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Mortality decline has historically been largely a result of reductions in the level of mortality at all ages. A number of leading researchers on ageing, however, suggest that the next revolution of longevity increase will be the result of slowing down the rate of ageing. In this paper, we show mathematically how varying the pace of senescence influences life expectancy. We provide a formula that holds for any baseline hazard function. Our result is analogous to Keyfitz's ‘entropy’ relationship for changing the level of mortality. Interestingly, the influence of the shape of the baseline schedule on the effect of senescence changes is the complement of that found for level changes. We also provide a generalized formulation that mixes level and slope effects. We illustrate the applicability of these models using recent mortality decline in Japan and the problem of period to cohort translation. [ABSTRACT FROM PUBLISHER]

This paper offers an empirical and analytic foundation for regarding period life expectancy as a lagged indicator of the experience of real cohorts in populations experiencing steady improvement in mortality. We find that current period life expectancy in the industrialized world applies to cohorts born some 40-50 years ago. Lags track an average age at which future years of life are being gained, in a sense that we make precise. Our findings augment Ryder's classic results on period-cohort translation. [ABSTRACT FROM AUTHOR]