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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
population’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.