## Mortality shifts and mortality compression in period and cohort life tables

**Nico Keilman**, *Department of Economics, University of Oslo*

*d*(

*x*)-column. We derive general analytical expressions for the moments of this distribution in a series of annual period life tables, written as functions of the moments in cohort life tables. The first moment is the life expectancy, while the second moment reflects compression of the age at death. The expressions are partly based on an empirical regularity that we found in the data for a number of countries with long data series in the Human Mortality Database (HMD).

We derive the conditions under which cohort life expectancy increases faster than period life expectancy. We also find expressions for the period life expectancy in the year a birth cohort reaches an age equal to its own life expectancy, and for the gap between the period life expectancy in a certain year and the cohort life expectancy for the cohort born that year. Furthermore, we establish a relation between the period life expectancy in a certain year *t*, and the lag λ that leads to an equally large cohort life expectancy for a cohort born in year *t* – λ (the number of years it takes a period life expectancy to reach the current level of cohort life expectancy).

Using the second moment of the AADD, we derive an expression for the variance / standard deviation of the period AADD. The expression shows that the cohort life expectancy and its variance drives the period variance up, while the period life expectancy presses it down. This sheds some more light on the dynamics of mortality compression in periods and cohorts.

Presented in Session 1197: Mortality and Longevity