Poor heath, large acute and long-term care medical expenses and spousal death are significant drivers of impoverishment among retirees. We document these facts and build a rich overlapping generations model that reproduces them. We use the model to assess the incentive and welfare effects of U.S. Social Security and means-tested social insurance programs, such as Medicaid and food stamp programs, for the aged. We find that U.S. means-tested social insurance programs for retirees provide significant welfare benefits for all newborn. Moreover, when means-tested social insurance benefits are of the scale in the U.S., all newborn prefer that Social Security be removed. Finally, we find that the current scale of means-tested social insurance in the U.S. is about right in the following sense. If we condition on the current Social Security program, the benefits of increasing means-tested social insurance are small or negative.

Half of U.S. 50‐year‐olds will experience a nursing home stay before they die, and one in ten will incur out‐of‐pocket long‐term care expenses in excess of $200,000. Surprisingly, only about 10% of individuals over age 62 have private long‐term care insurance (LTCI) and LTCI takeup rates are low at all wealth levels. We analyze the contributions of Medicaid, administrative costs, and asymmetric information about nursing home entry risk to low LTCI takeup rates in a quantitative equilibrium contracting model. As in practice, the insurer in the model assigns individuals to risk groups based on noisy indicators of their nursing home entry risk. All individuals in frail and/or low‐income risk groups are denied coverage because the cost of insuring any individual in these groups exceeds that individual's willingness‐to‐pay. Individuals in insurable risk groups are offered a menu of contracts whose terms vary across risk groups. We find that Medicaid accounts for low LTCI takeup rates of poorer individuals. However, administrative costs and adverse selection are responsible for low takeup rates of the rich. The model reproduces other empirical features of the LTCI market including the fact that owners of LTCI have about the same nursing home entry rates as non‐owners.