Linking period and cohort life expectancy in Gompertz proportional hazards models

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.