A Universal Pattern of the Evolution of Life Table Entropy and Life Expectancy

Andrew Noymer, University of California, Irvine
Ciarra Coleman, University of California, Irvine

Using the complete data collection of the Human Mortality Database (HMD), we demonstrate a striking and heretofore-undocumented regularity in the relationship between life expectancy, e(0), and Shannon entropy, H. We show that sqrt{H} is a 2-segment picewise-linear function of e(0) when the two quantities are considered in historical terms — viz., plotted over time for a given country. Entropy has often been considered as a candidate for a measure of life table rectangularization, but our work suggests that in real human life tables, entropy contains little information beyond that already conveyed by e(0). This does not imply that H is not of interest theoretically, but it does suggest that as an empirical matter, demographers should look elsewhere in their quest to find a quantity that measures rectangularization. Additionally, we explore the interpretation of the 2-segment cut-point in light of prior work on the modal age of death.