MEDICAL INSURANCE IN HEALTH CARE SYSTEMS
Remember Joe, who suffered a heart attack at the beginning of Topic 1? Things turned out quite well, both medically and financially, for our friend Joe. You see, Joe’s medical bills were covered by a Blue Cross PPO insurance plan he had obtained through his employer. Joe could thus afford the best and fastest hospital care money could buy, and the triple bypass surgery he received at the prestigious private teaching hospital was highly successful. Angela, his wife, and the two children are tickled pink now that Joe is back to his former self.
But how might events have differed if Joe had not been covered by medical insurance, or if Joe was enrolled in an HMO plan? Moreover, what are some of the reasons why Joe and his family were covered by health insurance? Also, why was Joe covered by an PPO rather than an HMO plan? What are the differences between the two types of plans? These are among the questions for which we search for answers in this topic.
As pointed out briefly in Topic 4 and further discussed in Topic 11, employment-related insurance is the dominant type of private health insurance coverage in the United States. Only a small percentage of the population purchases health insurance directly from insurance companies. Because most private health insurance is purchased through employers, many people believe that employers pay for their health insurance coverage. But economic theory suggests that nothing could be further from the truth because employees pay for their health insurance coverage in the form of reduced or forgone wages.
Economic theory implies that a trade-off exists between insurance premiums and wages because, during a particular time period, a worker tends to generate a certain value or marginal revenue product (MRP) for a company. The MRP that a worker generates depends on his or her marginal productivity and the price of the good or service in the marketplace that she helps produce (assuming that output is produced in a competitive market). More precisely, economic theory posits that MRP equals the price of the product times the marginal productivity of the worker. It follows that a higher price and greater productivity both increase a worker’s MRP or worth to a company.
Employers are typically pressured by competition in the goods and labor markets to compensate workers based on their market-determined MRP. That is, if an employer compensated its employees at a rate in excess of their MRP, that company would be forced to raise product prices and thereby lose business and profits to competitors in the goods market. At the same time, if the employer did not compensate its employees at a rate that at least matched the market-determined MRP, the company would lose productive employees to competitors in the labor market and thereby also lose business and profits. Consequently, economic theory predicts that workers are compensated for their MRP as long as markets are reasonably competitive. However, compensation comes in the form of both wages and fringe benefits such as life insurance, health insurance, and paid vacations. If you think in terms of total compensation, it follows that more expensive health insurance coverage leads to lower wages or reductions in other fringe benefits for a given level of the MRP. Thus, this trade-off can also be interpreted as meaning that employees actually pay for their health insurance coverage through a reduction in other types of compensation.
Of course, markets are not as frictionless as economic theory sometimes seems to suggest. For example, because of mobility costs, some workers find themselves with more or less health insurance coverage than they truly desire. Also market imperfections, such as wage discrimination, sometimes occur in the real world such that specific workers receive compensation that falls below the competitive rate. However, market forces tend to support long-run outcomes consistent with workers being paid their MRPs as frictions such as mobility costs become less inhibiting and competition for the best workers intensifies.
Representative of several studies, Miller (2004) empirically examines the wage and health insurance trade-off using data for a sample of male workers between ages 25 and 55 during the period of 1988-1990. As one might imagine, a wage-health insurance tradeoff is difficult to discern statistically because more productive workers tend to receive both higher wages and increased health insurance coverage (as well as greater amounts of other benefits). Thus, it is important that both observable (such as education and experience) and unobservable (such as motivation, dependability, and intelligence) indicators of productivity are held constant in the empirical analysis to isolate the hypothesized inverse relation between wages and the presence of employer-sponsored health insurance. Controlling for observable and unobservable measures of productivity and other factors, Miller finds empirically that health insurance coverage results in 10 to 11 percent less wages. However, Miller warns that his estimate of the trade-off between wages and health insurance may also reflect the presence of other types of fringe benefits such as paid vacations and sick leave, which he was unable to control for because of data limitations. But when health insurance is valued at 11 percent of average wages, the resulting figure of $2,000 compares very closely to the average annual cost of employer-sponsored insurance plans at that time. Thus, Miller’s study lends empirical support for the wage and health insurance trade-off and the idea that employees pay for their own health insurance benefits in terms of forgone wages.
The notion that employers do not pay for the health insurance benefits of their employees and therefore only sponsor the insurance is important for the discussion that follows. Both models of the demand for health insurance presented assume workers pay for and choose their own coverage. The first model, the so-called conventional theory or standard gamble model, assumes people purchase health insurance to avoid or transfer risk. In this case, insurance serves as a pooling arrangement to replace the high risk or variability of individual losses with the reduced risk or variability associated with aggregated losses. The second model, the Nyman model, views people as desiring financial access to medical care that health insurance offers. In this case, a pooling arrangement allows individuals, in the event they become ill, to receive a transfer of income from those who remain healthy. The transfer helps solve an affordability constraint that people face when their net worth falls below the cost of medical treatments. Both of these models offer important insights into the reasons why people demand health insurance and valuable lessons regarding the proper role of public policy with respect to health insurance markets.
The Conventional Theory of the Demand for Private Health Insurance
Because of imperfect information, many of the choices individuals make as health care consumers or providers involve a substantial amount of uncertainty. For example, for an individual consumer, many medical illnesses occur randomly, and therefore the timing and amount of medical expenditures are uncertain. Likewise, from the health care provider’s perspective, patient load and types of treatment are unknown before they actually occur. Because these events are unpredictable, they involve a substantial degree of risk. Because most people generally dislike risk, they are willing to pay some amount of money to avoid it.
Consumers actually purchase a pooling arrangement when they buy a policy from an insurance company. Pooling arrangements help mitigate some of the risk associated with potential losses. We will illustrate this point through an example. Suppose, two individuals, named Joe and Leo, face the same distribution of losses. We can think of a loss distribution as showing the probability of a number of different occurring outcomes, with the sum of the probabilities equaling 1 or 100 percent. More specifically, assume that both Joe and Leo each face a 20 percent probability of losing $20 and an 80 percent probability of losing nothing. Most individual loss distributions are characterized by a low probability of losing a large sum of money and a high probability of losing very little. The dollar losses are kept to a minimum to ease the calculations that follow. The ensuing discussion may be more meaningful if you think in terms of thousands or millions of dollars. Also assume that the losses of Joe and Leo are perfectly uncorrelated, or independent of one another. That is, Leo does not incur a loss just because Joe incurs a loss, and vice versa.
Standard statistics theory suggests that the expected value, m, of a distribution of outcomes such as losses can be computed as the sum of the weighted values of the outcomes, Li, with the probabilities, p, serving as the weights. The expected value serves as a summary measure of the distribution of outcomes. For our example, the expected loss equals:
(6-1) m = P1L1 + p2L2 = 0.2 × $20 + 0.8 × $0 = $4.
Equation 6-1 can be interpreted as meaning Joe and Leo can each expect to lose $4 on average.
But people are also concerned about the variability of the expected loss. It stands to reason that a distribution of likely outcomes involves greater risk when more variability exists around the expected value. For example, Joe and Leo are likely to feel financially more secure knowing they can expect to lose somewhere between $3 and $5 than between $1 and $7. Statistics theory suggests we can measure the variability or variance of a distribution of outcomes such as losses using the following formula:
Along with the expected value, the variance also serves as a summary measure of a distribution. Notice that the variance increases when the actual outcomes, Li, are further away from the expected outcome, m. It can also be shown that the variance increases when the probability of extreme outcomes increases. That is, the variance increases when extreme outcomes are more likely to occur than the intermediate outcomes along a distribution. Typically, the variability of a distribution of outcomes is represented by its standard deviation rather than its variance. The standard deviation, which is found mathematically by taking the square root of the variance, equals $8 in this case.
Both the expected loss of $4 and its standard deviation of $8, in this example, can be thought of as measures of risk. Generally speaking, more risk is associated with a higher expected loss and when the distribution of the expected loss, or standard deviation, exhibits wider variability. If both Joe and Leo are risk averse to some degree we can show that they might be better off by pooling their losses. Risk aversion occurs when people receive disutility from taking on additional risk and are willing to pay to avoid it or must be paid to accept it.
Let’s now explore how Joe and Leo might mutually gain from entering into a pooling-of-losses arrangement. The idea is that both Joe and Leo will share in covering the losses of the other if a loss occurs. If Joe and Leo enter into a pooling arrangement, four possible outcomes are likely. One likely outcome is that both Joe and Leo lose no money at all. The joint probability of both Joe and Leo facing zero losses is found by multiplying the individual probabilities of zero losses occurring, or 0.8 × 0.8 = 0.64. Notice that the probability of an extreme outcome is lowered by the pooling arrangement from 0.80 on an individual basis to 0.64 on a group basis. This is similar to the joint probability of flipping a coin and obtaining two consecutive heads. The probability of a head toss equals 0.50, so the probability of two consecutive head tosses equals 0.25. This result already provides a favorable sign that Joe and Leo may be better off by entering into a pooling arrangement.
The second likely outcome is that Joe loses $20 but Leo suffers no losses, and the third likely outcome is that Leo loses $20 but Joe does not. Each of these separate outcomes must be weighted by their respective probabilities of occurring, 0.2 and 0.8, respectively. The final likely outcome is that both Joe and Leo simultaneously suffer a loss of $20. The joint probability of this outcome occurring is found by multiplying the individual probabilities of occurrence, 0.2 × 0.2, which amounts to 0.04. Notice once again that the probability of an extreme outcome occurring is reduced by the pooling arrangement. Table 6-1 summarizes the four likely outcomes and their probable values. Notice that the probabilities of the four outcomes sum to 1 or 100 percent, as they should.
The calculations in Table 6-1 suggest that the pooling arrangement does not make either Joe or Leo better off in terms of the expected loss. Each person faces an expected loss of $4 with or without the pooling arrangement. But when people face the same distribution of outcomes, a pooling arrangement is not about reducing the expected loss; the pooling arrangement is all about reducing the standard deviation or variability of the loss. If we apply the formula for the variance in Equation 6-2, we can obtain the variability of the share of the losses faced by either Joe or Leo as
(6-3) Variance = 0.64(0 – 4)2 + 0.16(10 – 4)2 + 0.16(10 – 4)2 + 0.04(20 – 4)2 = 32
It follows that the standard deviation associated with the expected loss equals the square root of the variance, or $5.66.
Notice that the standard deviation of the loss distribution declines from $8 without the pooling arrangement to $5.66 with the pooling arrangement. Both Joe and Leo clearly gain from the reduced variability associated with their expected losses of $4. What may be unclear at this point, however, is the intuition behind the reduction in the variability of the losses that each individual faces because of the pooling arrangement. Entering into a pooling arrangement essentially replaces each person’s individual loss distribution with the average loss distribution of the group. The average loss distribution of the group involves a lower probability of extreme outcomes occurring because it is much less likely that both Joe and Leo will simultaneously lose nothing or lose $20. In other words, what happens to one individual will typically be offset by its not simultaneously happening to the other individual.
In addition, the variability of the expected loss decreases as more individuals with similar individual loss distributions join a pooling arrangement. Assuming losses are not perfectly correlated, more individuals joining the pooling arrangement help reduce the probability of the extreme outcomes occurring and thereby make the expected loss less variable and more predictable. It also can be shown that the group loss distribution becomes more symmetrical and bell-shaped, unlike an individual loss distribution, which is heavily skewed toward the left. A loss distribution heavily skewed toward the left means small dollar losses occur more frequently than large dollar losses.
The preceding discussion suggests that consumers typically gain from entering into pooling arrangements because the pooling helps reduce the variability of the expected losses. Certainly, consumers benefit when they enter into a medical expense pool. The individual loss function associated with medical expenses is heavily skewed toward the left, indicating that only a very few people will actually incur large medical expenses in the absence of insurance. Indeed for the United States as a whole, a mere 5 percent of all patients accounted for more than half of all health care spending in 1996 (Berk and Monheit, 2001). From an individual consumer’s perspective, a pooling arrangement can reduce the variability associated with medical expenses to some degree.
We have not yet established why insurance companies become involved in pooling arrangements. Certainly, people enter into simple forms of pooling arrangements on their own. For example, large families often provide informal sharing of losses, and businesses with a large number of employees sometimes self-insure. However, in cases involving people with no informal or formal relationships, personal pooling arrangements involve an unnecessarily large number of contracts written. The number of contracts would equal [n(n – 1 )]/2, where n equals the number of individuals in the pool. In contrast, when the pooling arrangement is developed by an insurance company, only one contract is written between each policyholder and the insurer. Also, if those in the personal pooling arrangement decide to increase the size of the group they must engage in marketing and underwriting (that is, determining whom and on what terms to cover) activities, among others. Most people lack expertise in these areas, but insurance companies can hire the necessary personnel and monitor their activities. Hence, insurance companies often serve as intermediaries and develop and sell pooling arrangements to individuals.
Thus, consumers pay an insurer a certain amount of income (that is, a premium), and the insurer covers some or all of the medical costs in the event an illness actually occurs. During any given period the actual benefits paid out by an insurer to any single consumer may be higher or lower than the premiums received from that consumer. By operating on a large scale, an insurer pools or spreads the risk among many subscribers so that, on average, the total premiums received at least compensate for the total cost of paying for medical services, particularly in the long run. In addition, given some amount of competition in the health insurance market, the difference between total premiums and total benefits paid out to all subscribers (or the loading fee) should approximate a “normal” amount.
Consumers differ in terms of the amounts and types of health insurance coverage they buy, and these differences are reflected in such items as the deductible amount, the coinsurance rate, and the number of events covered. (We will examine the health insurance product more closely later on in the topic.) In general, a high deductible and a high coinsurance rate reflect less extensive or less complete health insurance coverage. For example, some consumers purchase health insurance plans that offer first-dollar coverage for all types of medical services, including routine care. Others purchase health insurance plans with large deductibles and copayments that cover only catastrophic illnesses. Differences in health care coverage can be explained by a host of factors, including the price of obtaining health insurance, the individual’s degree of risk aversion, the perceived magnitude of the loss relative to income, and information concerning the likelihood that an illness will actually occur. The following section offers a model to address how each of these factors individually affects the demand for health insurance.
Deriving the Demand for Private Health Insurance
We can better understand how these factors influence the quantity demanded of health insurance by focusing on Figure 6-1, where the actual utility, U, associated with different levels of income, Y, is shown for a representative consumer (ignore the chord AB for now). The slope of this utility function at any point is AU/AY and represents the marginal utility of income. The declining slope, or marginal utility of income, is based on the premise that the individual is risk averse. This means the risk-averse person is opposed to a fair gamble where there is a 50-50 chance of losing or gaining one dollar because a dollar loss is valued more highly than a dollar gain. That is, for any given level of income, the pain of losing an incremental dollar exceeds the pleasure associated with gaining an additional dollar.
Suppose a person has an income of Y0 equaling $40,000. As indicated in the figure, this income level yields actual utility of U0, which amounts to 90 utils. For expository purposes, we assume utility can be measured directly in units called utils. Further, suppose the person faces a choice concerning whether to purchase health insurance. The decision is based partly on a belief that if an illness occurs, the medical services will cost $20,000. Consequently, if the illness occurs and the consumer pays the entire medical bill, income declines to $20,000 and the level of actual utility falls to U1, or 70 utils.
The two outcomes that can occur if the consumer does not purchase health insurance are represented by points A and B. At point A, no illness occurs and income remains at $40,000 such that actual utility equals U0. At point B, an illness occurs and (net) income falls to $20,000 such that actual utility equals U1. Because the resulting outcome is unknown before it actually occurs, the individual forms expectations concerning the probability of each outcome occurring. With these subjective probabilities, the expected (rather than actual) levels of utility and income can be determined. Specifically, the individual’s expected level of utility, E(U), can be determined by weighing the actual utility levels associated with the two possible outcomes by their subjective probabilities of occurrence, p0 and p1:
(6-4) E(U) = π0 × U0(Y0 = $40,000) + π1 × U1(Y1 = $20,000),
or
(6-5) E(U) = π0 × 90 + π1 × 70,
where π0 and π1 sum to 1. Based on Equation 6-5, the chord AB in Figure 6-1 shows the level of expected utility for various probabilities that the illness will occur. As the probability of getting ill increases, expected utility declines, and this outcome is associated with a point closer to B on the chord. The precise probability value the individual attaches to the illness occurring is based on his best personal estimate. It is likely to depend on such factors as the individual’s stock of health, age, and lifestyle.
Suppose the consumer attaches a subjective probability of 20 percent to an illness actually occurring. Following Equation 6-5, the expected utility is
(6–6) E(U) = 0.8 × 90 + 0.2 × 70 = 86
and the expected level of income, E(Y), is
(6-7) E(Y) = p0 × Y0 + p1 × Y1 = 0.8 × 40,000 + 0.2 × 20,000 = 36,000.
Equation 6-7 represents the weighted sum of the two income levels with the probability values as the weights. Thus, expected income equals $36,000 and the expected level of utility is 86 utils if insurance is not purchased (and full risk is assumed) given a perceived probability of illness equal to 0.2 and a magnitude of the loss equal to $20,000. The levels of expected income and expected utility are also shown in Figure 6-1.
Notice in the figure (not drawn to scale) that the person is just as well off in terms of actual utility by paying a third party a “certain” amount of $5,000 to insure against the expected loss of $4,000. The certain loss of $5,000 reduces net income to $35,000 and provides the consumer with an actual utility level of 86 utils, which equals the expected utility level without insurance. To the consumer, the $1,000 discrepancy, or distance CD, represents the maximum amount she is willing to pay for health insurance above the expected loss. It reflects the notion that a risk-averse consumer always prefers a known amount of income rather than an expected amount of equal value. This preference reflects the value the consumer places on financial security. It is for this reason that the typical person faces an incentive to purchase health insurance.
It is easy to see from this analysis why an insurance company is willing to insure against the risk. Assuming this person is the average subscriber in the insured group and the probability of an illness occurring is correct from an objective statistical perspective, the insurance company could potentially receive premium revenues of $5,000 to pay the expected medical benefits of $4,000 with enough left over to cover administrative expenses, taxes, and profits. The expected medical benefits can also be referred to as the actuarial fair value or “pure premium.” To the insurer, the difference between the total premium and medical benefits paid out, or pure premium, is referred to as the loading fee. In the economics of insurance literature, the loading fee is also typically referred to as the price of insurance.
Factors Affecting the Quantity Demanded of Health Insurance
The model in Figure 6-1 can be used to explain how the price of insurance affects the quantity demanded of health insurance. Under normal circumstances, the consumer purchases health insurance if the actual utility with health insurance exceeds the expected utility without it. The theoretically correct comparison is between the expected utility with health insurance and the expected utility without health insurance. Because the amount of the premium payment is perfectly certain with a probability of occurrence equal to 1, however, the expected and actual utility with health insurance are equal. We use actual utility here to avoid confusion. In Figure 6-1, that happens whenever the loading fee leads to an income level associated with a point between D and C on the actual utility curve for the given set of circumstances (that is, probability values, degree of risk aversion, and magnitude of loss). In terms of the present example, the consumer demands health insurance if the loading fee is less than $1,000 because actual utility exceeds expected utility at that dollar amount. If expected utility exceeds actual utility, the consumer does not purchase health insurance coverage because the price is too high (a loading fee producing actual utility between points D and B). This happens if the loading fee exceeds $1,000 in our example. Finally, if actual and expected utility are equal due to the loading fee, the individual is indifferent between buying and not buying health insurance (point D or a loading fee of $1,000). Both options make the consumer equally well off. Therefore, it follows that the loading fee, or the price of health insurance, helps establish the completeness of insurance coverage and the number of people who insure against medical illnesses. Specifically, as the price of insurance declines, actual utility increases relative to expected utility and the quantity demanded of health insurance increases – ceteris paribus.
At this point, it is useful to note that employment-related health insurance premiums, unlike cash income, are presently exempt from federal and state income taxes even though they are a form of in-kind income. For example, if an employer pays cash wages of $800 and provides health insurance benefits equal to $200 per month to an employee, only the $800 is subject to taxes even though total compensation equals $1,000. Assuming a 20 percent marginal tax rate, the individual pays $160 in taxes on $800 of cash income rather than $200 on $1,000 of total compensation.
Thus, relative to cash income (or all other goods purchased out of cash income), health insurance is effectively subsidized by the government because of its tax-exempt status. We can view this tax subsidy on health insurance benefits in another way. Each time the employer raises the employee’s wage by $1, the employee receives only 100 – t percent of that $1 as after-tax income, where t percent is the marginal tax rate. However, if employer health insurance contributions increase by $1, the employee receives the entire dollar as benefits. In effect, the government picks up t percent of the price of the health insurance in forgone taxes and the employee pays the remaining (100 – t) percent in forgone wage income (since both wages and in-kind benefits are substitute forms of compensation). Given t = 20, the government implicitly pays 20 cents and the employee pays 80 cents of the marginal dollar spent on health insurance. If we allow for the possibility that not all health insurance premiums are tax exempt (such as the health insurance premiums of some individuals who purchase individual policies), the user price of health insurance can be written as (1 – et/100)P, where e is the fraction of health insurance premiums exempted from taxes and P is the price of health insurance (the loading fee). The user price of health insurance obviously decreases with a higher marginal income tax rate and tax-exempt fraction.
Figure 6-2 provides a graphical illustration of the impact of the tax exemption of insurance premiums on the quantity demanded of health insurance. In the figure, the vertical axis captures the loading fee or price, P, and the horizontal axis indicates the amount of insurance coverage demanded, q. A rightward movement along the horizontal axis indicates policies with lower deductibles and copayments or more risky events covered by the plan, and consequently, a higher premium payment. An individual’s demand for insurance coverage is drawn as a downward-sloping curve to reflect the law of diminishing marginal utility. In addition, a downward-sloping demand for insurance might signify that people typically face relatively few high-risk situations but many more low-risk events. As price declines, people are therefore more willing to have more of these less-risky events covered by insurance.
Let’s simplify the discussion by taking the employer out of the picture. Suppose the demand in Figure 6-2 represents a self-employed worker’s demand for health insurance. Before 1996, self-employed workers were allowed to exempt only 25 percent of their premiums from taxable earnings. However, for discussion purposes, let’s suppose that initially the self-employed worker is not allowed a tax exemption on any type of spending and that her income is taxed at 20 percent. Let’s also assume that the self-employed worker earns $60,000 of annual income and the loading fee for an insurance policy is set in the marketplace at $400. The government therefore collects $12,000 in taxes ($60,000 times 0.2) from this self-employed worker.
Thus, price P0 in Figure 6-2 equals $400. The individual matches up market price with marginal benefit, as indicated by demand, and purchases q0 amount of insurance in the process of maximizing utility. We assume that q0 equals $4,000 worth of insurance coverage. Notice in this case that an additional dollar spent on health insurance comes at the same cost of an additional dollar spent on any other type of good or service because taxes are applied equally to all types of spending out of income. That is, an additional dollar of pretax income purchases only 80 cents of insurance and any other good or service the individual might buy because of the 20 percent tax rate on wage income. Alternatively stated, the opportunity cost of $1 of additional insurance coverage is $1 spent on all other goods and services.
Now suppose the government exempts all insurance premiums of the self-employed from income taxation, which reflects what actually occurred in 2003. Now, because of the differential tax treatment, an additional dollar out of pretax income purchases $1 of insurance but only 80 cents of all other goods and services. Thus, the opportunity cost of an additional dollar spent on insurance declines from $1 to 80 cents. In terms of our example, this means that the opportunity cost of purchasing health insurance is no longer $400 but now equals $320 or (1 – t)P0.
Figure 6-2 shows the impact of the lower after-tax price of health insurance on the quantity demanded of health insurance. As long as demand is not perfectly inelastic, the self-employed worker responds to the lower after-tax price by purchasing more health insurance, which for discussion purposes is set at $4,200. The government now collects $11,160 of taxes from the self-employed worker.
Thus, economic theory suggests people purchase more health insurance because of the preferential tax treatment of health insurance premiums. The tax exemption effectively serves as a subsidy for the purchase of health insurance coverage. As we saw in our example, the government effectively pays 20 percent of the loading fee and thereby reduces the individual’s out-of-pocket price when purchasing health insurance. Also, note that the government gives up tax revenues because of the preferential tax treatment of health insurance premiums. These lost tax revenues could have been used to finance various public goods and services. In this example, the government lost $840 of tax revenues. In the aggregate, estimates suggest the government lost roughly $150 billion of tax revenues in 2004 because of the tax exemption (Sheils and Haught, 2004).
The expected utility model in Figure 6-1 can also help explain other factors affecting the demand for health insurance. First, the subjective probability of an illness occurring affects the amount of health insurance demanded. In terms of the figure, as the probability of an illness increases from 0 to 1, the relevant point on chord AB moves from A toward B. Given the shapes of the two curves, the horizontal distance between the actual utility curve and the expected utility line, which measures the willingness to pay for health insurance beyond the expected level of medical benefits, at first gets larger, reaches a maximum, and then approaches 0 with a movement from A to B. Therefore, all else held constant, including the loading fee, the quantity demanded of health insurance first increases, reaches a maximum amount, and then decreases with respect to a higher probability of an illness occurring. The implication is that individuals insure less against medical events that are either highly unlikely (closer to A) or most probable (closer to B). In the latter case, it is cheaper for the individual to self-insure (that is, save money for a “rainy day”) and avoid paying the loading fee. For example, assume the probability of illness is 1. In this case, the expected and actual levels of utility are equal at point B in Figure 6-1. In this situation, it is cheaper for the individual to self-insure than to pay a loading fee above the medical benefits actually paid out. Alternatively stated, there is no need for insurance since the outcome is certain. The uncertainty of an illness occurring is one reason more people insure against random medical events than against routine medical events, such as periodic physical and dental exams, which are expected.
Another factor affecting the amount of insurance coverage is the magnitude of the loss relative to income. Assuming the same probabilities as before, the expected utility line (chord AB) in Figure 6-1 rotates down and pivots off point A if the magnitude of the loss increases. In this case, the new expected utility line meets the actual utility curve somewhere below point B. For the same probability values as before, the horizontal distance between the expected and actual utility curves increases. Thus, the willingness to purchase health insurance increases with greater magnitude of a loss. This implies that a greater number of people insure against illnesses associated with a large loss, at least relative to income. Insurance coverage is also more complete. The potential for a greater loss is one reason more people have hospital insurance than dental or eye care insurance coverage.
The final factor affecting the amount of health insurance demanded is the degree of risk aversion. Obviously, people who are more risk averse have more insurance coverage than otherwise identical people who are less risk averse. Greater risk aversion makes the utility curve more concave. In fact, if the person is risk neutral, the marginal pain of a dollar loss equals the marginal pleasure of a dollar gain and the slope of the utility curve is constant (a straight line through the origin). In this case, a person would be indifferent with respect to purchasing or not purchasing insurance because the expected and actual utilities are equal at different levels of income. For a risk lover, the pleasure of an additional dollar gained exceeds the pain of an incremental dollar loss and the slope of the utility curve increases in value. In the case of a risk lover, no insurance is purchased because expected utility is greater than actual utility at any level of income.
In sum, according to conventional theory, we can specify the quantity demanded of health insurance, Q, as a function of the following factors:
(6–8) Q = f [(1 – et/100) × P, Degree of risk aversion, Probability of an illness occurring, Magnitude of loss, Income].
Note that a change in the first explanatory factor results in a movement along a given demand curve, whereas an adjustment in any of the other four factors results in a shifting of the curve.
With suitable data, Equation 6-8 can be estimated to determine the user price and income elasticities of the demand for health insurance. In practice, however, it is very difficult to measure the user price and quantity demanded of health insurance. Therefore, various proxies are used depending on data availability. For example, the price of health insurance, P, is sometimes proxied by the size of the insured group. The expectation is that the loading fee, or the price of health insurance, falls with a larger group size due to administrative and risk-spreading economies. Some studies assume that the price of health insurance is the same for all individuals and allow only marginal tax rates, t, and the tax-exempt fraction, e, to vary.
Proxy measures for the quantity of health insurance must also be employed. The quantity of health insurance is usually measured by either total insurance premiums, some measure of insurance coverage completeness, or a coverage option (for example, less versus more restrictive health insurance plans). Table 6-2 displays some of the estimated price and income elasticities of the demand for health insurance reported in various studies. The studies reveal that individuals possess a price-inelastic demand for health insurance. Furthermore, while health insurance is considered a normal good (that is, it has an income elasticity greater than zero), the studies found a relatively small income effect. Even the demand for long-term care insurance is found to be inelastic, with price and income elasticities of about -0.39 and 0.18, respectively (Kumar et al., 1995).
However, these studies generally assume the individual is able to make marginal changes in the insurance policy. But employer-sponsored group insurance policies are largely beyond the control of the single individual employee. Typically, the employer or union representatives make decisions concerning the insurance package by considering the welfare of the overall group rather than that of any one individual employee. Nevertheless, most studies find that the demand for individual health insurance is also inelastic with respect to price. For example, see Marquis et al. (2004). See Goldstein and Pauly (1976) or Pauly (1986) for further discussion on this point. When employees can select from multiple similar plans offered by the employer and must pay more out-of-pocket for more expensive plans, demand is found to be much more responsive to price. For example, Dowd and Feldman (1994/95) found that the demand for a health plan is highly elastic with respect to price at about -7.9 when multiple similar plans are offered. Strombom et al. (2002) estimate elasticities ranging from -2.0 to -8.4 depending on the cost of switching plans as measured by age, job tenure, and medical risk category.
