Wednesday, January 25, 2012

Insurance and Pooling Equilibria

In the bad old days, insurance was a way to smooth cash flows from improbable but large expenses: fire, health, auto mishaps. Through repetitious metonymy, 'health care insurance' and health care are now synonymous.

I was struck by Obama's mention last night that:
I will not go back to the days when health insurance companies had unchecked power to cancel your policy, deny your coverage, or charge women differently than men.

Emprically, women use more health care, they cost more, estimates are around 35%. Some of this is childbearing, but a lot of it comes from the simple fact they go to the doctor more often (notice women see their gynecologists rather regularly, whereas men have no comparable service). So now charging women more for something they use more of is illegal because it discriminates.

Interestingly, in the 1970's there was a law passed so that upon retirement, the annual payments to female retirees had to be the same as for male retirees even though women live longer, statistically. That is, the present value of their retirement packages, by law, are larger for women than men.

Government seems to be doing more and more to make it difficult to prevent 'pooling equilibria', cases where different types of applicants get into a pool, eventually pushing out the 'better' or 'lower cost' people who don't want to subsidize the other group. For example, due to legal rulings, it is now very difficult to give job applicants explicit aptitude tests, even though this would be very useful, and avoid the charade from those Microsoft/Google IQ tests given verbally. Interestingly, Nobel Laureate and prominent Big Government advocate Joe Stiglitz's most famous paper relates to an inefficiency from a pooling equilibrium, and his take-away was that markets were inefficient because of this problem. In practice, government encourages pooling equilibrium where it was never a problem before by preventing rational discrimination based on projected costs/benefits based on observable characteristics.

While the equilibrium efficiency loss in Stiglitz-Weiss is abstract, it usually creates something pretty simple, as if you can imagine what would happen to insurance if it could not price based on risk and allowed people to opt out: healthy people would leave in droves, which is why Obama-care made insurance mandatory. Think about the lawsuits on disparate impact for mortgage lending in the 1990s, where whites were rejected less often than blacks, and this was presumed discriminatory (in an evil way), and so the only way to make unequal groups equal is to stop making distinctions that differentiate them, which led to simply the idea that down payments and having a job were unnecessary underwriting criteria.

It's rather funny that Stiglitz's main theoretical contribution to the academic literature is so starkly in contrast to not just his politics but his obsession, which is increasing the size and scope of government which prioritizes preventing firms from rationally discriminating. Remember that in Stiglitz's model, like everything else in this literature (he didn't invent it), failure to discriminate types somewhat known by participants is what causes all the problems, the 'bad equilibria.' I guess that highlights no one takes these models very seriously--change one assumption here or there, different result.


Mercury said...

I’m sure Stiglitz thinks his academic research supports his politics and isn’t contradictory at all. You only have to price risk if you’re running an (insurance) business. When you replace that with an entitlement it’s all about redistribution. Problem solved.

People like him actually know better than most that different people bring different abilities, risks and human attributes to the table and are therefore more advantaged/disadvantaged in particular areas of life because of them. And who would know best where to plug the holes, oil the joints and adjust the scales to fix these problems…than experts like Stiglitz?

The role of government of course is to make everyone as equal as possible, at least in those respects that are most glaring and politically sensitive. Equality for everyone except the noble, central planners who make life better for us all (no health insurance mandate for them!) that is.

The world of Harrison Bergeron is nigh upon us:

A perspiring aspiring academic said...

Well, pooling is the result of more fundamental problems--pooling itself need not be a problem.

The inefficiency stems from 1)Bank can't discern good from bad borrowers, AND 2) The good borrowers will take NPV<0 projects if the interest rate is too high (due to risk shifting). (1) by itself could lead to an ok pooling eqm (though of course the bad guys force the good to pay more), but (2) drives the inefficient rationing. The relevant question is then: what is the analog for (2) in the insurance market?

Government-induced pooling should only be a problem if it causes the 'good' guys to behave differently. It's possible that the pooled price of insurance is more than the good guys are willing to pay, in which case a pooling eqm must be mandated. A mandate would transfer welfare from the good to the bad types, but it is not clear to me that there is a direct analog to Stiglitz's inefficient credit rationing.

Bottom line: gov't induced pooling certainly benefits some at the expense of others, but it is not clear that it destroys overall efficiency like in Stiglitz's model.

A perspiring aspiring academic said...

As a follow up, an example in the spirit of Stiglitz-Weiss would be if the healthy types no longer had an incentive to stay healthy. Since I get the same coverage whether my diet consists of mostly vegetables or mostly twinkies, then the pooled eqm leads to inefficiently fat twinkie eaters that are expensive to cover. This eqm destroys social welfare, but we needed something in addition to the pooling.

Eric Falkenstein said...


A simple inefficiency is because if you charge women and men the same for services that cost women more, Women will use 'too much', men too little. Further, in general the mechanism is much more convoluted such as in mortgage lending, where the best way to meet minority loan targets was to lower criteria across the board, which didn't seem like a problem until 2007

mike said...

I think you have to distinguish efficiency and fairness. You also have to think about how fairness relates to long term efficiency.

If blacks are more likely to default on mortgages than whites. And being black is a sufficient statistic for predicting defaults, then it would be efficient to discriminate based on race. But, would it be fair to do so? And suppose there is a policy of discriminating based on race. What would be the long term costs of this to society?

And then you have the problem that perhaps race is not a sufficient statistic for defaults but used instead to implement racist policies. This is actually what Griggs v. Duke Power Co.was all about. You should read the details . it runs counter to your argument

Eric Falkenstein said...

Griggs put the burden of proof on the employer, basically making it impossible for jobs not involving plutonium, which is why the government doesn't give aptitude tests anymore. Most discrimination allegations are based on disparate impact, so again, the firm is required to prove there is rational story for disparate impact, which is practically impossible in most cases. So firms satisfice with quotas and remove qualifications, for all sorts of applications (lending, hiring, insuring).

As per efficiency vs. fairness, i think it's fair to pay more for something that costs the provider more, etc. it's a fact that the productivity/costs of various demographics is different, often for very benign reasons (eg, women live longer than men), so to force people to ignore this is unfair and inefficient.

Dave Pinsen said...


The government still gives aptitude tests to military recruits.

Patrick R. Sullivan said...

'If blacks are more likely to default on mortgages than whites.'

Which they aren't if income and credit history are controlled for. Which is what the infamous Munnell/Boston Fed paper neglected.

For want of a nail....

freebee34 said...

I work in health insurance consulting and have access to large amounts of transaction level data. It is true that women cost about 35% more than men but it is not true unconditionally. While women do consume more services they get less injuries than men and have fewer large health claims (i.e. heart attack). 40 year old women are the largest consumers (more than 2.5 times the average) and this is mostly due to extremely expensive menopause and cancer treatments that do not occur to men. 30 and under year old males claim at very low rates but conditional upon a claim have costs similar to the average. women and men after the age of 60 consume at exactly the same rate.

zby said...

I've read somewhere that in Europe (not just in one country but across the board) the health costs are a multiple times lower then in the USA and of better quality despite being mostly state funded.

Eric Falkenstein said...

zby: That's correct. Our system is so highly regulated, it's not obviously better than a state-monopoly. But there's more upside to creating a better private sector, and also our demographics are a lot different than Sweden and France.

Leo said...


You might want to have a look at the Swiss health care model.

Then we'd love to know something concrete about your "better private sector".

And lastly, what do your efficient models say about the millions of uninsured kids in the USA?

Dave Pinsen said...


One difference between Switzerland and the US is that we have mass immigration of unskilled, uneducated workers. These immigrants are often illegal and work off-the-books at jobs which don't provide health insurance (they and their children do, nevertheless, receive health care, as indigents are not denied emergency treatment in the US). This demographic group skews US stats on health insurance, education, etc.

Dave Pinsen said...

"zby: That's correct. Our system is so highly regulated, it's not obviously better than a state-monopoly."


There's been some research suggesting that survival rates for cancer patients, for example, are higher in the US than in Europe.

Another point to consider is the extent to which Europe and other first world regions free-ride on medical R&D financed by high spending in the US.

eh said...

I've read somewhere that in Europe (not just in one country but across the board) the health costs are a multiple times lower then in the USA and of better quality despite being mostly state funded.

Can't address the total cost issue (e.g. as % of GDP, or whatever), which is what I believe you are referring to (?). But I live and work in Europe, and from an employee's perspective, health insurance costs here are clearly greater than what I experienced in the US. Here I pay a percentage of my salary every month as a premium. There is a whole system of 'regulated insurers', so this premium varies little from insurer to insurer; current average is approx 14%, which is about what I pay (there are also private insurers). Since my employer pays (only) half, I pay approx 7% of my salary for heallth insurance. In the US, with only a couple of exceptions, my employer covered the entire premium. And my cost at the exceptions was minimal -- certainly nothing like 7% of my pay.

But everyone is covered, including the unemployed and those on Sozialhilfe. Which is, I suppose, one factor in the cost. And also a good thing.

Clearly reform is needed in the US.

But I want to throw some cold water on the idea that Europe is, in general, a model of efficient, low-cost, high-quality health care. For example, there are many, many of these 'regulated insurers', which no doubt ups the administrative cost -- i.e. there is no 'single payer'. So from my point of view, the point of view of a typical employee, the cost is clearly higher here.

Quality is, from my limited experience, comparable.

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