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Advanced Education and Mortality Compression in the United States 149
the open age interval is age 120 in order to avoid the truncation of
death at death. The mortality compression measures are calculated
by following the mathematical approach from Kannisto (2001) who
used the modal age of death (
M
). According to Kannisto, the mode
is not subject to bias when the age range is truncated in the life table.
Although life expectancy (LE) measure (the mean measure) could be
biased in presenting mortality compression, I still provide the
information because it is the most common measure of longevity.
The modal age of death (
M
) was obtained by the formula below:
(5)
where
x
is the age corresponding to the largest value in the life
table function,
d
x
, which is
the
number of deaths at
x
in the life
table,
d
x
-1
is
d
x
at age
x
-1 and
d
x
+1
i
s
d
x
at age
x
+1
.
The degree of compression is measured by the standard
deviation above the modal age of death [SD(
M
+)]. The formula of
SD(
M
+) is
(6)
where
x
i
>
M
, for
i
=1, 2, . . . ,
n
.
Therefore, the numerator is the sum of squared positive
deviations from the modal age of death, and the denominator is the
number of age intervals above the
M
(Cheung, Robine, Tu, & Caselli,
2005). The smaller SD(
M
+) represents the greater level of mortality
compression.
A bootstrapping technique is applied here to obtain standard
errors (Efron, 1987; Efron & Tibshirani, 1986) for the life
expectancies, modal ages of death, and the measures of mortality
compression. For further detail, please refer to the research of Cai
and his colleagues (Cai et al., 2010; Cai & Lubitz, 2007).