Human Lifetime Entropy in a Historical Perspective (1750-2014)

Although it is widely acknowledged that life is risky, it is difficult to provide an intuitive indicator of the riskiness of life, whose metric would have a concrete counterpart for the layman. This paper uses the Shannon entropy index to the base 2 to quantify, in terms of bits (i.e. the amount of information revealed by tossing a fair coin), the risk relative to the age at death in 37 countries from the Human Mortality Database. We identify 5 major stylized facts: (1) over the last two centuries, (period) life entropy at birth exhibits an inverted U shape pattern with a maximum in the first half of the 20th century (at about 6 bits); (2) over the last 150 years, Western countries have converged in terms of (period) life entropy at birth towards levels of 5.6 bits for men and 5.5 bits for women; (3) curves of (period) life entropy at birth for men and women crossed during the 20th century; (4) the entropy age profi le shifted from a non-monotonic profi le (in the 18th and 19th centuries) to a strictly decreasing pro file (in the 20th and 21th centuries); (5) men exhibit a higher life entropy than women below ages 50-55, and a lower one after ages 50-55.