Human lifetime entropy in a historical perspective (1750–2014)

This paper uses Shannon's entropy index to the base 2 to quantify the risk relative to the age at death in terms of bits (i.e. the amount of information revealed by tossing a fair coin). We first provide a simple decomposition of Shannon's lifetime entropy index that allows us to analyse the determinants of lifetime entropy (in particular its relation with Wiener's entropy of the event "death at a particular age conditional on survival to that age") and to study how the risk about the duration of life is resolved as the individual becomes older. Then, using data on 37 countries from the Human Mortality Database, we show that, over the last two centuries, (period) lifetime entropy at birth has exhibited, in all countries, an inverted-U shape pattern with a maximum in the first half of the twentieth century (at 6 bits), and reaches, in the early twenty-first century, 5.6 bits for men and 5.5 bits for women. It is also shown that the entropy age profile shifted from a non-monotonic profile (in the eighteenth and nineteenth centuries) to a strictly decreasing profile (in the twentieth and twenty-first centuries).