Health Insurance without Single Crossing: Why Healthy People have High Coverage

Abstract

Standard insurance models predict that people with high risks have high insurance coverage. It is empirically documented that people with high income have lower health risks and are better insured. We show that income differences between risk types lead to a violation of single crossing in an insurance model where people choose treatment intensity. We analyse different market structures and show the following: if insurers have market power, the violation of single crossing caused by income differences and endogenous treatment choice can explain the empirically observed outcome. Our results do not rely on differences in risk aversion between types.A well-documented problem in health insurance markets with voluntary insurance like the US is that people either have no insurance at all or are under-insured. 1 Standard insurance models -inspired by the seminal work of Rothschild and Stiglitz (1976; RS) and Stiglitz (1977) -predict that healthy people have less than perfect insurance or-in the extreme-no insurance at all. However, both popular accounts like Cohn (2007) and academic work like Schoen et al. (2008) show that people with low health status are over-represented in the group of uninsured and under-insured. 2 We develop a model to explain why sick people end up with too little (from a social point of view) or no insurance. We do this by adding two well-documented empirical observations to the RS model:(i) richer people tend to be healthier; and (ii) health is a normal good.Technically speaking, introducing the latter two effects can lead to a violation of single crossing in the model.There is another indication that the standard RS framework with single crossing does not capture reality in the health insurance sector well. The empirical literature that is based on RS does not unambiguously show that asymmetric information plays a role in health insurance markets. One would expect that people have private information about their health risks -think for example of preconditions, medical history of parents and other family members or lifestyle. However, some papers, like for We thank the editor (Martin W Cripps) and two anonymous referees of this JOURNAL for their suggestions. Comments by Cedric Argenton, Eric van Damme, Humberto Moreira, Florian Sch€ utt and seminar participants at Tilburg University are much appreciated. Financial support from the Dutch National Science Foundation (VICI 453.07.003) is gratefully acknowledged.1 In empirical studies, under-insurance is defined using indicators of financial risk. To illustrate, one definition of under-insurance used by Schoen et al. (2008) is 'out-of-pocket medical expenses for care amounted to 10% of income or more'. In our theoretical model, under-insurance refers to less than socially optimal/efficient insurance. 2 In the words of Schoen et al. (2008, p. 303): 'underinsurance rates were higher among adults with health problems than among healthier adults'.[ 1 ]

Incentivizing Efficient Utilization Without Reducing Access: The Case Against Cost-Sharing in Insurance

“…The latter determines insurance value -but not its cost -by assuming decreasing risk aversion. Boone and Schottmüller (2015) show how income dierences may explain the phenomenon of advantageous selection if income is negatively correlated with health risk and positively correlated with care utilization in case of sickness.…”

“…13 Here, I argue that an alternative 13 Boone and Schottmüller (2015) assume utilization to vary on the intensive margin with income, while access problems are more in line with variation on the extensive margin. Still, Boone and Schottmüller (2015) is the only work, that I am aware of, that recognizes the potential of cost-sharing to be a source of adverse selection. incentivization scheme based on boni can mitigate this source of heterogeneity.…”

The complementarity between risk adjustment and community rating: Distorting market outcomes to facilitate redistribution

“…Second, extending this logic, CR is no longer optimal if all high-cost types choose the "wrong" contract. Boone and Schottmüller (2017) present a model in which this can happen.…”

Basic versus supplementary health insurance: Moral hazard and adverse selection

“…This leads to a consistent ranking of types. See Boone and Schottmüller (2013) for an analysis of the case where types are not ranked consistently because the single crossing assumption is not satisfied.…”