Mini Review

Life expectancy in Germany until 2050

Eckart Bomsdorf*

Department of Economic and Social Statistics, University of Cologne, Albertus-Magnus-Platz, Cologne 50923, Germany

Received 23 July 2003; received in revised form 4 November 2003; accepted 5 November 2003

Abstract

The expected demographic shifts—already having commenced in many countries—have their origin primarily in decreasing birth rates

and increased life expectancy. This paper will show possible development paths for life expectancy at birth up until the year 2050. We will

distinguish between traditional period life tables and cohort life tables, the latter leading to more realistic values for life expectancy. It will be

shown that a marked increase in life expectancy up to over 90 years is to be expected.

q 2003 Elsevier Inc. All rights reserved.

Keywords: Life table; Cohort; Period; Death rate; Age-specific

1. Approach

Life expectancy in Germany—as in many other

countries—has increased significantly over the last 100

years. This is due, in particular, to a decline in infant

mortality from 20% to under 0.5%. However, age-specific

death rates have also decreased pronouncedly in all other

age groups.1 For example, the probability of a newborn

infant not reaching the age of 50 is today less than 5%,

compared to approximately 45% a century ago.2 The key

question is now, how life expectancy will continue to

develop. However, before we can answer this question we

must address some methodological issues.

Life expectancy is determined with the help of

survival or death rates. It is thus plausible to apply the

methods with which these probabilities are modeled

when projecting life expectancy. Although direct esti-

mation of life expectancy is conceivable, its assessment

using survival and death rates, and thus life tables, is

preferable. Life expectancy is merely a cumulative

statistic, and although it has high information content it

is, on its own, usually not a sufficient mortality measure.

In contrast, the distribution of deaths described by a life

table yields more interesting information for population

and pension calculations.3

In life tables age-specific survival and death rates, as

well as life expectancy, are indicated separately for the

male and female population groups. These life tables

were originally conceived as so-called cohort

(or generation) life tables, which present the mortality

development of a particular birth cohort—all persons

born in a particular year—from birth until no lives

remain in the group. To prepare a single complete cohort

life table thus requires data from a time period of at least

100 years, as life tables are generally constructed up to

the age of 100. Naturally, the death rates in these life

tables cannot be used as estimates for the death rates of

currently living age groups, as age-specific mortality will

have changed significantly over time.

These generation life tables are thus not commonly

used in practice. Instead, period (or current) life tables

that have the same structure as the cohort tables are

employed. However, in constructing period life tables no

specific cohort is described. Instead, sex-specific death

rates for each age group from 0 to 100 are established in

a certain year, or in a period comprising several years.

Based on these data, a full life table is calculated

separately for men and women reflecting actual current

mortality conditions as a cross-section. In Germany,

0531-5565/$ - see front matter q 2003 Elsevier Inc. All rights reserved.

doi:10.1016/j.exger.2003.11.002

Experimental Gerontology 39 (2004) 159–163

www.elsevier.com/locate/expgero

* Tel.: þ49-221-4702982; fax: þ49-221-4705074.

E-mail address: bomsdorf@wiso.uni-koeln.de (E. Bomsdorf).1 As a rule, survival and death rates (also called mortality rates) referred

to in this paper are single-year age-specific rates; multi-year rates can be

calculated directly from these. The term ‘life expectancy’ refers to the life

expectancy at birth.2 This data assumes complete life tables, i.e. a period treatment. 3 Cf. Bomsdorf, 2002, pp. 11–17.

complete life tables, in which data from a population

census are integrated, are distinguished from abridged

life tables. The former are generally of higher data

quality than the latter. This is mainly due to the fact that

abridged life tables are calculated on the basis of

population data that has repeatedly been adjusted over

time, and that no smoothing of death rates occurs as with

the complete tables. Additionally, no death rates for age

groups over 90 are specified in the abridged life tables.4

History, and in particular the last decade, has shown

that apart from a few exceptions death rates in Germany

have continually decreased, leading to higher survival

rates and thus higher life expectancy. Assuming a

continuation of this trend, differing approaches are

possible in the calculation of estimated death rates,

including the use of endogenous prognosis functions.

Employing these death rates in the estimation of survival

rates and life expectancy has proven to be appropriate.

To calculate the estimates for life expectancy at birth

up until 2050, death rates need to be determined based

on future mortality conditions.5 For Germany, model

calculations for death rates were undertaken using the

approach suggested by Bomsdorf and Trimborn.6

Here, the future single-year death rates, which depend

on the age x and year t; were determined using a

log-linear function with age- and sex-specific parameters.

This approach assumes that the logarithm of the single-

year death rates over time can be described sufficiently

well with a linear function. Lee and Carter independently

suggested and applied a similar approach in 1992 (Lee

and Carter, 1992).7 Estimations modeling life expectancy

until 2050 using log-linear functions were also applied in

a study for the G7-States done by Tuljapurkar et al.

(2000). However, both of the above-mentioned analyses

use the period approach, which causes a systematic

underestimation of life expectency.

The death rates used in computing future life expectancy

based on period life tables and cohort life tables are shown

in Table 1. Here, the cross-section perspective of the period

life table and the longitudinal approach underlying the

cohort life table is clearly demonstrated.

In order to take the most recent mortality trends into

account, the abridged life table 1998/2000 of the German

Federal Statistical Office (Statistisches Bundesamt)

was used to calibrate the extrapolations for future life

expectancy—in spite of the reservations expressed

above.8 In Method 1 the coefficients of the log-linear

prognosis model were determined based on the complete

life table for Germany. In Method 2 the abridged life

tables 1961/1963 and 1997/1999 were used to estimate

the coefficients.

From the model calculations for survival and death

rates described above, life expectancy at birth is

determined for 2005–2050. We differentiate calculations

according to which type of life table was used (cohort or

period life tables), according to sex and the approach used

in modeling. Method 1 provides a lower limit or path for

the development of life expectancy, while Method 2

indicates an upper path. The further in the future the

calculations lie, the more they should be understood as

possible scenarios rather than as a definite prognosis; this

Table 1

Single-year death rates

Age in years Period life table

(Year TÞ

Cohort life table

(Year of birth TÞ

0 q0;T q0;T

1 q1;T q1;Tþ1

2 q2;T q2;Tþ2... ..

. ...

98 q98;T q98;Tþ98

99 q99;T q99;Tþ99

100 q100;T q100;Tþ100

qx;t : Single-year death rates for people aged x in year t; x ¼

0; 1;…; 100; t ¼ T ; T þ 1;…; T þ 100:

Table 2

Life expectancy at birth in Germany 2005–2050 based on period life tables

Year of birth Life expectancy in years

Method 1 Method 2

Total Female Male Total Female Male

2005 78.6 81.6 75.7 79.0 82.1 76.1

2010 79.1 82.1 76.1 79.8 82.9 76.9

2015 79.5 82.6 76.6 80.6 83.8 77.7

2020 80.0 83.1 77.1 81.4 84.6 78.4

2025 80.4 83.6 77.5 82.2 85.3 79.2

2030 80.9 84.0 77.9 82.9 86.0 79.9

2035 81.3 84.4 78.3 83.6 86.7 80.6

2040 81.7 84.8 78.7 84.2 87.4 81.2

2045 82.0 85.2 79.0 84.8 88.0 81.9

2050 82.4 85.5 79.4 85.5 88.6 82.5

4 The age groups 90–100 of the 1998/2000 abridged life table were

estimated by applying a smoothing interpolation on the 1986/1988

complete life table in the model calculations. The life expectancy of 100-

year-olds is taken as the maximum of the adjusted life expectancy

according to the last complete life table and the life expectancy calculated

from the linear interpolation of death rates of those aged over 100 years.

Thatcher et al. (1998) investigate the modeling of death rates of high-aged

persons.5 The prognosis of the development of life expectancy in France, Japan

and the USA by Olshansky et al., (2001) is based on a reduction in

mortality, which is assumed to be similar for all age-groups. Birg and

Flothmann (2001), pp. 23–38) in their model calculations derive the life

expectancy in Germany from the median age.6 Cf. Bomsdorf and Trimborn, 1992.7 Regarding the quality of these approaches see, for example, Helberger

and Rathjen, 1998, pp. 406–411. 8 Cf. Bomsdorf, 2002, p. 16.

E. Bomsdorf / Experimental Gerontology 39 (2004) 159–163160

is particularly true for life expectancies based on the

cohort approach.

2. Results

Official statistics on life expectancy are internationally

often determined based on period life tables. However, due

to their cross-section treatment they systematically under-

estimate life expectancy. Thus, it seems necessary to

additionally specify estimates for life expectancy based on

cohort life tables.

All results point to a continued rise in life expectancy.

The period view indicates an increase in life expectancy

for women from currently 81 years to approximately 85.5

years in 2050 using Method 1. The equivalent values for

men are 75 and 79.4 years (see Table 2). The difference

Fig. 1. Life expectancy in Germany 2005–2050 based on period life tables.

Fig. 2. Life expectancy in Germany 2005–2050 based on period life tables.

Table 3

Life expectancy at birth in Germany 2005–2050 based on cohort life tables

Year of birth Life expectancy in years

Method 1 Method 2

Total Female Male Total Female Male

2005 83.4 86.9 80.1 88.0 91.2 85.0

2010 83.8 87.2 80.6 88.6 91.7 85.7

2015 84.2 87.6 80.9 89.2 92.2 86.4

2020 84.5 87.9 81.3 89.8 92.6 87.0

2025 84.9 88.3 81.7 90.3 93.1 87.6

2030 85.2 88.6 82.0 90.8 93.5 88.2

2035 85.5 88.9 82.3 91.2 93.8 88.8

2040 85.8 89.2 82.7 91.7 94.2 89.3

2045 86.1 89.5 83.0 92.1 94.5 89.8

2050 86.4 89.7 83.3 92.5 94.8 90.3

E. Bomsdorf / Experimental Gerontology 39 (2004) 159–163 161

between male and female life expectancy remains nearly

the same over time, which is also true for the results

according to Method 2. However, Method 2 estimates

life expectancy for both sexes to be approximately

three years higher in 2050 than according to Method 1.

The life expectancy independent of sex runs

accordingly.9

Figs. 1 and 2 graphically summarize the results over

the complete time span until 2050. In contrast to Table 2,

the graphs depict values for life expectancy for all years.

The illustrations show a near linear increase in life

expectancy over time. The slope is independent of sex, but

differs for the two approaches.10 The annual progression for

Method 2 is distinctly higher than the estimates given by

Method 1.11

The prognosis determined with the help of cohort life

tables shows a different picture (see Table 3 and Figs. 3

and 4). The estimates for life expectancy are naturally

markedly higher than in the cross-section treatment. In

Method 1 the life expectancy of women at birth rises to

89.7 years in 2050; that of men born in 2050 is projected

to be 83.3 years. The difference between the life

expectancy of women and men remains practically

constant. This, however, is not the case for Method 2.

Here male life expectancy increases more than female

life expectancy.12 In contrast to the situation for the

period treatment, the slope of the Method 2 curves in

Fig. 3 is not significantly higher than that of the Method

1 curves. It is interesting to note that the life expectancy

at birth in 2050 for men in Method 2 is higher than the

equivalent for women in Method 1.

3. Summary

While estimates for life expectancy based on a period

treatment are better suited for international comparisons,

statistics calculated on the basis of cohort data provide a

more realistic prognosis. In each case, Method 1 indicates a

moderate rise in life expectancy, while Method 2 designates

an upper path. The actual future life expectancy should—

provided no unexpected events occur—be found to lie in

this corridor.13

Fig. 3. Life expectancy in Germany 2005–2050 based on cohort life tables.

9 The aggregation of male and female life expectancy to one term is

methodologically problematic. All the same, this value is estimated

here, as internationally often only combined life expectancy is specified

(cf. e.g. Tuljapurkar et al., 2000).10 An accurate observation of the growth of life expectancy shows it being

slightly weaker than linear.11 If only the most recent trends in life expectancy in Germany were

extrapolated, even higher life expectancy than indicated by Method 2 would

have to be expected.

12 Due to the cohort approach it is not sensible to use the values of the

period tables when representing the development of future life expectancy.

It would be necessary to use the cohort life table for the respective current

birth cohort. This approach would estimate life expectancy at birth in 2003

at 86.7 years for women and 80.0 years for men using Method 1 and

equivalently 90.9 and 84.7 years with Method 2.13 It is not the function of this paper to demonstrate the consequences of

increasing life expectancy. However, we would like to refer to the Final

Report on Demographic Change by the Enquete Commission of the

Deutscher Bundestag (2002), which in detail looks into the effects of

demographic change, i.e. the shifting of the age structure in Germany and

its consequences. Of the numerous contributions to this topic we, in

particular, refer to Stauffer (2002), who quantitively analyses the effects of

changes in fertility, mortality and migration on the proportion of old-aged

people in society.

E. Bomsdorf / Experimental Gerontology 39 (2004) 159–163162

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Fig. 4. Life expectancy in Germany 2005–2050 based on cohort life tables.

E. Bomsdorf / Experimental Gerontology 39 (2004) 159–163 163