Risk Selection under Public Health Insurance with Opt-out

I study risk selection between the public and private sector when both types of health insurance coexist. In theory, a system that combines public and private provision of health insurance could overcome the disadvantages of each system on its own. Public insurance programs generally offer a one-size-fits-all policy. This leads individuals with higher than average demand for insurance to turn to private health insurance providers, which offer more comprehensive benefit packages, lower waiting times, higher amenities, etc. The resulting double coverage is inefficient. A purely private system, on the other hand, achieves little, if any, risk pooling and involves the full force of adverse selection. It can lead to underinsurance and even a complete market unraveling for some risks. Depending on its institutional design, a mixed public-private system might prove to be a viable alternative.

Germany is one of the few countries with such a dual health insurance system. To guarantee a certain extent of risk pooling in public insurance, relative low-income individuals are mandatorily insured under the public plan. Relative high-income individuals can stay in public insurance, or opt out and buy private health insurance instead. The main difference between public and private health insurance lies in the premium calculation: Public premia are community-rated and calculated based on income, while premia in private insurance depend mainly on risk. The difference in premium calculation creates incentives for individuals to engage in self-selection. A pronounced segmentation of risks across sectors, however, would undermine the advantages of a mixed public-private health insurance system and compromise financial sustainability of the public plan. This explains the importance of studying risk segmentation.

I model theoretically the choice of health insurance under the German institutional setup, borrowing the binary loss environment from Rothschild and Stiglitz (1976), and extending it to include a public insurance option (as in Olivella and Vera-Hernández 2013) and a continuum of risk types. I show that for those individuals who are eligible to choose, there exists a risk threshold above which they purchase public insurance and below which they purchase private insurance. I demonstrate how this threshold varies with the distribution of income and risk, which determines how much individuals can gain from risk pooling in public insurance versus how much they lose due to income redistribution, and how it depends on the level of coverage in public insurance.

Drawing on the 1995 to 2011 waves from the German Socio-economic Panel data set, I estimate the risk threshold as a function of an extensive set of covariates. The estimates allow me to characterize the extent of risk segmentation in the German health insurance system. I can further conduct rich counterfactual scenarios, such as, how risk segmentation is affected when there is a change in the public benefit package or in the threshold level of income which determines eligibility to purchase private insurance.

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