مدل رای دهنده میانه بیمه سلامت با خطر اکس پست اخلاقی

One of the main features of health insurance is moral hazard, as defined by Pauly [Pauly, M.V., 1968. The economics of moral hazard: comment. American Economic Review 58, 531–537), people face incentives for excess utilization of medical care since they do not pay the full marginal cost for provision. To mitigate the moral hazard problem, a coinsurance can be included in the insurance contract. But health insurance is often publicly provided. Having a uniform coinsurance rate determined in a political process is quite different from having different rates varying in accordance with one’s preferences, as is possible with private insurance. We construct a political economy model in order to characterize the political equilibrium and answer questions like: “Under what conditions is there a conflict in society on what coinsurance rate should be set?” and “Which groups of individuals will vote for a higher and lower than equilibrium coinsurance rate, respectively?”. We also extend our basic model and allow people to supplement the coverage provided by the government with private insurance. Then, we answer two questions: “Who will buy the additional coverage?” and “How do the coinsurance rates people are now faced with compare with the rates chosen with pure private provision?”.

No matter what system for the provision of health care—private or public—for which a country has opted, the consumer only pays a small part of the total cost out-of-pocket upon consumption. While insurance premiums pay for the bulk of the cost in a private system, tax receipts are used if provision is public. But irrespective of how health care is financed, we must deal with the fact that once people have fallen ill, they face incentives to consume more than optimal health care, since they do not have to pay the full marginal cost for the care they utilize. In the health economics literature, this is referred to as moral hazard (Pauly, 1968), or sometimes as ex post moral hazard (Zweifel and Breyer, 1997) to stress the fact that it arises after the bad state has occurred—as opposed to ordinary moral hazard which is a change in behavior before the actual accident. The problem of ex post moral hazard has attracted considerable attention in conjunction with private health insurance.1 The usual way of mitigating moral hazard is to require patients to pay some part of the costs out-of-pocket, i.e. to include a coinsurance in the insurance contract. The larger the part paid out-of-pocket (the higher the coinsurance rate), the lower is the excess utilization of medical care. On the other hand, the higher is the coinsurance rate, the lower is the risk reduction. So, there is an inherent conflict between reducing excess utilization and reducing risk when deciding on the coinsurance rate. It is in the interest of the buyer of insurance to reduce overconsumption, since the premium will depend on the expected costs for the buyer’s medical care. The optimal coinsurance rate makes an ideal trade-off between minimizing deadweight losses and reducing risk. Not everybody will want the same coinsurance rate, since people differ in how they want to strike this balance. With private health insurance, the market can offer buyers different contracts, so that people preferring a lower coinsurance must pay higher premiums. This is generally not the case when health insurance is fully tax-funded. Then, people cannot choose how much to pay and get a coinsurance in accordance with their contribution; instead one contract applies to everyone. It is quite different to have a uniform coinsurance rate determined in a political process, than different rates varying in accordance with one’s preferences. It will, for instance, have different consequences for efficiency and distribution. Our objective is to construct a political economy model in order to characterize the political equilibrium and answer questions like: “Under what conditions is there a conflict in society on what coinsurance rate should be set?” and “Which groups of individuals will vote for a higher and lower than equilibrium coinsurance rate, respectively?” It turns out that income elasticity and risk aversion are the two crucial parameters. For instance, if we have the empirically plausible situation of an income elasticity of health services smaller than one and constant relative risk aversion, low-income individuals will prefer a lower coinsurance than high-income individuals. First we study these issues under the assumption that public insurance cannot be supplemented with private insurance. However, a strong case can be made for supplementation usually being possible Besley and Gouveia, 1994, Breyer, 1995 and Gouveia, 1997, at least in health-care systems where financing is public but production is private. Gouveia (1997) mentions the Medigap insurances available in the U.S., which are sold by private firms to individuals entitled to Medicare, and are explicitly designed to supplement Medicare. Another example, also mentioned in Gouveia (1997), is the French two-tier system of ambulatory care. The second tier of providers, with above average quality, are allowed to charge patient fees above the levels regulated by the national convention. For these reasons, we extend our basic model and allow people to supplement the coverage provided by the government with private insurance. The private supplementary insurance will pay some part of the coinsurance in the public insurance. Then, we answer two questions: “Who will buy the additional coverage?” and “How do the coinsurance rates people are now faced with compare with the rates chosen with purely private provision?”. The answer to the first question is that low-income individuals will (under reasonable assumptions) be the ones purchasing supplementary insurance. The answer to the second question is that everybody will face a lower coinsurance rate with public than with private insurance. What coinsurance rate is set will affect how much health care people will consume. In the end, this will determine the aggregate level of health-care expenditures in the economy. Therefore, it is interesting to analyze what system, public supplemented with private or purely private, renders the highest aggregate spending on medical services. We argue that public insurance which allows a private supplementary insurance will actually result in larger aggregate expenditure than the purely private one. An objection to the claim that coinsurance rates determine demand could be that many types of medical services are rationed, so that people cannot choose to consume as much as they want to. We do not deny that rationing is an important aspect of health-care provision.2 But some types of care are easier to ration than others. Labor-intensive care can be rationed by restricting the supply of doctors and nurses, thus creating waiting lists for surgery for instance (see Besley et al., 1999 for an analysis of the importance of waiting lists as rationing devices). However, waiting lists is a rationing device not available for all types of care. Prescription drugs only require a prescription to be filled out by a physician—a not very time-consuming procedure—and then the patient can treat himself at home. An indication of the problem with rationing pharmaceutical drugs is that Medicare in the U.S. does not cover ambulatory drugs due to the fear of moral hazard (Schweitzer, 1997).3 So, although rationing is an important aspect of health care, we do believe that there are enough instances where rationing does not take place—or is so incomplete—that it merits a separate analysis. This paper is related to two separate research lines: one concerning the public provision of private goods in general, the other the provision of health care in particular. The first is represented by Usher (1977) and Epple and Romano (1996), for example. In these papers, the good is assumed to be uniformly provided to everybody. Wilson and Katz (1983), however, analyze what should characterize a non-rationed good that a political majority finds it beneficial to subsidize. Further, they analyze what determines the level of subsidization chosen by the majority. One conclusion is that goods with large compensated price elasticities are bad targets, because subsidies incur too much wasteful consumption, i.e. large deadweight losses. The two examples of goods they mention as actually being subsidized are education and health care. Deciding on a level for subsidization (as Wilson and Katz do), or setting a coinsurance rate (what we analyze), might seem like two sides of the same coin. But then we forget that even without public intervention, there will be a “subsidization” of health care at the time of utilization, since costs are reimbursed. So, the situation with which to compare the outcome under public provision is not one of zero deadweight losses, since there will be deadweight losses even with private provision. Another way of putting this is that the provision of health care should be analyzed in expected utility terms, and what the government provides should be considered as insurance. This is done in the second line of research to which this paper is related: the literature on the public provision of health insurance. See, e.g. Breyer (1995) and Gouveia (1997) where public provision of health insurance is analyzed from a positive perspective in voting models. In their models, rationing is possible, however, and voting takes place over the amount of health care provided rather than the level of subsidization, as in our paper. As discussed above, we believe the non-rationing assumption to be relevant for some types of care and that there is a moral-hazard problem with public insurance, although the problem has attracted most attention in conjunction with private health insurance. To point out the differences between voting over the level of subsidization (the coinsurance), rather than the level of provision, we include a section where our results are compared with those of Breyer (1995) and Gouveia (1997). We conclude that the results differ in some important respects.4 The rest of the paper is organized as follows. In Section 2, the theoretical model is introduced and some results for publicly provided health insurance are presented. Further, the conditions for a political equilibrium are discussed. In Section 3, we allow the public insurance to be supplemented with private insurance (we call this case non-exclusive public insurance), and in Section 4, we compare our results with those of Breyer (1995) and Gouveia (1997). In Section 5, we discuss whether the aggregate utilization of medical care will be larger with a non-exclusive public insurance than with a purely private insurance. Finally, Section 6 summarizes and concludes.

In this paper, we have analyzed a situation where rationing is not possible and ex post moral hazard arises; the reason for this has been argued earlier in the paper. We do also believe that the problem of moral hazard may be present even with rationing, but it will be harder to model in such a setting. The model does not contain voting over whether provision should be public or private, but rather the extent of the subsidization. Thus, we have focused on how the demand for medical services and risk reduction differs between individuals. We find risk aversion and income elasticity to be key parameters in this decision. If we assume constant relative risk aversion and an income elasticity equal to 1, there will be no conflict on the level of insurance. However, using the more plausible assumptions of constant relative risk aversion and an income elasticity lower than 1, we find the demand for insurance to decrease with income. Further, we find that if adding the possibility of buying supplementary insurance, it will be in demand by low-income earners. This result is in contrast with Breyer (1995), for example, where high-income earners will want to supplement the public insurance. Finally, we want to point out some limitations of our study and indicate what could be done in the future. First, it is probably too strong an assumption that no rationing takes place at all. Even for the type of services where rationing is hard, e.g. pharmaceuticals, the no-rationing assumption is quite strong. Second, in our model, everybody faces the same probability of falling ill. A more realistic model would account for the differences in this probability which we know to exist, and for the negative correlation between health and wealth (Smith, 1999).