Uncertain lifetime, health investment and welfare

Abstract. 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.
JEL Codes: C60, D15, D81, I12, I18.
Keywords: life cycle, uncertainty, health, welfare.