Health and Mortality Delta: Assessing the Welfare Cost of Household Insurance Choice

Abstract

We develop a pair of risk measures for the universe of health and longevity products that includes life insurance, annuities, and supplementary health insurance. Health delta measures the differential payoff that a policy delivers in poor health, while mortality delta measures the differential payoff that a policy delivers at death. Optimal portfolio choice simplifies to the problem of choosing a combination of health and longevity products that replicates the optimal exposure to health and mortality delta. For each household in the Health and Retirement Study, we calculate the health and mortality delta implied by its ownership of life insurance, annuities including private pensions, supplementary health insurance, and long-term care insurance. For the median household aged 51 to 58, the lifetime welfare cost of market incompleteness and suboptimal portfolio choice is 28 percent of total wealth.