Friday, June 19, 2009

Perverted Insurance

Now that we've gone through a rigourous treatment of how insurance works, let's look at how "health care coverage" works, and how this is different from insurance, even though the terms are sometimes used interchangeably.

Many people expect that for a monthly or annual fee, some organization will pay all of their medical bills for them, much as a traditional insurance plan would in the event of a catastrophe. The more procedures covered, the better the plan, and typically more expensive. Organizations that provide this service are called Health Maintenance Organizations, or HMO's.

Like insurance, the costs of providing this care are spread among a large population. Unlike insurance, the actual cost of doing this is much easier to calculate, because there is very little risk or uncertainty involved.

Why is that? Well, most people typically will visit the doctor or hospital, and most over a lifetime will incur significant medical expenses. The total cost to the HMO of paying for all of these people is simply calculated as follows:

Number of members * average cost of medical bills + overhead = total cost

Of course, overhead is significant and will likely include some profit for the HMO. The total price per person for these services is the total cost divided by the number of people. Obviously there is some variation in price based on coverage, prior conditions, etc.

Let's look at the total cost of paying for medical service directly:

Number of patients * average cost of medical bills = total cost

This total cost is the same total cost as before minus the overhead from the HMO. Simply by existing and having customers, the HMO is increasing the cost of medical care to society overall by having overhead. They are the quintessential middle-man.

In fairness, the HMO is going to have some value for those interested in mitigating the financial risk of an expensive procedure. However, any of those people who are able to afford routine care on their own will be better off purchasing insurance for catastrophes they can't afford and paying for the routine care on their own, thereby eliminating all overhead for the routine care and saving money.

Also, for the unhealthy people who use a lot of care and have high bills, the HMO may be a good deal. But for just as many people, it's a bad deal because they are sharing the cost of everyone's routine procedures. Because of overhead, there are more of those people than there are people who benefit.

In other words, due to the overhead, it is a mathematical certainty that a system with HMOs will cost more overall than a system without.

Is that difficult to believe? Let's take a moment to consider what would happen if you didn't pay for groceries directly, but instead had a grocery plan that paid for them for you. Your total grocery bill would no longer be just the price of the groceries, but also whatever your grocery plan charged for the service of paying your bill.

We don't do this, because it doesn't make any sense to have another middleman paying for your food when you're perfectly capable of doing it on your own. Such a system would increase the price of groceries for everyone.

Let's assume now that in order to purchase catastrophic health insurance, you also had to purchase this grocery plan. Seems ridiculous and wasteful, no? But that's exactly what we're doing when we pay for a health plan that covers routine care.

Economics of Insurance, Part 3

To wrap this all up, think about this gamble.

Flip a coin. If it's heads, you win $10, if it's tails, you lose $10.

You may only play once, and you must either play the game or pay someone $1 and they will play the game for you, taking your winnings and eating your losses.

Mathematically, your expected return is better if you play. You have a 50% chance of gaining $10, and a 50% chance of losing $10. It's break-even.

If you opt to pay the dollar, overall you have a 50% chance of winning $9, and a 50% chance of losing $11. Now it's no longer break-even; you're at a $1 disadvantage.

Only a fool would pay that dollar, right?

Let's keep the same game but scale the numbers a bit. If you win, you make $1,000,000. If you lose, you lose $1,000,000. Or, you can pay $100 to get out of playing. You are not a rich person and losing $1,000,000 would ensure you'd be poor for the rest of your life.

Now, your expected return is still break-even if you play, so what do you do?

I think in this case more people would opt-out of the game, because the potential for a life-ruining outcome is now 50% instead of none. Most people probably would not take that gamble.

Let's examine the company that takes the $100. Let's assume that a large number of people play this game. On average, the company makes $100 per game. Since the game is fair, they pay out in losses just as much as they win in winnings, so they break even there, since they are able to play the game many times. The more they play, the less risky the game is for them, and they still make a $100 profit each time.

This illustrates the value that insurance companies create. Even in a completely fair, break-even situation, the stakes might be so high that a reasonable person would like to bow out completely, and would even pay money to do so.

And that's why you would want to buy insurance.

Economics of Insurance, Part 2

Let's examine insurance even closer using statistics.

What if I want to calculate exactly what insurance is worth to me, so I can decide if I'm getting a good deal or not?

Let's take our lightning-strike example from before and apply it to a single person making the decision to buy insurance for medical costs resulting from being struck. This person is 20 years old, expects to live at least 50 more years, and has a 1 in 1000 chance of being struck by lightning each year, costing him $20000 in medical expenses.

The odds of him being struck at least once in those 50 years are very close to 5%. (He actually has a 4.76% chance of being struck once and a 0.12% chance of being struck twice. The odds of being struck three times or more are negligible.[1])

Anyway, he has a 4.76% chance of paying out $20,000 in fifty years, and a 0.12% chance of paying out $40,000. Taken together, his expected lifetime medical expenses from lightning strikes is almost exactly $1000.

This works out to an annual cost of $20.

If he can buy insurance for less than that, the odds are very much in favor of him making money. If he is a risk-averse person, he might even be willing to pay slightly more than that for the feeling of security, or if the consequences of him having to pay a $20,000 medical bill all at once would severely impact his life.

It should be noted, however, that if this man is willing to keep aside $20,000 to cover possible medical costs, buying lightning insurance for anything over $20 per year is a bad deal for him.

In real life, of course, this calculation is complicated by the fact that we don't know exactly how long we will live, we don't know exactly how likely it is that we personally will be struck by lightning, etc.

Insurance companies, however, do know all of these things, and this is one way that they make money. If our man pays the insurance company $20 a year for lightning insurance, by his calculations he is breaking even. The insurance company may know from extensive data and research that this man also has a 1% chance of getting hit by a car over those 50 years or dying of natural causes, in which case they wouldn't be paying his lighting-strike medical bills. More specifically, they won't know that for a fact about that particular man, but they'll know that on average over a large population, these things will be true, and they can still make a profit by charging what the man calculates to be a break-even price.

In effect, by being very good at statistics and by spreading out the cost over an entire population, the insurance company profits by mitigating risk. The insurance company has very little financial risk because over a large population, they can calculate extremely accurately their costs. An individual, being only one person, cannot calculate his costs with as high a certainty. In effect, we buy this certainty from them.

Let's use another example. I may be able to say with a very high degree of confidence that given 1000 New Yorkers, half of them will be Yankees fans. However, given a single person, even knowing that half of New Yorkers are Yankees fans, I have at best a 50/50 chance of guessing correctly whether that person likes the Yankees.

At this point, buying insurance may seem like a fool's deal, but that depends on how risk-averse you are. If you will spend more than your expected return for the peace of mind that if something bad happens to you you won't lose your life or your house, then insurance has value to you.

However, if you are able to afford any such expenses either through savings or other means, you have essentially no reason to buy insurance to cover those costs, because that will likely end up costing you more money than you would otherwise spend.

In short, you should only ever buy insurance to cover possible costs that are so large that you could not otherwise pay them. Otherwise, you are losing money to insurance company overhead.

Since most people don't realize this, insurance companies actually can make quite a bit of money by covering expenses that people can easily pay for out-of-pocket. The premiums will be much higher, but when people don't actually pay or even see the cost of the premium (my company has great insurance!) they never have to make this decision.

The sad part is that we could significantly reduce health care costs simply by teaching people statistics.



  1. For those of you wondering where these numbers are coming from, the Binomial Distribution accurately calculates the probability of k number of events occuring within n trials.


Thursday, June 18, 2009

Economics of Insurance

In my humble opinion, a big part of the problem with today's system of health care is what amounts to legalized insurance fraud. To understand what I mean, we must first examine why insurance exists and do a bit of math.

Simply by being alive we encounter some level of risk to our lives, health, and financial condition. Some people are happy to accept high levels of risk, while others want to mitigate that risk as much as possible, and are willing to pay money to do so.

Consider buying a car; you might think that it's worthwhile to pay a bit extra for some safety features, or purchase a newer car with more advanced airbag system than a lower-priced used car without those safety features. Those safety features are there to mitigate the risk of injury or death in the event of a collision, and are worth money to some people.

Nobody buys a car with the intention of crashing it (well, almost nobody). Most people would consider the risk of getting into a serious collision to be rather small, or they wouldn't drive at all. Still, we consider it worthwhile to pay for safety features just in case we are unlucky. Therefore, risk mitigation has a definite financial value.

In other words, nobody ever thinks "That was really stupid of me to pay for the side-impact airbag since I never had an accident in that car," or "I was so wrong to wear a life-preserver on my boat, I never fell off once."

Likewise, buying insurance is a way to mitigate the risk of an unlikely catastrophe. Insurance does this by spreading the cost of an unlikely event among a group of people, with the assumption that a small minority of them will need the money.

Here's where the math comes in. Assume I have 1000 people who find the costs of being struck by lightning unacceptable, and would like to share the burden of that risk among themselves. Also assume that these people's chances of getting struck by lightning is equal at 1 in 1000, so that in a given year, one of those people is probably going to get struck by lightning. Finally, assume that the medical costs associated with recovering from a lightning strike are $20,000.

To cover these people annually would cost $20,000 divided among 1000 people, or $20 a person. However, someone is going to have to collect the payments and spend the time handling the claims and doing research into the probability of a lightning strike, so there is overhead involved. Assuming these 1000 people designate a single person to handle their lightning insurance and agree to pay him $1 each for his trouble, and to cover the cost of mailing them a bill. Total cost per year in that case is $21,000 divided evenly, or $21 per person.

These 1000 people find this cost acceptable because even if they were to live 100 years, the total they would pay for this insurance is $2100. If they do not enter into the insurance agreement, it's possible they will end up responsible for a $20,000 bill they may be unable to pay, so they're willing to pay $21 a year to eliminate that risk.

And that's how insurance works, in a nutshell. Now, let's change the scenario a bit, and assume that a few of those 1000 people have jobs installing flag poles and antennas on rooftops, and are fifty times as likely to get struck by lightning as the others. The man handling the insurance realizes this and calculates that the overall cost of annual payment will be higher.

How much higher? Well, with a 1/1000 probability summed over 1000 people, the annual probability of a lightning strike is 1, with a cost of $20,000. [1] When there are five people with a 50/1000 chance of a strike, and 995 with a 1/1000 chance, the probability of one strike is still nearly certain, with the probability of two strikes increased. The average annual payout is as follows:


1 50
( ---- * 995 + ---- * 5 ) * $20,000 = $24,900
1000 1000


The increased probability of a lighting strike will, on average, cost the group $4900 a year. This money has to come from somewhere. The group gets together and decides that it's only fair for the people who are at increased risk for lightning strikes to foot the bill, so these five people will now pay $981.

The other option would be for these at risk people to form their own insurance group, however, since they aren't sharing the risks among as many people, their rates would be even higher.

"But wait!" you say. "This means that the larger the group, the lower the premium for everyone!" Although this can be true on a small scale, on a large scale the difference is minor or non-existent as long as the risk is the same. Consider another 1000 people with the same probability of getting struck enters into the agreement; the annual cost would double, but the incidents of lightning strike would double similarly.

We also are neglecting that in the real world, calculation of risk is an inexact science. Realize that the incentive for the flagpole installers is to downplay the risk of their own lightning strike, such that the insurance man cannot accurately calculate how much his annual payout will be. He will likely come up short, and the result will be a larger premium for everyone next year to cover the cost.

Also, in a very small group, the odds of a flagpole installer being in the group at all become much lower. Let's assume that a lot of people are not fully disclosing their flag installing tendencies, driving up costs for everyone. A group of 800 people may split off and decide that they will not just raise premiums for the flagpole installers, but will exclude them entirely from the group, keeping costs low and providing nearly the same risk mitigation.

Now that that's out of the way, let's examine what would happen if the risks assumed by the insurance group increased for the entire original group. Let's say that the climate changes and there are twice as many thunderstorms as before, so everyone is twice as likely to be struck. Obviously, costs would double, and premiums would now be $40 each plus overhead. The cost of handling twice as many claims may be more, but probably not double, so let's say the total premium would be $41.50 each, or there will not be enough money to pay the medical costs for everyone.

So, as the risk of paying expenses goes up, so do the costs, and it's a nearly linear relationship. What happens if the lightning gets so bad that everyone is almost guaranteed to be struck once during a year? The insurance man now is handling claims as a full-time job, so the overhead would be at least $30,000. The annual cost to provide this would now be:

1000 people * $20,000 + overhead = $20,030,000

Divided among 1000 people, the annual premium is $20,030.

What we've shown is that as the probability of the "risky" event approaches certainty, the cost of providing insurance becomes greater than if each person paid for their own expenses directly. There is essentially no reason to have insurance for an event that is certain to happen, and it is in fact an extremely inefficient way to pay for things.

In fact, as the probability of the costly event becomes more certain, the smart financial move is to NOT buy insurance. If I have a $20,000 premium and the cost of the medical care is $20,000, I am better off without insurance because on the off-chance I don't get struck by lightning, I've paid nothing and am $20,000 richer.

The overhead in the above example was kept small to make the math easy, but consider what the actual cost of providing insurance to 1000 people each year would be, and you'd see it would be much greater than $30,000. You'd average 2-3 claims a day, would have to verify and support each of those claims, detect fraud, do extensive paperwork and keep accurate records, etc. That's probably more work than one person could do alone.

How does this affect our current health care situation? As it exists right now, many insurance companies are required by law to pay for things that aren't risky at all, in fact a large part of them are routine. This is an abuse of the purpose and notion of insurance, and it guarantees increased costs, because there is little risk of not experiencing routine medical costs like annual checkups.

When insurance is required to act as an intermediary between a doctor and a patient instead of managing risk, higher costs and higher prices overall result.

The conclusion is: it is mathematical fact that in order for insurance to provide value, the services it covers have to be unlikely among a given population.

The irony is that people with "good health insurance" are probably very happy that their plan covers "almost everything," when in reality, they are indirectly paying through the nose for something that would be cheaper if they paid for it directly. And when people willingly pay for insurance plans that include coverage for routine care, insurance companies have little incentive not to provide these services.

In fact, if I were an unscrupulous insurer and the government tried to force insurance companies to cover certain routine procedures, I may be quite happy that they just gave me a license to make a profit on something that's not in my customers' best interest to buy. The only drawback for me would be that some of my customers would no longer be able to afford the premiums and would drop coverage entirely. Notice that neither case benefits the customer.



  1. The probabilities discussed here are simplified and would only be true averaged over a long time. If the probability of getting struck by lightning is 1/1000, the chance of a single lightning strike in a year among 1000 people is closer to 37%. The chance of no strike at all is also about 37%. However, the probability of two strikes is about 18%, three about 6%, and so forth. Taken together, over many years, you'd average about 1 strike per year.


Ethics and Freedom

The basic premise of "Universal" health care is that someone else, namely the federal government, should be responsible for paying the medical bills of the entire nation. Some go further and want to see the federal government provide the medical service much as it already provides a military. Either way, the premise is the same: health care is a "basic right," and should be provided to citizens by the government with little to no restriction.

Of course in our society as in just about every other, "the government" is funded via taxes, which means that universal health care effectively mandates that an individual's health care is not just his own responsibility, but mine, yours, and all citizens.

In a free-market system, each individual is financially responsible for his own care. Obviously there is a problem with this simple, effective idea, or nobody would be trying to change the system. The problem is that most people are unwilling, or unable, to pay for the entire cost of their medical service.

Of course, we see a lot of these struggling people on the news who don't qualify for Medicaid but are still too poor to afford health insurance or pay their own bills. Or there's the woman battling a life-long illness and the money's finally run out. Anecdotal evidence abounds.

We'd have to have a heart of stone wish this situation on these people, so we think something should be done. Heck, shouldn't the government pay for it?

Let's examine our current situation. Instead of involving the government, wouldn't it be far more efficient if a group of people were to give this desperate person money directly? Why doesn't that happen consistently? Why aren't people knocking on my door asking for money to pay their health care bills? I have some neighbors and friends who I'm sure I could help, if they only asked. Why aren't they asking?

The answer is partly that for a person to directly ask for financial assistance is considered an imposition, rude, or impolite, and partly because the expected return on such activity (begging) is low. Also, going door-to-door to ask for money would be impractical, especially for a busy, sick person.

To that end we have charities, which exist to connect the people in need with the people who are willing to help them. Consider St. Jude Children's Hospital, certainly a worthy charity. St. Jude is a case that works largely through voluntary private funding.

Most, if not all, people would commend St. Jude as an admirable and worthwhile enterprise. What would happen, however, if St. Jude hired a particularly annoying telemarketing firm to collect donations? Probably there would be less good will toward St. Jude and such a move would hurt their reputation.

What if St. Jude hired a bunch of gangs who would intimidate people into giving donations? What if these gangs gave people a year to donate voluntarily, then kidnapped people who refused and held them in prisons? What if the gangs were paid handsomely by St. Jude to do this work?

Odds are quite a few people would have a problem with St. Jude at that point, because to accomplish a worthwhile goal, they would be using violent methods of coercion.

The government, in this case, is directly analogous to the gangs hypothetically hired by St. Jude's hospital. Just like the gangs, government power comes from the threat of violence and imprisonment. If you don't believe that, try voluntarily not paying your taxes and see what happens.

The ethical question comes down to this: if you are not willing to personally threaten someone with violence so that they pay for your medical bills, why is it acceptable for an intermediary to do it for you?

Is it because a majority of people think it's ok? If yes, then is it ethical for a majority of people to vote to legally censor, imprison, or persecute a minority? Until you can logically answer these questions, the basic premise that one person is responsible for another person's health care, and should be held to that responsibility through use of government force (taxes backed by threat of violence), is inconsistent.

As a hint, if you still would like to argue for universal health care, "the ends justify the means," and "ethics are completely relative and defined by the strongest party (might makes right)" are your two options for a logically consistent basis for your argument.

Personally, I'm willing to accept that in some extreme cases the ends do justify the means. An example is killing in self-defense, which I find perfectly reasonable, and is an adequate reason for the feds to fund a military. Also public-works and infrastructure projects seem reasonable to me. The U.S. Constitution specifically allows for road-building to support a postal service, and although I wouldn't threaten to kill someone for not paying for a road, it's reasonable to assume that roads are popular enough (even historically) that I wouldn't have to.

Reasonable people recognize that transportation would be nearly impossible, or certainly very difficult and costly, if the government were not involved. A single small entity could block building of an interstate highway by asserting property rights. I don't think there's a clear ethical answer here; only the very hard-core libertarians would argue the validity of eminent domain in all cases.

That medical care falls under the same category as national defense and highway building, however, is quite a stretch. We'll examine why later.

Be that as it may, if you think that the ends justify the means and that is your ethical basis for universal health care, continue to the next part of this argument, which examines the inevitable result of socialized medicine. At that point you can decide what means are appropriate to achieve that end.

"Universal Health Care" -- why not?

The words "Universal Health Care" are all over the news, mostly because a large proportion of the baby-boom generation, realizing that they will quickly be overcome by expensive medical bills they haven't prepared for, are now pushing a socialist health care system to once again stick the younger American generations with the bill for their irresponsibility. Among my naive generation are willing accomplices who the boomers have sold on this idea.

It's time for people to wake up to this scam. These people are voting to siphon money from future generations for benefits that won't exist by the time the young people need them. This will bankrupt our country even faster than Medicare, Social Security, and countless other social programs are already doing. It's a pyramid scheme, and the fact that it's sanctioned by the Federal Government does not make it less of one. Look at UAW and General Motors for a private-sector example.

The following simple, but extensive, thought experiment is offered to counter this idea. I am going to disagree with the idea that we need "Universal Health Care" on two counts. The first is a disagreement with the premise of the entire system, which is that one person should be forcibly held responsible for another's health care. The second is that a truly "Universal" health-care system is an economically inefficient way to handle people's health care needs.

Health Care

My wife is taking a persuasive writing class and is arguing against "Universal Health Care." The professor is giving her a difficult time, and the illogical arguments for "Universal Health Care" have got my hackles up.

The following entries will be an extensive treatise on why "Universal Health Care" in the United States would not be pretty. Enjoy.

Grand intentions

Today, my intentions are to write about things I find interesting or funny here because I enjoy reading things I've written in the past.

Also, my mother is constantly asking for my slightly-more informed opinion on political matters, and it will be easier to refer her to my blog than to actually explain things off-the-cuff. Besides, I'm in the generation that does things like that.

What is much more likely is that I'll post a few times before forgetting this blog exists.