Life Expectancy

Lent term is about to end. I learned several things during this term. But I'm sure I'm going to forget them in a month or so. So let me write them down here. The first instalment is about life expectancy. If you spot any inaccurate descriptions below, let me know by leaving a comment.

1. Life expectancy is visualized as follows. Take age on the x-axis and take the proportion of survivors to a certain age on the y-axis. From the data on death rates for each age cohort, you can plot the proportion of survivors for each age. The area surrounded by the x and y axes and the plot curve is life expectancy at birth. (Added on 16th March: Of course, one cannot estimate life expectancy for each cohort because then you need to track this cohort until the last person dies. For practicality, demographers assume that each cohort will face the same survival probability as the one currently faced by older cohorts. Special thanks to Bessho-san (his Japanese blog), who emailed me on this point.)

2. In the demography literature, various ways to decompose change in life expectancy between two points in time have been developed during the past 25 years. But the most useful is still one of the first proposals: Arriaga, E.E. (1984). "Measuring and explaining the change in life expectancies", Demography, 21, pp.83-96.

3. Crude death rates are sensitive to age composition of the population. Even if the death rates for every age group doesn't change, the crude death rate of the population goes up if the proportion of old people to the population goes up. A solution to this is standardized death rates, in which the population death rate is calculated with the age structure fixed. But then the arbitrariness of the choice of a "standard" age composition is a problem.

4. A good reference of these issues is Demography: Measuring and Modeling Population Processes, by Samuel H. Preston, Patrick Heuveline, and Michel Guillot (Blackwell Publishing, 2001).