Yaari's Lifecycle Model in the 21st Century: Consumption Under a Stochastic Force of Mortality

Abstract

We extend the life-cycle model (LCM) of consumption over a random-length life-cycle (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt their consumption strategy to new information about their mortality rate (a.k.a. health status) as it becomes available. We compare and contrast the optimal consumption paths to investigate the impact of mortality rate uncertainty vs. simple lifetime uncertainty, but assuming the actuarial survival curves are the same. In addition to deriving the optimal consumption function, our main result is that when utility preferences are logarithmic the initial consumption rates are identical to the Yaari model. But, in a CRRA framework in which the coefficient of relative risk aversion is greater (smaller) than one the consumption rate is higher (lower) and a stochastic force of mortality changes optimal behavior even when faced with the same probability of survival. Numerical examples are provided to illustrate the magnitude of this effect. Our results should be relevant to researchers interested in calibrating the life-cycle model as well as those who provide normative guidance (a.k.a. financial advice) to retirees based on the LCM.