Dynamics of life expectancy and life span equality

Abstract

As people live longer, ages at death are becoming more similar. This dual advance over the last two centuries, a central aim of public health policies, is a major achievement of modern civilization. Some recent exceptions to the joint rise of life expectancy and life span equality, however, make it difficult to determine the underlying causes of this relationship. Here, we develop a unifying framework to study life expectancy and life span equality over time, relying on concepts about the pace and shape of aging. We study the dynamic relationship between life expectancy and life span equality with reliable data from the Human Mortality Database for 49 countries and regions with emphasis on the long time series from Sweden. Our results demonstrate that both changes in life expectancy and life span equality are weighted totals of rates of progress in reducing mortality. This finding holds for three different measures of the variability of life spans. The weights evolve over time and indicate the ages at which reductions in mortality increase life expectancy and life span equality: the more progress at the youngest ages, the tighter the relationship. The link between life expectancy and life span equality is especially strong when life expectancy is less than 70 y. In recent decades, life expectancy and life span equality have occasionally moved in opposite directions due to larger improvements in mortality at older ages or a slowdown in declines in midlife mortality. Saving lives at ages below life expectancy is the key to increasing both life expectancy and life span equality.

Keywords: aging; demography; life span variation; mortality; pace and shape.

Fig. 1.

Association between life expectancy at birth ${\mathit{e}}_{\mathit{o}}$ and life span equality $\mathit{h}$.

Fig. 2.

(A) Association between changes in life expectancy at birth ${\mathit{e}}_{\mathit{o}}$ and life span equality $\mathit{h}$. (B) Association between changes over 10-y rolling periods.

Fig. 3.

Weights for the changes in life expectancy $\mathit{w}\left(\mathit{x}\right)$ (A and B) and life span equality $\mathit{w}\left(\mathit{x}\right){\mathit{W}}_{\mathit{h}}\left(\mathit{x}\right)$ (C and D). Each line refers to a given period and represents how life expectancy and life span equality react to age-specific mortality improvements for Swedish women in selected periods.

Fig. 4.

(A) Association between 10-y changes in life expectancy at birth ${\mathit{e}}_{\mathit{o}}$ and life span equality $\mathit{h}$ because of mortality changes below the threshold age. (B) Association between 10-y changes in ${\mathit{e}}_{\mathit{o}}$ and $\mathit{h}$ because of mortality changes above the threshold age. The dotted lines show the directions of the relationship below and above the threshold age.

Fig. 5.

Life expectancy at birth ${\mathit{e}}_{\mathit{o}}$ and life span equality $\mathit{h}$ for three different scenarios: 1) observed points: Swedish females, 1751 to 2017; 2) youngest equality: life span equality derived by matching observed life expectancy levels by reducing the youngest age; and 3) constant change over age: death rates in each year at all ages are reduced at the rate $\mathit{\rho }$ to achieve the observed change in life expectancy at birth.