The sad tale of Sam 1 and Sam 2 (more on health insurance)

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My previous blog commented on both health and education. Some of the comments on that blog had been addressed in my earlier posts on health insurance. See herehere and here. But the basic message still seems to be getting lost. Australia’s health insurance system penalises the ill. It is a form of anti-insurance. That is why needs to be fixed.

To show this let’s try another story.

Suppose, on Monday, that there are two individuals. They are identical in every way. Let’s call them Sam 1 and Sam 2. Both of the Sams are risk averse and both face a risk of illness that will require hospitalisation sometime in the future. So both Sams would like comprehensive health insurance that is fairly priced (i.e. priced at an actuarially fair rate).

The chance of getting ill in the future is a random event.  So let’s suppose that on Tuesday, Sam 1 is lucky and Sam 2 is unlucky. Sam 1 finds out that his chance of becoming ill in the future is relatively low. In contrast, Sam 2 finds out that his chance of becoming ill in the future is relatively high.

On Wednesday, Sam 1 and Sam 2 make their decisions on health insurance.  What will they do?

Sam 1, who has the low chance of becoming ill, will choose to rely on Medicare. It is not worth his while to buy private health insurance because he is not likely to need it. Even though he is risk averse, his optimal choice in Australia is to choose the taxpayer-funded partial health insurance called Medicare.

In contrast, Sam 2 has a high chance of becoming ill and needing hospital treatment in the future. He cannot take the risk of just relying on Medicare and so chooses private health insurance. But the price that he has to pay for private health insurance is higher than he expected for two reasons.

First, because of the overlap between the public health insurance scheme and the private health insurance scheme, his private health insurance has to cover some services that he would receive without extra payment under Medicare. As he has already paid his taxes for Medicare, he is essentially paying twice for these overlapping services.

Second, because only people like Sam 2, who have a high risk of needing hospital care, take out private health insurance, the price of that insurance has to be high to cover this ‘adverse selection’ problem.

Now before you say this is all just tough luck for Sam 2, let’s note a couple of things:

  1. Remember that the only difference between Sam 1 and Sam 2 is that Sam 2 has a higher chance of becoming ill. There is no difference in income. Indeed by any sensible welfare measure Sam 2 is worse off than Sam 1 because of his health risk. But it is Sam 2 that will buy the private health insurance – he can’t take the risk not to buy given his health status.
  2. If we went back in time to Monday, before each individual learnt of their individual health risk, both individuals would agree that the outcome on Wednesday was undesirable. They would both prefer to live in a society where full health insurance was available at a fair price. The problem is that people make their decisions about health insurance when they know their health risk. The healthy rely on Medicare. Those more likely to require hospitalization (often the elderly) buy private health insurance. Put simply, individuals act in their own self-interest and their own information about their health risk.

Australia’s current health insurance scheme systematically penalises those, like Sam 2, with high health risk. The rebate partly rectifies that inequity. In other words, on Monday, before they know their individual health risk, both Sam 1 and Sam 2 would prefer a society where there is a rebate on private health insurance. Of course, on Tuesday, Sam 1 will decide that the rebate is a bad idea and lobby the government to get rid of it. The government has just responded.

Australia’s health insurance system, which systematically penalises those most at risk of illness, is bizarre. We can design a better health insurance system. That may mean a more comprehensive Medicare scheme with the associated taxes to support it. However getting rid of the rebate is not a way to help improve health insurance for Australians.

Some final points.

  1. Please note that being in favour of the rebate is not the same as being against Medicare. It is being against a stupid distortion in our current system.
  2. Using the health insurance system as a hidden tax on the rich creates an undesirable distortion – it also makes those most likely to need hospitalisation worse off.
  3. Note that health insurance is a separate issue to health provision. The above argument says nothing about public or private hospitals. Confusing the two is like confusing car insurance with a car manufacturer.
  4. Finally, the proofs of all the above are in Gans and King “Anti-insurance: Analysing the health insurance system in Australia”, Economic Record, 79, (2003), 473-486.
23 Responses to "The sad tale of Sam 1 and Sam 2 (more on health insurance)"
  1. This ‘Rawlsian’ scenario would suggest that what Sam 1 and Sam 2 actually want ex ante is a top-quality health care system funded from a progressive taxation system. To bring the issue into sharper focus, imagine that they were in fact born on Tuesday, and the illness is severe and incurred early in life, so that Sam 2 will never be in a position to earn the income required to buy private health insurance. It is this type of issue that I think is of considerably more concern when it comes to the design of the health care system.

  2. Thanks for posting this. What I still don’t understand is why Sam 2 in your example ‘cannot take the risk of just relying on Medicare’. The obvious inference is that the health care Medicare provides is insufficient to deal with any illness, and therefore the only option is to buy PHI. But what is the additional care that PHI is providing? How is the treatment better? All other things being equal, are the survival rates for people with PHI greater than for those without for, say, breast cancer? At the moment I think people have the impression that they can’t rely on Medicare. What is the evidence that this impression is justified? 

  3. Stephen,

    I reread you’re post dated Jan 22 and this is what I think you’re saying.

    Let p: public health infrastructure, P: private health infrastructure, x: medicare levy, y: PHI.

    Patients who take out PHI pay x+y. Patients without PHI pay x.

    Let p intersect P represent infrastructure that PHI provides which overlaps with the public health infrastructure. This doesn’t include things like GP’s for example.

    Let u be p intersect P contained in p. Let v be p intersect P contained in P.

    Essentially there is a duplication in some health infrastructure.

    What you’re saying is that patients with PHI pay for p intersect P twice, once as a percentage of x which funds u, and a second time through a percentage of y which funds v, even though private patients will only ever use v.

    Ok, I get it, but your preferred ’third alternative’ in the Jan 22 post is not taking into account institutional factors, i.e people aren’t homogenous. Without price regulation what will happen over time is the poor will be priced out of quality health care. (I’m assuming price depends on quality of service, i.e. better quality is more expensive; I’m also equating quality with outcome, better quality = better health/education outcome). Your funding follows the student model suffers from the same problem.

    I don’t know your political views are so maybe you put a premium for efficiency over equality but if that isn’t the case then I agree with derrida’s comment in your last post, economists need to put the poli back into the econ (both political economy and public choice). Standard economics might be good at telling us about efficiency of outcomes but it tells us very little about the change in status quo in the distribution of income for example. You need to include institutions in the analysis. 

  4. It seems to me that your example really amounts to a case for greater public health insurance rather than reducing the ‘tax’ on private health insurance.
    If Sam 2’s high health risk is known to the insurer then he will face a higher premium – which will be more important than any insurance ‘tax’. If not known, then adverse selection (only people like Sam 2 taking out insurance) will lead to the same result. So I don’t think it makes sense to imply that private health insurance is better than public  because it provides more to people with the greatest health needs.
    The best way to ensure that those with high health needs receive greater services is take out the insurance on Monday – before the health risks are known – and to provide services based on health needs. That sounds a lot like public health provision to me.
     

  5. Stephen,
    After all this confusing discussion, I would say that your previous post http://economics.com.au/?p=8291 makes the point well that the current system is quite good.  Your main recommendation appears to be tax the rich more so that they can avoid ‘double payment’ of the overlapping portion of health insurance in the public and private systems.  So if we avoid what is really a small bit of redundant insurance cover, all will be good in the world.
    Two other assumptions you require stand out to me to fail the reality check test
    1.     1. priced at an actuarially fair rate
    2.    2.  he cannot take the risk of just relying on Medicare and so chooses private health insurance. 
    For a start, the point of public insurance is that people contribute based on their ability to pay, not their individual risk.  Second, I would agree with Stephen Wood that the pubic system is very good for serious life-threatening illness and injury.  For elective procedures, Chopper 2 can always simply pay cash, and yet still receive the drugs required for an operation as subsidised prices – now there’s a distortion.  If a lady gets her chest enhanced she still gets a subsidised for this choice. 
    The simplest way to test whether your argument holds is to replace health with some other publicly provided service for which private alternatives are available.  If the logic holds for these other services, then maybe you have a point.
    Let’s revisit the public provision of police services (where the privately insured will ultimately depend on the public system in some form anyway).
    We have two identical individuals, Chopper 1 and Chopper 2, both are risk averse and will require security services (as a crime deterrent and for investigation of crimes) in the future.  Both Choppers would like comprehensive crime insurance (policing) that is fairly priced (i.e. priced at an actuarially fair rate). 
    The chance of requiring police services in the future is a random event.  So let’s suppose that on Tuesday, Chopper 1 is lucky and Chopper 2 is unlucky. Chopper 1 finds out that his chance of being targeted by a hitman in the future is relatively low. In contrast, Chopper 2 finds out that his chance of being targeted by a hitman in the future is relatively high.
    On Wednesday, Chopper 1 and Chopper 2 make their decisions on crime insurance.  What will they do?
    Chopper 1, who has the low chance of being targeted by a hitman, will choose to rely on the State police. It is not worth his while to buy private security guards because he is not likely to need it. Even though he is risk averse, his optimal choice in Australia is to choose the taxpayer-funded partial security insurance called Police.
    In contrast, Chopper 2 has a high chance of assassination, and needing security services in the future. He cannot take the risk of just relying on the State police and so chooses to engage private security firm as a form of insurance. But the price that he has to pay for private security insurance is higher than he expected for two reasons.
    First, because of the overlap between the public police and the private security services, his private security firm has to cover some services that he would receive without extra payment from State police. As he has already paid his taxes for State police, he is essentially paying twice for these overlapping services.
    Second, because only people like Chopper 2, who have a high risk of needing security services, take out private security, the price of that security has to be high to cover this ‘adverse selection’ problem.
    Now before you say this is all just tough luck for Chopper 2, let’s note a couple of things:
    Remember that the only difference between Chopper 1 and Chopper 2 is that Chopper 2 has a higher chance of being killed. There is no difference in income. Indeed by any sensible welfare measure Chopper 2 is worse off than Chopper 1 because of his health (death) risk. But it is Chopper 2 that will buy the private security– he can’t take the risk not to buy given his security status.
    If we went back in time to Monday, before each individual learnt of their individual security risks, both individuals would agree that the outcome on Wednesday was undesirable. They would both prefer to live in a society where full security and policing insurance was available at a fair price. The problem is that people make their decisions about security insurance when they know their risk. The healthy rely on the State police. Those more likely to require security and crime deterrence (often the elderly?) buy private security insurance (home security alarms, etc). Put simply, individuals act in their own self-interest and their own information about their risk.
    Australia’s current security and crime insurance scheme systematically penalises those, like Chopper 2, with high security risk. The rebate partly rectifies that inequity. In other words, on Monday, before they know their individual security risk, both Chopper 1 and Chopper 2 would prefer a society where there is a rebate on private security costs. Of course, on Tuesday, Chopper 1 will decide that the rebate is a bad idea and lobby the government to get rid of it. The government has just responded.
    Australia’s police system, which systematically penalises those most at risk of illness, is bizarre. We can design a better police system. That may mean a more comprehensive State police scheme with the associated taxes to support it. However getting rid of the rebate is not a way to help improve security and crime prevention for Australians.

  6. “But the basic message still seems to be getting lost. Australia’s health insurance system penalises the ill. It is a form of anti-insurance. That is why needs to be fixed.”

    Sorry, the basic message is being lost. Are you trying to say that private insurance is subject to adverse selection?  Or that if private insurers know medical information the actuarial premiums are more costly for the more ill?  Isn’t that the whole reason for having a public system? Since the poor ill people cannot access medical care themselves? So you are really talking about a small group of rich, sick people, who happen to get insurance for non-urgent health care by pooling their funds with other rich people who require a lot of non-urgent health care?

    That will always be the case even with a top-up type of insurance you propose.  Only the rich ill people will tkee out such insurance.

  7. Great comments – thank you. Let me respond.

    On income and PHI – agree, that there is an issue of inequality in Australia. I think this should be addressed through the taxation system, not by distorting the health system.

    On Medicare – it seems to me that the big extra health risk associated with Medicare is waiting lists. That’s why I keep going on about the elderly. They appear to be the big losers (think hips, knees, cataracts to name a few) where without PHI they face significant waiting lists and associated pain and suffering. Of course, this may reflect that I am getting older.

    On politics – agree. I would like a rather modest change in the current system. I recognise that public health insurance will never be complete. There will be waiting lists because the government will always want to keep costs down. But we could have a broad public health insurance (paid for by more progressive taxes) with PHI as a true top up insurance. Health provision could be public and/or private. What I care about is the insurance – not who employs the medical staff who treat me. 

    An alternative would be required private health insurance (with community rating to get around the issue of higher risk individuals facing higher premiums). This would require subsidies for low income earners to buy the minimum level of cover. But given where we start, I think tinkering with the current system is better. (And as I noted before, we are starting at a pretty good system by international standards).

    Finally, on Chopper 1 and Chopper 2 – excellent analogy. And in societies where the public policing is inadequate and the risk of violence is high, this would be a big problem and I would probably advocate the same sort of reform for security as I am advocating for health insurance. However, fortunately I dont think we live in that sort of country! That said, private insurers do give people who take private security measures lower premiums. So in a sense, in Australia, the private system does offer a rebate for those who take private security measures.

  8. This is now a bit redundant as Stephen has just responded to comments but here’s my two cents anyway …

    I think that ideally, under Stephen’s and Joshua’s proposal, the community would agree on a basic standard/level of health care services that the Government would fund through the tax system (regardless of whether service delivery was in the public or private system). Then, hey it’s a free world, individuals who wished to top up on extras would take out PHI. 

    I confess that I don’t see any problem, on equity or other grounds, with this approach.  

  9. Kobs, I’m not sure how different this is to the current system, except that if you want to ‘top-up’ your private insurance you get a subsidy.

    I would like to see some research on how much overlap there really is between the systems, because I suspect the overlap works both way – that private patients do get care that would otherwise have been financed from public health, but on the flip side, that private patients do get some of their ‘top-up’ procedures partly funded from public health – e.g. pharmaceuticals.

    Anyone got any pointers to this type of research.  If the subsidies go both ways, I’m not sure whether the overlap is so important. 

  10. No-one knows the costs and outcomes of all hip replacements, for example, over a given period in both private & public systems. The Productivity Commission’s portfolio on  Performance of Public and Private Hospital Systems explains why the necessary data are absent. Doesn’t that make argument based on individual, informed choice a little … premature?

  11. I’m not sure that your claim that “only people like Sam 2, who have a high risk of needing hospital care, take out private health insurance, (so) the price of that insurance has to be high to cover this ‘adverse selection’ problem” is true.
    There have been a few papers that have found the opposite.  For example the paper of Buchmueller et al (2009) linked to below.
    http://ideas.repec.org/p/her/chewps/2008-2.html
    It finds that people who have PHI are actually healthier than those who don’t have it, suggesting there is in fact favorable selection.
     

  12. Someone who knows more about the healthcare sector can correct me if I’m wrong but isn’t the main expense in healthcare (apart from drugs) the fees paid to healthcare professionals?

    So as an alternative how about expanding the supply of doctors/surgeons instead of exacerbating inequality? The professional bodies act like typical rent-seeking groups by inhibiting entry to the profession so there is already grounds for reform based on competition.

    We can expand supply through international students via immigration policy.

    The advantage of increasing supply through international students over already qualified foreign professionals is it solves the adverse selection problem in recognising foreign educational credentials and english proficiency and any objections the professional bodies have based on adverse selection. Furthermore, professional bodies can’t complain that we are lowering the quality of potential doctors/surgeons as supply of top students from around the world is greater than the amount of top students produced locally.

  13. DavidN,

    You may be correct that traditionally this was the case. But in QLD at least, many doctors have been imported to cover gaps in hospitals, and in the past 5 years or so the domestic intake of university places for doctors has been very high.  So high in fact, that the wave of new doctors coming through the ranks is too large for the hospital system to cope with, and the rotations for interns are having to be more ‘virtual’ medicine while hospitals catch up.  They call it a tsunami of young doctors. 

    Also, if increasing the supply of doctors though immigration decreases doctor salaries, then that decreases the incentive for intelligent domestic students, with plenty of other career options, to persevere through a decade of study to become a doctor.  There is a balance here to be struck, and importing foreign workers is a shonky solution to most problems.  

  14. Cameron,

    Just to be clear, I’m not advocating importing foreign workers. I’m advocating increasing the local supply of health professionals, though yes, via permanent as opposed to temporary emigration.

    As you say, if we increase the supply of local health professionals wage inflation should flatten out over time and this may discourage smart local students from taking up the profession. Even though it wasn’t addressed directly to your concern from my comment above I don’t think this should affect the quality of candidates as the global supply of intelligent students outnumber local ones. Secondly, our ability to attract intelligent students isn’t dependent on local wages. Our quality of life and absence of racial/religious/gender discrimination etc. is also an attractive feature over many developing countries , even for the well off within those countries (I’m thinking of China, India, Malaysia etc.). 

    With respect to the ‘tsunami of young doctors’, I’m not suggesting the market will be in equilibrium over night, increasing the supply of new doctors will not immediately drop fees of surgeon for example. It will take time, and yes, if physical infrastructure isn’t available (though I’m sceptically of this) then we would need to invest to match the increase in human infrastructure.

    But more importantly, if as I believe the professional bodies are acting as rent-seekers, health care costs are higher than they can be, and the difference is pure rent, then we have a ‘free lunch’ policy where everyone is better off except rent-seeking health professionals.

    I will concede I may be completely off the mark as I don’t know what the health sector is really like.

  15. “Sam 1, who has the low chance of becoming ill, will choose to rely on Medicare. It is not worth his while to buy private health insurance because he is not likely to need it. ”

    Are you supposing at that point that the insurance isn’t actuarially fairly priced?

  16. No. If both ‘Sams’ are privately insured at the same price (the insurer doesn’t know which Sam is which, or the government requires community rating) then the premium will reflect the average risk. This is actuarially unfair for Sam 1 but better than fair for Sam 2. But it may not be an equilibrium (depends on degree of risk aversion and the beenfits under Medicare) so Sam 1 may drop out of private insurance. The price of insurance rises to the actuarially fair price for Sam 2 who takes out insurance. 
     

  17. Are health insurers not able to discriminate on the basis of risk factors known by the customer in Australia?

  18. Prof King
    Does the posts that you’ve made also mean that you support school vouchers or a similar funding arrangement for private schools?
    Thanks
    Matthew

  19. Rob – my understanding is that private health insurers cannot explicitly discriminate on the basis of health status or risk factors (this is called community rating). They can of course design products that are more attractive to people with certain risk factors (and they do this) so there is (to use the economics term) self selection by different risk types to different policies. 
    This is very different to what used to occur in the US, where, for example, a diagnosis with cancer meant a massive increase in insurance premium (that really was anti-insurance. I am not sure how much – if at all – the recent US policy reforms have changed this).

    Matthew – I haven’t got back to blogging on education funding. Too much on! I tend to favour a ‘type’ of voucher system that involves means testing and could allow schools (both public and private) to charge top-up fees subject to equity considerations. Joshua and I wrote about this is Finishing the job.

  20. It’s interesting that adverse selection hasn’t brought down the system. Are those with private health insurance overwhelmingly in bad health?

    “This is very different to what used to occur in the US, where, for example, a diagnosis with cancer meant a massive increase in insurance premium (that really was anti-insurance. I am not sure how much – if at all – the recent US policy reforms have changed this).”

    That seems like total madness. Surely the point of getting health insurance is that if you turn out to be more sick than expected you are covered not just for that insurance period, but beyond it. Can’t businesses offer to lock in the current trajectory of premiums if you fall ill? Or be obliged to continue treatment for illnesses diagnosed while you have health insurance? Surely that is a much more attractive product to customers.

  21. Rob

    in Australia community rating requires premiums to be the same irrespective of risk (although there are variations depending on age at joining.) 
    i.e. The insurance premium is the same regardless of the health status or claims history of a member or new member.

    However, reinsurance supports the principle of community rating by sharing between health insurers the hospital and medical costs of high risk members admitted to hospital. Funds with a greater proportion of low risk members contribute into a reinsurance pool and those with a greater proportion of high risk members receive transfers from it.

    Also because private health insurance coexists with a universal public scheme, the potential cost of what you are insuring for is less than the cost in a system without a universal base.

  22. Why hasn’t adverse selection made the reinsurance market unviable? Is it just too important for funds to have reinsurance?

  23. Rob

    I think its probably because the Australian system has a floor of universal public coverage.  Say for example I develop some incredibly expensive long-term illness, then in all likelihood I would go into the public health care system, where the costs would be spread across all taxpayers.  Even though we have a small health insurance levy, most of the cost of the health care system is paid for out of general government revenue.  We also have effective price control of pharmaceuticals as well. But in addition, the reinsurance element means that all private insurers bear the cost of heavy risks equally.  In a sense, there is adverse selection affecting private health insurance, but since the private system doesn’t have to bear the full costs, and there are no advanatages from shifting high risks onto other companies, it is sustainable

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