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Fun With Power Laws

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Interesting article by Malcolm Gladwell in the latest New Yorker. This week, the Great Popularizer picked distribution models -- basically, the trend lines made by graphed data -- as the lucky subject to be translated into Gladwellese (a rare but increasingly popular dialect consisting of engaging anecdotes tangentially related to an interesting, superficially counterintuitive theory of behavior).

The focus here is on the difference and differing implications between bell curve and hockey stick distributions. The former is the shape you're most familiar with -- a smooth slope upwards that gracefully arcs into a gradual descent, with the majority of the relevant data points falling in the middle. A hockey stick distribution, by contrast, sees all the action on one end. The majority of points cling to the X (horizontal) axis, but a set along the tail spikes upward. This, he argues, is how the homeless problem actually looks, with most of the afflicted affected for mere days (the vast group sticking to the X axis, if you make the Y axis time spent on the street), while a small subset are chronic cases that cost cities remarkable amounts of money and resources. From past work on the subject, I can attest that poverty functions much the same way. And, most relevant for our purposes, so does health spending.

We tend to think in terms of bell curves, and when solving societal problems, we tend to solve them in ways that make sense when applied to a bell curve model. But many problems actually follow the hockey stick model, with the vast majority of folks not needing serious help but a couple chronic cases requiring massive intervention. The dissonance results in policies addressing the 80 percent who would be fine without the aid, but not doing nearly enough for the problem children on the tail. Welcome to the health policy debate.

Health spending follows the 80/20 rule: 80 percent of the resources go to 20 percent of the population. That 20 percent is the hockey stick. They're the chronically ill, the terminally ill, the folks falling from trees and crashing their cars. And they chew up the health care budget with MRIs, chemotherapy, complicated operations, pharmaceutical cocktails, and all the rest. If you're wondering where our $2.7 trillion a year goes, look there, not at your annual physical.

The problem is, no one knows what to do about that 20 percent. Denying them treatment is out of the question, and rationing, on any level, is apparently taboo. There's no system to evaluate and rule or suggest against end-of-life treatments, and no insurer I know of even incentivizes towards a living will. Our dysfunctional relationship to death aside, though, the bulk of this spending is beneficial, exactly the sort of complex, needy cases we expect our health system to treat.

But since we're unable to flatten outlays on the sick and expensive, we naturally return to the bell curve model, trying to change the behaviors of the 80 percent spending barely anything. That, for instance, is what HSA's attempt to do. All HSA's, by law, come with catastrophic insurance -- the insurance that the 20 percent routinely defaults into. No behaviors are changed at that level. Without rationing, no behaviors can be changed at that level. So policy makers are instead left to muck around with yearly check-ups and how long you wait to decide if your cough really requires antibiotics.

But attacking the middle of a bell curve when you're really dealing with a hockey stick distribution is like boxing a ghost -- you can punch all you want, but you're not hitting anything. There's just not a lot of money to be saved there. And for that reason, HSAs aren't going to fix our health care system, particularly not its rocketing costs. They address the portion of the population that's basically blameless for the bill. Now, granted, it's easier to ring a bell than make a slapshot, and I understand why this weakened administration is going for the simpler target. But the bottom line is, when it comes to health care, we're playing hockey, and becoming an expert bell ringer does you little good out on the ice. Policy makers who do want to suit up, though, and are willing to take some knocks, could do worse than to start with Henry Aaron and his new book Can We Say No?


3 Comments

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Excellent post Ezra. Excellent.

 "Can We Say No" seems interesting and provocative. I can't really imagine reading it in addition to my current coursework load within the next year, though. If you were to post a summary of the argument and a cursory look at the evidence presented, I and probably others would be grateful. The Amazon page doesn't exactly radiate information.

mike

Interesting, I thought the Gladwell article was good, too, but I have no idea why he or anyone else would think that certain problems, such as police brutality or, say, medical malpractice, would follow a bell curve.  He correctly points out that they don't--but, I would argue that they intuitively do not.  I'd have guessed a power-law-type distribution for police brutality, and i'm sure most others would, too.  His homelessness example is probably better.  His smog one is, too, but ignores global warming. 

 However, Ezra, your point on HSAs dealing with a "bell curve" problem when a "hockey stick" approach is warranted is a VERY good one.  good job. 

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