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A Gravity Model of Mortality Rates for Two Related Populations.

Cairns, A.J.G.; Blake, D.; Dowd, K.; Khalaf-Allah, M.; Coughlan, G.D.


A.J.G. Cairns

D. Blake

M. Khalaf-Allah

G.D. Coughlan


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 parameters 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.


Cairns, A., Blake, D., Dowd, K., Khalaf-Allah, M., & Coughlan, G. (2011). A Gravity Model of Mortality Rates for Two Related Populations. North American Actuarial Journal, 15(2), 334-356.

Journal Article Type Article
Publication Date 2011-04
Deposit Date Nov 20, 2012
Journal North American Actuarial Journal
Print ISSN 1092-0277
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 15
Issue 2
Pages 334-356
Public URL