﻿ 歐美研究季刊第47卷第2期  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).