This paper studies redistributional effects of competition between private and public insurance on health insurance markets based on the example of Germany. Public and private insurance co-exist and are mutually exclusive. Private insurance maximizes profits. Public insurance balances budget and is financed by an income tax with a cap. In addition, customers of public insurance have the option to opt out once income is sufficiently large.
On a more abstract level, we study a two-dimensional linear taxation problem with price cap,
23Analogous results hold if there are more than two private insurances.
24Note that as a consequence, PRs do not survive competition with other PRs since very wealthy but unprofitable customers cannot be deterred from entering and cause a loss to the insurance.
opt-out for high types under a budget balancing constraint and regulation. Public health premia may only depend on income types but health costs depend on health types of customers. This regulation in combination with the potential of opt-out gives rise to cream skimming (risk selec-tion) by a competing private insurance.
Private insurance discriminates between healthy and unhealthy customers. If possible, she de-ters unprofitable customers while attracting customers who will generate a gain by varying the premium. In the face of cream skimming, opt-out by rich customers and budget balancing, the public insurance sets the public contribution rate.
As first result, we derive a condition under which a unique, redistributive, budget balancing public contribution rate exists. We show, increasing the opt-out threshold up to the level of the public insurance’s price cap decreases the premium for all customers, public and private, since the type area where the private insurance may cream skim vanishes. Increasing the opt-out threshold further, leads to even lower public and private premia since health and income types are positively correlated.
Considering a systematic improvement of the population’s health and income25, we show that even though the change clearly improves the population’s characteristics, the public contribution rate might increase. Healthy and wealthy customers may opt out and insure privately so that an improvement does not benefit all customers via redistribution in the public insurance but instead is pocketed by private insurance.
Increases in correlation between income and health may increase public health prices to keep a balanced budget: On the one hand, less wealthy types insure publicly and become on average less healthy which causes additional costs to public insurance. On the other hand, higher earning types become more healthy after the increase in positive correlation but may opt out so that the gain in health and decrease in costs is lost to private insurance.
While some characteristics of our model are Germany specific (opt-out and price cap), simpler versions still constitute a contribution to the literature: Health and income types are continuous which in combination with regulation of public insurance and budget balancing leads insurance markets to collapse under voluntary insurance. In particular, this result is not due to adverse selection and may deliver a rationale for why health insurance is compulsory in Germany, France and Switzerland.
In addition, continuous types allow for modeling of maximum and factual health benefit levels and thus over insurance which drives customers’ contract choice.
In Germany as in Italy, customers have the choice between public and private insurance. When setting the opt-out threshold at infinity our model corresponds to a completely public, non-profit, earnings-based redistributive health insurance system as in France.
25In the sense of first-order stochastic dominance
We formulate the model under the assumption that private insurance perfectly observes cus-tomers’ health types. We believe this is plausible since private insurances in Germany often require potential customers to fill out binding questionnaires about their medical history. More-over, insurances can draw on internal statistics to precisely estimate the likelihood that a customer falls sick with a certain disease. We think of an agents’ health type as average health over her life time rather than a reflection of a particular moment. By modeling health types as observable and fix over lifetime, we circumvent the moral hazard problem in health insurance: Insured agents do not overuse their insurances. The motive to insure is hence not by risk-sharing but imposed by regulation to redistribute along the income and health dimension. Public health premium as percentage of income is set at an ex ante stage by the public insurance for we implicitly assume that the general income-health risk distribution of the population is known to both public and private insurance.
In our model, the public insurance commits to running a balanced budget rather than maximiz-ing profits. We offer two possible justifications for this behavior. First, we may assume that a benevolent government sets up a health insurance fund to provide large parts of the population with health insurance at lowest possible costs.26 Second, we can regard public insurance as a representative for an entire competitive public insurance market in which every public health in-surance operates at her (identical) costs.27 Either explanation motivates the objective to balance budget.
26In fact, in years in which German public health insurances make significant profits, customers obtain a refund in form of a price deduction.
27In Germany, for example, customers can choose from several similar public health insurances, and switching insurances within the public sector is simple.