Journal of the Institute of Actuaries

Research Article

The expectation of life and its relationship to mortality

J. H. Pollard


The complete expectation of life at birth ė0 is frequently used as a measure of the level of mortality of a population. It is also used for assessing trends in mortality and trends in mortality differentials. Although the relationship between mortality and expectation of life is essentially reciprocal, the exact connexion is rather more complicated, and becomes important when, for example, trends in differentials are analysed.

In this paper, the relationship between mortality and expectation of life is explored in some detail, and formulae are developed for analysing the effects of mortality changes on expectation of life, and trends in mortality differentials on ė0 differentials.

Unlike Keyfitz (1977), who concentrates on the proportional change in ė0 corresponding to equal proportional changes in mortality at all ages, we study the relationship between absolute changes in mortality, generally different at different ages, and the corresponding absolute change in ė0.

It is demonstrated that two populations may experience diminishing mortality differentials and at the same time widening ė0 differentials. Numerical examples are given using Australian data over the periods 1921–71 and 1971–79.

Although the formulae in the paper relate solely to the expectation of life at birth, the methods and formulae are readily adapted to expectations of life at other ages and indeed, temporary expectations.