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Julie Rehmeyer, Math Trek

For new federal plan to buy medical supplies, devil is in the details

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SN Prime | January 7, 2013 | Vol. 3, No. 1

Medicare could waste billions of dollars, bankrupt small businesses and leave seniors without crucial medical equipment, 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 like oxygen tanks and wheelchairs 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 … in my 20 years in this business,” says economist 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 one bid increment more than the highest losing offer.)

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.

So what about Medicare’s system? Would it set the same prices as other approaches? It had never been mathematically analyzed before implementation, so no one knew. 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 every-one does this the price will collapse and no one will make the equipment.

Cramton teamed up with economist Brett Katzman and mathematician Sean F. Ellermeyer of Kennesaw State University in Georgia to compute 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, and his colleagues tested the system out on real people and found that most participants indeed ended up lowballing.

Medicare is now 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 Medicare’s administrators to do what he says they 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.

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