@techreport{NBERw17325,
 title = "Health and Mortality Delta: Assessing the Welfare Cost of Household Insurance Choice",
 author = "Ralph Koijen and Stijn Van Nieuwerburgh and Motohiro Yogo",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "17325",
 year = "2011",
 month = "August",
 URL = "http://www.nber.org/papers/w17325",
 abstract = {We develop a pair of risk measures for the universe of health and longevity products that includes life insurance, annuities, and supplemental health insurance. Health delta measures the differential payoff that a product delivers in poor health, while mortality delta measures the differential payoff that a product delivers at death. A life-cycle model of insurance choice simplifies to replicating the optimal health and mortality delta through a portfolio of health and longevity products. 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, and long-term care insurance. We then compare them to the optimal health and mortality delta implied by the life-cycle model. For the median household aged 51 to 58, the lifetime welfare cost of market incompleteness and suboptimal insurance choice is 6 percent of total wealth.},
}