Old, frail, and uninsured: Accounting for puzzles in the U.S. long-term care insurance market

Half of U.S. 50-year-olds will experience a nursing home (NH) stay before they die, and a sizeable fraction will incur out-of-pocket expenses in excess of $200,000. Given the extent of NH risk, it is surprising that only about 10 percent of individuals over age 62 have private long-term care insurance (LTCI). This market also has a number of other puzzling features. Many applicants are denied coverage by insurers. Coverage of those who have insurance is incomplete. Insurance premia are high relative to an actuarily fair benchmark. Using a model that features agents with private information about their NH entry risk and an insurer who optimally chooses menus of LTCI contracts subject to participation and incentive compatibility constraints, this paper shows that these puzzles can be attributed to adverse selection, overhead costs on the insurer, and Medicaid. The model also accounts for the lack of correlation between NH entry and LTCI ownership. This final property is novel because our setup has only one dimension of private information.