This paper develops a model of health insurance that incorporates behavioral biases. In the traditional model, people who are insured overuse low value medical care because of moral hazard. There is ample evidence, though, of a different inefficiency: people underuse high value medical care because they make mistakes. Such "behavioral hazard" changes the fundamental tradeoff between insurance and incentives. With only moral hazard, raising copays increases the efficiency of demand by ameliorating overuse. With the addition of behavioral hazard, raising copays may reduce efficiency by exaggerating underuse. This means that estimating the demand response is no longer enough for setting optimal copays; the health response needs to be considered as well. This provides a theoretical foundation for value-based insurance design: for some high value treatments, for example, copays should be zero (or even negative). Empirically, this reinterpretation of demand proves important, since high value care is often as elastic as low value care. For example, calibration using data from a field experiment suggests that omitting behavioral hazard leads to welfare estimates that can be both wrong in sign and off by an order of magnitude. Optimally designed insurance can thus increase health care efficiency as well as provide financial protection, suggesting the potential for market failure when private insurers are not fully incentivized to counteract behavioral biases.
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