Long-term care and myopia: Optimal linear subsidies for private insurance

This paper studies optimal linear policy directed at private long-term care insurance in the context where individuals are myopic, that is, underestimate their dependency risk. Without government intervention, myopic individuals underinsure, while the first-best optimum requires full insurance. To decentralize the first-best, one needs personalized linear subsidies on private insurance premiums combined with personalized lump-sum taxes to finance these subsidies and redistribute resources among individuals. In the second-best setting where only uniform instruments can be used, the determination of the optimal insurance subsidy rate includes three main considerations: standard efficiency concern, correction for myopia, and redistributive concerns. While the correction for myopia pushes for a higher subsidy rate, the analysis of the redistributive concerns is far less straightforward. Overall, the redistributive concerns depend on three main factors: whether wealthier individuals are less myopic, how the probability of dependency varies with wealth and what is the type of absolute risk aversion exhibited by individual preferences.