Healthcare Economics

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Chapter 4 Health Insurance Healthcare demand is inextricably associated with insurance demand due, fundamentally, to individual risk aversion that reflects willingness to pay for reducing the financial risk one faces. Since the financial burden of an episode of illness is often large with respect to most individuals’ incomes and the illness itself unpredictable, individuals demand insurance, i.e. they want to spread and smooth out such random variations in their wealth. Moreover, since this illness-related financial burden is mostly invariant to one’s income1, health insurance is regularly provided publicly as part of social insurance in a large number of countries. Public health insurance is also motivated by the fact that, by increasing coverage and hence producing a positive impact on the workforce, it may boost earning power. Ironically, as higher incomes positively affect health, there exists a simultaneity (Lynch [2004]). Yet, in many countries that build universal coverage health insurance systems, coverage is neither uniform nor publicly provided. This chapter includes a simple but rigorous presentation of individual demand for insurance while deferring the details of healthcare provision as social insurance to the part on healthcare system analysis. Both aspects of healthcare insurance were first rigorously analyzed in Arrow [1963]. Whereas personal demand for insurance arises from individuals’ concern for sharp variations in their wealth, social insurance is a social solidarity phenomenon. Although there may be economic efficiency reasons, such as a healthier workforce (Deaton [2002]) and economies of scale in administration, favouring social insurance (Hussey & Anderson [2003]), the insurance affordability prevails as the main reason for public provision (Besley & Gouveia [1994]). Many countries have developed differing institutional arrangements and varying amounts of coverage in the provision of health insurance. a. Demand for insurance Risk-averse individuals facing risky prospects demand insurance. We will first break down this loaded statement into its four components. Firstly, a risky prospect is simply the possibility that a decision-maker will face mutually exclusive future financial states of the world, i.e. any one of those states may turn out to be the case. These may be, for example, a state where one continues to possess his car as is and another where the car is stolen or subject to an accident as a result of which the owner incurs a financial loss. A loss state implies a significantly different financial state than the one in which the owner continues to possess his car. In the case of health, a serious but curable illness possibility implies different financial prospects as the unhealthy individual will have to pay for medical care and his financial situation is significantly worse than in a healthy state. Secondly, in both cases, the difference in financial outcomes implies that the individual would have enjoyed different levels of wealth in the two states and, correspondingly, different marginal utilities of wealth, higher with lower wealth and vice versa. If neither state can be ruled out ex ante, i.e. neither is assigned zero probability, then the

1 There exists, however, some evidence that there is an “income gradient”, i.e. higher income means better health (see Deaton [2002], Lynch et al. [2004]).

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individual’s expected utility2 will be higher if some wealth can be transferred from the high to low wealth state. This happens because the marginal utility of low wealth is higher than that of high wealth (see Figure 4.1). If a dollar is transferred from a high to low wealth state, the marginal utility lost from the former exceeds that gained from the latter. This, then, is a net increase in the individual’s total utility. Thus, thirdly, the risk- averse3 individual would be willing to pay for a transfer of wealth across states because the transfer increases her total utility. This transfer requires contracting with a third party that could assure the individual that, in return for a sure fee (i.e. a fee paid regardless of the state), compensation will be available in case of financial loss. The availability of such a contract turns the demand for insurance into a market insurance contract. Finally, there is evidently a strong link between demands for healthcare and for healthcare insurance (Dusansky & Koc [2006]), i.e. those who are to demand healthcare (and that would be all of us) do demand health insurance beyond the pure insurance motivations. As we saw in the previous chapter, the health stock is desirable in itself as well as it enables one’s earning capacity. Combined with the inherent unpredictability of healthcare expenses, not only demand for healthcare influences individuals’ healthcare insurance contract choices but also a feedback phenomenon exists in the form of the terms of insurance contracts and affects the demand for healthcare. It goes without saying that the availability (that insurers are willing to offer contracts) and affordability (that insurance is available at prices lower than the price at which demand is choked) of insurance also depends on the supply side. Since insurance is a transfer of risk from insuree to insurer, insurers’ profitability will determine the existence of market provision to which we will return below. We now consider Figure 4.1, below, where the utility function reflects decreasing marginal utility by its concavity. As explained below, this property of individuals’ utility functions will yield risk aversion and, hence, demand for insurance. The wealth levels wB0 = W – L and wG0 = W are, respectively, the individual’s wealth in loss and no-loss states of the world. Correspondingly, she would derive utilities u(wB0) and u(wG0) in the respective states. However, none of these states are to occur with certainty when, ex ante, the individual is making an insurance decision. Of course, ex post, the individual is in one of the two mutually exclusive states. The likelihoods of the ex post states, whether computed objectively or subjectively4, are p for the loss state and (1 – p) for the no-loss state. The loss is given by L = wG0 – wB0 whereas we = pwB0 + (1 – p)wG0 is the expected wealth and w0 the certainty equivalent of the risky prospect because u(w0) = pu(wB0) + (1

2 The expected utility consists of the weighted average of her utilities in the two states. Since the insurance decision precedes the knowledge of the exact state of the world, economic analysis typically postulates that individuals maximize their expected utility, the weights representing the likelihood of a state’s occurrence. These weights may be endogenous (or at least partially determined by the decision-maker) or exogenous, and objective or subjective. See any microeconomics textbook for a discussion of the expected utility hypothesis. 3 A risk-averse individual strictly prefers the expected value of a risky prospect to the risk. In the current case for health insurance, it amounts to u(we) > pu(wB

0) + (1 – p)u(wG 0) in Figure 4.1.

4 The objective determination of these probabilities is simply based on count data on past group occurrences. Insurers use this information in designing and supplying contracts. Individuals, on the other hand, form their own subjective evaluations of the states’ occurrences when forming their demands for insurance contracts.

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–p)u(wG0), the utility provided by w0 is equal to the expected utility from the risky prospect. In fact, the difference (we – w0) is called the risk premium. u u(wG0) u(w) EU0 EU0 = pu(wB0) + (1 – p)u(wG0) u(wB0) wB0 w0 we wG0 w we = pwB0 + (1 – p)wG0 wG wG0 w0 EU(wB,wG;p) = u(w0) = EU0

slope = – p

p −1

450 wB0 w0 wB Figure 4.1 Derivation of state-space indifference curves

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Figure 4.1 graphically displays the concept of risk aversion. Those individuals who exhibit a positive risk aversion have positive demands for insurance. They are willing to pay to transfer the financial risk onto others. In fact, such a transfer would be acceptable if the contract premium is low enough that the individual attains at least the expected utility EU0 she would have had on her own, facing the risky prospect. This means that the choking price for coverage L would be exactly equal to (wG0 – W) because, for a higher premium, she would do better on her own. Thus any premium lower than (wG0 – W) combined with the full coverage L would leave the individual better off with insurance. The economic analysis of insurance is best represented graphically in a state-space diagram that allows the explicit representation of the demand and supply prices5 of insurance or, in other words, of indifference curves and a budget constraint. Moreover, the analysis of informational problems of adverse selection, ex ante and ex post moral hazard finds intuitive representations in state-space diagrams. Figure 4.1 explains the transition from the introductory explanation, above, of risk- aversion and demand for insurance to a state-space diagram. The individual’s initial bundle or endowment is (wB0,wG0). The slope of the indifference curve passing through this bundle is evidently very steep as the marginal utility of wB0 far exceeds that of wG0. Note how wG0 in the bottom panel is derived from the top by using the 450 line as the reflector. The slope of the indifference curve when it crosses the 450 line is equal to – p/(1 – p) (as explained in Appendix 4A) and of course much flatter than at (wB0,wG0). This graphically yields the convexity of the indifference curves towards the origin. Intuitively, the convexity of the indifference curves corresponds to risk aversion. Since a risky prospect in the current context is where wealth is significantly different in the two states, the marginal utilities will likewise be different, a high marginal utility for low wealth in the loss state and a low marginal utility for high wealth in the no-loss state. The high marginal utility in the bad state with low wealth (the numerator of the slope) will quickly fall whereas the marginal utility in the good state with high wealth (the denominator of the slope) will slowly increase when the gap closes towards full insurance. These opposite changes in marginal utilities indicate that the slope becomes flatter and converges to – p/(1 – p) along the 450 line where wealth is equalized across states or, in other words, no risk exists any longer. In Figure 4.2 below, two full coverage contracts are shown, w0 and w1. The former yields as much utility as the individual would have enjoyed without insurance at the initial situation whereas the latter strictly increases her utility above the initial level. An individual’s demand price6 for an extra dollar of coverage is then simply the slope of his indifference curve as the slope represents the maximum amount the individual is willing to sacrifice in the no-loss state in order to buy the one-dollar coverage in the loss 5 Keeping with conventions, the price of insurance, as different from the contract premium, is defined as the unit price for insurance, i.e. the amount payable per dollar of coverage. 6 The demand price is the maximum unit price that a potential buyer is willing to pay for a given quantity of a good. The willingness to pay is also constrained by the ability to pay. The collection of demand prices, as a schedule, constitutes a demand curve.

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state. Consistent with standard demand curves, the convexity of the indifference curve towards the origin ensures a decreasing demand price or marginal willingness to pay for extra coverage. wG w0 wG0 • Complete coverage

wFI slope = – p

p −1

π = 0 U(wB,wG) = U0 450 wB0 wFI wG0 wB Figure 4.2 Complete coverage insurance contract The budget constraint in Figure 4.2, originating at the individual’s initial endowment and with slope – p/(1 – p), is called a fair odds line and represents an actuarially fair transfer of funds from the good to the bad state. It reflects competitive insurance provision under the rather strong assumption that insurance companies face no administrative costs. Competitive insurance provision implies that any demanded contract will be supplied by some company provided it makes a non-negative profit. In such an environment, an insurance company’s expected profit can be formulated as a function of the loss probability, the premium R7 and the coverage Q as πe = p(R – Q) + (1 – p)R.

7 The premium can always be expressed as a fraction r of the chosen coverage Q without affecting the derivation.

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Noting that (Q – R) = dwB and (– R) = dwG and, also, under perfect competition, expected profits will be driven down to zero8, one obtains πe = – pdwB – (1 – p)dwG = 0 and the slope of the budget constraint is thus obtained as

B

G

dw dw

= – )1( p

p −

.

Given that the initial endowment point is part of the budget set, the budget line is hence obtained. Returning to Figure 4.2, facing such a budget constraint, the individual will choose Q = L, i.e. full coverage and the corresponding premium R1 will be equal to the actuarially fair cost of the coverage, i.e. R1 = pL = wG0 – w1. This corresponds to a premium of p per dollar covered. Note that, if the full coverage contract happened to be w0, then the premium would have been equal to R0 = pL + (w1 – W) = wG0 – W. As seen in Figure 4.2, this latter contract leaves the individual indifferent between remaining uninsured at {W – L, W} and purchasing full coverage at w0, with the high premium R0. The last incremental step towards the demand curve for insurance is the addition of loading costs, i.e. the costs of actually running the insurance firm. Although theoretically simple, loading costs constitute a significant proportion of premia in general9. In case loading costs are proportional to coverage, the actuarially fair premium per dollar of coverage is just augmented by the unit loading cost r = p + t. We note that, as above, [Q – R] = dwB and [– R] = dwG. Thence, the slope of the budget line, as developed in Appendix 4B and shown in Figure 4.3 below, is steeper and individuals will purchase incomplete coverage and the loading cost imposes a lower utility on insurees. The zero expected profits requirement for the existence of insurance10 implies that the addition of loading cost t reduces the demand for insurance as individuals facing a premium exceeding the actuarially fair rate choose less than complete coverage. The intuition for the incomplete coverage solution hinges on the individual’s willingness to pay for extra coverage or, simply, her demand price for insurance. As the supply price of insurance is higher with loading costs added (i.e. p+t rather than just p), the individual’s demand price falls to p+t faster in terms of coverage demanded. In other words, the demand price falls below the supply price well before full coverage Q = L. 8 If any insurance contract is expected to yield strictly positive profits, it will be offered. And, of course, loss contracts will be withdrawn. 9 American private insurance loading costs have been estimated at 24 cents in the dollar. See Wolf [2007]. 10 See Appendix 4B. The dissipation of expected profits is, however, to be qualified because, in reality, insurance firms are also risk-averse and they would build risk premia into their pricing. However, for a first approximation, the expository and pedagogical gain to assuming zero expected profits outweighs the lack of realism therein.

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wG w0 wG0 Incomplete coverage

wGINC slope = – p

p −1

π < 0

450 slope = – tp

tp −−

+ )1(

and π = 0

wB0 wBINC wB Figure 4.3 Loading cost and incomplete coverage Insurer loading costs consist of overheads and other administrative costs. It must be noted that insurees incur loading costs averaged over the number of insurees rather than their individual coverage. Consequently, if the loading cost component of an individual’s premium is taken as constant, it provides some incentive for the individual to spread it over a larger coverage. The demand for insurance is thus defined as the coverage required in response to the market premium that is the price for dollar of coverage. Tracing the amount of coverage demanded in response to changes in premia thus yields the demand curve for insurance, as drawn in Figure 4.4 below. There is graphic congruence between this case and the two other reasons why insurance demand may fall short of complete coverage. The incompleteness of coverage also arises of informational problems in insurance markets. The budget constraint introduced above will be key to understanding the two informational problems of adverse selection and moral hazard that we now turn to.

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wG wG0 EU(wB,wG;pL) = EU(wB0,wG0;pL) Complete coverage

wFull slope = – L

L

p p −1

π(pH) = 0 π(pL) = 0 450 wB0 wFull wG0 wB a pH pL QD QFI Q Figure 4.4 Insurance coverage demand

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b. Insurance markets and information problems The economics of information has found perhaps its most fertile application in insurance because, plainly, insurance markets are inextricably grounded in elicitation and integration of information into contract design. The information in question relates to the identification of different pools of insurees with similar characteristics and, once in the pools and covered, to their behaviour that is costly to observe. Insurers’ two fundamental concerns are the matching of contracts to potential insurees and the design of contract incentives so as to affect insuree behaviour upon being covered. The first concern is the self-selection (or adverse selection) problem and the second the moral hazard problem. In turn, the moral hazard problem has the ex ante and the ex post components. The first refers to the insuree’s effect on the likelihood of a loss covered under the contract and the second on the size of the loss. As an example of adverse selection, consider the case of the chronically ill11. The self- selection problem would arise if insurers offered premia based on averages whereas policies are purchased only by chronically ill who are normally expected to make frequent and large claims, if not for treatment but for medications. Thus, insurers would earn negative profits if a larger percentage of such people purchased policies than anticipated by insurers. Provided all buy the average contract, the insurers would not lose. However, if not, the marketplace would force insurers to try to segment the general pool of potential insurees into more homogeneous pools by designing profitable contracts that are relatively more attractive and specific to each pool. If any pool supports profitable contracts then the insurance market ought to work properly, matching a particular pool of insurees with corresponding insurance contracts. If not, a market failure12 will arise due to this first type of information problem. The adverse selection problem thus arises when there is a mismatch between the type of insuree, not necessarily known to the insurer, and the contract designed with a particular insuree in mind. Surprisingly, this may occur as a result of ex ante mismatch in which wrong people joining a particular insurance plan or, simply, a plan retaining only the wrong people (Altman et al. [1998]). To understand the problem, let us consider Figure 4.5a below and assume, temporarily, that the insurer has complete information on potential insurees, i.e. the insurer knows their risk types. To simplify the exposition, we will henceforth consider two risk types represented by illness probabilities pL and pH corresponding, respectively, to low-risk and high-risk insurees. As in Figure 4.4, these two homogeneous groups, whose members

11 This is an interesting category because, quietly, most types of cancer joined the chronic illness category where the ill carry the illness at bay for the long term. 12 A market failure is a market outcome that is an equilibrium but a suboptimal one in that the market allocation can be improved upon had it not been for reasons impeding the proper functioning of markets. These reasons typically include non-competitive behaviour arising from such sources as market entry and exit restrictions that induce market power, lack and/or asymmetry of information on tastes and technology of market participants, ill-defined property rights leading to public goods and externalities, transactions costs that prevent a market’s functioning and, finally, technologies that induce large scale economies.

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being perfectly known to the insurer, are offered the complete coverage contracts {wL,wL} and {wH,wH} with respective premia rL = wG0 – wL and rH = wG0 – wH such that rH > rL simply because pH > pL. Thus the riskier class members pay a higher premium. We note that both complete coverage contracts yield zero expected profits, an outcome consistent with perfect competition. If insurer information is incomplete, i.e. the insurer no longer is able to identify members of a risk group, the high-risk group members adversely self-select into purchasing the contract {wL,wL}, the one designed for the low-risk group and that would break even only if low-risk members purchased it. Understandably, the threat of negative profits from high-risk members purchasing low-risk type contracts would have insurers anticipate this adverse selection phenomenon and respond. While we will return to the impossibility of pooling (or blending) contracts below in Figure 4.5b, we now consider an attempt at separating risk groups. In Figure 4.5a, {wH,wH} and {wBL,wGL} allow separation, the first weakly preferred by high-risk types and the second strongly preferred by low-risk types. We note that the market fails due to incomplete information (as the insurer has less information than individual risk group members on their own risk categories) in that the overall welfare is lower than in the case of complete information. Although the high-risk group members do not suffer a welfare loss, their presence imposes negative externalities on the low-risk members whose loss of utility is equal to (UL1 – UL2). wG UL2 UL1 (wB0,wG0) • wGL πL = 0 and

slope = – L

L

p p −1

UH1 UHADVERSE

slope = – H

H

p p −1

450 and πH = 0 wBL wH wL wB Figure 4.5a Adverse selection and incomplete coverage

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A set of uniform-premium contracts or a pooling one (identical for all) for all will not arise under competitive market conditions because cream-skimming insurers will break ranks and pry away healthy individuals with lower premia in return for accepting some risk. Consider Figure 4.5b below with uniform-premium case illustrated, {wH1,wH1} chosen by high risks as more than complete coverage will not be available and {wBL1,wGL1} for low risks. The wedge-shaped area enclosed by the two individuals’ indifference curves and the fair premium budget line for low risks includes profitable contracts that attract only low risks. Thus the market will be segmented and the emerging equilibrium can only be of a separating type where low and high risks pay different premia13. wG UH Cream-skimming contracts UL (wB0,wG0) • wGL wH

slopeL = – L

L

p p −1

UH and πL = 0 slopeAVERAGE and πAVERAGE = 0

slopeH = – H

H

p p −1

450 and πH = 0 wBL wH wB Figure 4.5b Adverse selection and community rates We can now proceed to analyze the case of incentives in health insurance. As an example of ex ante moral hazard, consider the behaviour of an insuree vis-à-vis lowering the

12 A separating equilibrium may not exist if the proportion of low risk types is so large that separation may break down due to insurers offering a pooling contract that would trade off low risks’ low premium for lower risk in such a way to make them better off pooling with high-risk types. Thus, in Figure 4.5a, the pooling budget line would be closer to that for low risks’ and allow them an increase in utility.

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likelihood of ill health by improving one’s diet and physical activity (AAFP [2007]). Eating well necessarily imposes a constraint thus requires some effort and physical activity not only requires effort but also is typically costly. In the absence of positive incentives (or strong inner motivation) lowering the cost of taking these preventive measures, individuals would normally choose suboptimal levels. The failure therein of an individual to undertake these preventive measures upon purchasing insurance that would mitigate some of the harmful consequences through medical care leads to the ex ante moral hazard problem. In other words, complete coverage over the consequences of one’s actions tends to impel complacency, in particular if one is predisposed to have an inadequate diet and lead a sedentary lifestyle14. The very existence of health insurance coverage generates, ironically, a disincentive for conditions conducive to good health (see Osterkamp [2003] for incentives under public insurance). This, in turn, increases the cost of insurance on the average as illness becomes more likely. Law of the unintended consequences at work! Figure 4.6 below depicts the ex ante moral hazard problem with the potential insuree facing the initial allocation {wB0,wG0} in which case, on her own, she would have chosen a high level of effort as we will see from the following reasoning. The insurer lacks information on the potential insuree’s health-enhancing effort choice, either plain impossible or too costly to observe. The consequence of this asymmetry in information is that complete coverage would simply induce a suboptimal allocation because the insuree would choose a lower than optimal level of effort. To see this, first consider the complete coverage contract w1. Clearly, this contract would give a higher utility to the low effort choice by virtue of the fact that a low effort costs less whereas, in terms of benefit consequences, no difference exists because the contract is one of complete coverage at {w1,w1}. Thus, adopting the simpler notation U(wB,wG) = p(e)u(wB) + (1 – p(e))u(wG), UL1 = U(w1,w1) – v(eH) < U(w1,w1) – v(eL) = UH1 simply because low effort is less costly whereas the benefits are equal due to complete coverage. Since high effort is desired and the uninsured individual would have chosen a high level of effort, a movement along the budget line with slope equal to slopeL from {w1,w1} towards the original non-insured allocation {wB0,wG0} makes high effort more and more attractive over low effort because such a movement corresponds to increasing risk via incomplete insurance. Thus a higher effort starts dominating the low effort when incompleteness reaches a certain level where the incremental cost of high effort is more than compensated by its beneficial effect in reducing the likelihood of illness. That point is {wB2,wG2} in Figure 4.6 below. As for the insurer, it can afford to offer that allocation as a zero-profit and incomplete coverage contract with premium equal to (wG0 – wG2), which corresponds to a premium rate of pL/(1 – pL), and a deductible of (wG2 – wB2) or a

14 Regular exercise is well known to bring about numerous health benefits. It lowers high blood pressure, reduces obesity and abates the risk of heart disease, osteoporosis and diabetes. It keeps joints, tendons and ligaments flexible so it is easier to move around. It contributes to your mental well-being and helps treat depression, and helps relieve stress and anxiety. It improves sleep. It boosts one’s metabolism (the rate of of burning calories) and thus helps maintaining a normal weight. It reduces some of the effects of aging. It increases endurance and the energy level. (AAFP [2007]) In short, all consequences of regular exercise lower the probability of ill health.

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co-insurance rate of (wG2 – wB2)/L0 = (wG2 – wB2)/(wG0 – wB0). wG UL2 = UH2 (wB0,wG0) wG0 • UL1 < UH1 wG2 w1 w1 slope = – pL /(1 – pL) slope = – pH /(1 – pH) 450 wB0 wB2 w1 wG2 wB Figure 4.6 Ex ante moral hazard and incomplete coverage With ex ante moral hazard, the behavioural incentives are combined with the partially endogenous risk. Consequently, the insuree’s health status is not entirely determined by her behaviour but some randomness as well. Despite the fact that nobody would desire bad health, the presence of insurance, desirable in its own right against risk and lumpy expenditure upon illness, may induce a change in behaviour for the worse resulting in a higher probability of a poor health outcome. Contrastingly, the ex post moral hazard concerns the ex post behaviour in seeking treatments whose marginal costs may exceed their marginal benefits or, in other words, seeking unnecessary treatments. Thus the ex post moral hazard problem arises in succession to a partial resolution of the uncertainty surrounding the health status of the insuree. For example, when the insuree is ill, the illness vs. health dichotomy is resolved. However, if completely covered, she has an incentive to consume all medical services with positive benefits whether her net benefits are positive or not. This behaviour generates the ex post moral hazard with hidden knowledge as the seriousness of the illness is not precisely known to the insurer (Koc

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[2005]). The presence of this information asymmetry causes the moral hazard problem and the resulting sub-optimality. Technically, this case can be understood with the exact tools we used to explain adverse selection. Under complete coverage, the insuree has no incentive to economize on medical resources. This can be thought of as, whereas an insuree with a heavy illness need not economize, the presence of one with a light case who would mimic the heavy case would then engender the moral hazard with hidden information15, formally akin to adverse selection. The insurer, however, possesses less information on the insuree’s ex post health status (i.e. the severity of illness once the insuree is ill)16. The behavioural problem is to get the insuree to choose the treatment corresponding to her illness level rather than having a light case choosing the treatment corresponding to a heavy case or, in other words, exaggerating the required treatment. The light and heavy cases require treatments costing mL and mH as in Figure 4.7 below. As higher treatment expenditure is better and higher coinsurance rate worse, the two types’ utilities increase in the southeast direction. If the insurer possesses complete information on the claimant’s illness status then the allocation is optimal in the sense that light and heavy cases receive the proper treatments. What distinguishes the two cases is that, whereas the light-case insuree wouldn’t benefit much from extra treatment and hence wouldn’t be willing to pay in terms of coinsurance, the heavy case would benefit and hence be willing to pay more. Graphically, the marginal willingness to pay (or the subjective price of insuree for extra coverage) is given by the slope of the indifference curves in Figure 4.7. In the complete information case, (mL,0) and (mH,0) are, respectively, the optimal allocations for the light and heavy cases. These allocations yield Yet, if the insurer is asymmetrically informed and can’t distinguish between types, the light-case insuree will benefit by declaring he is a heavy case and, correspondingly, choosing the treatment mH. This is misallocation of resources and suboptimality. Though the misallocation problem may be resolved through coinsurance, suboptimality will remain due to information asymmetry. Since coinsurance is costlier to the light-case insurees, the imposition of the rate c0 deters them from taking up mH. Thus, their utility remains at uL*. However, their presence costs the heavy-case insurees in terms of utility as the bundle (mH,c0) yields them uH1, a lower level of utility than under complete information. Related to ex post moral hazard, there are three issues remaining to be discussed. First, insurance contracts typically provide incomplete coverage, whether to solve the adverse selection and the moral hazard of the ex ante variety or the ex post moral hazard.

15 Moral hazard with hidden information arises when, originally endowed with symmetric information under uncertainty, one of the parties to the contract gains an informational advantage upon the resolution of uncertainty. This is certainly the case in the present problem as, when the insuree is ill, he alone knows whether the illness is light. In this latter case, the insuree has an incentive to pretend to be a heavy case. 16 A related case of ex post moral hazard in which ex ante behaviour has an alleviating effect on ex post damages would be handled by inducing the insuree to commit to ex ante preventive measures that would, should the illness state arise, result in lower damages. These preventive measures are typically verifiable thus contract enforcement would be easy.

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Deductibles and/or coinsurance appear as insurers’ standard tools for reducing coverage for purposes of sharing risk with insurees and providing incentives to reduce moral hazard. The choice between the two types of risk-sharing tools is crucial depending on the nature and the interactions of the problems (The Economist [1995]). An eminent c uH1 uH* uL* uL0 c0 mL mH m

Figure 7 Ex post moral hazard and incomplete coverage feature of healthcare is the progressive nature of many known illnesses and, hence, the importance of early detection and intervention. Since early intervention is significantly less costly, contractual disincentives to contact one’s physician (such as a copayment or user fee17) may be counterproductive when the patient chooses to delay reporting the symptoms and the illness progresses to a level where substantial intervention becomes necessary. Moreover, the determination of contractual coverage with incentive considerations also depends on whether the insuree is able to affect the likelihood of an illness and the costs of treatment should she develop it. As opposed to adverse selection and ex ante moral hazard, the existence of an ex post moral hazard problem is essentially questionable. Once an insuree with an average understanding of medicine enters the health care system with some symptoms and channeled by the primary care physician, he then is under the care of physicians. Therefore, the choice set before the patient is characteristically defined by medical norms18 with little patient leeway although the patient selects options from choice sets along the way. That the patient is restricted reduces the relevance of ex post moral hazard 17 As opposed to a deductible, a user fee is a fixed amount per use whereas the deductible is a fixed amount for use of insurance benefits per contract period. 18 One must bear in mind the “small area variations”, an awkward term to translate the idea that medical norms are not uniform spatially and that different treatments may be the preferred choice of the local medical profession in response to same symptoms and diagnostics.

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but, in turn, increases the importance of physician agency problems, in the first as patient’s agent and in the second as the payer’s agent.19 Thus, the alleviation of the ex post moral hazard problem is more intimately related to the physician’s role as agent than the patient herself. As such, the institutions and incentives surrounding the physician will have to be the primary focus of analysis. Second, when the insurer designs insurance contracts, three ex ante states of nature are consistent with the above discussion of asymmetric information problems. However, when the first uncertainty unfolds, the insuree is either healthy or unhealthy. If she is unhealthy the seriousness of illness becomes a matter of information asymmetry and generates a problem of moral hazard with hidden knowledge. Methodologically, the insurance contract design will take as given the coinsurance necessary to solve this ex post moral hazard problem and then choose the risk-sharing and incentives to address the ex ante problems. Thus the contract design proceeds backwards whereas parties to the contract are forward-looking. We note that risk-sharing and contract incentives influence insurees’ healthcare demands in various ways. First, the initial self-selection induced through a menu of contracts aims at alleviating adverse selection. Second, the premium and coverage in each contract target stronger preventive effort on the part of insurees thus targeting the ex ante moral hazard problem. Finally, the coinsurance rate20 provides a strong incentive for the insuree, if ill, to self-select into the correct illness pool thus zeroes in on the ex post moral hazard problem. Finally, ex post moral hazard is intimately connected to social considerations. If healthcare insurance is unaffordable to an individual in the absence of social insurance and he accesses healthcare in its presence, technically speaking he is generating ex post moral hazard. Thus the presence of insurance changes his behaviour in such a way that his consumption of healthcare rises above the uninsured level. This is, of course, an expected response to changing incentives. Since insurance works by lowering the price of insured services by transferring funds from non-claimants (or insured but healthy) to claimants (insured but ill), the affordability of such services increases. To claim that this is a net welfare loss is to ignore the increase in benefits the extra service consumption provides and that would not have been available to the uninsured, who would be willing to pay but cannot21. This case is an example of second-best welfare analysis where departures from what would have been the first-best do not necessarily worsen social welfare. In fact, as claimed in Nyman [2004], the net welfare gain of social insurance, by increasing the number of insured, may be positive. c. Social insurance and public provision of insurance The healthcare insurance issue reveals to be deeper and more controversial than the fairly technical individual health insurance framework presented above. For, the powerful and justifiable social solidarity consideration retains the issue of universal healthcare insurance in policy agendas, if not for its introduction always for various modifications to 19 These agency problems are analyzed in the next two chapters. 20 See Zeckhauser [1995] for a discussion of copayments and coinsurance. 21 Economic theory has been largely quiet on this till recently (see Nyman [2004]) yet the problem was first identified by Pauly [1983]. Bundorf & Pauly [2006] revisits the issue.

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existing structures. This section will thus end the chapter with an introduction to social insurance that will be examined in detail in the later chapter on alternative organizations of healthcare systems. The bumpy history of social healthcare insurance descends to 19th century German unification under Bismarck22. The corporatist system established by the 1883 legislation in Germany was rooted in Illness Funds established along vocational boundaries. Workers in a trade became mandatory members of these insurance funds based on cost sharing by workers and employers. This structure continued, by and large, till 1990s when, in order to induce both horizontal and vertical competition, mandatory membership in one’s vocational fund was relaxed in favour of mobility across funds. This modification to the German health insurance system introduced both horizontal and vertical competition. It has relaxed the inefficient spatial and vocational locks. Moreover, it allows vertical competition in quality. As part of the social insurance framework but at a wider scale of universality, the newly elected Labour government introduced the national health insurance (and the NHS23) in 1948, based on the well-known Beveridge24 report of 1942 (Musgrove [2000]). As opposed to the German system with regulated insurance markets (Files & Murray [1995]), the British system exhibits the government as the primary insurer as well as a small but significant private parallel insurance system (Colombo & Tapay [2003], Tapay & Colombo [2004]) for those who opt out (i.e. who want to complement or supplement) and even for those who ride the fence for rainy days when they might need the swiftness of private delivery. Until recently, NHS was a unitary system with public funding and public provision. Whereas public funding continues, NHS recently started purchasing services from the private sector providers (Csaba & Fenn [1997]). The Bismarck vs. Beveridge is important in the evolution of healthcare systems as historical benchmarks in the evolution of healthcare systems with substantial regulation and universal coverage of the population. However, the set of real healthcare systems is significantly richer as they combine public and private provisions of insurance and healthcare services to varying combinations (Besley & Gouveia [1994]). Ironically, as the recent NHS experiment demonstrates, a public system can even relax the monopoly in provision of services by introducing internal markets, i.e. competition amongst providers within the public system. A further dimension along which healthcare systems can be differentiated is the degree of incompleteness of the universal public insurance coverage.

22 Otto von Bismarck (1815-1898), chancellor of Germany for a long time, 1867 to 1890, introduced components of the modern welfare state. The decentralized health insurance was introduced in 1883 and it worked locally through participation of employers and workers in its administration and with cost sharing by employers and, mostly, by workers themselves. This latter phenomenon conferred majority representation in insurance boards for workers with the consequential political advantage accruing to German Social Democrats and, eventually, setting an example to other social democratic parties elsewhere. 23 The National Health Service (NHS) is a publicly funded unitary provider of comprehensive healthcare services. 24 William Beveridge (1879-1963) served as consultant to the Liberal government (1906-1914) on old age pensions and national insurance. After serving as the director of LSE from 1919 to 1937, the wartime Conservative government commissioned him, in 1941, to produce a report on postwar social reconstruction. He reported to parliament, in 1942, on social insurance part of which was the new comprehensive health insurance scheme.

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This incompleteness may transpire in two forms, first services that are simply not covered and second the lack of complete insurance coverage for covered services. The first incompleteness potentially creates a complementary coverage market and the second the supplementary coverage market. For example, there is a surprising and remarkable resemblance between the essentially public French system with its supplementary coverage markets (Buchmueller & Couffinhal [2004]) and the Medigap insurance market in the US (Browne & Doerpinghaus [1994]) providing not only complementary but also supplementary coverage to essentially public Medicare insurance system. For the rest of US population above the official poverty level, private insurance markets in different markets cover a high percentage of the population with wildly different baskets but leave about 45 million without basic coverage (Vanness & Wolfe [2002], Woolhandler & Himmelstein [2002]). Whereas supplementary insurance is not legal in Canada with public insurance covering a substantial basket of healthcare services25, complementary insurance markets are reasonably thick (Emery & Gerrits [2006], Gordon [1998]). References AAFP (American Academy of Family Physicians) [2007], “Benefits of regular exercise”, http://familydoctor.org/online/famdocen/home/healthy/physical/basics/059.html Altman, D., D.M. Cutler & R.J. Zeckhauser [1998], “Adverse selection and adverse

retention”, American Econ. Rev., Papers and Proceedings 88(2), 122-126 Arrow, K. [1963], "Uncertainty and the Welfare Economics of Medical Care", American Econ. Review 53(5), 941-973 Besley, T. & M. Gouveia [1994], “Alternative systems of health care provision”,

Econ. Policy October, 200-258 Browne, M.J. & H. Doerpinghaus [1994], “Asymmetric information and the demand for medigap insurance”, Inquiry 31, 445-450 Buchmueller, T.C. & A. Couffinhal [2004], “Private health insurance in France”, OECD Health Working Papers No. 12 Bundorf, M.K. & M.V. Pauly [2006], “Is health insurance affordable for the uninsured”, J. Health Econ. 25(4), 650-673 Csaba, L. & P. Fenn [1997], “Contractual choice in the managed health care market: An

empirical analysis”, J. Health Econ. 16, 579-588 Colombo, F. & N. Tapay [2004], “Private health insurance in OECD countries: The benefits and costs for individuals and health systems”, OECD Health Working Papers No. 15 Colombo, F. & N. Tapay [2003], “Private health insurance in Australia: A case study”, OECD Health Working Papers No. 8 Deaton, A. [2002], “Policy implications of the gradient of health and wealth”, Health

Affairs 21, 13-30 Dusansky, R. & C. Koc [2006], “Health care, insurance, and the contract choice effect”,

Econ. Inquiry 44(1), 121-127 (The) Economist [1995], “Economics focus: An insurer’s worst nightmare”, July, 70 25 This structure grants the insurer a monopsonistic purchasing power over providers (Herndon [2002]). Of course, the extent of the basket of services covered will in turn affect the complementary insurance markets (Stabile & Ward [2006]).

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Emery, J.C.H. & K. Gerrits [2006], “The demand for private health insurance in Alberta in the presence of a public alternative”, in Beach et al. [2006] Files, A. & M. Murray [1995], ''German risk structure compensation: Enhancing

equity and effectiveness'', Inquiry 32, 300-309 Gordon, M. et al. [1998], ''Funding Canada's health care system: a tax-based alternative

to privatization'', CMAJ 159(5), 493-496 (plus discussion, 497-501) Herndon, J.B. [2002], “Health insurer monopsony power: The all-or-none model”,

J. Health Econ. 21, 197-206 Hussey, P. & G.F. Anderson [2003], “A comparison of single- and multi-payer health

insurance systems and options for reform”, Health Policy 66, 215-228 Koc, C. [2005], “Health-Specific Moral Hazard Effects," Southern Econ. J. 72(1), 98-118 Lynch, J. et al. [2004], “Is income a determinant of population health? Part 1”, Milbank Quarterly 82, 5-99 Musgrove, P. [2000], “Health insurance: The influence of the Beveridge Report”,

Bulletin of the World Health Organization 78(6), 845-855 Nyman, J.A. [2004], “Is ‘moral hazard’ inefficient? The policy implications of a new

theory”, Health Affairs 23(5), 194-199 Osterkamp, R. [2003], “Public health insurance: Pareto efficient allocative improvements through differentiated copayment rates”, European J. Health Econ. 4, 79-84 Pauly, M.V. [1983], “More on moral hazard”, J. Health Econ. 2(1), 81-85 Stabile, M. & C. Ward [2006], “The effects of delisting publicly funded health-care services”, in Beach et al. [2006] Tapay, N. & F. Colombo [2004], “Private health insurance in the Netherlands: A case study”, OECD Health Working Papers No. 18 Vanness, D.J. & B.L. Wolfe [2002], “Government mandates and employer-sponsored

health insurance: Who is still not covered?”, Int. J. Health Care Finance and Econ. 2(2), 99-135

Wolf, W.J. [2007], “An Overview of Maine’s Health System”, Legislative Policy Forum on Health Care, Maine Health Access Foundation Woolhandler, S. & D.U. Himmelstein [2002], “Paying for national health insurance – And not getting it”, Health Affairs 21(4), 88-98 Zeckhauser, R.J. [1995], “Insurance and catastrophes”, Geneva papers on Risk and

Insurance Theory 20(2), 157-175 Discussion questions 1. Why do societies include healthcare with social insurance? 2. Does the public provision of health insurance pose institutional difficulties compared to market provision? 3. Are there incentive and information problems specific to public health insurance? 4. What is adverse selection in health insurance? 5. Does the fact that public insurance generates a single pool really solve the adverse selection problem? 6. What are the advantages and the disadvantages of public over private health insurance?

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7. “Even if there were no informational problems in insurance markets, complete coverage would still be unavailable.” Why? 8. Are the social insurance concepts of Beveridge and Bismarck different? 9. What is moral hazard in health insurance? 10. Distinguish between the concepts of ex ante and ex post moral hazard. 11. Define and explain user fees, co-payments, deductibles and co-insurance. 12. When should co-insurance replace deductibles? 13. Is there a friction between social insurance and incomplete coverage insurance? 14. Does the fact that a household doesn’t buy health insurance constitute market failure? Problems 1. Show that the demand for insurance increases with the illness probability or the cost of treatment. 2. Does an insuree’s demand for insurance increase when he becomes more risk-averse? 3. Explain why an insurance contract ought to include a deductible. 4. Explain risk-pooling, one of the principles on which insurance is based, in the case of just two individuals. 5. Explain why the presence of loading costs rules out complete coverage. 6. Show that total welfare is decreased when, in a competitive insurance market, the presence of adverse selection prevents insurers offering complete coverage. 7. Show that total welfare is decreased when, in a competitive insurance market, the presence of moral hazard prevents insurers offering complete coverage. 8. Under what circumstances deductibles would dominate co-insurance? 9. How would the co-insurance rate vary with the insurer’s perception of the composition of the insurees pool under ex post moral hazard? 10. Is it possible that a deductible may generate perverse incentives for moral hazard? 11. How would incompleteness of coverage reduce ex ante moral hazard? 12. Carefully explain the relationship between coverage incompleteness and the second- best solutions to adverse selection and ex ante moral hazard. 13. Why can’t insurers offer as many contracts as the number of types of potential insurees? 14. How does an increase in the co-insurance rate affect the demand for healthcare? 15. Does incomplete coverage due to loading costs depend on insurer size? Appendix 4A Slope of the indifference curves in state-space diagrams The slope of an individual’s indifference curves in a state-space diagram is the subjective (or demand) price for insurance as the slope yields what the individual is willing to pay in the good state for an extra dollar of coverage in the bad state. The individual’s expected utility function is given as

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EU = pu(wB) + (1 – p)u(wG). The derivation simply consists of taking the total derivative, noting that utility is constant along an indifference curve and obtaining the slope expression on the right-hand-side of the resulting equation. First, we take the total derivative and equate it to zero: dEU = pu’(wB)dwB + (1-p)u’(wG)dwG = 0 and solve for the slope:

B

G

dw dw

= – )(')1(

)('

G

B

wup wpu

− .

An important property of indifference curves in state-space diagrams is that their slope when they cross the 450 line is always equal to the slope of fair-odds line

– )1( p

p −

.

This use of the property will prove crucial in the analysis of the basic insurance problems of adverse selection and moral hazard. Appendix 4B Competitive premia and loading costs Incorporating a loading cost T > 0 and rewriting a competitive insurer’s expected profit becomes πe = p[R – T – Q] + (1 – p) [R – T] and, assuming linear premia and loading costs, = p[rQ – tQ – Q] + (1 – p) [rQ – tQ] = [r – t – p]Q which yields, due to profit dissipation (i.e. expected profits reduced to zero) under perfect competition, r = p + t. This implies that the potential insuree’s budget line is now steeper. To see this, consider the individual’s payoffs in the two states of the world. wG = W – rQ wB = W – rQ + Q – L.

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Isolating Q in the second, substituting it into the first and rearranging the resulting equation yields the budget line

BG wr r

LW r

r Ww

− −

  

− −

+= 1

)( 1

for wB ≥ W – L

that is represented in Figure 4.3 with the slope r/(1 – r) steeper than p/(1 – p), the slope pf the fair odds line at which the individual would have purchased complete coverage, i.e. Q = L. To see this, consider the individual’s expected utility maximization problem )()1()(max

}{ rQWupLQrQWpuU

Q −−+−+−=

where W – rQ + Q – L = wB and W – rQ = wG. The first-order condition for this maximization is given as 0)(')1()1)((' =−−− rwuprwpu GB which, rearranged, yields

p

p r

r wup

wpu dw dw

G

B

B

G

− >

− =

− −=

11)(')1( )('

.

This inequality implies

1 )(' )(' >

G

B

wu wu

which, in turn, yields wB < wG. Thus, as shown in Figure 4.3, the individual chooses incomplete coverage. Appendix 4C Moral hazard and health-enhancement costs In the presence of moral hazard, as explained in the text, individuals’ control over the likelihood of healthy outcomes has to be explicitly treated, with its benefits and its costs. Individuals’ health-enhancing activities (from better eating habits to good sleep to physical exertion) are typically costly, not only in terms of time allocated but also in terms of the purchased inputs (from gym time to quality food) into activities. The benefits accrue as healthy time that can be used for work or leisure, or simply enjoyed as health. The utility function introduced in Appendix 4A can be augmented to incorporate these benefits and costs as follows. EU = p(e)u(wB) + (1 – p(e))u(wG) – v(e).

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The first part of this utility function, p(e)u(wB) + (1 – p(e))u(wG), is as above except that the probabilities are now determined by the individual’s costly effort e. An increase in this effort increases the probability of the healthy state G (i.e. 1 – p(e)) but, of course, this increase is slower than the increase in the effort. The second and new part v(e) is the cost of effort and it is increasing in effort. Consistent with typical cost functions, the cost increases faster than the effort. For notational simplicity, we can interchangeably use U(wB1,wG1;eL) = UL1 = p(eL)u(wB1) + (1 – p(eL))u(wG1) – v(eL). Of course, given the assumed structures, the individual would choose an optimal prevention level in the absence of insurance so as to maximize his expected utility. Appendix 4D Ex post moral hazard Since the ex post moral hazard problem arises when and if the insuree turns into a patient, the health vs. illness dichotomy ceases to exist and illness turns into shades of illness. The informational problem is one of moral hazard with hidden knowledge where the patient, knowing her illness better than the insurer may choose to exaggerate the level of her illness by consuming medical care services with negative net benefits. Under symmetric information, the heavy-case and light-case patients receive treatments mH and mL respectively as in Figure 4.7. However, if the insurer is unable to distinguish cases, the light-case patient prefers the heavy-case treatment in the absence of a screening mechanism, as follows uL* = uL(mL,w – R) < uL(mH,w – R) = uL0. If a screening mechanism in the form of a coinsurance payment c0 is chosen so as to minimize the cost of separation of light and heavy cases, separation would occur if the light case prefers the treatment level corresponding to her illness. Separation then requires uH(mH,w – R – c0mH) ≥ uH(mL,w – R – c0mH) uL(mL,w – R) ≥ uL(mH,w – R – c0mH). As shown in Figure 4.7, if the contract specifies a coinsurance c0 applied to the heavy- case treatment level, then proper separation takes place. In fact, since the coinsurance aims at forcing the light case to separate, the coinsurance rate is solely determined by the light-case patient’s willingness to pay for treatment. Of course, this is just a demonstration that tools are available to improve allocation. On a separate note, note the negative externality imposed on the heavy-case by the mere presence of the light case as the heavy-case is worse off in comparison to the symmetric information case.

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