بیمه سلامت: درمان پزشکی در مقابل پرداخت از کار افتادگی

We present arguments for treating health insurance and disability insurance in an integrated manner in economic analysis, based on a model where each individual’s utility depends on both consumption and health and her income depends on her earning ability. When purchasing insurance, she may choose a contract that offers less than full medical treatment. We find that high-ability individuals demand full recovery and equalize utility across states, while low-ability individuals demand partial treatment and cash compensation and suffer a loss in utility if ill. Our results carry over to the case where health states are not observable.

Random changes in health, e.g. due to illness, affect a person’s well-being in several ways. One way is the direct effect of health on well-being. But there are also some indirect effects. First, reduced health may affect the person’s utility from consumption. Secondly, medical expenses necessary to recover from illness reduce affordable consumption. Finally, illness may affect the ability to generate income. In this paper, we argue that a proper treatment of health risk and health insurance should take all these effects of an illness into account, and we offer a theoretical model in which to do this. In this model, an individual’s utility depends on both consumption and health and her income depends on her earning ability. When purchasing health insurance, she may choose to receive less than full medical treatment when ill, and support consumption from a combination of cash compensation and her remaining earning ability. While health insurance and disability insurance are in fact integrated in a number of European countries with public tax-financed (social) insurance systems, the economics literature has treated the two risks as separate problems, with the risk of medical expenditures to be covered by health insurance and the risk of losses in labour market productivity to be covered by disability insurance. The present work is an attempt at correcting this, putting a coordinating perspective on health and disability insurance. In particular, we expand the concept of health insurance to include not only coverage against medical costs but also against permanent loss in earning ability, arguing that these are two types of consequences of the same risk, i.e. the risk of suffering a loss in health. Whereas health and disability insurance in most European countries is heavily subsidized–in effect, a cross-subsidization takes place from individuals with high earning abilities to those with low abilities–our analysis addresses the question of what the outcome would be without any transfers. We find that individuals with low earning abilities indeed trade off health for consumption. Letting insurance contracts offer individuals various combinations of medical treatment and cash compensation of income loss if they become ill, we find, in particular, that high-productivity individuals choose contracts providing full medical treatment while low-productivity individuals choose contracts offering partial medical treatment and partial compensation for loss in earnings. Low-productivity individuals consequently choose not to fully recuperate from an illness but rather receive cash payment that partly offsets the income loss due to partial impairment. 1 Moreover, even in this setting where there is symmetric information about health risks and health states, such low-productivity individuals end up being less than fully insured, in the sense that they have lower utility when ill than when healthy. These results have interesting policy implications. Whereas there is much focus among many policy makers on the issue of providing health insurance that covers all individuals in a fair and uniform manner, our analysis points to reasons for offering a menu of health insurance contracts, where cash compensation may substitute for the right to full recovery.2 In the case where health insurance schemes are also used as a means of redistributing income, our analysis indicates that this issue is related to redistribution in cash, i.e., through the tax system: a low-productivity individual may actually prefer to receive support from government in the form of cash rather than in the form of improved health, since better health has a smaller effect on consumption for low-skilled people than for high-skilled ones. 3 Like the traditional literature on health insurance, we focus on illnesses for which a treatment is available that fully restores pre-illness health and ability. However, in other work, individuals’ desire to restore health is taken for granted.4 In Marchand and Schroyen (2005), for example, there is no loss of health for an individual who falls ill, only a loss of time caused by illness. In their model, high-productivity individuals get well immediately at a private practice, while low-productivity ones suffer a time loss while waiting in the public health-care system. This time loss constitutes an inefficiency, whereas the outcome in our model is efficient, with low-productivity individuals getting compensation in cash instead of full treatment. In other work where non-monetary consequences of illness are taken into account, it is assumed that utility is state dependent and that health is either irreplaceable or not restorable.5 In this paper, we allow for both monetary and non-monetary consequences of illness without imposing assumptions either that health will always be fully restored or that it is irreplaceable. Thus, we provide a bridge between the health-insurance literature, which typically takes only monetary consequences of illness into account, and the disability-insurance literature postulating that health is irreplaceable or non-restorable. Our model has the following crucial features. First, we make the reasonable assumption that an individual’s productivity is affected by her health: If she suffers an illness and health is not fully restored, then her productivity will be negatively affected by the illness. The effect is that individuals with low full productivity have lower incentives for restoring health and therefore will tend to prefer contracts with cash compensation for illness.6 Second, we use a bivariate formulation of utility that allows for interactions between consumption and health. In particular, we make the assumption that the two are complements, i.e., that an individual’s marginal utility of consumption is increasing in health. 7 Our main analysis takes place in a world of symmetric information about health risks and health states, while the individuals’ ability may be private information. However, we show that our findings hold also in a situation where an individual’s health is non-verifiable, i.e., when insurers face problems of ex-post moral hazard. In fact, if ex-post moral hazard is a problem, then integrating medical insurance (with in-kind provision of medical treatment) and disability insurance (with cash compensation) reduces the insured individual’s incentive to falsely claim to be ill when in good health; in other words, integration induces self-selection. 8 The outline of this paper is as follows. The model is presented in Section 2 while our main findings are derived in Section 3. We discuss the case of ex-post moral hazard in Section 4. Our results are discussed in a concluding Section 5. Proofs are relegated to an Appendix.

Our focus has been on how an individual’s inherent ability at full functionality (i.e., when healthy) influences her ex-ante choice of insurance contract. Insurance allows the individual to allocate income between the two health states prior to knowing which state occurs and, if falling ill, between consumption and health. It is of no importance, in a world of symmetric information, whether the coverage for medical costs is paid in cash intended to cover medical bills, or directly in the form of medical treatment. The individual’s ex-ante decision concerning what level of treatment to choose is unaffected by the way she is compensated; the fundamental decision concerns to what extent health is to be restored. 12 However, as discussed in Section 4, if health state is not easily verifiable, then it becomes essential whether medical expenditures are compensated in cash or in kind. When information about health state is asymmetric, integration of a cash compensation of income loss and an in-kind compensation of medical expenditures reduces the individual’s incentive to falsely claim to be ill. Our findings are driven by the fact that the potential loss in income is larger, the higher the ability. This implies that the prices of the two types of contracts differ depending on the individual’s ability. The higher the potential income loss due to reduced ability, the cheaper is the contract offering indemnity in kind (i.e., treatment), compared to a contract offering cash compensation of income loss. Thus, the cost–benefit ratio on medical treatment is lower the higher the level of ability at full functionality.