Experiences in modelling complex demographic processes

Experiences in Modtlling Complex Demonraphic Processes Thomas Biittntr') Multistate mathematical demography, Population analysis and forcast, Marital status of Population. The Paper deals with a special aspect of the family-dimension of population dynamics: the population disaggrtgated by age, sex and marital status and its development. First, the methodological approach of the multistate analysis is outlined and second some results of an application are given. The connection between population development and other social processes needs an intensivied scientific treatment under the condition of an intensively extended economy, of socialist ways of living and of long term changes in the patterns of demographic rtproduction. Thus, the so called process aging population< involving significant changes in the age structure of the GDR's population, describes a complex and complicated phenomenon, having consequences to many spheres of lift. Social sciences have to recognize and, finally, quantify this changes and its implications. Therefor modelling of essential demographic processes art an important precondition. Methodology: The central concept in demography is the life table, describing the evolution of a (hypothetical) cohort (a generation, let say) of individuals born at the same time and exposed to an unchanging agespecific schedule of vital rates. The starting point for constructing a life table is the differential equation that defines l(x), the probability of surviving to a certain tgt function): d (x) l(x) 2, l(x) = -p TX

x (survivorship

(1)

The classic life table approach was only able to deal with the transition between two states of existence, mostly from being alive to being dead. To tackle more complex problems a gentralisation of classic life tables to increment-decrement life tables (multistate life tables) were developed in the last decade. (l), (4). This approach is also founded on equation (l), but with matrices replacing scalars. The procedure of estimating en age-specific matrix of transition probabilities P(x) between several states (including death) from observed data is described in the literature.(2) (3). '1) I titute for Sociology and Social Policy, Academy of Sciences, G%, 1080 Berlin, Otto-Huschke-Str. lo/l1 2) Note, that the chance/risk of dying between age cland U+ du for anq- year-old person ist a (&) d%; in (1) x stands for exact age

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The survivorship function is then @Yen L(x+h)

=

by

L(x) P(x)

(2)

In the multistate perspective of population analyeis there ist a set of several life table functions (statistica), all of them originating from the transition probabilities P(x). A discret age-time model of multistate population development expresses the population projection process bytmeans of matrix operations. Given the multistate population as a vector Kt+disaggregated by age and states at t=O, and tranafonning the transition probabilities P(x) into the survivorship proportiona S(x), that refer to individuals who are not at exact age x but in age groups x to x+h, by

S(x)

s

[I

+

P(x+hy.. P(x) * (I + P(x)] -l

(3)

(note, that I is the identity matrix), then the basic projection equation may be expresaed as follows: Kt+' (x+h) = S(x) Kt(x) (For computing Kt+' (0). d.e. the surviving babies born in the unit time interval, see (3)) Application: The flows between marital states, recorded in the official statistic, are given as followa1) Never married-

Marmwed 1

Divirced

For analysing the patterns of marital status behaviour, after estimating P(x), the life table statistic 'Life expecttancyby state of existence at age x* was computed. Table 1 gives an impressive comparison between these statistics for 1975 and 1982. Reducing a large number of observed data to condensed figures it is visible that the remaining married life time decreases but the years to be divorced increased for an 2o-year-old female between 1975 and 1982 significantly; the aame for males. An aspect of this phenomenon is the increase of *paperless" marriages ('cohabitions') within younger age groups.

1) Note, that from each state (and each sge, consequently) deaths are possible.

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Table

1.

Bxpectancies

of

of

- old

20 - year

remaining

Remaining Status age

at

life

time

in

each

marital

state

females

life

expectancy

(in

years)

Wever

20

married

Widowed

Married

Divorced

Total

1975 5.08

55.63

9.31

5.86

55.00

20.45

3.09

53.87

10.31

55.56

a. 00

6.08

56.09

8.93

8.16

56.45

20.08

5.28

54.04

8.46

14.99

56.17

5.30

36.31

8.94

Married

0

40.63

Widowed

0

29.53

Divorced

0

36.15

9.10

Bever married

9.87

32.14

Married

0

39.36

Widowed

0

29.48

Divorced

0

32.72

Never

married

1982

Population projections are frequently used for making present and possible tendencies clearly vieible. Yore than that they are important

sources

of

data

for

policy

making.

The changes in marital behaviour refered above in connection with the given age structure of the population may effect the percentage distribution of all marital states and both sexes. There

is

and that population of

a trend the

the will

development

will

far-reaching

provided

that

unmarried

for

problems; persons

of

portion

of

increase. bring

persons

In general,

society

especially advanced

married face

in terms age

- most

of

the to

of

face care

will

decrease

future with to

a host

be

them will be un-

married women. References: K.C., Rogers, A.: Multidimensional Mathematical Demography: An overview, International Institute for Applied SgsternsAnalysis (IIASA), Eaxenburg 1982, RR-82-35. (2) Ledent, J.: Some methodological and empirical considerations in the construction of increment-decrement life tables, IIASA,

(1) Land,

(3) (4) (5)

Laxenburg 1978, RR-78-25. F.: Spatial Rogers, A., Wlllekens, Population Analysis: Methods and Computer Programs, IIASA, Laxenburg 1978, RR-78-18. Rogers, A. (Rd.): Resays in Multistate Mathematical Demography, IIASA, Laxenburg 1980, RR-80-10.

Tables of Working Life: The Increment-Decrement Yodel, U.S. Department of Labor, Bureau of Labor Statistics, Washington 1982, Bulletin 2135.

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