بیمه سلامت بهینه برای پیشگیری و درمان

This paper reexamines the efficiency-based arguments for optimal health insurance, extending the classic analysis to consider optimal coverage for prevention and treatment separately. Our paper considers the tradeoff between individuals’ risk reduction on the one hand, and both ex ante and ex post moral hazard on the other. We demonstrate that it is always desirable to offer at least some insurance coverage for preventive care if individual consumers ignore the impact of their preventive care on the health premium. Using a utility-based framework, we reconfirm the conventional tradeoff between risk avoidance (by risk sharing) and moral hazard for insuring treatment goods. Uncompensated losses that reduce effective income provide a new efficiency-based argument for more generous insurance coverage for prevention and treatment of health conditions. The optimal coinsurance rates for prevention and for treatment are not identical.

One of the major themes in health economics since the field began has been the behavior of patients and providers in the presence of health insurance that covers part or all of the cost of healthcare. Much of the economic literature on optimal health insurance focuses on “the fundamental tradeoff of risk spreading and appropriate incentives”; see Cutler and Zeckhauser (2000, p. 576) for a review of this literature. Specifically, it examines either the dead-weight losses from moral hazard, the tradeoff between moral hazard and the gains from insuring against financial risk, or the differential coverage of multiple goods with varying degrees of risk. Our primary interest in this paper has to do with extending the literature to directly address issues of optimal insurance in markets with two healthcare goods, namely preventive activities/care and treatment of poor health when it arises. For this paper we define preventive care to mean a service with no direct utility or benefit other than it reduces the probability of being in relatively sick states of the world. Although our main focus is on primary prevention, which prevents bad health states from happening altogther (as with immunization), a simple extension of our model partially captures certain dimensions of secondary prevention which include the detection and prevention of a deteriation of a chronic disease. In the process of deriving an expression for the optimal coverage of preventive care, we contrast how privately and socially optimal choices of preventive care differ, and how these choices are affected by the presence of insurance coverage for treatment services. We also examine how the optimal coverage of preventive care should be influenced by cost sharing on healthcare treatment in a second best optimal insurance policy that covers both prevention and treatment. One of the questions that we answer is: should preventive services be covered at all? Should they be covered to the same extent as other healthcare treatments, such as for accidents, curative care, or paliative care to relieve pain? There is a view held by some in the field that prevention is less uncertain than illness itself and may thus merit less generous coverage. Others have argued for coverage for prevention based on criteria other than economic efficiency (e.g., concerns about cost sharing hampering compliance among those with serious chronic health conditions). However, few have addressed the efficiency arguments for covering prevention based on an expected utility framework. We present a series of models where consumers’ choices about prevention affect expected health status as well as affect expenditures on healthcare treatment. Risk averse consumers value their health, their consumption of non-health goods and services, and protection from financial risks. We provide theoretical support for coverage of prevention to reduce insurance premiums and the cost of bearing risk, especially when the individual's premiums do not fully reflect savings from his or her own individual preventive activity. This paper makes three basic contributions to the existing literature. First, we differentiate coverage for prevention from that for treatment in determining optimal insurance. Second, we examine how health insurance coverage for both prevention and healthcare treatment are influenced by the presence of uncompensated losses. For example, in a world where consumers are imperfectly insured for loss of income from ill health, or there are uncompensated healthcare treament costs (such as for over-the-counter drugs and supplies) how do these uncompensated losses affect the optimal cost sharing on healthcare treatment? In a parallel manner, how do uncovered costs of prevention (the time and discomfort costs of screening tests, for instance) affect optimal cost sharing on preventive services and healthcare treatment? The third contribution is that we explicitly examine the implications of non-monetary losses, such as blindness or pain, that healthcare treatment may ameliorate but not eliminate. How do such direct utility losses of poor health affect optimal insurance design? As we show below, uncompensated treatment and prevention losses provide an additional rationale for reducing cost sharing both for both preventive care and healthcare treatment goods, while direct utility losses impact optimal preventive care cost sharing only. Since optimal insurance is a topic of considerable interest to many researchers and policymakers – both economists and non-economists – much has been written on this topic. We do not address these other rationales for insurance coverage that can be found in the health economics and public health literatures. These other important rationales for insurance coverage include correcting for externalities, such as those that can occur with communicable diseases; altruism or public good arguments; corrections of informational problems (i.e., uninsured consumers may make the wrong ex ante decisions about health insurance or preventive activity); distributional concerns that may underlie some forms of social insurance (such as goals of elimination of poverty, or achieving social solidarity); or fostering more complete coordination among healthcare providers and patients. Without denying the relevance of these other arguments for more generous health insurance coverage, we reexamine the efficiency-based arguments for insurance, and derive new results which refine our understanding of the value of generous insurance coverage from the consumer's point of view in the absence of other market or social imperfections.

In this article, we have extended the literature on efficiency-based models of optimal insurance for both health care treatment and prevention, while focusing purely on demand-side incentives. Using a linear demand specification to derive the major findings11 but which exhibits zero income effects on the demand for healthcare treatment, we have been able to derive closed form solutions for optimal cost sharing on both preventive care and healthcare treatment in a variety of specifications. Our work indicates that insuring preventive care can be second-best optimal when either of two major conditions hold. First, if preventive activity is not contractable between the insurer and the consumer, then the privately optimal coinsurance rate does not equal the socially optimal rate, because the consumer will ignore his or her impact on premium costs. Second, the second-best optimal coinsurance rate for both treatment and prevention depend on health-related losses typically not covered by health insurance. In fact, if the losses are large and strongly correlated with health care treatment, then it may be optimal to have a negative coinsurance rate for prevention. Although we have derived these results under a simple set of assumptions, we fully expect that they can be generalized qualitatively to a broader set of circumstances. These would include situations with externalities (contagious disease), inadequate information and other decision-making problems, decisions made by other parties (such as an employer) rather than by a social planner, as well as a wider range of assumptions about the specification of the demand for medical care. Our model examines a simple form of third-party insurance, but could apply in part to managed indemnity, managed care, and various supply-side arrangements. Although the details of each alternative are important, the addition of moral hazard on the part of the consumer (with respect to his or impact on insurance premiums) and non-health losses that are associated with health care use will both require some type of correction in the incentive structures to patients under these more elaborate extensions or assumptions about behavior. For example, if managed care or pay-for-performance rewards providers for keeping up immunization or screening rates, then there is still a concern that the patient may still not fully internalize the costs of his or her actions or to compensate for health-related but not otherwise insurable actions. To do that may require lowering the copayment or coinsurance rate as well. How far would depend on the specifics of the supply-side incentives, as well as the demand parameters that we have modeled. The new results that we find most interesting are those for uncompensated costs of treatment and prevention, and uncompensated health shock losses that have not received significant attention in the previous literature on optimal insurance. Uncovered costs of treatment and prevention include the time costs of these services, as well as perhaps the uninsured losses of income, or need to purchase uninsured medical care goods (over the counter drugs, for instance). The additional financial risk imposed by these types of losses provides a rationale for reducing cost sharing on both prevention and treatment services. On the other hand, uncompensated health shock losses – direct health losses that do not affect the marginal utility of income – make coverage of preventive care less important and do not affect optimal treatment cost sharing. The intuition is clear. On the one hand, if consumers face uncovered health-related losses, then they already have an incentive to expend effort on prevention, and do not need as much financial inducement to do so. On the other hand, if consumers face uncertain income losses which are correlated with healthcare spending shocks on certain treatment goods, then “over-insuring” (more generously covering them than would occur otherwise) those treatment goods is a second best response to reduce the individual's associated risk. It is worth highlighting the limitations of our study. While we were able to generalize our optimal preventive care cost sharing results to an arbitrary demand and utility functions, our optimal treatment coverage results were all derived using a very specific demand structure. Both in our basic model and our utility-based framework, we consider only one period, one good demand functions that are linear in prices and have additive errors with constant variance.12 We have ignored supply side incentives throughout, and hence our results assume that the level of healthcare treatment spending when uninsured is ex post efficient in the sense that the marginal cost is equated to the ex post marginal benefit. We have also assumed that the demand for treatment is income inelastic, which is troubling to both us and no doubt many of the journal readers.13 Our zero income assumption may be problematic. By making this choice, we assume away income distributional issues and corner solutions, which are particularly relevant in any equity discussions of optimal health insurance. In our model, subsidizing healthcare does not affect relative incomes, although it does affect those with poor health. We recognize that these are relatively restrictive assumptions, although our models remain more general than many others that have used only consumer surplus or assumed only two healthcare states or one healthcare good. Our zero income elasticity assumption sidesteps the concerns of Nyman (1999) that there are income effects on behavior generated by insurance coverage. We are not very worried about this possibility for three reasons. The first is that the Health Insurance Experiment's findings on income effects suggest that they are quite modest once one adequately controls for the endogeneity of insurance and have reliable measures of health status. The second reason is that neither of us are convinced that the positive income effects of a few individual's with large healthcare expenditures are not offset by the cumulative smaller negative effects of the resulting premiums on a larger population. We are aware of no direct evidence on this compositional effect, given that almost none of the literature explicitly measures and estimates the two components. The third and more pragmatic reason for not being concerned about large income effects is we are not considering the effects of going from no insurance to optimal insurance, but rather the characteristics on the margin of an optimal insurance policy, where redistributive effects are smaller. We have also repeatedly used a linear approximation of the marginal utility of income which is consistent with approximating the utility function with a constant absolute risk aversion function. We are not especially troubled by this assumption because our results should hold as an approximation for any arbitrary function, as long as the absolute risk aversion parameter is not varying too much across states of the world. Our uncompensated loss function and optimal savings function were also approximated using linear functions. Again, we believe that our results should hold as an approximation for more general nonlinear functions. The other restrictive assumption that we have made for tractability sake is that the variance in healthcare expenditure is a constant, conditional on the health state. Specifically we have assumed that the variance (as well as the higher order moments) in healthcare treatment does not depend on either the level of preventive activity Z , nor the level of cost sharing, that is View the MathML source∂σθ2/∂Z=0 and View the MathML source∂σθ2/∂cX=0. We do not need these restrictive assumptions to achieve our conclusions. Conditional on being sick, we might expect that more preventive activity Z also reduces the variance in expenditures conditional on health state. For example, earlier detection leads to earlier, less expensive and less variable expenditures. This would lead to a lower coinsurance rate for preventive activity, in part because there would be an additional element in the ∂π/∂Z term that acts as a wedge between the socially and privately optimal levels of prevention. Perhaps the area most in need of empirical work is to document the magnitude of uncompensated treatment and prevention costs to consumers. Significant uncompensated costs provide a rationale for zero or even negative cost shares on treatment goods and prevention goods, reflecting a second best correction in the absence of perfect insurance markets. It would be interesting to know how large are the adjustments needed to the conventional model results.