کنترل انگیزه های انتخاب زمانی که قراردادهای بیمه سلامت درون زا هستند

The paper examines the nature of health insurance contracts when insurance companies pool high- and low-risk individuals. In a spatial product differentiation model, the normal forces of competition induce quality provision, but selection incentives induce insurers to under-provide quality. To offset selection incentives, the government can reimburse some of the insurers’ costs. However, such a subsidy can in some cases reduce quality further, as well as discourage production efficiency. In such cases the optimal reimbursement rate is negative.

The issue of risk selection in health insurance markets, and the design of policies to control it, has received growing attention in recent years (see, for example, Newhouse, 1996; Glazer and McGuire, 1998). Recognizing that financial incentives are central to the analysis of this phenomenon a number of authors (Ma, 1994; Newhouse, 1996) have adopted techniques from the optimal regulation literature of Laffont and Tirole (1994) to the health insurance context to examine the implications for optimal reimbursement policies.1 However, it is arguable that the mechanism of risk selection requires somewhat more specific modelling than is available in the standard literature. Insurance companies have incentives to select good risks ahead of bad risks because the latter are more expensive to cover. A major strand of the literature on selection control examines the use of risk-adjusters to offset these incentives. Exogenous characteristics correlated with expected health care utilization are used to predict costs, and correspondingly adjust premiums paid to health plans. Glazer and McGuire have recently investigated the design of such risk adjusters in the context of the model of insurance under adverse selection of Rothschild and Stiglitz (1976) and Wilson (1977). An alternative natural way for the government to remove these incentives is for it to pay for some of the realized costs of coverage: indeed, by reimbursing all of the insurance claims paid, a government would cause insurers to be indifferent between covering either risk type. The problem with such a solution is, of course, that insurers would have no incentive to provide insurance efficiently, since the signal upon which transfers are based is no longer exogenous. This is an example of the multi-task agency problem identified by Hölmstrom and Milgrom (1991). By reducing incentives to select good risks, the government also waters down incentives for production efficiency. In this paper selection is socially undesirable because it can lead to low quality insurance. There is a sense in which this occurs in the standard Rothschild–Stiglitz model. An equilibrium in that model (if one exists) is characterized by full insurance of high-risk individuals, but with low-risk individuals being under-insured. One might interpret this as under-provision of quality (of insurance bought by low risks) in order to deter high risks from purchasing the wrong contract. However, the ‘quality’ of insurance purchased by high risks is not distorted. In addition, competition eliminates the possibility of cross subsidization of high risks by low risks (firms earn zero profits on each contract they sell in equilibrium), so insurers have no particular incentive to alter the risk mix of their insurance pools. It is arguable that this kind of model misses a fundamental issue in the analysis of selection incentives, namely, that such incentives derive from the benefits associated with better risk pools, and that they can lead to under-provision of quality for all consumers. To allow the possibility of positive profits I endow insurers with some market power, specifically by use of a spatial model of product differentiation. I also assume that consumers cannot be quantity constrained, or more generally, that insurers cannot offer non-linear screening contracts. This second assumption, which induces a kind of pooling, means that insurers must earn positive profits on at least some of their clients if they are to remain in the market. 2 Insurers may then have incentives to reduce the terms of insurance (i.e., its quality) in order to increase the share of profit-generating low risks they cover. Whenever insurers have access to information about the risk-types they cover, they will have incentives to sell to low risks – ‘cream-skimming,’ and deny coverage to high risks – ‘dumping’ (see Ellis, 1998). Government regulations often attempt to ban such activities, by requiring open enrollment periods and community rating. This paper assumes that such regulations are effective, so without loss of generality insurance companies have no private information about the characteristics of individuals (although they do know the distribution of risks in the population). As Newhouse notes however, insurers have other subtle methods of inducing self-selection by good risks, including staffing policies and physician incentive contracts, which are difficult to regulate directly. To capture this idea, I will assume that although the insurance contract offered by firms is a very simple linear scheme, it is impossible for the government to impose its desired scheme on insurers. That is, consumers and insurers are fully aware of the terms of the contract, but these cannot be directly controlled by the government. If under-provision of quality is to be corrected by subsidizing claims paid, then the effects on endogenous insurance company effort (production efficiency) need to be modelled. Ignoring the effects on effort, and possible feedback effects on quality, it is straightforward to interpret subsidization of expensive plans as a kind of risk adjustment (Cutler and Zeckhauser, 1997), with claims being used as a signal of the average risk of a firm’s enrollees. Appealing to the literature on optimal regulation under asymmetric information, it is natural to infer that, accounting for effort incentives, a positive but sub-unitary fraction of claims should be reimbursed. A contribution of this paper is to show that in fact, allowing feed-back effects from effort choice to quality, a negative subsidy may be optimal. The simple intuition for this result is as follows. In the absence of subsidies, the effects of effort are fully internalized, so firms make socially efficient effort choices, but they may under-provide quality. Given the level of effort, a direct effect of a small proportional claims subsidy is to reduce the difference between the expected claims of high- and low-risks born by the insurer, and thus to reduce selection incentives. The subsidy also reduces effort, the direct social cost of which is second order. However, to the extent this effort reduction increases the cost differential between high- and low-risk individuals, it increases the incentive to select low risks, offsetting the direct effect of the subsidy on selection incentives. If this feedback effect is large enough, it is optimal (at least locally) to impose a negative subsidy. Finally, let me compare the structure of this model with those of the regulation under asymmetric information literature. In that literature, firms have private information about their inherent efficiency (which is exogenous), and about the effort they supply. The realized cost of production (excluding the costs of effort borne directly by the firm), is observable by the government and is a function of these unobservable components. The optimal regulatory transfer takes a ‘cost-plus’ form. In this paper, an insurer’s ‘inherent efficiency’ corresponds to the average risk of the pool it covers, which is endogenous, and is a function of the quality of insurance offered by all (in our model, both) firms, but not the effort they exert. Realized costs of production (net of effort costs) are again observable by the government.3 However, the endogeneity of a firm’s inherent efficiency means that the optimal regulatory transfer can be either a ‘cost-plus,’ or a ‘cost-minus’ contract. The next section describes preferences, insurance provision, market structure, and welfare. Section 3 examines market equilibrium and the conditions under which selection incentives are operative. Section 4 introduces subsidies, and investigates their effect on effort and quality choices, and welfare. Section 5 offers some concluding comments.

This paper has proposed a model for examining the mechanisms that might be used by insurance companies to indirectly select good risks, and the effects of possible government responses to these mechanisms. I have deliberately removed all avenues by which direct selection on the part of insurers, and direct regulation on the part of the government, could be effected. Thus, issues of ‘risk adjustment’, whereby insurance premiums are corrected for exogenously observable client characteristics (e.g., age), are ruled out, by assuming that there are no such characteristics to observe. This focus on indirect mechanisms of selection is meant to capture the idea that policymakers may be concerned about the quality of insurance offered, the supposition being that insurers might undersupply quality in order to deter consumers who value quality more (i.e., the high risks) from purchasing from them.