insurance products — such as those offered by employers or in the health insurance marketplaces — only about 1 percent of policyholders reach a catastrophic level of expenditures at which reinsurance kicks in. (Mr. Miller and I are co-authors of an editorial about Ms. Jung’s and Mr. Feldman’s study, which also appears in Health Services Research.)

Reinsurance is the fastest-growing component of Medicare’s drug program, expanding at an 18 percent annual rate between 2007 and 2016. In 2007, it accounted for 17 percent of government spending for Part D. In 2016 it was 44 percent.

The Affordable Care Act hastened this growth. The law requires pharmaceutical manufacturers to pay some of the cost of the drug benefit. (The Bipartisan Budget Act of 2018 further increased how much manufacturers must contribute.) For the purposes of reaching the catastrophic threshold and triggering reinsurance, these industry contributions count as out-of-pocket payments for enrollees, even though they are not.

That means enrollees don’t have to spend as much as they otherwise would to trigger the reinsurance program. Although this is of great benefit to enrollees, it also pushes up taxpayer liability for the program.

Changing the extent to which manufacturer’s contributions count as enrollee out-of-pocket spending is one potential reform of the program. Other solutions include increasing the liability of insurance company plans in the catastrophic range and decreasing the liability of taxpayers.

This would have the effect of bringing premiums more in line with program spending. Doing so would “return Part D to the market-based program it was intended to be,” Ms. Jung said. As it stands, there is a substantial divide between what Part D was billed as and what it actually is.