Why Do Mortality Variability Trends for the Young and Old Diverge? A Perturbation Analysis

Michal Engelman, Johns Hopkins University
Hal Caswell, Woods Hole Oceanographic Institution
Emily M. Agree, Johns Hopkins University

Variability in longevity has recently been shown to follow strikingly different trends for the young and old: while overall mortality variation decreased as life expectancy at birth rose, survivors to older ages have become increasingly heterogeneous in their mortality risks. These diverging trends reflect changes in the underlying demographic parameters determining age-specific mortality. To understand these changes, we employ a Siler model -- which describes the mortality hazard across the full lifespan and allows for the representation of distinct improvements in early-life, later-life, and background mortality. Using maximum likelihood parameter estimation techniques and newly-developed Markov-chain-based matrix calculus perturbation methods, we then quantify the sensitivity of age-specific mortality variance trends to the changing Siler model parameters. Our results suggest that the slower pace and later start of survival improvements in adulthood relative to those at younger ages form the dynamics that foster the growing inequalities observed for survivors to older ages.