Uncertain Lifetime, Health Investment And Welfare

We build a life cycle model to study the implications of two types of lifetime uncertainty on investment in health and welfare. We show that when the hazard rate of death depends on age, uncertainty increases health investment. Instead, when hazard rate depends on human frailty, uncertainty decreases health investment. In both cases, uncertainty reduces welfare. The size of the effects depends on an aggregate parameter related to the natural increase in human frailty with age, to the marginal return on health investment and to the rate of time preference. We first derive the main results from a small model which admits an analytical solution, before generalizing them in a larger model using numerical simulations. We conclude that the role of uncertainty depends on how death is modeled; and that if death is linked to frailty, as suggested by empirical evidence, a health policy reducing health uncertainty would stimulate individual investment in health promoting activities and improve welfare.