Greg Mankiw links to an article that illustrates the challenges of interpreting raw numbers causally. This would really be a great example for your introductory statistics or economics classes, because the article, by Robert Book, starts off by identifying a statistical error and then goes on to make a nearly identical error of its own! Fun stuff.

Book sets up the story:

Many advocates . . . claim that a public health plan will save money compared to private health insurance because “everyone knows” that the largest government health program, Medicare, has lower administrative costs than private insurance. . . . Advocates of a public plan assert that Medicare has administrative costs of 3 percent (or 6 to 8 percent if support from other government agencies is included), compared to 14 to 22 percent for private employer-sponsored health insurance . . .

He then points out the problem with this raw comparison:

Medicare patients are by definition elderly, disabled, or patients with end-stage renal disease, and as such have higher average patient care costs, so expressing administrative costs as a percentage of total costs gives a misleading picture of relative efficiency. Administrative costs are incurred primarily on a fixed or per-beneficiary basis; this approach spreads Medicare’s costs over a larger base of patient care cost.

Excellent point. Don’t forget about the denominator, as we always tell our students.

The next step, I’d think, is to compare costs for different groups of potential patients, characterized by age, health status, and socioeconomic and demographic background variables.

But that’s not what Book does–instead he just compares average administrative costs per patient: $509 per primary beneficiary for Medicare, $453 for private insurers. But this can’t be right: of course, Medicare patients, who are older, sicker, and are going to the doctor and hospital more often, will have higher administrative costs! It seems silly to jump all over the first set of unadjusted numbers and then take the second set of unadjusted numbers at face value, leading to this claim:

If recent cost history is any guide, switching the more than 200 million Americans with private insurance to a public plan will not save money but will actually increase health care administrative costs by several billion dollars.

I don’t buy it–for essentially the same reason that I find Book’s first argument persuasive. It would seem to make more sense to compare comparable groups of people. (But see Book’s comment below, defending his calculations.)

Disclaimer

I’m no expert in health policy. These are just my impressions as a teacher of statistics. It’s great to find such examples that are so relevant to policy. I was surprised to see Mankiw quote the above article without criticism; but I’m pretty sure he’s studied these issues in a lot more detail than I have, and so perhaps he has additional knowledge that makes him confident in the substance of Book’s reasoning.

In particular, I expect that Mankiw has spent some time talking with the faculty at Harvard’s world-class Department of Heath Care Policy. I don’t know if any of their professors are Eagle Scouts, but they do have this guy, who was the founding editor of the Journal of Health Economics, a member of the editorial board of the New England Journal of Medicine, vice chair of the Medicare Payment Advisory Commission, etc etc. Also on the board of directors of Aetna so it looks like he has experience on both sides. Perhaps Newhouse or one of his colleagues has done a more detailed study that support’s Book’s conclusions.

P.S. Krugman links to an article by political scientist Jacob Hacker that questions Book’s numbers. I doubt Mankiw reads my blog very often, but I expect he’ll respond to Krugman, so perhaps he’ll supply some more data to rebut this. Could be interesting.

P.P.S. Book responds on Krugman’s blog, explaining why in his opinion the Hacker report does not shoot down Book’s numbers. I’m still skeptical of his claim that, “The appropriate measure is administrative cost per person.” Perhaps he can address this.

P.P.P.S. Book does address the cost-per-person issue in a comment below. At this point, I’ll just have to say that the answer depends on specifics of billing, administrative costs, etc. I don’t think I have anything further to add. But I still think it will be a great teaching example.