On the relationship between period and cohort mortality

In this paper I explore the formal relationship between period and cohort mortality, focusing on a comparison of measures of mean lifespan. I consider not only the usual measures (life expectancy at birth for time periods and birth cohorts) but also some alternative measures that have been proposed recently. I examine (and reject) the claim made by Bongaarts and Feeney that the level of period is distorted, or biased, due to changes in the timing of mortality. I show that their proposed alternative measure, called “tempo-adjusted” life expectancy, is exactly equivalent in its generalized form to a measure proposed by both Brouard and Guillot, the cross-sectional average length of life (or CAL), which substitutes cohort survival probabilities for their period counterparts in the calculation of mean lifespan. I conclude that this measure does not in any sense correct for a distortion in period life expectancy at birth, but rather offers an alternative measure of mean lifespan that is approximately equal to two analytically interesting quantities: 1) the mean age at death in a given year for a hypothetical population subject to observed historical mortality conditions but with a constant annual number of births; and 2) the mean age at death, , for a cohort born years ago. However, I also observe that the trend in period does indeed offer a biased depiction of the pace of change in mean lifespan from cohort to cohort. Holding other factors constant, an historical increase in life expectancy at birth is somewhat faster when viewed from the perspective of cohorts (i.e., year of birth) than from the perspective of periods (i.e., year of death).