Compressing or Expansion of Morbidity? The Demand for Annuity and Long-term Care Insurance

Individual retirees face two important risks: rising health care costs and increased life expectancy. Health shocks and longevity risk are inherently connected since death represents the end state in an individual’s health state transition process. A longer life expectancy can be attributed to a prolonged time span during which the individual stays healthy, i.e., compression of morbidity (Fries 2005), or associated with a relatively more increase in the length of an unhealthy state, i.e., expansion of morbidity (Olshansky et al. 1991). A third hypothesis (the dynamic equilibrium theory) points to an overall stable relative length of unhealthy life expectancy. There is still no consensus in the literature on which pattern truly captures individuals’ evolution of health states. In this paper, we use a life-cycle model to investigate how the health state transition process affects an individual’s demand for long-term care insurance and life annuity, in addition to other standard investment products such as bonds and stocks. Our paper contributes to the existing literature in several ways. First, we develop a dynamic multistate transition model where the transition probabilities depend on age and calendar time. Second, we answer the question as to what is the demand for long-term care insurance and life annuity under the compression, expansion and dynamic equilibrium hypothesis, respectively.