Deinonychus antirrhopus

Moral Hazard, Adverse Selection and Insurance

Since I did a post on adverse selection (well, pointed to a post on adverse selection), I thought one that was a bit more detailed on the underlying theory would be a good idea.

What is moral hazard? Moral hazard occurs when a person can take actions that can influence the probabilities of various outcomes occurring. For example, an individual who is diriving a car who has no insurance will probably be much more careful than if he did have insurance. The reason is the down side to not having insurance when you get into an accident can be pretty bad. Instead of getting a payment from your insurance company the other person (if you are at fault) will sue you and go after your assets. Whereas if you have insurance you don't have to worry about this.

Insurance basically reduces the gap between different states of the world. Suppose there are two states of the world, good and bad. When the good state obtains you suffer no losses. When the bad state obtains you suffer a loss of say $5,000, and your initial wealth is $20,000. Now suppose, the probability of the bad state occuring is 0.1 and obviously 0.9 for the good state. This person will be willing to pay up $567 for insurance.¹, and the competitive insurance permium (assuming perfect information, and that the insurance market is competitive) is $500. Now if the bad state occurs the person's wealth is $19,500 and if the good state occurs wealth in good state is $19,500.

Moral hazard creeps in when the person's actions can influence the probabilities, and taking preventive actions is costly, adn there is imperfect informatin (i.e., the insurance company does cannot tell what precautions you have taken). For example, to protect against fires in your house, you might install smoke alarms, buy fire extinguishers, and keep flamable substances to a minimum. But this takes work. With insurance, since the impact of the bad state occuring is reduced you might be less inclined to take all of these precautions. In this case, insuring fully against the loss is can lead to moral hazard. That is, if the probability of the bad state prior to insuring was 0.1 when you took all the precautinos, with full insurance you might not take all the precautions and the probability now becomes .15. In this case, the competitive premium should be $750 to reflect in increased risk the insurance company faces. To get around this the payoff in the bad state might be $19,100, and the payoff in the good state $19,500. Now there is an incentive to take precautions so that the good state obtains.

Pretty boring I know, but it is important in looking at insurance markets, especially for automobile insurance. Adverse selection is more of a problem in health insurance markets. For example, you might know if you or people in for family tend to have a specific problem. In this case you offer insurance plans that say offer complete coverage (with a higher premium) and partial coverage (with a lower premium). The preimiums and covereage are structured so that the low risk person selects partial coverage adn the high risk full coverage.

Note that a pooling equilibrium is not possible. A pooling equilibrium is one where the insurance company offers a plan with a premium that is the average of the high risk and low risk premiums. The problem is that with such a strategy, bot the high risk and low risk will end up with the same coverage. But at this point, another insurance firm can come along and offer a policy that offers a premium/coverage combinationt that is attractive to the low risk individuals, but is unattractive to the high risk individuals. So all the low risk individuals take the new plan, leaving only high risk (and high cost) individuals with the initial plan/insurance company.

This is why with universal coverage legislation you see in all the legislative mumbo-jumbo a section which outlaws private insurance. The universal insurance program offered by the government is basically a big pooling equilibrium. So if private insurance is not outlawed, then the government is left with only the high risk/high cost people. It should also be noted that in this situation (i.e., pooling equilibria), the low cost individuals are subsidizing the medical care for the high risk/high cost individuals.
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¹Assuming the person's utility is a natural logarithm of wealth.