**DISCUSSION PAPER PI-1110**

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.