A Gravity Model of Mortality Rates for Two Related Populations

Kevin Dowd, Andrew J.G. Cairns, David Blake, Guy D. Coughlan, and Marwa Khalaf-Allah

The mortality rate dynamics between two related but different-sized populations are modeled

consistently using a new stochastic mortality model that we call the gravity model. The larger

population is modeled independently, and the smaller population is modeled in terms of spreads

(or deviations) relative to the evolution of the former, but the spreads in the period and cohort

effects between the larger and smaller populations depend on gravity or spread reversion param-

eters for the two effects. The larger the two gravity parameters, the more strongly the smaller

populationâ€™s mortality rates move in line with those of the larger population in the long run. This

is important where it is believed that the mortality rates between related populations should not

diverge over time on grounds of biological reasonableness. The model is illustrated using an

extension of the Age-Period-Cohort model and mortality rate data for English and Welsh males

representing a large population and the Continuous Mortality Investigation assured male lives

representing a smaller related population.