Life Expectancy in Developed Countries is Higher Than Conventionally Estimated. Implications from Improved Measurement of Human Longevity

Abstract

Both the centuries-long tradition of conventional lifespan indicators and the more recent criticism to them ignore the true exposures of individuals to prevailing mortality levels. These exposures form a genuine part of a more comprehensive picture of the prevailing mortality conditions. In low-mortality countries, our estimated duration of human life exceeds the conventional estimates by 15 years. Our theory implies that mortality dynamics are characterised by a considerable inertia. This is used to develop new methods of forecasting, leading to a more optimistic outlook for future mortality.

Appendix. Additional Derivations and Detailed Tabulations

Derivation of the Formula for Exposure-Adjusted Life Expectancy at Age x

Given the adjusted mortality schedule μ*(·), one may compute the life expectancy at age w in the exposure-adjusted life table in a usual way:

$$ e*(w) = \int\limits_w^{\infty } {{e^{{ - \int\limits_w^s {\mu *(v)dv} }}}ds} . $$

(A1)

After applying the transformation (3) to change variables in both integrals $\left( {s = y(z),v = y(u),{\text{i}}{\text{.e}},ds = k(z)dz,dv = k(u)du} \right)$ and using Eq. 4, this yields:

$$ e*(w) = \int\limits_{{{y^{{ - 1}}}(w)}}^{\infty } {{e^{{ - \int\limits_{{{y^{{ - 1}}}(w)}}^{{{y^{{ - 1}}}\left( {y(z)} \right)}} {\mu *\left( {y(u)} \right)k(u)du} }}}k(z)dz} = \int\limits_{{{y^{{ - 1}}}(w)}}^{\infty } {{e^{{ - \int\limits_{{{y^{{ - 1}}}(w)}}^z {\mu (u)k(u)du} }}}k(z)dz} . $$

(A2)

This implies for the life expectancy at age x for those currently observed at that same age:

$$ e_x^{*}(x) = e*\left( {y(x)} \right) = \int\limits_x^{\infty } {{e^{{ - \int\limits_x^z {\mu (u)k(u)du} }}}k(z)dz}, $$

(A3)

which is a general form of the relation (7) presented in the main text.