MPIDR Working Paper
Linking period and cohort life expectancy in Gompertz proportional hazards models
Lenart, A., Missov, T. I.
MPIDR Working Paper WP-2010-024, 21 pages.
Rostock, Max Planck Institute for Demographic Research (April 2010)
Adult mortality decline was the driving force of
life-expectancy increase in many developed countries in the second
half of the twentieth century. In this paper we study one of the
most widely used models to capture adult human mortality - the
Gompertz proportional hazards model. In its standard settings we,
first, derive analytic expressions for period and cohort life
expectancy. In addition we formulate a necessary and sufficient
condition for the unboundedness of life expectancy. Secondly, we
prove that if mortality decreases in time at all ages by the same
proportion, both period and cohort life expectancy at birth
increase linearly. Finally, we derive simple formulae that link
period and cohort life expectancy to one another. They imply that
if period life expectancy at birth increases steadily by three
months per year, which has been the case for the best-practice
country since 1840, then the corresponding cohort life expectancy
rises constantly by four months per year.
Keywords: mathematical demography