Obamacare vs. Arithmetic

Back in 2008, I wrote one of my first pieces for PJM: “Today’s Health Insurance Ain’t Insurance.”  I just re-read it and it stands up pretty well: today’s health insurance still ain’t. Have a look at it, as it has some more detailed explanations for the points I’m going to make in this article, but the point is this: there’s basic mathematics behind all real insurance, and while actuarial math can get pretty hairy, we don’t need it to see the underlying and essential flaw of the whole approach taken by the Affordable Care Act.


At the heart of it, insurance is a bet. You are making a bet with someone else that some bad thing will happen to you, while they’re making a bet that it won’t. If you buy the simplest and cleanest kinds of insurance, like term life, you are betting that you are going to die during the term of the insurance, and the insurance company is betting you won’t. (“Whole life” and “universal life” policies are more complicated things that mathematically act like combining a term life policy with an annuity. This is where the math can get hairy, but you pretty much find out what you need to know when you realize an insurance company would far rather sell you one of these policies than term life and a separate annuity.)

All insurance is based on a really simple equation called expectation value, or more commonly risk. In life insurance, you start by deciding how much money your survivors need if you were to fall over tomorrow. Let’s say it’s $100,000. (Your spouse can get a job.) So the amount at risk for the insurance company is $100,000. That’s called the hazard, H. They look at your your age, your sex, your health, and possibly your profession or hobbies (base jumping? Race car driving?) and come up with a probability that you will die during the term of the insurance. That’s a number P where 0 ≤ P ≤ 1. Then they compute the expectation value R of that $100,000 as

R = P × H

The way to interpret that is: if you sell enough insurance policies to people with the same characteristics, the insurance company can expect to pay out about R dollars for every $100,000 worth of policies sold. I just went online, and as a 58-year-old man with diabetes, the best rate I found was $495 a year. That would actually be a little more than the actual risk; insurance companies need to have some room for runs of bad luck, and they need to have some margin over that to pay for all those people running the insurance company and some profits for the stockholders. (Which, contrary to what you hear from the usual suspects, isn’t very large — Aetna, for example has profits between 2 and 6 percent.) So the real premium for a term life insurance policy is a little more than just the expectation value. How much depends on a whole bunch of things, so let’s just say x. Your total premium is going to be R+x and we know x > 0.


When we look at what we call health insurance now, though, that all breaks down, because many of the things that are covered happen — colds and flu, childhood illnesses, and so on — with probability near 1.

Guess what? If P is about 1, that premium is going to be the total cost plus x. Always. No matter what.

We got away with the current scheme for as long as we did because, dating back to Harry Truman’s administration, we let companies buy their group health insurance using pre-tax dollars. In other words, they got a pretty substantial discount for buying health care for their employees instead of paying them more.

Now, when you give people an incentive like that, they’re going to do more of it; what used to be “major medical” starts adding regular doctor visits and such. At the same time, the insurance companies want to control their costs, so they started adding more administration to the whole thing. That increases x but it doesn’t change the relationship.

What does change the relationship is that we start to run into something Milton Friedman called “Gammon’s Law,”  which originated with a study of Britain’s National Health Service done by Dr. Max Gammon. Friedman called it the Theory of Bureaucratic Displacement:

In a bureaucratic system, increases in expenditure are paralleled by a corresponding decrease in production.

Translated from the economist-ese, that means in a bureaucratic system, the more you spend on something, the less you get of it.

Gammon’s original work in which he identified this found the correlation was very nearly perfect: as the number of pounds spent on the National Health System increased, the number of hospital beds declined. The correlation was -0.99.

Aside: for those of you who don’t eat and breathe statistics. Imagine you have a loaf of sliced bread. You weigh the bread, then take out a slice, then weigh it again; keep taking out slices of bread and re-weighing.

The correlation between the number of slices taken out, and the weight of the remaining bread, will be around -0.99.


Why does this happen? There are at least a couple of reasons. As more money goes into the bureaucracy, there’s more pressure to make sure it’s being spent well, which means more forms, more auditors, more independent review boards. All of that takes time and money, and that time and money are being taken away from what used to be the goal.

The second reason is that as administration develops, it becomes its own constituency. Administrators are more important that the people doing the work — they must be, right? I mean, they’re the managers. Administrators get paid more, and in a bureaucracy, administration is the route to higher pay, better offices, and more perks. What’s more, the people doing the work have to do more work to support the administrators. Doctors are seeing that now — new record-keeping requirements, from HIPAA to electronic record systems.

The upshot, though, is that once a system becomes bureaucratic, adding money makes it worse.

And that’s the arithmetic of Obamacare. You start off with something that makes some sense — it’s perfectly reasonable to want insurance against the chance you’ll be hurt in a car accident or develop cancer. Then, because of weird tax incentives, you start doing something that makes less sense: asking insurance companies to pay for things instead of giving you the money to pay for them yourself. Then we start mandating coverage too — so I have to pay for maternity and OB/GYN coverage, even though I’m a 58-year-old single man with no obvious prospect of impending pregnancy.

This is the way I put it back in 2008:

Here’s where things start to get tricky, though. Some people — young people just out of school for example — aren’t making a lot of money, but then don’t really want to spend a lot of money on insurance. Normally, they wouldn’t have to: other than accidents and very rare diseases, a 25-year-old shouldn’t normally need anything more than minor maintenance and occasional hangover cures. The idea of the mandate, though, is that if you include these low-risk people in the whole insurance pool, the premiums they pay can be added back to the pot for older people and people with serious illnesses, which makes the insurance more “affordable” — for them.

It’s exactly the same situation as if we charge a 25-year-old the same amount for a year’s term life insurance as we charge his 75-year-old grandfather: it may make the insurance more affordable for Granddad, but it does so by overcharging young Elmo. Add in the “mandate,” so Elmo can’t opt out, and we have a universal care plan that forces Elmo to pay for services he doesn’t get so that Granddad can pay less for the services he gets. But it’s “voluntary” — you get to pick your insurance plan to some extent — and it’s not “tax-supported” because you are just paying the insurance company directly.

Except for the cost of administering the plan itself, and the wages they take through a garnishee if I don’t “volunteer.”

So in this mandated universal coverage plan, the government comes and makes me give someone money so it can be distributed to other people, and I don’t have any choice about participating. Where I come from, we call that a “tax.”


Since this seems to have been my month for I-told-you-so’s, I’ll point out that (with the exception of the garnishee) this is exactly how the Supreme Court sorted it out too.

So, the current plaintive cry from the Left is “what have you got to replace it with?” I’ve got to admit that my instant reaction to that is “if you’re doing something stupid, then replacing it with not being stupid isn’t a bad thing.” But we can actually make some sense of the question if we instead ask “what can we do with health care where the arithmetic makes sense?”

Here are some ideas:

  1. Let everyone buy health care with pre-tax dollars.Right now, if you have a corporation buying your health “insurance,” they can call it an expense; it comes out of the pocket before it’s taxed. If you’re buying it as an individual, though, you buy the insurance with after-tax dollars, which means that you’re automatically paying more. Often much more.The “flexible spending account” was one solution to that — you could at least put away enough money to cover your deductibles and any expenses you expected with pre-tax dollars. It wasn’t a great deal, because you had to guess right — anything that was left at the end of the year went back to the government.So, instead, let’s do this: You can put whatever you want into a flexible spending account, which can only be spent on healthcare items, just like an FSA now. Oh, we’d let you spend it on over-the-counter drugs too, something they took away from FSAs a few years ago.If you haven’t spent it all at the end of the year, it stays in your account. You can adjust your contribution if you need to. You keep the FSA in any bank you like — and if you don’t like the bank’s policies, you can move your account any time. Yes, the account pays interest, and that’s not taxable either. (Idea: this is also a retirement account; you can start withdrawing cash at age 65 and your heirs get the leftovers if you die.)
  2. Let everyone buy whatever insurance they want, with one exception (that’ll be point 3.) Open market, and you pay for it with your FSA from point 1.
  3. Establish a minimum acceptable standard for a basic major medical plan. No daily health care, no mandated chiropractic. Everyone has to have this. Yes, a mandate. The differences: first, you pick the plan you like. If you want fancier insurance, it costs more, but everyone has to have at least the basic plan. If you don’t make enough money to afford it, okay, you get a subsidy. You still pick the plan you like on an open market.

So now, what does this scheme do? First of all, it restores something like competition, and removes insurance companies from the day to day payments to medical providers. You pay them out of your FSA using a debit card. If you want to see a “concierge doc,” you can, and you pay them effectively in cash. If you don’t use up all the money this year, you can cut your contribution next year — that’s more cash in your pocket and an incentive not to spend more than you have to. There’s no insurance company doing the paperwork, just a bank making sure you’re charging an authorized item.

If the insurance companies want to stay in the loop, then they have to provide some useful service — helping you find better docs, or negotiated discounts, or something. As it stands right now, they have almost no incentive whatsoever to try to provide better service.

Second, it means freelancers and small businesses are now on a level playing field with big companies. Everyone is using pre-tax dollars, and if a union or whatever wants to negotiate a subsidy to be added to your pretax account, then it can. Maybe there’s a limit on the amount, maybe not.

Whatever solution we look for though, the really important point is this: the whole basis of Obamacare, the notion that we can have more people, getting more benefits, and pay less, is just impossible. The arithmetic doesn’t work. And if you think that’s “unfair,” I’m sorry.

But arithmetic isn’t sorry. Arithmetic doesn’t listen. Arithmetic doesn’t care.



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