Prior health expenditures and risk sharing with insurers competing on quality.

Insurers can exploit the heterogeneity within risk-adjustment classes to select the good risks because they have more information than the regulator on the expected expenditures of individual insurees. To counteract this cream skimming, mixed systems combining capitation and cost-based payments have been adopted that do not, however, generally use the past expenditures of insurees as a risk adjuster. In this article, two symmetric insurers compete for clients by differentiating the quality of service offered to them according to some private information about their risk. In our setting it is always welfare improving to use prior expenditures as a risk adjuster.

1. Introduction

* To create incentives for cost containment, several countries relying on public funds to cover part or all of their health insurers' expenditures have introduced a prospective financing mechanism into their health insurance system. In this mechanism, competing health insurers do not get their costs reimbursed by the state, but receive capitation payments from the regulator. If insurers raise additional premiums, these have to be community rated. It is well known that the combination of prospective financing and community rating of additional premiums may create incentives for risk selection, i.e., "actions of economic agents on either side of the market to exploit unpriced risk heterogeneity and break pooling arrangements, with the result that some consumers may not obtain the insurance they desire" (Newhouse, 1996, p. 1236). To mitigate this problem, the capitation payments are adjusted on the basis of observable risk factors. However, existing risk-adjustment schemes are based mainly on demographic and socioeconomic variables, and they reflect only a small fraction of the heterogeneity in risks. Insofar as the insurers have better information than what is captured in the risk-adjustment system, there remains room for risk selection (van de Ven and Ellis, 2000). (1)

One way to reduce the incentives for risk selection is to introduce a mixed reimbursement scheme, in which payments from the regulator to the insurers are a combination of a prospective capitation and actual costs (Newhouse, 1986, 1996, 1998). Such a mixed reimbursement (or partial capitation) system can be interpreted as a form of risk sharing between the regulator and the insurers. Although its aim is to reduce the incentives for risk selection, it dilutes the incentives for efficiency. The optimal system will therefore depend on the weights given by the regulator to these two considerations (risk selection and efficiency) and on the behavioral reactions of the insurers. Risk sharing can take different forms, from a simple proportional rule in which the reimbursement is a linear combination of capitation and actual expenditures, to sophisticated systems of outlier or condition-specific risk sharing. The consequences of these different systems in terms of the tradeoff between efficiency and risk selection have been analyzed empirically by Beebe (1992) and van Barneveld et al. (2001). These articles do not contain an explicit description of insurer behavior and/or market equilibrium. In the present article, we want to model explicitly the tradeoff between efficiency and selection in the context of a theoretical model of insurer competition in which social welfare objectives are stated explicitly. To keep the model tractable, we focus on the simple proportional scheme, which has received much attention in the theoretical literature and is applied in countries such as the Netherlands and Belgium.

The tradeoff between selection and efficiency in the context of risk adjustment has been analyzed recently in a set of articles by Encinosa and Sappington (1997), Glazer and McGuire (2000), Frank, Glazer, and McGuire (2000), and Jack (2001). These articles model a situation of adverse selection, in which the patients have superior information about their own health status and insurers or HMOs differentiate benefits and/or quality to let the good risks self-select. We focus rather on the selection activities of the insurers, i.e., on the other side of the market. While quality differences are also central in our model, we will introduce them as an explicit risk-selection device in a model of competition between two profit-seeking insurers who can distinguish between different types of insurees. This is one of the main risk-selection issues in the European compulsory insurance schemes we have in mind, but it is also relevant in other systems when there is concern about the equal treatment of different risk groups.

Two assumptions are crucial to our approach. First, the risk-adjustment system is imperfect and the insurers are better informed than the regulator about the relative risks of different patients. To model this, we concentrate on a group of patients who are identical with respect to the observable variables appearing in the risk-adjustment formula but who differ with respect to other health characteristics about which the insurers have superior information. In this situation it will be profitable for insurers to attract good risks and discourage bad risks--where "good" and "bad" refer to the relative expected health expenditures of individuals within a given risk class as defined by the risk-adjustment scheme. Second, we assume that explicit cream skimming is forbidden and that the insurers use quality differentiation to discriminate between patients having different expected health expenditures. (2) Our concept of quality includes aspects, such as the timeliness of payments or friendliness of staff, that are related to the services provided by insurers and not to health care itself.

Our model has some similarities to the one proposed by Ellis (1998). He analyzes different forms of risk selection (including explicit dumping of patients) within a duopoly model. However, he does not allow explicitly for cost-reduction efforts by insurers and is therefore not explicit about the efficiency-selection tradeoff. We characterize the equilibrium in the model of quality competition and derive comparative statics with respect to the policy instruments. This is the first contribution of this article.

More important, however, we analyze the consequences of introducing insurees' prior expenditures into the risk-sharing system. It is well known that prior expenditures are a good predictor of actual expenditures (Newhouse, 1986; van Vliet, 1992; van de Ven and Ellis, 2000; van Barneveld et al., 2001). Their use in the risk-adjustment scheme has not been very popular, however, because of their diluting effect on the incentives for efficiency. (3) It has been argued that, apart from a discount factor, including past expenditures is similar to a simple cost reimbursement. Although this may be true, the conclusion that prior expenditures should not be used no longer follows once some risk sharing is introduced. In that case we introduce actual expenditures anyway, and this is certainly (although perhaps marginally) worse from the point of view of efficiency. Even then, Newhouse (1986, 1994, 1998) has consistently advocated the use of actual rather than prior expenditures in the partial-capitation system. Apart from practical reasons, he argues that actual expenditures are more efficient to reduce risk-selection incentives because they yield a more sensitive measure of predictable variation in expected cost. The latter argument is not obvious, however. As a matter of fact, it is possible that the use of prior insurees' expenditures is more effective at reducing risk selection than the use of actual expenditures, because prior expenditures might be more strongly correlated with the (imperfect) signal used by insurers to distinguish different risk groups. We model this effect explicitly and derive the (broad set of) conditions under which the introduction of prior expenditures into the risk-sharing mechanism is welfare improving. To do so, we have to distinguish two periods in our model. This two-period specification will force us to solve a subgame-perfect Nash equilibrium by backward induction.

The details of the model are described in Section 2. Section 3 characterizes the symmetric equilibrium in the insurance market. The comparative statics with respect to the policy instruments are analyzed in Section 4. Section 5 formulates the conditions for the optimal government policy. We compare the second-best solution to the hypothetical first-best case in which the regulator has direct control on the qualities offered to the different types of insurees. Section 6 concludes.

2. Description of the model

* We consider two symmetric insurers, denoted k = A, B, who compete for clients in a regulated health insurance market. They have to cover the costs of all medical treatments supplied by health care providers to their insurees (or clients). To do so, insurers receive from the state some capitation and cost-based payments financed by tax revenue. There is no private premium or copayment paid by insurees.