age structure

Age pyramid of Germany (2017)

Global Age Pyramid (2017)

The age structure or age distribution is the statistical distribution of people according to their age at the time of recording. It is a tool for demography and supports forecasts of population development .

Instead of referring to people, however, it can also refer to specified utensils such as cars, washing machines or computers.

Age structure of the population

In common parlance, however, the age structure almost always means the age distribution of the population . The graphical representation of this distribution is called the age pyramid or population pyramid . In these, the age structure is shown separately for women and men on two pages. Such a graphic is structured as follows (see example on the right):

X-axis : number or proportion of people in a year (age)
Y-axis : Age of people, shown in 5 year steps.
By arranging the Y-axis in the middle of the X-axis, the proportions of women are shown in one direction of the X-axis and the proportions of men in the other direction of the X-axis.

This arrangement of the axes and values gives rise to various graphic forms that have a wide variety of causes and results in their creation and social impact.

The term age pyramid emerged from the first such representations, which look like a pyramid, since the youngest years, which form the basis of the graphic, represent the most representatives and the number of members of a year decreases with increasing age. Even if the age structure in the vast majority of industrialized countries has long since developed away from the original age pyramid due to the reduced mortality rate (mortality or death rate), the increased life expectancy and the lower birth rate (term of obsolescence ), this term is still used in general. In developing and emerging countries , the pyramid shape that gives it its name can still be found in some cases.

According to the history of a population, certain graphic forms are to be expected as a result. Different events in the development of the population cause recognizable changes or deformations. Examples of this are wars , natural disasters and changes in the cultural and social behavior of people (for example ' pill break ').

The median age (value that divides the population into the two halves of those who are younger or older than this value) of the world population in 2012 is 28.4 years according to the CIA's World Factbook .

Typical forms of age structures

The six basic forms of the age structure

Population pyramid of Venezuela - classic pyramid shape (2000)

The terms pyramid, bell and urn go back to Friedrich Burgdörfer .

a) Linear or classic pyramid shape (isosceles triangle shape)

An almost linear decrease in the number of children per age group with increasing age results from the large number of children born and the same mortality across all age groups, that is, the life expectancy of all newborns is low, or there is only a slight decrease in the number of children per woman, which nevertheless is above 2.1. This form of the pyramid is common in South America and India, but also in conservative Christian counties in the USA ( Holmes County , Ohio ). This structure was also present in Germany and Austria around 1890.

A population pyramid now leads to exponential population growth due to the sharp drop in mortality across all age groups.

b) Broadened or modified pyramid shape (pagoda shape)

With a constantly very high or even rising birth rate , the pyramid has a base that widens exponentially downwards. This goes hand in hand with a mostly low life expectancy and an early onset, high mortality rate across all ages, if this pyramid describes a developing country. Such pyramid shapes are common in the poorest countries on earth, in some African countries such as Nigeria , DR Congo or Uganda .

The pagoda shape also leads to exponential population growth.

c) beehive shape

The beehive shape arises from a slowly converging age structure, which contracts suddenly in old age. It is considered an ideal because the population neither increases nor decreases. The prerequisites for this are that there is a higher life expectancy, a late onset, high mortality rate and the birth rate is almost constant at the replacement level of 2.1 children per woman. If the number of children remains constant, the US will achieve this form in the near future.

d) bell shape

This form is characteristic of a population that, after a long period of time with low fertility and mortality rates, is confronted with an increasing fertility again. An example of this type of age pyramid are the industrialized countries around 1960, at the time of the baby boom .

Population pyramid of Munich - mixed form between onion shape and Christmas tree shape

e) onion shape or urn shape (exaggerated onion shape)

Many industrialized countries show this type of age structure, as a low birth rate in transition leads to an overhang of older people. At the same time, the younger age groups decrease from year to year. This phenomenon is usually referred to as aging . The prerequisites are the total fertility rate of less than 2.1 children per woman, a high life expectancy with a late onset, high death rate. The age-specific mortality remains the same, however. Age pyramids of economically highly developed countries like that of Western Europe can be assigned to this type.

f) Fir tree shape or teardrop shape

The fir tree shape consists of a very narrow trunk in the young age groups, which becomes massively wider from the 20-year-olds and slowly contracts from the 35-40 year olds. The largest age groups are the 25-30 year olds. Especially in industrialized countries, big cities and especially the inner cities of these big cities have fir tree-shaped population pyramids. This has to do with the fact that the inner-city districts are not very attractive for families and older people, but are very attractive for young adults. The Christmas tree shape is particularly pronounced in university towns or trendy areas such as Shibuya , Friedrichshain-Kreuzberg , Jena or Manhattan .

The transitions between these forms are fluid, but they can be predicted from the cultural and social conditions of the population under consideration. Even if a country's level of development cannot be equated with its demographic level, this can often be guessed at from the shape of the age structure. If the percentage of under 20 year olds is greater than or equal to 50%, this is usually referred to as a developing country.

The typical order is: ${\ displaystyle a) {\ xrightarrow {\}} b) {\ xrightarrow {\}} f) {\ xrightarrow {\}} c) {\ xrightarrow {\}} e)}$

It should be noted that forms e) and f) are not stable, ie these structures cannot be maintained in the long term. The structure evolves into a different, stable form, in extreme cases with a birth rate of zero.

Estimation of the age distribution

Weibull simulated age distribution functions with area normalized to 100

The same curves rotated 90 ° to the left and mirrored

The age structure observed can be approximated using different distribution functions . A first approach to describe the age distribution with only one parameter, mortality , is the exponential distribution . If a population is the size of B people and gives the number of deceased in relation to age, then the number of those still alive is. The age distribution is therefore: ${\ displaystyle F (x)}$ ${\ displaystyle BF (x) = S (x)}$ ${\ displaystyle S (x)}$

{\ displaystyle S (x) = {\ text {const.}} \ cdot e ^ {- m \ cdot x}}

With

{\ displaystyle m}

: Mortality.

The constant is chosen so that the sum over just gives the population . ${\ displaystyle S (x)}$ ${\ displaystyle B}$

The expected value of the exponential distribution is the reciprocal of mortality, the life expectancy value . For the examples above it is years for Germany , 211 years for Mexico, 144 years for China and 65 years for Russia. The high values for Mexico and China result from the high proportion of young people due to population growth. The exponential distribution knows no aging, which is why it allows unrealistically old age. ${\ displaystyle {\ tfrac {1} {m}}}$ ${\ displaystyle {\ tfrac {1} {0 {,} 01044}} \ approx 96}$

An improved approach models the distribution with an age-dependent mortality rate : ${\ displaystyle m (x)}$

{\ displaystyle m \ rightarrow m (x) = m_ {0} \ cdot x ^ {b-1}.}

Inserted into the distribution function results in the Weibull distribution with the two parameters and : ${\ displaystyle S (x)}$ ${\ displaystyle m_ {0}}$ ${\ displaystyle b}$

{\ displaystyle S (x) = e ^ {- m_ {0} \ cdot x ^ {b}}.}

The diagram shows one age distribution for the exponential distribution and two for the Weibull distribution. The parameters are listed in the table. The total number (area integral) is 100 for all three curves (for example 100 million people).

Curve parameters of the diagram
Curve	${\ displaystyle {\ tfrac {1} {m_ {0}}}}$	${\ displaystyle b}$	${\ displaystyle {\ tfrac {1} {m (1)}}}$	${\ displaystyle {\ tfrac {1} {m (20)}}}$	${\ displaystyle {\ tfrac {1} {m (50)}}}$	${\ displaystyle {\ tfrac {1} {m (80)}}}$	${\ displaystyle S (1)}$	${\ displaystyle S (60)}$	${\ displaystyle S (90)}$
1	60	1.0	60	60	60	60	1.9	0.7	0.5
2	100	1.4	100	30th	21st	17th	4.0	0.2	0.04
3	10 ¹³	6.8	10 ¹³	3 · 10 ⁵	1400	91	1.3	1.2	0.2

Curve 1 is an exponential distribution with a life expectancy value independent of time. For years 1, 20, 50 and 80 it is a constant 60 years. The proportion of one-year-olds is 1.9 (i.e. 1.9 million here), that of 90-year-olds 0.5.
Curve 2 has a life expectancy value of with the constant . This results in an age dependency of , which falls from 100 years at an age of one year to 17 years at an age of eighty. The distribution is pyramidal. ${\ displaystyle {\ tfrac {1} {m_ {0}}} = 100}$ ${\ displaystyle b = 1 {,} 4}$ ${\ displaystyle {\ tfrac {1} {m (x)}}}$
Curve 3 simulates a constant distribution with a decrease at sixty years due to a very high life expectancy value of 10 ¹³ at an age of one year, which decreases very quickly with increasing age due to the large value of . ${\ displaystyle b = 6 {,} 8}$

To compare the curves with an age pyramid, turn them 90 ° to the left so that the age becomes the ordinate. If further parameters are introduced, the observed values can be reproduced more precisely. On the other hand, the interpretation of the meaning of the parameters becomes more difficult.

country	Raw death rate	Average life expectancy at birth	Basic form of the age pyramid
Germany (2008)	1.08 / 1000	79.01 years	Urn shape
Mexico (2008)	4.78 / 1000	75.84 years	Pyramid shape
China (2008)	7.03 / 1000	73.18 years	Beehive shape
Russia (2008)	14.62 / 1000	67.88 years	Urn shape

Web links

Commons : Age pyramids - collection of images, videos and audio files

Wiktionary: Age structure - explanations of meanings, word origins, synonyms, translations

Berlin Institute for Population and Development . Retrieved October 12, 2016.
Federal Statistical Office Germany - Age pyramid 1950-2060, 13th coord. Population forecast, destatis.de. Retrieved October 12, 2016.
Austria 1991 - dynamic Excel population pyramid of the University of Klagenfurt ( Memento from February 17, 2006 in the Internet Archive )
Graphic: Age structure - Germany , from: Figures and facts: The social situation in Germany , www.bpb.de
Graphic: Age structure - Europe , from: Figures and facts: Europe , www.bpb.de
Graphic: Age structure EU - USA - China , from: Figures and facts: Europe , www.bpb.de

Individual evidence

↑ Median age online at the World Factbook of the CIA ; As of September 27, 2012. (English)
↑ J. Bähr , C. Jentsch , W. Kuls : Population geography . (= Textbook of General Geography. Volume 9). New York / Stuttgart 1992, pp. 177-181. online at Google Book Search . As of January 30, 2009

^ W. Kuls: Population geography . An introduction. Stuttgart 1980, p. 65.

↑ ^a ^b Karl Husa, Helmut Wohlschlägl : Introductory seminar “Basics of Population Geography”. ( Memento from December 5, 2010 in the Internet Archive ) University of Vienna , Institute for Geography and Regional Research, p. 42.

^ Friedrich Burgdörfer: People without youth. Birth loss and aging of the German national body. A problem of the national economy - of social policy - of the national future. Berlin 1932, p. 112.

[1] Median age online at the World Factbook of the CIA ; As of September 27, 2012. (English)

[2] J. Bähr , C. Jentsch , W. Kuls : Population geography . (= Textbook of General Geography. Volume 9). New York / Stuttgart 1992, pp. 177-181. online at Google Book Search . As of January 30, 2009

[3] W. Kuls: Population geography . An introduction. Stuttgart 1980, p. 65.

[Bevölkerungsgeographie-4] Karl Husa, Helmut Wohlschlägl : Introductory seminar “Basics of Population Geography”. ( Memento from December 5, 2010 in the Internet Archive ) University of Vienna , Institute for Geography and Regional Research, p. 42.

[5] Friedrich Burgdörfer: People without youth. Birth loss and aging of the German national body. A problem of the national economy - of social policy - of the national future. Berlin 1932, p. 112.