Adverse Selection

Consider the used-car market. While the sellers of used cars know the quality of their cars, the buyers do not know the exact quality (imagine a world with no blue book information available). From the buyer’s point of view, the car may be a lemon. Under such circumstances, the buyer’s offer price reflects the average quality of the cars in the market.

When sellers approach a market in which average prices are offered, sellers who know that their cars are of better quality do not sell their cars. (This example can be applied to the mortgage and housing crisis in 2008. Sellers who knew that their houses are worth more prefer to hold on to them, instead of lowering the price in order to just make a sale). When they withdraw their cars from market, the average quality of the cars for sale goes down. Buyers’ offer prices get revised downward in response. As a result, the new level of better-quality car sellers withdraws from the market. As this cycle continues, only lemons remain in the market, and the market for used cars fails. As a result of an information asymmetry, the bad-quality product drives away the good-quality ones from the market. This phenomenon is called adverse selection.

It’s easy to demonstrate adverse selection in health insurance. Imagine two individuals, one who is healthy and the other who is not. Both approach an insurance company to buy health insurance policies. Assume for a moment that the two individuals are alike in all respects but their health condition. Insurers can’t observe applicants’ health status; this is private information. If insurers could find no way to figure out the health status, what would it do?

Suppose the insurer’s price schedule reads, “Charge $10 monthly premium to the healthy one, and $25 to the unhealthy one.” If the insurer is asymmetrically informed of the health status of each applicant, it would charge an average premium $\left(\frac{10+25}{2}=\text{\$}17.50\right)$ to each. If insurers charge an average premium, the healthy individual would decide to retain the health risk and remain uninsured. In such a case, the insurance company would be left with only unhealthy policyholders. Note that these less-healthy people would happily purchase insurance, since while their actual cost should be $25 they are getting it for $17.50. In the long run, however, what happens is that the claims from these individuals exceed the amount of premium collected from them. Eventually, the insurance company may become insolvent and go bankrupt. Adverse selection thus causes bankruptcy and market failure. What is the solution to this problem? The easiest is to charge $25 to all individuals regardless of their health status. In a monopolistic marketA market with only one supplier. of only one supplier without competition this might work but not in a competitive market. Even in a close-to-competitive market the effect of adverse selection is to increase prices.

How can one mitigate the extent of adverse selection and its effects? The solution lies in reducing the level of information asymmetry. Thus we find that insurers ask a lot of questions to determine the risk types of individuals. In the used-car market, the buyers do the same. Specialized agencies provide used-car information. Some auto companies certify their cars. And buyers receive warranty offers when they buy used cars.

Insurance agents ask questions and undertake individuals’ risk classification according to risk types. In addition, leaders in the insurance market also developed solutions to adverse selection problems. This comes in the form of risk sharing, which also means partial insurance. Under partial insurance, companies offer products with deductiblesInitial part of the loss absorbed by the person who incurs the loss. (the initial part of the loss absorbed by the person who incurs the loss) and coinsuranceSituation where individuals share in the losses with the insurance companies., where individuals share in the losses with the insurance companies. It has been shown that high-risk individuals prefer full insurance, while low-risk individuals choose partial insurance (high deductibles and coinsurance levels). Insurance companies also offer policies where the premium is adjusted at a later date based on the claim experience of the policyholder during the period.

Moral Hazard

Adverse selection refers to a particular kind of information asymmetry problem, namely, hidden information. A second kind of information asymmetry lies in the hidden action, if actions of one party of the contract are not clear to the other. Economists study these problems under a category called the moral hazard problem.

The simplest way to understand the problem of “observability” (or clarity of action) is to imagine an owner of a store who hires a manager. The store owner may not be available to actually monitor the manager’ actions continuously and at all times, for example, how they behave with customers. This inability to observe actions of the agent (manager) by the principal (owner) falls under the class of problems called the principal-agent problemThe inability of the principal (owner) to observe actions of the agent (manager)..The complete set of principal-agent problems comprises all situations in which the agent maximizes his own utility at the expense of the principal. Such behavior is contrary to the principal-agent relationship that assumes that the agent is acting on behalf of the principal (in principal’s interest). Extension of this problem to the two parties of the insurance contract is straightforward.

Let us say that the insurance company has to decide whether to sell an auto insurance policy to Wonku, who is a risk-averse person with a utility function given by $U\left(W\right)=\sqrt{W}\text{.}$ Wonku’s driving record is excellent, so he can claim to be a good risk for the insurance company. However, Wonku can also choose to be either a careful driver or a not-so-careful driver. If he drives with care, he incurs a cost.

To exemplify, let us assume that Wonku drives a car carrying a market value of $10,000. The only other asset he owns is the $3,000 in his checking account. Thus, he has a total initial wealth of $13,000. If he drives carefully, he incurs a cost of $3,000. Assume he faces the following loss distributions when he drives with or without care.

Table 3.3 "Loss Distribution" shows that when he has an accident, his car is a total loss. The probabilities of “loss” and “no loss” are reversed when he decides to drive without care. The E(L) equals $2,500 in case he drives with care and $7,500 in case he does not. Wonku’s problem has four parts: whether to drive with or without care, (I) when he has no insurance and (II) when he has insurance.

We consider Case I when he carries no insurance. Table 3.4 "Utility Distribution without Insurance" shows the expected utility of driving with and without care. Since care costs $3,000, his initial wealth gets reduced to $10,000 when driving with care. Otherwise, it stays at $13,000. The utility distribution for Wonku is shown in Table 3.4 "Utility Distribution without Insurance".

When he drives with care and has an accident, then his final wealth (FW) $\left(\text{FW}\right)=\text{\$}\mathrm{13,000}-\text{\$}\mathrm{3,000}-\text{\$}\mathrm{10,000}=\text{\$}0\text{,}$ and the utility = $\sqrt{0}=0\text{.}$ In case he does not have an accident and drives with care then his final wealth (FW) = $\left(\text{FW}\right)=\text{\$}\mathrm{13,000}-\$\mathrm{3,000}-\$0=\$\mathrm{10,000}$ (note that the cost of care, $3,000, is still subtracted from the initial wealth) and the utility = $\sqrt{\mathrm{10,000}}=100\text{.}$ Hence, E(U) of driving with care = $0.25\times 0+0.75\times 100=75\text{.}$ Let’s go through it in bullets and make sure each case is clarified.

• When Wonku drives without care he does not incur cost of care, so his initial wealth = $13,000. If he is involved in an accident, his final wealth $\left(\text{FW}\right)=\text{\$}\mathrm{13,000}-\text{\$}\mathrm{10,000}=\text{\$}\mathrm{3,000}\text{,}$ and the utility = $\sqrt{\mathrm{3,000}}=54.77\text{.}$ Otherwise, his final wealth $\left(\text{FW}\right)=\text{\$}\mathrm{13,000}-\text{\$}0=\text{\$}\mathrm{13,000}$ and the utility = $\sqrt{\mathrm{13,000}}=114.02\text{.}$ Computing the expected utility the same way as in the paragraph above, we get $\text{E}\left(\text{U}\right)=0.75\times 54.77+0.25\times 114.02=69.58\text{.}$
• In Case I, when Wonku does not carry insurance, he will drive carefully since his expected utility is higher when he exercises due care. His utility is 75 versus 69.58.
• In Case II we assume that Wonku decides to carry insurance, and claims to the insurance company. He is a careful driver. Let us assume that his insurance policy is priced based on this claim. Assuming the insurance company’s profit and expense loading factor equals 10 percent of AFP (actuarially fair premium), the premium demanded is $\$\mathrm{2,750}=\$\mathrm{2,500}(1+0.10)\text{.}$ Wonku needs to decide whether or not to drive with care.
• We analyze the decision based on E(U) as in Case I. The wealth after purchase of insurance equals $10,250. The utility in cases of driving with care or without care is shown in Table 3.5 "Utility Distribution with Insurance" below.

Notice that after purchase of insurance, Wonku has eliminated the uncertainty. So if he has an accident, the insurance company indemnifies him with $10,000. Thus, when Wonku has insurance, the following are the possibilities:

• He is driving with care

  • And his car gets totaled, his final wealth = $\$\mathrm{10,250}-\$\mathrm{3,000}-\$\mathrm{10,000}+\$\mathrm{10,000}=\$\mathrm{7,250}\text{,}$ and associated utility = $\sqrt{7250}=85.15\text{.}$
  • And no loss occurs, his final wealth = $\text{\$}\mathrm{10,250}-\text{\$}\mathrm{3,000}=\text{\$}\mathrm{7,250}\text{.}$

  So the expected utility for Wonku = 85.15 when he drives with care.

• He does not drive with care

  • And his car gets totaled, his final wealth = $\$\mathrm{10,250}-\$\mathrm{10,000}+\$\mathrm{10,000}=\$\mathrm{10,250}\text{,}$ and associated utility = $\sqrt{10250}=101.24\text{.}$
  • And no loss occurs, his final wealth = $10,250 and utility = 101.24.

  So the expected utility for Wonku = 101.24 when he drives without care after purchasing insurance.

The net result is he switches to driving with no care.

Wonku’s behavior thus changes from driving with care to driving without care after purchasing insurance. Why do we get this result? In this example, the cost of insurance is cheaper than the cost of care. Insurance companies can charge a price greater than the cost of care up to a maximum of what Wonku is willing to pay. However, in the event of asymmetric information, the insurance company will not know the cost of care. Thus, inexpensive insurance distorts the incentives and individuals switch to riskier behavior ex post.

In this moral hazard example, the probabilities of having a loss are affected, not the loss amounts. In practice, both will be affected. At its limit, when moral hazard reaches a point where the intention is to cheat the insurance company, it manifests itself in fraudulent behavior.

How can we solve this problem? An ideal solution would be continuous monitoring, which is prohibitively expensive and may not even be legal for privacy issues. Alternatively, insurance companies try and gather as much information as possible to arrive at an estimate of the cost of care or lack of it. Also, more information leads to an estimate of the likelihood that individuals will switch to riskier behavior afterwards. So questions like marital status/college degree and other personal information might be asked. Insurance companies will undertake a process called risk classification. We discuss this important process later in the text.

So far we have learned how individuals’ risk aversion and information asymmetry explain behavior associated with hedging. But do these reasons also hold when we study why corporations hedge their risks? We provide the answer to this question next.