Christoph Schottmüller publish paper in Economic Journal
People with high health risks are underinsured while people with low health risks buy insurance coverage. That is an observation often made in countries with private health insurance systems like the US. It seems to contradict standard insurance models in which people buy high insurance coverage because they have private information that their risk is high.
Schottmüller and his co-author Jan Boone from Tilburg University add two well established observations to the standard insurance model in the paper Health insurance without single crossing: why healthy people have high coverage:
First, health is a normal good (i.e. richer people consume more health care conditional on being ill).
Second, there is a positive correlation between health and wealth.
The paper shows that a model containing these two observations can explain why healthy people buy high insurance coverage. This result holds, however, only if insurance companies have (some) market power and not in a perfectly competitive insurance market. For the case where insurance companies have market power, policy interventions trying to increase the insurance coverage of poor people (like the Affordable Care Act) can increase efficiency.
The results cast doubt on the so called positive-correlation test which tested for the presence of asymmetric information in a market by testing for a positive correlation between coverage and (realized) risk: While asymmetric information is present and relevant in our model, we derive equilibria in which the correlation between risk and coverage is negative.