The Life Table is a fascinating tool that provides us with an estimate of life e
The Life Table is a fascinating tool that provides us with an estimate of life expectancy. It computes, for every age group, how many years of life are left to the average person in that age group.
The Life Table should really be called the Death Table, because it begins with an arbitrary number of births in a given year and calculates how quickly the newborns die off.
The first person to perform such calculations was John Graunt (1662), a hat maker living in London in the seventeenth century. He took a keen interest in the weekly death bulletins issued by the various parishes[1]. He estimated that, out of 100 people conceived in London in his day, only 64 percent would survive to age 6, only 40 to age 16, and so forth. Three of every one hundred newborns would make it to age 66, and only one to age 76. Graunt was not able to say, however, how long the average newborn could be expected to live. The complete method for estimating life expectancy would be delineated later by the astronomer Edmond Halley.[2]
To compute life expectancy at birth, as well as life years remaining at any particular age, age-specific mortality rates are manipulated in a series of calculations that are best organized in the rows and columns of a table or spreadsheet. Life Tables are constructed for men, women, or both. When data suffice, a Life Table could be constructed for other sex identities. Life Tables are constructed for particular occupational categories, ethnicities etc. by interested parties such as life insurance companies.
The entire Life Table depends on the age-specific mortality rates that are inputted. We use the latest data available. But the Life Table will soon be out of date, because mortality rates are constantly changing. As a matter of fact, Queen’s University in Kingston, Ontario was found in the 2010s to have under-invested in its professors’ pensions. Actuaries[3]advising the University had failed to realize that Queens professors’ mortality rates were declining faster than the mortality rates of other groups.
Typically, each life table begins with 100,000 hypothetic newborns. The actual number doesn’t matter, since we’re only concerned with the proportion that dies in any age group. We like to begin with a nice big number so that, when we multiply by mortality rates, we won’t get tiny fractions. We like a number divisible by ten so we can easily calculate percentages. In the Life Table below, the one hundred thousand newborns are Canadian females born in 2019. You’ll find them in first row of numbers, fifth column, the column labeled “l” (lowercase “L”).
Have a look at those 100,000 newborns highlighted in Table 6-1. In the cell to the left of the highlighted cell, you see the number q=0.0038297. This is the probability that a newborn will die before it reaches the age of 1. The number to the left of that is the mortality rate expressed as a decimal, M. M=.0038429.
Why is M, the mortality rate, not the same as q, the probability of dying? Recall