We explore the hierarchy of two instruments, waiting time and coinsurance for medical treatment, for optimally solving the tradeoff between the economic gains from risk sharing and the losses from moral hazard. We show that the optimal waiting time is zero, given that the coinsurance rate is optimally set.
Most health insurance plans do not use indemnity payments that depend on health status, but reimburse the costs of the care actually provided to consumers. The reason is that the health status of a person can only be imperfectly observed. When insurance reimburses health care expenses, it subsidizes the price of health care at the margin, giving rise to a dead-weight loss. An optimal insurance contract thus involves copayments by the consumers. Coinsurance solves the tradeoff between risk sharing and the incentives to consume increased medical care.
User charges apply in social health insurance systems in many countries. Some services, such as dental care, may be excluded from the social insurance package, and deductibles and copayment rates are used to restrain the demand for health services. Countries with a national health service, however, do not generally employ coinsurance to curb demand for health care. They instead use waiting time for this purpose.
There is a vast literature analysing waiting times and waiting lists in the provision of health care services (for an overview see Cullis et al., 2000). Lindsay and Feigenbaum (1984) develop a model in which waiting list queues function as a rationing device. Waiting time matters because the value of health care decays the longer the treatment is postponed after the diagnosis. Iversen (1993) outlines a supply side model in which waiting lists for inpatient care are the result of a political bargaining process over resources. Iversen (1997) and Olivella (2002) analyze the effect of a private sector on waiting in the national health care system. Another strand of literature explores the scope of using waiting as a method of rationing health care in order to meet distributional objectives. Hoel and Sæther (2003) show that queuing in the public health care system might entice high-income persons to opt out and buy health care privately while still participating in the financing of the public system. If sufficient weight is given to equity, welfare can be improved by using the self-selection mechanism. In the absence of distributional motives, however, it is never optimal to have a positive waiting time for health treatment.
Smith (2005) analyzes user charges for different treatments under an exogenous health care budget. For a given treatment, all consumers have the same benefit, but, as the consumers’ wealth differs and marginal utility of wealth is decreasing, coinsurance reduces the demand for health services by discouraging poorer consumers from seeking treatment. In line with optimal taxation rules, the coinsurance rate for a treatment is inversely related to the price-elasticity of demand.
Gravelle and Siciliani (2008a) extend the Smith model by introducing heterogeneity with respect to the consumers’ benefits from treatment and a public health care system which uses queuing to ration demand. Prioritization among treatments again follows an elasticity rule: the more elastic demand is with respect to the waiting time, the longer the optimal wait is. Adding user charges to the model, Gravelle and Siciliani demonstrate that Ramsey waits and prices apply simultaneously. While they do not check whether the optimum requires the use of both instruments, in a subsequent paper, they find a corner solution with respect to waiting time (see Gravelle and Siciliani, 2008b). If the disutility of waiting is higher for patients with large benefits of treatment, the optimal waiting time is zero.
In this paper we address the complementary use waiting time and coinsurance in a representative consumer model, which includes health and consumption as arguments of the utility function and a linear coinsurance scheme designed to restrict moral hazard. We add the investment aspect of health, determining the consumer's income in the process, and waiting time, which reduces income since an untreated ill person cannot work. We show that the optimal coinsurance rate is positive (due to moral hazard) and smaller than one (due to the consumer's risk aversion). For a given coinsurance rate, the optimal waiting time may or may not be positive. However, if the coinsurance rate is optimally set, it is not optimal to have a positive waiting time for treatment.
National health services use queuing as a rationing device like centrally planned economies do (Kornai, 1980). Social health insurance systems depend more on user charges to signal the scarcity of resources to the consumers of health care. In this paper, we demonstrate that an optimized design does not generally use a positive waiting time for medical treatment. The reason is that coinsurance sufficiently solves the tradeoff between risk-sharing and moral hazard, thereby rendering waits a redundant instrument. Still, a positive waiting time might be optimal if the choice of the coinsurance rate is restricted or if health status is subject to an excessive risk.
This paper restricts the analysis to a constant coinsurance rate in the tradition of Zeckhauser (1970) and Feldstein and Friedman (1977), among others. With a non-linear scheme, the optimal coinsurance rate tends to be smaller for high health care expenses (Blomquist, 1997). Since for high expenses the optimal waiting time might be positive, it would be interesting to analyze a non-linear coinsurance scheme combined with waiting time, an issue we leave to future research.
