Latest Issue of Science News


Math Trek

Devil is in the details of a new Medicare plan to buy medical supplies

Math Trek

Sponsor Message

Medicare could waste billions of dollars, bankrupt small businesses and leave seniors without crucial equipment like oxygen tanks and wheelchairs, some economists warn, with a new auction-based purchasing plan that ignores mathematical principles of competitive bidding.

The new plan began with an apparently good idea: Medicare has started buying durable medical equipment through a competitive bidding process rather than through fixed prices influenced by industry lobbying. In theory, this could save the government a big chunk of the $14 billion it has spent on such equipment in a year. But in reality, mathematicians and economists say, the bidding system Medicare has chosen is so flawed it will create chaos in the market, fail to meet the demand and waste money.

“I have never seen a poorer auction or poorer government auction … in my 20 years in this business,” says Peter Cramton of the University of Maryland. “It is very sad.”

In its broadest strokes, the bidding system Medicare designed is similar to many others: Producers submit sealed bids saying how many units they can produce at what price, and Medicare fills the contract by purchasing from the lowest bidders. In the most common approach, called a “second-price auction,” all the winners are paid the price of the lowest bidder who lost out. (EBay uses an analogous approach, with the winner paying a dollar more than the highest losing bid.)

But Medicare decided instead to pay all the producers the median of all the winning bids. Federal officials explained in a rule-making document that they considered using the maximum of the qualifying bids, but that “this approach would have led to program payment amounts that were higher than necessary because some suppliers were willing to provide these items to beneficiaries at a lower cost.”

Cramton calls that statement absurd, and says it illustrates officials’ ignorance regarding auctions. Change how much producers get paid, he points out, and you change how much they’ll bid.

Take, for example, eBay. Had they set their system up so that you pay the full amount you bid and you were willing to pay up to $500 for a ring, you probably wouldn’t bid that amount. Instead, you’d take a guess about how little you might be able to get it for and bid, say, $401 in the hopes that the next highest bidder would stop at $400.

Remarkably enough, it’s been proven mathematically that in this alternate system, if everyone bid optimally, the final prices would be exactly the same as they are on eBay now — though the bids themselves would be different.

The median-price system had never been analyzed when Medicare chose it, so no one knew whether it would produce the same prices as other systems. But even without analysis, it has a clear problem: Half the winning producers will get less than they bid, and quite possibly less than what it costs them to make their product. To deal with that, Medicare made the bids nonbinding, so that a winning bidder can bow out without penalty.

But this solution brings its own problems. As a bidder in this system, the rational thing to do is to bid really, really low. After all, your bid doesn’t determine what you’ll be paid, and since 10,000 suppliers might participate, one lowball bid will barely change the median price. If the price turns out to be profitable, you take the contract, and if not, you can just bow out. Of course, if everyone does this the price will collapse and no one will make the equipment.

Cramton, together with economist Brett Katzman and mathematician Sean F. Ellermeyer of Kennesaw State University in Georgia, analyzed Medicare’s system to see whether it would set the same price as other systems. They computed what’s called the “Bayesian Nash equilibrium,” which is a bidding strategy for all participants in which no one could earn more money by changing their own bid, assuming that everyone else’s bids stay the same. Over time, bidders would be expected to converge toward the Bayesian Nash equilibrium strategy.

The team got a bizarre result: There were infinitely many Nash equilibria. That means that the bidders shouldn’t be expected to converge on a single price. The strategy in which everyone lowballs — and everyone then refuses the ridiculously low contract price — is one equilibrium. And indeed it’s the most tempting of them: Charles Plott, an economist at Caltech, tested the system out on real people and found that most participants indeed ended up lowballing.

Medicare is currently using the median-bid system in nine areas of the country. The program’s administrators claim great success, with costs reduced by 35 percent and no significant problems. But Cramton says that Medicare has refused to provide basic data to support these assertions.

Representative Tom Price of Georgia has a bill before Congress that would force the Centers for Medicare and Medicaid Services (CMS) to do what he says it should have done in the first place: Ask bidding experts for help designing an efficient system.

If Price’s bill doesn’t pass, Medicare will expand its program to half the country in 2013.

Note: To comment, Science News subscribing members must now establish a separate login relationship with Disqus. Click the Disqus icon below, enter your e-mail and click “forgot password” to reset your password. You may also log into Disqus using Facebook, Twitter or Google.

X