Volume 24 - Article 21 | Pages 497–526

Variance in death and its implications for modeling and forecasting mortality

By Shripad Tuljapurkar, Ryan Edwards

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Date received:01 Aug 2010
Date published:22 Mar 2011
Word count:8007
Keywords:entropy, inequality, proportional hazards


The slope and curvature of the survivorship function reflect the considerable amount of variance in length of life found in any human population. This is due in part to the well-known variation in life expectancy between groups: large differences in race, sex, socioeconomic status, or other covariates. But within-group variance is large even in narrowly defined groups, and changes substantially and inversely with the group average length of life. We show that variance in length of life is inversely related to the Gompertz slope of log mortality through age, and we reveal its relationship to variance in a multiplicative frailty index. Our findings bear a variety of implications for modeling and forecasting mortality. In particular, we examine how the assumption of proportional hazards fails to account adequately for differences in subgroup variance, and we discuss how several common forecasting models treat the variance in the temporal dimension.

Author's Affiliation

Shripad Tuljapurkar - Stanford University, United States of America [Email]
Ryan Edwards - University of California, Berkeley, United States of America [Email]

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