# COHORT LIFE TABLES

Life tables are used to describe the mortality experience of a population. Several summary statistics can be calculated using life tables, such as life expectancy at birth, a summary statistic which estimates longevity. The basic unit of a life table is the probability of dying at specific ages. There are two types of life tables, which can be distinguished by the methods used to calculate age-specific probabilities of death. Life tables for which age-specific probabilities of death are calculated using the number of deaths and population size in the current year are known as current, or period, life tables. For cohort, or generational, life tables, agespecific probabilities of death are calculated using mortality data from a group of individuals born in the same year and followed until all cohort members have died.

Estimates of life expectancy obtained from period life tables are based on a hypothetical population. For example, the 1994 life expectancy at birth for Canadian women was estimated as eighty-three years, using a period life table. This life expectancy is interpreted as the average age of death for all women born in 1994, and this average is determined by assuming that these women will experience the same age-specific mortality rates as women who died in 1994. No similar assumptions are required when determining life expectancy using cohort life tables because the actual longevity of a population is being measured. The requirement that all cohort members have died, however, limits construction of cohort life tables to demographic data from one hundred or more years prior to construction of the tables.

An illustrative example is provided by F. Pelletier et al. (1997), who investigated mortality in Quebec, Canada, during the 1800s. Using Quebec mortality data from 1891 to construct a period life table, they estimated female life expectancy to be forty-five years. However, cohort life tables show that the life expectancy of Quebec women born in 1891 was, in fact, fifty-one years. The underestimation of life expectancy obtained using period life tables was largely a result of a decline in infant mortality over time. Estimates of life expectancy obtained using period life tables will match cohort life tables only when there has been no change in mortality over time, an extremely unlikely scenario.

Both period and cohort life tables are typically constructed by assuming a population at birth of 100,000 individuals, denoted by l0 = 100,000. The estimated number of survivors by age X is then denoted by lx.

Demographers have identified improvements in health in many countries. These improvements in health began during the 1800s and tended to be even more marked during the 1900s. Cohort life tables will therefore continue to prove valuable in the future both as a benchmark against which to compare period life tables and as an additional tool for investigating mortality trends.

Neil Klar

## Bibliography

Pelletier, F.; Légaré, J.; and Bourbeau, R. (1997). "Mortality in Quebec During the Nineteenth Century: From the State to the Cities." Population Studies 51:93103.

Weeks, J. R. (1994). Population: An Introduction to Concepts and Issues, 7th edition. Belmont, CA: Wadsworth Publishing Company.

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