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

Summary 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.