A Note on Some Historical Data on Old Age

The main purpose of this brief factual note is to bring together a selection of historical data which seem to the author to provide an interesting long-term perspective on the changes in the force of mortality at high ages since the 17th century.

As a by-product, the data can also be used to produce an estimate of the proportion of people who might have been expected to survive from birth in 1700 to reach age 100 in 1800. It is of interest that this is consistent with the estimates given by Zhao and by Vaupel and Jeune elsewhere in this monograph, and which they derived from model life tables with a life expectancy at birth of between 35 and 40 years.

The data which are used in this Note relate to the following periods, starting from the present and working backwards:

(a)	England and Wales in 1980-1990. For ages 0-85, the figures are derived from English Life Table No 14. For ages 85 and over they are derived by an extension of the method of extinct generations (Thatcher, 1992).
(b)	England and Wales in 1841. The figures are derived from English Life Table No 1, which was compiled by William Farr and published by the Registrar General (1843).
(c)	Halley's life table for Breslau in 1687-1691. Halley's life table is reproduced and discussed by Karl Pearson (1978) and by Anders Hald (1990).
(d)	British Members of Parliament who died from 1550 onwards. The data on ages at death of British Members of Parliament (M.P.s) are the subject of an on-going study by Peter Razzell, who has published some preliminary results (Razzell, 1993, 1994). Further results are expected from a joint study by Peter Razzell and Jim Oeppen. The particular figures in Table 1, relating to M.P.s who died at ages 50 and over in the periods 1550-1699, 1700-1799 and 1800-1875, and whose ages at death were known, were calculated by Julia Hynes from data provided by Peter Razzell and the History of Parliament Trust.

The data for M.P.s who entered Parliament before 1660 are not as reliable as the later material, and of course there are problems in estimating life table values from ages at death. Thus the M.P. figures should be regarded as preliminary, pending the forthcoming study by Razzell and Oeppen. They are, however, based on far more data than the comparable estimates for the British aristocracy (Hollingsworth 1977).

Tables 1, 2, 3 summarise the relevant survival functions and the derived forces of mortality, averaged over 5-year age groups. These were calculated by the formula

where ľ is the average force of mortality between ages x and x+5, and where l_x and l_x+5 are the numbers surviving to these ages.

Figure 1 illustrates some of the survival curves. Figure 2 shows the changes of mortality over time between the successive groups of M.P.s. Figure 3, in which Halley's life table and the English life tables are plotted down to the age range 30-35, shows the most comprehensive perspective of all.

Halley's life table does not start from the exact age 0, but the value of l₀ has been reconstructed by Bockh and is given by Hald (1990) as 1238. Using this, we find from Halley's table that the probabilities of survival at Breslau in 1687-91 were 0.279 from age 0 to age 50, and 0.118 from age 50 to age 80. (The Members of Parliament give 0.080 from age 50 to age 80 in 1550-1699 and 0.135 in 1700-1799). In order to estimate the probability of survival from age 80 to age 100, we take the average value of the force of mortality in this age range as 0.4, which is a reasonable extrapolation of the curves in Figure 3. This implies that the probability of survival from 80 to 100 would be about 1 in 3,000. On combining all these estimates, we find that the probability of survival from age 0 to age 100, for a life table cohort born in 1700, comes to about 1 in 100,000. This is consistent with the estimates derived by Zhao and by Vaupel and Jeune from the model life tables.