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Over the course of a year, individuals are at risk for a variety of unfortunate and unpredictable events, e.g., property damage due to fire or hurricane, property loss due to burglary, or physical and mental pain and suffering due to adverse health events. In most cases, affected individuals can purchase goods or services to replace the loss or to alleviate the adverse effects of an untoward event. In some cases, it is possible to reduce the probability that an adverse event will occur. In many instances, through the purchase of insurance, it is also possible to reduce financial loss associated with an adverse event. In general, people dislike risk and are willing to trade a small amount of money, in the form of an insurance premium, for protection against a potentially large loss in income. (Depending on what kind of health insurance system, particularly whether it is a private or public system, the payment can be either a private insurance premium paid out of pocket or through a reduction in wages or a public premium in the form of taxes. For simplicity, we will refer to the payment as a premium. Similarly, the bearer of risk under insurance can be a private company or a public governmental body. We will refer to the bearer of risk as the insurer.)
This research paper outlines the basic economic models of health insurance, emphasizing the relationship between risk and insurance demand. It also discusses the distortions in the market for health care services created by health insurance.
1. Risk And The Demand For Insurance
The relationship between risk and insurance demand is derived from the relationship between utility and wealth (for additional discussion see Arrow 1963). Utility is a function of wealth, with more wealth leading to higher levels of utility or satisfaction. Although utility rises with wealth, it is generally assumed to do so at a decreasing rate. This property is called diminishing marginal utility. Each incremental increase in wealth provides a smaller incremental increase in utility. It therefore follows that the gain in utility associated with any incremental gain in wealth is less than the loss in utility associated with an equivalent loss of wealth.
The property of diminishing marginal utility implies individuals are risk a verse. That is, individuals would prefer to have any level of wealth with certainty than a gamble providing the same level of wealth on average. For example, a risk averse individual would prefer $100 dollars with certainty as opposed to a gamble with a 50 percent chance of winning $200 and a 50 percent chance of winning $0. Risk aversion is an inherent property of a concave utility function. Because risk averse individuals prefer certainty, the premium they are willing to pay for an insurance policy that removes risk exceeds the actuarially fair premium (AFP) of the insurance, which is the amount that the insurer would have to pay out, on average, for this policy. The gap between the premium individuals are willing to pay and the AFP is termed the risk premium (Phelps 1997).
The risk premium allows insurers to cover expenses above the medical payout, e.g., claims processing. Several factors determine the size of the risk premium an individual will be willing to pay. First, risk aversion is likely to vary with wealth. For very different reasons, both individuals with very high and those with very low levels of wealth are less willing to pay a risk premium (Feldstein 1999). The marginal disutility of an incremental decrease in wealth falls at high levels of wealth, reducing any utility gain to avoiding risk. In contrast, the marginal disutility becomes very large at very low levels of wealth, making the opportunity cost of purchasing insurance too high.
Second, the probability of a loss will influence the size of the risk premium. As the probability of the loss approaches 1, the willingness to pay for insurance rises, but more slowly than the increase in the AFP for that individual. Thus the risk premium falls. In the extreme case, when the probability of a loss equals 1, the risk premium goes to zero. In this case, there is no risk and individuals would not be willing to pay any risk premium. Similarly as the probability of a loss goes to zero, both the willingness to pay and AFP fall, but the willingness to pay falls faster and eventually the risk premium equals zero. Individuals would not pay for insurance if the probability of a loss equaled zero.
Third, the magnitude of the loss affects the risk premium individuals are willing to pay. A greater loss represents an increase in the variance of income. An individual will be willing to pay a higher risk premium for a higher cost illness.
The utility curve depicted in Fig. 1 can be used to analyze the demand for insurance described above. Throughout the analysis we assume individuals know the probability they will suffer a loss (or benefit from a gain). Because greater wealth leads to higher utility, the utility at point C, U(C), is greater than the utility at points A or B. Diminishing marginal utility implies that if point B is equidistant from points A and C, the utility gained from moving from B to C is less than the utility lost from moving from B to A.
Consider an individual at wealth B evaluating a gamble with outcomes A and C, each of which has a 50 percent probability of occurring (e.g., tossing a fair coin). If point B is equidistant from points A and C, the expected wealth resulting from the gamble, i.e., where on a erage the individual could expect to be if tossing the coin, is the initial level of wealth, B. The expected utility of such a gamble, EU (gamble), is the probability weighted sum of the two outcomes A and C and, because each outcome has a 50 percent chance of occurring, can be determined by finding the midpoint on the chord connecting A and C. Because the utility curve is concave, even though the initial level of wealth is the same as the expected wealth of the gamble, the utility of B, U(B), will exceed the expected utility of the gamble, EU (gamble). This utility gain of avoiding risk is key to the demand for insurance.
Models of health insurance fit exactly into this model. For simplicity, assume a world in which there is only one type of adverse health event and spending in the unhealthy state is unaffected by the presence of insurance. Individuals are assumed to start with wealth level C and remain there if healthy during the year. If they suffer an illness shock, they will then spend C-A on health care services. Assuming the probability of a loss is 50 percent, the expected loss is C-B. Expected wealth, under uncertainty, is B. Without insurance the individual would have expected utility of EU (gamble).
Now imagine individuals could purchase an insurance contract that would pay the costs of medical care in the event of an illness. With a 50 percent chance of each individual incurring the loss, the expected cost to the insurer of each enrollee is C-B. The AFP therefore is C-B. If individuals pay the AFP, their wealth level is B, regardless of whether the illness occurs. In other words, the risk of financial loss has been eliminated. The individual has turned a potentially large loss in income into a smaller known loss of income (in the form of the AFP). In this situation, the utility would be U(B) because the income level B is achieved with certainty. As is clear from the figure, the individual prefers to purchase insurance relative to self-insuring. The amount of the utility gain is equal to the vertical distance between U(B) and EU (gamble). The greater the concavity of the utility curve, the greater the risk aversion and the greater the utility gain from insurance.
The utility curve depicted in Fig. 1 also can be used to assess the amount that an individual would be willing to pay for insurance. Utility of a wealth level of x, with certainty, is equivalent to the expected utility of remaining uninsured (facing the risk of having a loss that leaves them at wealth level A). Thus an individual would be indifferent between being uninsured or paying a premium of C-x for insurance. This premium is their maximum willingness to pay for insurance (WTP), with C-B the AFP and B-x the risk premium.
2. Moral Hazard
Up until now, the magnitude of the loss associated with an illness was not affected by the presence of insurance coverage for the desired medical care services. Substantial theoretical and empirical work suggests that this is not the case (Pauly 1968, Manning et al. 1987, Newhouse 1992). Specifically, because health insurance lowers the price of medical care services faced by the consumer at the time of purchase, individuals will often consume more care than they would if they paid the full price. The providers of this care are paid the full price, however, receiving out of pocket payments from the patient and reimbursement from the insurer.
The consequences of this behavior, known as moral hazard, depend in part on the difference between the cost of the care and the value individuals place on that care. Because individuals do not demand this same level of care without insurance, standard economic models assume that the value they place on the care is less than the full cost of that care. If this is true, insurance causes a loss in consumer welfare because of the insurance-induced increase in consumption, whose costs are passed back to the consumer in the form of higher insurance premiums. The welfare loss is thus incurred by the enrollee at the time the insurance premium is paid, not when care is received. This welfare loss accrues even if, as is the case in most complex insurance markets, the individual is not purchasing health insurance directly and may in fact not be aware of the welfare loss. In aggregate, adjusting for transfers between individuals, the amount paid through premiums exceeds the value of care financed by the insurance.
This analysis is depicted graphically in Fig. 2. The demand curve tells us how much medical care will be demanded for any given price. For example, assume the price of care, as paid to the provider of care, is denoted Pp. In this case, uninsured individuals would purchase q* units of care. If insurance lowered the individual’s out of pocket price to Pc, insured individuals would then consume q** units of care.
The demand curve is taken as the measure of value because it also represents the maximum amount an individual would be willing to pay for any given quantity of care. For example the maximum amount an individual would pay for q* is Pp. The overall value placed on all care up to any quantity is the area under the demand curve up to that point. For an uninsured individual, the value of care consumed would be the area under the demand curve up to q* (ABq*0). For an insured individual, it would be represented by ACq**0.
The total cost of care, paid by the individual and insurer, is the price paid to the provider times the quantity of services provided. In the case of an uninsured individual, it would be Pp times q* (PPBq*0). Notice that the value of care to the consumer exceeds the costs of the care by the portion of the area under the demand curve not included in the box (PPAB). This net value to the consumer is termed consumer surplus (CS).
If the individual purchases insurance and then increases consumption, the total cost of care increases to PpDq**0. Notice the incremental cost of the care purchased, BDq**q*, exceeds the incremental value to the consumer, BCq**q*. The amount by which the incremental cost exceeds the incremental value represents the welfare loss (WL) of insurance and is represented by the triangle BDC.
At the time that care is consumed, the individual only pays a price of Pc, so the out of pocket cost is PcCq**0. The actuarial cost of the care to the insurer, however, is PpDCPc. It is this cost, not the out of pocket cost, that determines the AFP. As noted above, the welfare loss is thus incurred at the time of insurance purchase. If the demand curve were inelastic, that is, if the level of consumption were not very responsive to changes in price, the welfare loss would be relatively small. Consumers, if aware of the welfare loss, would prefer to consume less in exchange for an appropriately lower premium, particularly in cases in which the welfare loss is large (elastic demand).
There are three important assumptions that would affect the size of the welfare loss. First, the analysis assumes that individuals other than the patient receiving the care do not receive positive utility from that consumption. If this positive externality exists, the welfare loss is reduced. Second, the analysis assumes that the price paid to providers is equal to marginal cost (as would be the case if it were set in a competitive market). If the price were set in an imperfectly competitive market, so that it exceeded marginal cost, the welfare loss from a societal prospective would be diminished. Third, the preceding analysis assumes that income effects associated with paying the premium and the transfer of income from healthy to sick individuals have only small effects on the consumption of medical care. Nyman and Maude-Griffin (2001) suggests that if these effects are large, the welfare loss is considerably reduced.
Many different approaches might be taken to minimize the welfare loss associated with insurance. For example, increasing consumer cost-sharing for medical care services would reduce utilization but has the disadvantage of increasing the size of the financial risk faced by the consumer. Increasing provider costsharing through a variety of financial incentive systems would reduce utilization, but has the potential disadvantage of too little care being prescribed. Private regulatory mechanisms, such as utilization review, can be implemented to constrain both where and what kinds of covered treatments an individual can receive. Managed care plans in the United States have been using these and other approaches to restrain use. In some cases, plans select providers whose preferred practice style leads to lower levels of utilization, particularly of higher cost alternatives. Some plans also educate both enrollees and providers to keep utilization below that which would otherwise occur. The extent to which various strategies are used will depend on the extent to which plans are in competition with other plans and the preferences of purchasers.
Nationalized systems can use similar strategies, limiting the resources available to provide care or providing financial and nonfinancial incentives to both providers and consumers to keep utilization at lower levels. Nationalized systems may also use their bargaining power to obtain favorable prices for medical care services.
3. Insurable Hazards
Given the analysis above, the theory of insurance would make several predictions regarding for which types of risks individuals would likely seek insurance coverage. First, they would seek insurance for services to treat events for which the probability of occurring is neither zero nor one. In other words, individuals would not want to buy insurance for protection against events for which they are not at risk, either because they know they will seek these services or because they know that they are at minimal risk of needing those services. Theory would predict that events with intermediate probabilities, that is, services with high-risk premiums, would generate the most demand. Thus the model would predict that most individuals would not purchase insurance to cover preventive services. The use of preventive services is not stochastic; that is, individuals know the probability of using these services in advance. Second, services that are costly would also have high risk premiums and would be attractive to insure. Third, individuals would not seek coverage for services for which demand is very elastic because such insurance would generate substantial welfare loss.
4. Adverse Selection
The preceding discussion was based on the utility curve for a single individual. To move the analysis to the market level, one must consider the behavior of many individuals, each with their own utility curve, initial wealth, and risk. Some individuals will be relatively low risk with low AFPs and others will be higher risk with high AFPs. Most models assume that individuals have more information about the risk that they face than do the insurers. If an insurer were to base the premium it charged to a defined group of individuals on the estimated average AFP of all these individuals plus some mark-up, there would be some whose WTP was below the premium and others whose WTP was above the premium. If insurance purchase were voluntary, the individuals whose WTP was below the premium would opt not to purchase coverage, leaving a smaller pool of higher risk buyers. The average AFP for those remaining in the pool would rise. Of course as the AFP rose, the insurer would need to raise the premium in the next cycle. Some of the individuals who had remained in the first cycle would find the new premium above their WTP and would also opt out of buying coverage. This nonrandom selection out of the pool would result in an increase in the average AFP for the decreasing number of everhigher risk individuals still interested in insurance.
Several papers outline scenarios in which insurance markets may collapse due to adverse selection (Akerlof 1970, Rothschild and Stiglitz 1976, Cutler and Reber 1998). In their seminal work, Rothschild and Stiglitz (1976) demonstrate that the set of policies that will be offered in the market is constrained by the ability of insurers to enter the market with new policies. This situation arises because insurers cannot perfectly ascertain the characteristics of the individuals they enroll. Certain policies cannot be offered in equilibrium because new insurers could enter the market and attract the lowest cost enrollees, leaving incumbent insurers with the higher cost enrollees, whose premiums do not cover their expected losses. In this environment, if an equilibrium does exist, it will be a separating equilibrium characterized by high risk individuals purchasing their most preferred actuarially fair policy and low risk individuals purchasing an insurance policy inferior to their most preferred actuarially fair policy, which will not be offered. Equilibrium is more likely to exist when there is a relatively large number of high-risk individuals and when the variation in risks is great.
Subsequent work indicates that the constraint on the set of policies offered depends on the equilibrium concept employed. Specifically, alternative equilibrium concepts can give rise to pooling equilibria (Wilson 1977) or even equilibria in which insurers may use profits on one product to subsidize losses on another (Spence 1978). All of the work in this area emphasizes the point that free entry into a market with asymmetric information limits the set of policies available because of adverse selection. Feldman et al. (1998) demonstrate that compulsory partial coverage may improve consumer welfare relative to a competitive equilibrium or compulsory comprehensive coverage.
Nationalized systems of insurance can reduce or eliminate adverse selection, depending on the degree to which coverage is compulsory and competition occurs within the system. Typically this would benefit those with the highest expected expenditure, at the expense of those with less expected expenditures. The benefits of reducing adverse selection must be weighed against reductions in the ability of individuals to select their most preferred benefit design.
5. Empirical Evidence
5.1 Magnitude Of Moral Hazard
The magnitude of moral hazard associated with the purchase of health insurance depends directly on the elasticity of the demand for medical care, i.e., how responsive consumers are to changes in the price. Manning et al. (1987) report estimates from a randomized trial indicating that the overall elasticity of medical care is – 0.17, that is, a 0.17 percent increase in utilization occurs for every 1 percent decrease in price. Demand for hospital services was estimated to be the least elastic (-0.14) and demand for well visits was estimated to be the most elastic (-0.43). These estimates are broadly consistent with other estimates derived from non-randomized settings (Feldstein 1999).
Estimated elasticities for other services tend to be somewhat higher than those for hospital and physician services. For example, elasticity of demand for pharmaceuticals has been estimated at about -0.40 (Smith and Garner 1974). Demand elasticity for nursing home care has been estimated at -0.76 (Lamberton et al. 1986).
5.2 The Demand For Insurance
The theory outlined above suggests that insurance demand is likely to be greatest for services with a high expected expenditure. In general, the evidence is consistent with the theory: services with a large estimated loss were more likely to be covered with insurance (Feldstein 1999). In addition, we would expect insurance demand to be greatest for services with highly inelastic demand. Again, evidence is consistent with theory. That is, the less price responsive the demand for the services, and therefore the smaller the moral hazard and associated welfare loss, the higher the level of insurance coverage (Phelps 1997).
Taken together, these factors explain much of the variation in service coverage witnessed among working adults in the U.S. For example, 76 percent of all employees participate in the medical care benefit offered by their employer, whereas only 59 percent participate in the dental care benefit, and 26 percent in the vision care benefit ( USDOL, BLS, p. 6). Of those participating in the medical care benefit, 100 percent have coverage for hospital room and board, inpatient surgery, and inpatient physician visits; 85 percent have coverage for home health care, 60–66 percent for well baby care, physical exams, and hospice care, 52 percent for immunization and inoculation, and only 35 percent for hearing care (same source, p. 48).
Although measuring risk aversion is difficult, Barsky et al. (1997) used survey responses from the Health and Retirement Study regarding a respondent’s willingness to take a new job with uncertain earnings to classify individuals based on their degree of risk aversion. They then related this measure of risk aversion to a variety of behaviors, including the purchase of health insurance. Stratifying by employment status (self-employed, employed, and not employed), they find that within each strata, the more risk averse respondents are more likely to purchase insurance.
5.3 Adverse Selection
Considerable evidence suggests that when given a choice individuals make health plan decisions based on their anticipated medical expenditures, thus generating nonrandom and, from the insurer’s perspective, adverse selection. Much of the literature examines enrollment patterns when individuals face multiple insurance options that vary in terms of generosity. Even though a variety of data sources and methods have been used to investigate the self-selection into a range of plan options, the evidence suggests that adverse selection is quantitatively large (Cutler and Zeckhauser 2000).
6. Conclusions
Health insurance provides value to individuals by reducing the risk of a large financial loss associated with an adverse health event. This allows individuals to obtain medical care that they otherwise might not be able to afford. The payment from the insurer serves as a transfer of income to individuals who become ill.
However, if left unchecked, health insurance markets generate two deleterious effects. First, by lowering the patient’s cost of consuming medical care, insurance leads to an increase in utilization (moral hazard). This increased consumption results in welfare loss. Second, insurance markets have a tendency to be unstable because of adverse selection. In the extreme, non-random selection could cause insurance markets to unravel, leaving some or all individuals uncovered and distorting the set of plans offered in the market.
Most health insurance systems, whether private or public, incorporate a variety of strategies to limit the welfare loss from the overconsumption of medical care and the effects of adverse selection. Inherently these strategies involve restrictions on individual behaviors. The challenge in most systems is to mitigate the unwanted consequences of insurance as much as possible while still accomplishing the fundamental goal of reducing risk.
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