Part II Data and Methods
14.1 German Life History Study
1.The German Life History Study (GLHS) is a long-term project con-ducted by the Max Planck Institute for Human Development (Berlin).
The main data source of this project is a series of retrospective surveys in which members of selected birth cohorts were asked to provide detailed information about their life courses. Part of these data are available for
1We speak ofnon-official surveysin order to signify that these surveys are conducted, not by official statistics, but by a variety of institutions of social research. Additional differences depend on circumstances. Most often the sample size of non-official surveys is much smaller than the sample size of official surveys. Furthermore, while some official surveys (e.g., theMikrozensus) are based on an obligation to give information, participation in non-official surveys is always a matter of free decision. Consequently, there is often a substantial proportion of non-respondents in non-official surveys; see, e.g., Porst (1996).
the general scientific public:2
a) Data from the first survey (LV I) were sampled during the years 1981 – 83 and included 2171 members of the birth cohorts 1929 – 31, 1939 – 41, and 1949 – 51.
b) Data from a second survey (LV II) were sampled in two parts, both relating to persons born in the years 1919 – 21; a first part was con-ducted in 1985 – 86 and included 407 persons (LV IIA), a second part was conducted in 1987 – 88 and included 1005 persons (LV IIT).
c) Data from a third survey (LV III) were sampled in 1989 and included 2008 members of the birth cohorts 1954 – 56 and 1959 – 61.
All surveys were conducted in the territory of the former FRG. For our present study we take into account all female respondents from the surveys LV I, LV IIT, and LV III (only cohort 1959 – 61). The case numbers and how they distribute over the five cohorts is shown in the following table:3
Birth cohort Birth years Male Female Interview date
C20 1919−21 373 632 1987−88
C30 1929−31 349 359 1981−83
C40 1939−41 375 355 1981−83
C50 1949−51 365 368 1981−83
C60 1959−61 512 489 1989
We also mention that all members of our subsample have a German citizen-ship. — In the remainder of this section we use this data set to investigate changes in the distribution of ages at first childbearing and the number of children across the five birth cohorts.4
Age at First Childbearing
2.Denoting our subsample of the GLHS by Ω, we can define a three-dimensional variable
(C, T, D) : Ω −→ C ט T ט D˜
2For an overview, see Wagner (1996). The data are available from theZentralarchiv f¨ur empirische Sozialforschung (K¨oln). We thank Karl Ulrich Mayer, the director of the GLHS, for the permission to use the data sets.
3Of the 632 women of birth cohort C20 three did not give valid birth years for their children and will be excluded in further calculations.
4We mention that the GLHS data have already been used in quite a large number of earlier studies. Concerning the questions of the present section, see, in particular, Huinink (1987, 1988, 1989), Blossfeld and Huinink (1989), Tuma and Huinink (1990).
Table 14.1-1 Age at first childbearing in our GLHS subsample.
C20 C30 C40 C50 C60
τ d= 1 d= 0 d= 1 d= 0 d= 1 d= 0 d= 1 d= 0 d= 1 d= 0
D, with property space ˜D:={0,1}, records whether a women has given birth to at least one child;5 andT, with property space ˜T :={0,1,2, . . .}, records the age of the women which, depending on the value ofD, is the
5The GLHS allows to distinguish women’s own children, step children, and adoptive children. For the present investigation we only take into account women’s own children.
age of first childbearing (ifT(ω) = 1) or the age in the interview year (if T(ω) = 0). The distribution of this three-dimensional variable, in terms of absolute frequency, is shown in Table 14.1-1.6 For example, there are 68 women in birth cohort C20 who gave birth to a first child at age 24, 41 at age 25, and so on. In total, 520 women of this birth cohort had at least one child, and 109 remained childless.
3.The data from Table 14.1-1 can be used to estimate distributions of the age at first childbearing. We use the formal framework introduced in Chapter 12 and refer to a duration variable
Tˆc : Ωc −→ T˜:={0,1,2,3, . . .}
where the indexc specifies one of the birth cohorts in our sample. Since each birth cohort comprises three birth years, and the interviews extend over up to three years, also the censoring times extend over several ages.
However, as seen from Table 14.1-1, for birth cohorts C20, C30, and C40, censoring only occurs after the last observed event (first childbearing). For these birth cohorts, the data can therefore directly be used to calculate a frequency distribution of ˆTc:
P[ ˆTc](τ) = | {ω∈Ωc|T(ω) =τ} |
|Ωc|
For example, referring to birth cohort C20, one immediately finds P[ ˆTC20](25) = 41
629 = 0.065
that is, 6.5 % of the members of C20 gave birth to a first child at age 25.
These values can then be used for the calculation of distribution functions, survivor functions, and rate functions.
4.The situation is slightly different for birth cohorts C50 and C60 where event times and censoring times overlap in some years. To illustrate, we refer to birth cohort C50. Obviously, for ages under 30, one can calculate frequencies directly. For example, forτ = 25, one gets
P[ ˆTC50](25) = 13
368 = 0.035
However, this direct calculation is no longer possible for ages τ ≥ 30.
We therefore use the Kaplan-Meier procedure introduced in Section 8.3.4.
Table 14.1-2 illustrates the calculations for birth cohort C50. Notice that, until age 29, results are identical with those from a direct calculation of frequencies.
6Note that the ages are not contiguous because the table refers to the realized property spaces. Note also that birth cohort C20 only contains 629 members because we have excluded three cases with unknown birth years of children.
Table 14.1-2 Kaplan-Meier procedure to calculate the survivor function for the age at first childbearing. Data refer to cohort C50 in Table 14.1-1.
survivor τ at risk events censored rate 1 – rate function
16 368 3 0 0.0082 0.9918 1.0000
17 365 4 0 0.0110 0.9890 0.9918
18 361 10 0 0.0277 0.9723 0.9809
19 351 30 0 0.0855 0.9145 0.9537
20 321 34 0 0.1059 0.8941 0.8722
21 287 36 0 0.1254 0.8746 0.7798
22 251 26 0 0.1036 0.8964 0.6820
23 225 22 0 0.0978 0.9022 0.6114
24 203 16 0 0.0788 0.9212 0.5516
25 187 13 0 0.0695 0.9305 0.5081
26 174 20 0 0.1149 0.8851 0.4728
27 154 22 0 0.1429 0.8571 0.4185
28 132 14 0 0.1061 0.8939 0.3587
29 118 12 0 0.1017 0.8983 0.3206
30 106 13 21 0.1226 0.8774 0.2880
31 72 3 22 0.0417 0.9583 0.2527
32 47 3 35 0.0638 0.9362 0.2422
33 9 1 8 0.1111 0.8889 0.2267
34 0.2015
5.The survivor functions for all five birth cohorts are shown in Figure 14.1-1. Several points are remarkable.
a) Until an age of about 27, the distribution for cohort C30 is quite similar to the distribution for cohort C20. After this age, that is, beginning at the end of the nineteen-fifties, a substantially greater proportion of the women belong to cohort C30 give birth to a child. Eventually, the proportion of childless women is quite smaller in C30 than in C20.
b) Compared with C30, members of birth cohort C40 begin childbearing at younger ages, but overall, both distributions are quite similar. In particular, in both cohorts, a high proportion of women, about 90 %, have at least one child.
c) Like the members of C40, also the members of C50 begin childbearing at younger ages. However, beginning in the mid-sixties, birth rates begin to decline, and it might be supposed that the proportion of women who eventually remain childless will be substantially greater than it was in the two preceeding cohorts.
d) Finally, members of birth cohort C60 delay the birth of a first child, and although the data do not allow definite conclusions, it seems quite possible that the proportion of finally childless women will again be greater than in the preceeding cohorts.
15 20 25 30 35 40 45
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
C20
C40 C30 C50 C60
Fig. 14.1-1 Distribution of age at first childbearing described by survivor functions, calculated from the data in Table 14.1-1.
15 20 25 30 35 40 45 50 0
0.5 1 1.5 2
C30 C40 C20
C50
C60
Fig. 14.1-2 Cumulated cohort birth rates calculated from the data in Table 14.1-3.
The results can be compared with the distribution of age at first marital childbearing. This was already done in Section 12.2.2.
Number of Children
6.The next step is to investigate the number of children born of women in theGLHSsubsample. We begin with the calculation of cumulated cohort birth rates. Table 14.1-3 shows the data. For example, 44 women belonging to birth cohort C20 have given birth to a child at an age of 21. The data can be used to calculate cumulated cohort births rates. The following table shows these rates, denoted byCCBR(τ), until ageτ as specified in the second column:
Cohort τ CCBR(τ) CCBR∗(τ)
C20 45 1.80
C30 43 2.19 2.15
C40 40 1.99 1.96
C50 31 1.38 1.39
C60 29 0.82 0.99
The final column, labeledCCBR∗(τ), shows corresponding cumulated
co-Table 14.1-3 Number of children in the GLHS subsample, classified with respect to mother’s birth cohort and age (τ).
τ C20 C30 C40 C50 C60
15 1
16 1 3 3
17 2 1 5 4 6
18 11 5 16 11 11
19 25 16 22 30 17
20 34 26 34 40 18
21 44 26 33 48 26
22 72 44 48 40 33
23 80 37 60 44 27
24 105 44 67 32 34
25 77 49 64 37 56
26 68 53 56 42 44
27 76 66 56 50 67
28 67 48 54 41 46
29 54 62 35 35 13
30 57 63 39 37 2
31 64 35 23 15
32 41 43 23 9
33 41 35 22 1
34 42 33 13
35 36 26 14
36 39 22 11
37 29 17 5
38 19 15 1
39 18 7 4
40 10 2 2
41 10 7 2
42 3 5
43 2 1
44 3 1
45 1
46 1
Total 1132 789 709 519 404
hort birth rates calculated from official statistics.7 Except for the youngest cohort, the rates are surprisingly similar. The difference for the youngest cohort is possibly due to the fact that the official statistics also includes births of immigrants.
7.Figure 14.1-2 presents a graphical view of the cumulated cohort birth rates. It is remarkable that we do not find a simple relationship between age at first childbearing and completed cohort birth rates. This can be seen, for example, by comparing cohorts C30 and C40. Although members of C40 begin childbearing at younger ages, compared with members of C30
7These are mean values of the year-specific rates published in Fachserie 1, Reihe 1 (1999, p. 198 -200). No official data are available for C20; for C30, the mean value refers to the years 1930 and 1931.
Table 14.1-4 Number of women with 0, 1, 2, 3, 4, and 5 or more children, calculated from the data in the GLHS subsample. Percentage values relate to all women in each of the cohorts who have at least one child. Percentage values in brackets provide the proportion of finally childless women.
C20 C30 C40 C50 C60
Children N % N % N % N % N %
0 109 (17) 38 (11) 39 (11) 86 231
1 185 35.6 75 23.4 78 24.7 106 37.6 145 56.2
2 168 32.3 126 39.3 139 44.0 134 47.5 86 33.3
3 104 20.0 61 19.0 64 20.3 30 10.6 21 8.1
4 40 7.7 36 11.2 23 7.3 7 2.5 6 2.3
≥5 23 4.4 23 7.2 12 3.8 5 1.8
(see Figure 14.1-1), the completed cohort birth rate is lower for C40 than for C30. Of course, a delay of childbearing might be accompanied by a decline in the total number of births; this will probably be true for cohort C60. However, a decline of birth rates can not be explained by simply referring to changes in the distribution of ages at first childbearing.8 8.Cumulated and completed cohort birth rates provide information about the total number of children born, but not about the distribution of the number of children. So we should finally also look at the number of births per women. The data are shown in Table 14.1-4. Since members of birth cohorts C50 and C60 have not reached the end of the reproductive period by the time when the interviews were performed, an interpretation should be confined to the cohorts C20, C30, and C40.
a) Compared with C20, more women of C30 gave birth to at least one child. Moreover, the proportion of women with only one child declined, resulting in an increase of the mean number of children per women, from 2.2 in C20 to 2.5 in C30. The substantial increase in the com-pleted cohort birth rate is therefore a result of both, the decline in the proportion of childless women and the increase in the mean number of children per women.
b) The proportion of childless women in C40 remains roughly the same as it was in C30. There is, however, a tendency to reduce the number of children per women. In particular, the proportion of women with four or more children declines while the proportion of women with two children increases. The result is a decline of the mean number of children per women, from 2.5 in C30 to 2.3 in C40, and consequently also a decline in the completed cohort birth rate.
It remains to be investigated how these tendencies continued in younger
8See also the discussion in Section 12.2.5.
birth cohorts. We already know from official statistics that the completed cohort birth rates continued to decline at least until birth cohort C60 (see Section 11.4). However, the data in our GLHS subsample do not allow to identify the changes in the distribution of children from which this tendency results.