Concentration in Percentile Scale Inter-Quartile Age

4. Shortest Age Interval of Deaths

We now propose to measure compression in terms of the shortest age interval in which a given proportion of deaths in a life table takes place. Free from both the age scale and the percentile scale, it will point out compression wherever it may occur. We shall accordingly denote this indicator by the letter C, followed by specification of the desired percentage. In Figure 4, the historical development of C10, C25 and C50 is shown in five countries.

(Figure 4 here)

All three indicators show in all countries a consistent long term decline which has more recently slowed down. Though the development has been approximately similar in all countries, significant differences between them can be noted in certain periods and particularly in the last decades when the values have stabilized in England and perhaps in the U.S. while continuing to decline in the others. As the three indicators give a roughly similar account of the course of events, it may be appropriate to select only one of them for recommended use. It would seem that C50 is the most expressive of the rapid fall, the ensuing slowdown and the current differences. It also has the merit of representing a larger segment of deaths. The development of C50 is therefore shown in the last column of Table 1.

We shall conclude the presentation of the C-family of indicators by introducing C90 which would be the ultimate touchstone of rectangularization. It is only realistic to grant that even a completed demographic cycle may be less than absolutely so. Fries himself made allowance for a certain number of cases which would not conform to the rule but die at varying ages. If it is judged that this residual variability in the age at death should not affect more than ten percent of all cases, it follows that compression of mortality is not essentially completed until C90, together with the lower order indicators, is reduced to one year.

It should be noted that C90 becomes meaningful only when early childhood mortality is small enough to be excluded from it. Until then, it simply indicates the age to which 90 percent of the new-born survive. As premature deaths become fewer, this age grows. Once the early mortality is excluded from it, C90 begins to decline with declining mortality and show compression. For the time being this decline is going on quite vigorously and shows hardly any sign of slowdown in the seven countries given in Figure 5.

(Figure 5 here)

Table 2 summarizes the present level of compression in 22 countries in the light of C-indicators at 10, 50 and 90 percent levels. In a very general way, the countries most advanced in compression - on top of the table - are those with lowest mortality while many of those with relatively higher mortality are found at the bottom of the table, affected as they are by still frequent premature deaths. Exceptions, however, abound and the situation varies depending on each particular indicator. In addition, C90 is in some cases affected by volatility.

(Table 2 here)

With two minor exceptions in C90, all data in Table 2 show that mortality of females is on every level of measurement more compressed than that of males. This difference is particularly pronounced in the case of France, Hungary and Slovenia and less so in Japan, Sweden and the Netherlands - a situation which is in line with sex differentials in life expectancy in these countries.

 

Concentration in Percentile Scale Inter-Quartile Age

Measuring the Compression of Mortality
Väinö Kannisto
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871
http://www.demographic-research.org/Volumes/Vol3/6