On the correspondence between CAL and lagged cohort life expectancy

Michel Guillot, University of Pennsylvania
Hyun Sik Kim, University of Wisconsin at Madison

It has been established that under the linear shift assumption, CAL(t) is equal to the life expectancy for the cohort born at time t-CAL(t), or, equivalently, e0c(t) is equal to CAL for the period t+e0c(t). This correspondence is important, because the cohort life expectancy for the cohort currently reaching its life expectancy, or lagged cohort life expectancy (LCLE), has been discussed in the tempo literature as a summary mortality measure of substantive interest. In this paper, we establish that the CAL-LCLE correspondence holds in a variety of empirical situations, present or historical, including ones in which the linear shift assumption doesn't apply, and provide some more general principles about the extent to which CAL can be used as an estimate of LCLE. Finally, we discuss the implications of the CAL-LCLE correspondence for using CAL (or LCLE) as a summary mortality measure, and for the projection of cohort mortality.