## Abstract

This study examines educational reproduction of East and West German men and women born between 1930 and 1950. In a prospective design, we study the importance of mobility and fertility pathways of reproduction, considering not only the social reproduction of education as an attribute but also the demographic reproduction of individuals who carry this attribute. Using data from NEPS and SOEP, we introduce a method that estimates prospective models based on retrospective data commonly available in surveys. The analysis offers new estimates of the expected number of high- and low-educated children born to men and women of different levels of education. Findings show that the importance of the fertility pathway of educational reproduction was higher in West than in East Germany, higher for women than for men, and higher for earlier than for later cohorts. For West German women of earlier cohorts, the fertility pathway tempered educational reproduction among the high-educated and reinforced it among the low-educated. Population renewal models show that differential fertility slightly lowered educational attainment and slightly increased inequality in educational attainment in the offspring generation. Across cohorts, the fertility pathway declined in importance, a result of fertility convergence between education groups and educational expansion in postwar Germany. We conclude that prospective designs advance our understanding of educational reproduction. The method that we introduce substantially reduces the data requirements of prospective analysis, facilitating future prospective research on social stratification.

## Introduction

What is the role of fertility in intergenerational reproduction and social mobility? Conventional studies of intergenerational reproduction cannot answer this question because they are retrospective, focusing on the association between social origin and status attainment (Blossfeld et al. 2016; Breen 2010; Breen and Jonsson 2005; Breen et al. 2009a, b; Erikson and Goldthorpe 1993; Shavit and Blossfeld 1993). Looking backward from anchor persons to their parents, conventional social mobility research examines how parents transmit their social position to children or, conversely, how children inherit their social position from parents.

A limitation of this approach is that it conditions on fertility: two family generations are required to transmit or inherit social positions. Yet, an analysis that is conditioned on the existence of a second generation ignores the process by which this second generation came into existence. In other words, the analysis of intergenerational reproduction is limited to the social reproduction of individual attributes, ignoring the demographic reproduction of individuals who carry these attributes. As a result, the retrospective approach treats social origin as an exogenous factor rather than as a phenomenon explained by processes of intergenerational reproduction. To understand intergenerational reproduction more fully, we have to examine the way one entire generation of individuals transmits advantages and disadvantages to the next generation.

This aim can be achieved by a prospective approach to intergenerational reproduction, considering not only the social reproduction of attributes (such as social position) but also the demographic reproduction of individuals carrying these attributes (Lawrence and Breen 2016; Mare and Maralani 2006). Prospective studies put exceptionally high demands on the data and therefore remain rare in stratification research. Recent work has demonstrated the relevance of demographic mechanisms in educational reproduction among Indonesian women (Mare and Maralani 2006); South Korean women (Kye and Mare 2012); Black and White U.S. women (Maralani 2013; Mare 1997; Song and Mare 2017); high school graduates from Wisconsin (Lawrence and Breen 2016); and, most recently, men and women in the United Kingdom (Breen and Ermisch 2017). For many European countries that differ from these contexts both demographically and in terms of social inequality in educational opportunity, almost no prospective studies exist.

In this study, we adopt a prospective approach to examine intergenerational educational reproduction in Germany, focusing on the demographic and social reproduction among men and women born between 1930 and 1950. We study the transmission of educational (dis)advantage and the relative importance of demographic (fertility) and social (mobility) pathways of reproduction.

Our contribution is twofold. First, we add a prospective view to examine educational reproduction not only comparatively across the East and West German context but also across cohorts. The prewar, war, and postwar cohorts born between 1930 and 1950 represent an intriguing setting to examine contextual differences and changes over time in the demographic and social pathways of intergenerational reproduction. These cohorts built their lives in a divided Germany characterized by stark differences between the socialist German Democratic Republic (GDR) and the market-oriented Federal Republic of Germany (FRG) in terms of economic development, fertility, family policy, and education systems. Moreover, in the German context, the 1930–1950 cohorts were the engine of the second demographic transition unfolding at different rates and pace in East and West Germany. The offspring of these birth cohorts—born mostly in the 1960s and 1970s—grew up in times of educational reforms and rapidly expanding educational opportunities, again with important differences between East and West Germany. Our study examines how these changes and sociohistorical differences shaped the educational reproduction among East and West German men and women. In line with previous prospective research, our study measures the educational reproduction rate by the expected average number of children attaining a certain educational category born to men and women of the target cohorts born in 1930–1950.

Second, our study contributes methodologically to research on intergenerational reproduction. We introduce a model of educational reproduction that allows studying trends over time while accounting for population-level and family-level effects of fertility on educational reproduction. Moreover, we introduce a decomposition technique that separates education gaps in reproduction rates into fertility and mobility components. This technique allows quantifying the role of differential fertility in the process by which men and women transmit their educational advantages or disadvantages to their children.

Most important, our method allows us to estimate prospective models using retrospective data commonly available in surveys. Previous prospective methods placed high demands on the data, requiring long-running panel data that track the process of fertility in the parent generation and the process of status attainment in the child generation.

For our empirical analyses, we use harmonized and pooled educational mobility data from the German National Educational Panel Study (NEPS) and the German Socio-Economic Panel Study (SOEP). Starting from a child generation comprising respondents born between 1944 and 1988, our adjustment method reconstructs a generation of their potential parents born 1930 to 1950. We use inverse probability weighting to minimize retrospective sampling bias and complement retrospective data on parents and family size with external data on childlessness to estimate educational reproduction of men and women born from 1930 to 1950.

## A Retrospective View on Educational Reproduction in Germany

Retrospective studies of have focused on inequality of educational opportunity (IEO) as a chief mechanism driving social reproduction and mobility (Breen 2010). A general finding from this literature is that over the past decades, educational expansion, policy reforms, and equalization of living conditions have reduced IEO in European societies, fostering social mobility for younger generations of men and women (Breen et al. 2009a, b).

Germany is an example for relatively rigid social class structures and low levels of fluidity (Erikson and Goldthorpe 1993) due to social class inequality in educational attainment (Müller and Pollak 2004). The German model of schooling is characterized by early tracking—typically at age 10—into a tripartite system of vocational, polytechnic, and academic track schools (Blossfeld et al. 2016). Germany’s rigidly tracking and highly stratifying education system became infamous as a sorting machine with large social background effects on track allocation and strong track persistence in secondary school careers (Buchholz et al. 2016; Schneider and Tieben 2011).

Blossfeld’s (1993) results on change across the West German birth cohorts of 1916 until 1965 showed persistent correlations between fathers’ and children’s educational attainment. Other evidence on West Germany has suggested that social class inequality in educational attainment has decreased over these birth cohorts (Breen 2010; Breen et al. 2009a, b; Müller and Pollak 2004), especially at the transition to tracked secondary education (Müller and Haun 1994). For the West German birth cohorts born in 1912–1977, Breen (2010) concluded that the increase in social fluidity was driven simultaneously by educational expansion (i.e., compositional effects) and a trend of declining IEO by social class of the origin family. Yet, despite strong educational expansion and a variety of education reforms, equalization seems to have stalled for more recent birth cohorts. Studying trends in educational mobility for the 1940–1978 West German birth cohorts, Heineck and Riphahn (2007) found that although educational attainment and absolute rates of educational upward mobility have increased, gaps in relative opportunities of children from high- versus low-educated parents have remained largely stable for people born in the 1950s and later.

For the 1956–1988 West German birth cohorts, Schneider and Tieben (2011) found persistent social inequality in access to upper secondary schooling. Persistent inequality was also found for access to postsecondary training and tertiary education in West Germany (Reimer and Pollak 2010). Similarly, Blossfeld et al. (2015) found that although IEO decreased at the transition to secondary schooling, social inequalities in access to university education remained stable and for West Germany, even increased slightly from the 1919 to 1980 birth cohorts.

In a divided Germany (1949–1990), large economic, political, social, and cultural contrasts emerged between the East and the West, with important consequences for education systems. The West German FGR retained the tripartite system, whereas the state-socialist GDR regime in the East rebuilt the education system and integrated it into the planned economy, abandoning tracking in lower-secondary education and implementing educational policies to promote educational opportunities for working-class children (Sieben et al. 2001).

A few retrospective studies have compared trends in educational inequality and mobility between East and West Germany. Hadjar and Berger (2010) found that across the 1925 to 1974 birth cohorts, schooling levels increased in West Germany. In East Germany, schooling levels stagnated as a result of restricted access to higher education to 10% of a birth cohort, a policy that the GDR introduced in the 1970s. IEO, however, was smaller in East Germany than in West Germany (Hadjar and Berger 2010), although it increased before reunification (Klein et al. 2019; Sieben et al. 2001). Following reunification in 1990, patterns of IEO converged after the West German education system was reintroduced in the new federal states in the East. Riphahn and Trübswetter (2011) showed that although schooling levels caught up rapidly in the East immediately after reunification, educational inequality increased to West German standards.

## A Prospective View on Educational Reproduction in Germany

The aforementioned retrospective studies on changes in educational reproduction adopted the conventional social mobility approach focusing only on the social pathway of transmission, measured by the association between social origin (such as parental class or education) and social destination (such as occupational or educational attainment). Because this approach conditions on fertility, it does not fully capture the process of educational reproduction by which earlier cohorts transmit educational advantages or disadvantages to later cohorts. If educational attainment in the earlier cohorts is associated with completed fertility, rates of intergenerational educational reproduction would differ by education even in the extreme case of perfect social mobility (i.e., no educational inequality) in the offspring cohorts. Moreover, as levels of completed fertility change over cohorts, rates of educational reproduction change as well. Thus, the blind spot of previous retrospective research on educational inequality in Germany is the demographic pathway of educational reproduction.

In the German context, East-West differences and cohort change are not limited to the previously discussed social mobility pathway; they extend to the demographic pathway of educational reproduction, most notably to family policy and fertility. A first key difference can be found in the long-term trends in fertility rates in postwar Germany. In West Germany, delays and declines in fertility commenced in the 1960s. By the mid-1980s, the total fertility rate (TFR) of West German women had dropped below 1.3 (Kreyenfeld 2004). This decline was partly due to a rise in childlessness but also to a decline in transitions to higher parities (Bujard and Sulak 2016). Initially fertility declined also in East Germany, but a substantial East-West difference emerged in the 1970s as the TFR in East Germany almost returned to replacement levels for a short period, only to decline again in the 1980s. This rise might be explained by pronatalistic socialist family policies (Kreyenfeld 2003). Before the collapse of the GDR, the TFR again declined to 1.5, converging to West German levels.

Regarding our study cohorts, estimates on cohort fertility rates (CFR) are more informative than period-based TFR estimates. The CFR reveals similar levels of fertility for East and West German women born in the early 1930s (2.1 children). Subsequent cohort declines were temporary in the East and continuous in the West (Kreyenfeld 2004). CFRs converged again for the birth cohort of 1950 to 1.8 in East Germany and 1.7 in West Germany (Statistisches Bundesamt 2020).

Apart from differences in completed fertility, East and West German women differed substantially in levels of childlessness, the age at first motherhood, and the extent to which these fertility indicators were stratified by education (Goldstein and Kreyenfeld 2011; Kreyenfeld 2003, 2004). Childlessness was more prevalent in the West, particularly for cohorts born after 1940. Among the 1950 cohort, the proportion of childless women was 8% in the East and 17% in the West. This gap grew further in later cohorts (Kreyenfeld 2003). At the same time, educational differences in rates of childlessness were low in the East and high in the West (Kreyenfeld 2004). Of West German women born in 1933–1948, 28% of tertiary-educated remained childless, compared with only 12% of low-educated (Skopek and Leopold 2017). In East German cohorts, 9% of tertiary-educated women and 8% of low-educated women remained childless. Conditioning on motherhood, however, East and West German mothers did not differ much in terms of family size.

Theoretical explanations for the association between education and women’s fertility include postponement of childrearing due to prolonged educational participation, human capital and opportunity costs of childrearing, knowledge and contraceptive behavior, and the timing of union formation (Kravdal and Rindfuss 2008). Only a few demographic studies have looked at men’s fertility. Evidence suggests that the educational gradient in fertility is substantially weaker or even reversed for men (Kravdal and Rindfuss 2008). Skopek and Leopold (2017) reported slightly lower childlessness for high-educated men compared with low-educated men in East Germany and not education differences in childlessness among West German men.

Because conventional retrospective mobility studies do not take into account fertility as a demographic pathway of reproduction, it remains largely unknown how the second demographic transition has affected educational reproduction of men and women. To our knowledge, only one study has examined educational reproduction in Germany prospectively (Buis et al. 2012). Based on population rates obtained from pooled microcensus and survey data, this study concluded that differential fertility of West German women born in 1925–1945 had only a minor effect on the educational distribution of their offspring. Yet, this study was restricted not only in terms of population coverage but also in terms of modelling fertility effects. The analysis used a simulation approach based on aggregated rates, ignoring within-family effects that require linked-generation data at the micro level.

## The Current Study

Against the backdrop of major societal, political, and institutional divides, rapid educational expansion, and a demographic transition toward lowest-low fertility in the second half of twentieth century, our study examines trends in educational reproduction of men and women in Germany. In contrast to previous research, we adopt a prospective approach to study how demographic and social pathways jointly shaped processes of educational reproduction. Our aim is to examine contextual differences and changes over time in the role of both pathways, drawing on prewar, war, and postwar cohorts (1930 to 1950) in East and West Germany.

To achieve this aim, we introduce a method that partly overcomes the high data requirements of previous prospective studies. We explicate a prospective method that is compatible with conventional retrospective mobility data, solving two problems: retrospective sampling bias and the identification of representative cohorts of potential parents. Using a new decomposition approach, we assess the role of fertility in the reproduction of inequality in East and West Germany, disentangling demographic and social pathways in processes of educational reproduction. The analysis is based on data pooled from the German National Educational Panel Study (NEPS) and the German Socio-Economic Panel Study (SOEP).

## Methodology and Data

We first describe the general model of educational reproduction underpinning our analysis as well as a decomposition method that allows us to assess the role of fertility in the process of educational reproduction among East and West German men and women. This general model defines all relevant variables. Next, we introduce a method that allows obtaining prospective estimates from retrospective data. We develop this method because suitable prospective data are not (yet) available for the German context. Finally, we describe the data sets and all adjustment steps applied to use retrospective data for prospective analyses.

### Modelling the Role of Fertility in Educational Reproduction

Our general model considers fertility as the only demographic pathway of educational reproduction. This model is simple but practical and suitable for the descriptive purpose of analyzing trends in educational reproduction and the importance of differential fertility for reproduction outcomes. More complex formulations of reproduction models consider other demographic processes, such as assortative marriage as additional pathways linking educational distributions between generations (see e.g., Lawrence and Breen 2016; Mare and Maralani 2006).

Following the notation of Song and Mare (2015), the link between educational distributions of two entire generations—rather than only parents and children—is given by the (unconditional) rate of educational reproduction (RER), which expresses the number of children attaining educational level j that a person of educational level i is expected to produce:
1

Equation (1) identifies three components of the RER: (1) the probability of remaining childless as a function of education, P(F = 0| I = i); (2) the distribution of positive fertility outcomes conditional on having children and educational level, P(F = f | F > 0, I = i); and (3) the probability that the child attains education level j given the parent’s education level i and family size f, denoted P(J = j | I = i, F = f ). The third component captures educational mobility from a retrospective view and is typically estimated in conventional studies of educational mobility and IEO.

Multiplying children’s attainment probability with family size (number of children f ) yields the conditional RER. For example, if the probability of attaining high education ( j = h) for a child of a high-educated mother (i = h) who has one sibling ( f = 2) is .75, a high-educated mother with two children would be expected to produce 1.5 high-educated children. Aggregating conditional RERs over the parents’ (observed) fertility distribution yields the average conditional RER. For example, if high-educated mothers’ chances of having either one or two children were 50-50, and if P(J = h| I = h, F = 2) = .75 and P(J = h| I = h, F = 1) = .85, the average high-educated mother would produce .5 · 1 · .85 + .5 · 2 · .75 = 1.275 high-educated children.

Additional consideration of childlessness yields the central outcome of our study: the aggregated unconditional RER. Given that childless persons do not directly transmit (dis)advantage to the next generation, the right side of Eq. (1) reduces to the average conditional RER weighted by the complementary probability of remaining childless. If 20% of high-educated women remained childless in the preceding example, the unconditional rate of producing high-educated offspring is (1 − .2) · 1.275 = 1.02.

Fertility enters the model in two steps—parenthood and, conditional on parenthood, the number of children—both of which can be associated with education. If fertility is negatively associated with education, then it tempers the educational reproduction of high-educated individuals. Eq. (1) specifies both population-level and family-level effects of fertility. The relevance of considering family-level effects is that a larger family size may reduce educational attainment as a result of resource dilution within the family (Downey 1995) or birth order effects (Black et al. 2005). Differences and changes in family size thus may drive educational reproduction outcomes through their associations with children’s educational attainment. Therefore, modelling family-level effects is required to study the role of fertility in the process of educational reproduction.

### Decomposing Fertility and Mobility Effects in Educational Reproduction

Our study interest, in a first step, is in education differences in unconditional rates of educational reproduction (Eq. (1)). This difference represents the joint demographic and mobility effect (Song and Mare 2015) when comparing persons of educational level i with persons of educational level i′ in producing offspring of educational level j:
$∆j=rji−rji′.$
2
For example, the gap between high-educated (h) and low-educated (l) individuals in producing high-educated offspring can be written as
$∆h=rhh−rhl.$
3
How much of this difference is attributable to differential fertility and how much is due to mobility (i.e., inequality of educational opportunity)? In a second step, we decompose the gap (i.e., the joint effect) into a fertility and a mobility component. Based on an additive decomposition, we write the joint effect as a linear combination of a fertility component attributable to differences in fertility between education groups ($∆fh$) and a mobility component attributable to inequality of educational opportunity ($∆mh$):
$∆h=∆fh+∆mh.$
4

The calculation of $∆fh$ and $∆mh$ involves counterfactual rates of educational reproduction. Counterfactual RERs are hypothetical values derived from swapping the fertility distributions of low- and high-educated groups. We describe the procedure in detail in the online supplement (section C1). We do not use the term counterfactual in a causal sense because our models do not allow us to estimate the causal effect of education as a treatment. Instead, we use the term counterfactual to underline the hypothetical nature of rates calculated based on exchanging fertility distributions of groups. The goal of calculating counterfactual rates is to understand structural differences in rates of reproduction across educational groups.

The fertility component is represented by the difference between the factual joint effect and two counterfactual scenarios: the joint effect if (1) the high-educated had the same fertility patterns as the low-educated and (2) the low-educated had the same fertility patterns as the high-educated. The average difference between the factual and the two counterfactual effects represents the fertility component. The mobility component is calculated analogously, but we can also derive it from Eq. (4) once h and $∆fh$ are known.

If cohort fertility rates of low- and high-educated individuals are known, we can calculate reproduction rates for the two outcomes of producing low-educated children and producing high-educated children. The absolute size of the mobility component is the same for both outcomes with reversed signs. We provide a formal proof in the online appendix (section C1). A two-way educational mobility table (parent education in rows, offspring education in columns) provides an intuition by showing that the social background gap in offspring’s probability of attaining high education equals the probability gap by social background in attaining low education with reserved sign. However, the joint effects for the two outcomes are not necessarily of the same direction and magnitude because the size of the fertility component can differ by outcome (see section C1 of the online appendix for details).

### Linking Educational Distributions Between Generations

We use the concept of educational reproduction rates to link educational distributions between generations via population renewal models (Kye and Mare 2012; Mare and Maralani 2006; Song and Mare 2015). Let C1 denote a birth cohort of individuals who either become parents (G1) or remain childless (CL1). Total cohort size is defined as NC1 = NG1 + NCL1. Let G2 denote the progeny of cohort C1. The number of children in G2 who attain educational level i and have a parent G1 with educational level j is then given by
$NijG2=NjC1·rij.$
5
The total number of children who attain education level i is given by
$Ni.G2=NjC1·rij+Nj′C1·rij′,$
6
and the total number of children is given by
$NG2=Ni.G2+Ni′G2.$
7

These analytical tools are useful to estimate the size of G2, the distribution of education in G2, and inequality in educational opportunity in G2 (e.g., via odds ratios obtained from the G2 mobility table; see section C2 of the online appendix). Applying these models for scenario analyses allows us to assess, for example, how educational mobility patterns of G2 would differ if high-educated persons of C1 had the fertility behavior of low-educated persons. Such hypothetical scenarios are useful not only for exploring the relative role of fertility and mobility in processes of educational reproduction but also for better understanding how differential fertility in C1 is associated with educational outcomes and educational inequality in G2.

### Data

We examine the educational reproduction of the 1930–1950 birth cohorts using retrospective social mobility data—that is, data on survey respondents and their parents. Our data strategy for estimating prospective models with these retrospective data involves two keys. The first key is having an anchor sample representative of the child population that descended from individuals born in 1930–1950. After defining this anchor sample providing retrospective data, we can reconstruct parents born in 1930–1950 adjusting for retrospective sampling bias. Obviously, those who became parents are only a subset of the population born in 1930–1950. Therefore, the second key to our approximation strategy is matching information on rates of childlessness to the parent-child data.

We construct an anchor sample for the 1930–1950 cohorts by pooling two data sets containing retrospective respondent-parent data on social mobility: Starting Cohort 6 of the NEPS (NEPS-SC6) and the SOEP. Pooling improves the precision of the estimates as we compare trends in educational reproduction of men and women for East and West Germany.

NEPS-SC6 (Blossfeld et al. 2011, data version 5.1.0) comprises individuals born between 1944 and 1988 who have been followed up annually since 2009 or 2010. To maximize case numbers, we select the fourth wave of 2011/2012, which includes a refreshment sample in addition to the original sample. The SOEP (Wagner et al. 2007, data version v.32) is an annual panel survey of households and individuals started in 1984. We select a cross-section from the year 2012 that is highly comparable to the NEPS sample and retain only subsamples that are part of the overall probability sample of persons living in German households. Both data sets have been used for educational mobility research before (e.g., Buchholz et al. 2016; Heineck and Riphahn 2007) and provide data on education of respondents and their parents. Moreover, both data sets include information on respondents’ year of birth, sex, number of siblings, mothers’ and fathers’ year and place of birth, and whether the parents lived in East or West Germany before reunification in 1989. All measures were harmonized across data sets.

We assess education in both generations using a dichotomous measure of having an Abitur degree (upper secondary schooling degree in Germany) or not. Although more detailed data on education levels (e.g., years of education) are available, we use a dichotomous measure for three reasons. First, Abitur degrees are comparable across generations; across East and West Germany; and, in terms of measurement, across the two data sets that partly used different coding schemes. Second, although entry into higher education in Germany has become more flexible in recent decades, the Abitur degree has been and still is the major route into university. Thus, the dichotomy captures a highly relevant aspect of educational inequality and path dependency of educational careers in Germany. Third, Abitur is usually completed at age 18 or 19, after 13 years of schooling in a more (West) or less (East) stratified school system. As a result, our measure is less affected by right-censoring than other measures of highest educational attainment. This benefit is crucial for our purposes because it allows us to reduce the minimum length of the observation window (see the next section).

### Defining Retrospective Anchor Samples

We use these pooled data as anchor data to reconstruct a representative sample for C1 individuals born in East and West Germany between 1930 and 1950. This anchor sample includes birth cohorts from 1944 to 1988 and has a sufficient coverage of offspring (G2) that individuals born from 1930 to 1950 (C1) could have potentially produced during their reproductive period. For example, the oldest respondent in G2 (born 1944) represents the first potential birth year of a child of C1, assuming a minimum fertility age of 14. Likewise, the youngest respondent in G2 (born 1988) represents the last potential birth years of a child of C1, assuming an upper bound of regular fertility of nearly 40 years. The upper bound can be justified demographically by population data showing that having a child after age 40 is rare for both women (Billari et al. 2007) and men (Prioux 2005). In our sample, 99.2% of respondents’ mothers and 97% of fathers were aged 40 or younger when their child (i.e., the respondent) was born (and 99.9% and 99%, respectively, for age 45). These numbers suggest that potential bias due to right-censoring in the fertility process is small—and if anything, concentrated in the later cohorts (1945 to 1950).

To define anchor samples, we first remove all cases with missing information on respondent or parent variables. Next, we restrict the SOEP sample to cover an interval of birth cohorts identical to the NEPS. This yields a total sample size of 28,526 anchor respondents. Because this sample was drawn from panel studies, we use weights that both surveys provide to adjust for nonrandom sampling and attrition. Our anchor sample is representative of noninstitutionalized persons born between 1944 and 1988. Table 1 shows descriptive statistics separately for both data sets and the pooled data.

The distribution of parent variables shows that these data are representative of (parental) conditions in which respondents grew up but not of any earlier population that could be identified. For example, the birth years of parents spanned almost one century (1877 until 1972). Even when looking only at the span between the 5th and the 95th percentile, the cohort spans remain large, ranging from 1914 to 1960 for mothers and from 1910 to 1957 for fathers. Moreover, fathers were, on average, three years older than mothers, reflecting age preferences in assortative mating (Skopek et al. 2011). From an unadjusted retrospective view, fathers were from older birth cohorts than mothers. Furthermore, the average number of siblings was 1.8, suggesting an average of almost three children per parent—much higher than what demographic data show for the respective target cohort C1 (individuals born in 1930–1950) of East and West Germans (Kreyenfeld 2003). Finally, the retrospective nature of the data misrepresents the relation between children and their parents. Each case is treated as having two unique parents, although in the population, siblings have the same parents. Fig. A1 in the online appendix summarizes these findings visually.

In a second step, we restrict the offspring sample to respondents whose parents were born in 1930–1950—the population C1 who could have produced offspring born in 1944–1988 during their reproductive period (i.e., assuming that C1 had not produced children before 1944 or after 1988). If we restrict the anchor sample to children of parents born between 1930 and 1950, we approximate a sampling frame for G2, the offspring of C1. Based on the G2 sampling frame, we can approximate a sampling frame for G1 (i.e., parents in C1).

Note that the youngest child born to members of C1 must be old enough to complete the process of educational attainment at time of interview. In our observation window, the latest-born offspring (cohort 1988) had 24 years to attain an upper secondary degree. Given that Abitur degrees are rarely obtained beyond age 21, right-censoring in the educational attainment process can be considered minimal.

In a third step, we define anchor samples separately for G1 mothers and fathers. For the mother sample, we select respondents who met three criteria: (1) their mother was born between 1930 and 1950, (2) their mother was born in Germany, and (3) their mother’s education level was known. For the father sample, we apply analogous restrictions. Fourth, we further split the mother and father samples into East and West Germany based on the information obtained from the respondents, assuming that parents born between 1930 to 1950 resided in the part of Germany where the respondent was born.

Finally, for our analysis of time trends, we further distinguish four nearly equidistant cohort groups: 1930–1935 (prewar cohorts), 1936–1940 and 1941–1945 (war cohorts), and 1946–1950 (postwar cohorts). We split all samples according to the cohort group of parents. In total, this yields 2 × 2 × 4 = 16 anchor subsamples and 27,732 anchor respondents distributed over all subsamples (see Table 2).

### Minimizing Retrospective Sampling Bias

The anchor data on G1 (parents born in 1930–1950) is still not representative of C1 (the entire birth cohort 1930–1950). First, data on higher-parity parents are overrepresented. Second, childless members CL of cohort C1 are not accounted for in the anchor data. To adjust the sampling frame accordingly, we use a two-step method proposed by Song and Mare (2015) that introduces two correction factors: (1) the number of children of each respondent’s family of origin, and (2) the fraction of childless individuals born between 1930 and 1950. The first factor can be obtained from data about respondents’ (G2) number of siblings, allowing us to correct for the overrepresentation of data from higher-parity parents by calculating weights for family size:
$wk=1fk,$
8
where k is an enumerator for respondents, and fk = siblk + 1—that is, the number of siblings plus the respondent. After these weights are applied, a G1 parent’s number of children is unrelated to the probability of being included in the retrospective respondent data.
Reweighting the retrospective respondent data yields prospective pseudo-data on G1. Eq. (1), can now be used to calculate G1’s educational reproduction rate in two steps. First, we estimate Pr(J = j | I = i, F = fk) on the unweighted G2 sample using a logistic regression model (we denote estimates by Pr instead of P). These are retrospective estimates of educational mobility in G2—that is, the probability that a child attains education level j given the parent’s education level i and family size f. Second, we approximate the conditional prospective educational reproduction rate (Eq. (1)) by calculating
$r̂ji∣f>0=1∑kniwk∑kniwk·fk·PrJ=jI=i,F=fk=1∑kniwk∑kniPrJ=jI=iF=fk,$
9
where ni is the number of respondents whose parents have education level i. The formula shows that reweighting effectively adjusts the denominator of the mean expression to equal the sum of the family size weights instead of the sum of respondents.

The second correction factor adjusts for childlessness in C1. To estimate childlessness for individuals born between 1930 and 1950, we could impute the probability of remaining childless from younger cohorts of respondents in the same data set, a technique proposed by Song and Mare (2015). This method assumes that childlessness does not change across cohorts. In our case, this assumption cannot be defended because childlessness in East and West Germany changed substantially across the relevant study cohorts (Kreyenfeld 2003).

Therefore, we estimate probabilities of childlessness across educational groups and gender on the basis of external fertility data covering the target cohorts C1. In their analysis of U.S. data, Song and Mare (2015) argued that matching of external data is difficult because retrospective parent data are not representative of any previous generation. Yet, in our case, the parent cohorts are clearly defined, allowing us to match estimates on childlessness obtained from external fertility data to our anchor samples based on education level, part of Germany, gender, and year of birth.

To increase the precision of fertility estimates for the cohorts under study, we pool external fertility data from several surveys providing data on the relevant variables: childlessness, education level, date of birth, born in Germany, and having lived in East or West Germany. In total, we use 16 surveys, including 12 repeated cross-sections from the German General Social Survey (ALLBUS), starting and refreshment samples from three waves of the German Ageing Survey (DEAS), and the German sample of the European Social Survey (ESS) from 2006. From these surveys, we retrieve a total of 17,589 respondents (N = 5,645 for East Germany, N = 11,944 for West Germany) born between 1930 and 1950 and providing information on all relevant variables. Table B1 in the online appendix provides details on surveys.

Next, we use a joint logit model with interaction terms to predict probabilities of being childless by cohort groups (1930–1935, 1936–1940, 1941–1945, and 1946–1950), part of Germany (East or West), gender, and education level. The model adjusts for survey effects and accounted for right-censoring in the fertility process by adjusting for age at interview (find detailed model specification in section C3 of the online appendix).

In a final step, we match these probabilities to the G1 parent samples based on cohort, gender, education level, and part of Germany (covariate vector X). Complete weights that adjust for retrospective sampling bias are then
$fwk=wk·11−PrF=0X.$
10

Using these weights, we can recover marginal distributions of education levels that are representative of the C1 population born between 1930 and 1950. Furthermore, by combining external data on group-specific childlessness and anchor data on family size, we can estimate cohort fertility for men and women of different education groups. Table 3 shows estimation results on childlessness and cohort fertility by educational levels for the cohorts under study.

Group-specific estimates for childlessness allow us to approximate our main outcome of interest, the unconditional educational reproduction rates of C1 (Eq. (1)), by
$r̂ji=1−PrF=0I=i)·r̂ji∣f>0.$
11

Note that educational reproduction rates are calculated separately for education groups, birth cohorts, gender, and part of Germany based on the samples described in Table 2. Fig. A2 in the online appendix visually summarizes population proportions of men and women from the target cohorts and their offspring after all retrospective adjustments.

## Results

Our analysis proceeds in three steps. First, we examine differential fertility of low- and high-educated men and women born between 1930 and 1950 in East and West Germany. Second, we present conventional retrospective estimates on educational mobility. Third, we integrate demographic and social pathways in a prospective model of educational reproduction. Using decomposition models and scenario analyses, we assess the relative importance of both pathways in processes of educational reproduction.

### Trends in Differential Fertility

Table 3 shows the proportion of childlessness, the average number of children for parents (PFR), and the average number of children for all cohort members (CFR) across analytic categories. Figure 1 illustrates fertility trends. We calculate all statistics by matching external fertility data to our anchor samples. Fig. A3 in the online appendix demonstrates that our method provides a close fit with trends in cohort fertility reported in official data.

For men, educational gaps in cohort fertility (CFR) were small and nearly absent in the most recent cohorts. This applies to West and East Germany, although low-educated men in East Germany more frequently remained childless. A notable difference is that fertility among West German men declined steeply across our study cohorts to levels substantially below those found in the East. The increase in childlessness among the West German men’s cohort is a major cause of these contrasts.

For women’s fertility, we see substantial educational differences. Consistent with previous demographic research (e.g., Kreyenfeld 2004), the strongest educational gradient in fertility is found among West German women—a pattern that is driven mainly by differential childlessness. Quite persistently over cohorts, at least 20% of women who grew up in West Germany and attained higher education remained childless, compared with a maximum of 14% of low-educated women. Conditioning on motherhood, the number of children (PFR) was also higher among low-educated women, although these differences vanished across cohorts. Overall, the CFR remained rather stable among East German women but declined among West German women. This cohort trend was stronger for low-educated than for high-educated women.

### Trends in Educational Attainment and Offspring’s Educational Mobility

Figure 2 shows trends in educational distributions across the 1930–1950 cohorts and their offspring generations separately by gender and part of Germany. In the upper panel, for cohorts born between 1930 and 1950, we see that women’s disadvantage in education remained stable across cohorts in the West, whereas the gender gap narrowed across cohorts in the socialist East Germany. In these cohorts, education levels were generally higher in the East than in the West, particularly among women. The lower panel, for the offspring of these cohorts, shows a strong increase in educational attainment across West German offspring cohorts, reflecting rapid educational expansion. Expansion was slower for East German offspring cohorts, reflecting quotas on higher education degrees (see Sieben et al. 2001). For later-born offspring, educational careers were increasingly completed in a unified Germany.

The average marginal effects shown in Fig. 3 are based on a model for educational attainment as a function of parental education and family size. This model for the chances of attaining higher education in G2 yields conventional retrospective estimates for educational mobility of the offspring of men and women born between 1930 and 1950. We employ logistic regression models that condition on parents’ education and family size separately for all offspring samples in East and West Germany. We use a linear specification of family size effects for reasons of parsimony. Alternative specifications yielded similar results. Additionally, we adjust for differences between surveys in the outcome.

Figure 3 shows selected results in terms of the probability of attaining higher education (see Tables B2 and B3 of the online appendix for detailed results). For both men’s and women’s offspring, educational mobility is generally higher in the East than in the West of Germany. Across cohorts, the results show no substantial changes in mobility. The patterns for the offspring (born in 1946–1988) of our study cohorts (born in 1930–1950) are substantively similar to earlier findings obtained from retrospective studies on educational mobility in Germany (see Heineck and Riphahn 2007, who studied East and West German birth cohorts 1940 to 1978).

Family size effects were substantial in both parts of Germany. Chances of attaining higher education decreased, on average, by 4 to 6 percentage points for each additional child in the family. This result demonstrates the importance of family size for our main analysis: a higher number of children strengthens population-level reproduction, but it weakens family-level reproduction through negative effects on children’s educational attainment. Analyses that omit family size would therefore overestimate educational reproduction of parents that have a higher number of children.

### Trends in Educational Reproduction

Next, we integrate fertility and mobility pathways into a prospective model of trends in educational reproduction. Figures 4 and 5 plot key estimates of our analysis. Figure 4 shows cohort estimates on rates of educational reproduction of men and women (see Eq. (1)), in both parts of Germany (see Table B4 in the online appendix for precise estimates). The left panel shows the production of high-educated offspring, and the right panel shows the production of low-educated offspring. Counterfactual estimates, represented by gray dashed lines, show the predicted rates if fertility distributions were swapped between education groups.

Figure 5 shows joint effects directly, along with mobility effects—that is, the counterfactual difference in educational reproduction rates if there were no fertility differences between low- and high-educated individuals. The difference between the lines of joint and mobility effects captures the fertility effect. Precise estimates on joint effects as well as fertility and mobility components including statistical tests are provided in Tables B5 and B6 of the online appendix.

#### Men

In East Germany, educational reproduction rates were stable across cohorts and almost unaffected by differential fertility, as indicated by the flat cohort lines and the overlap between the lines for factual and counterfactual fertility distributions (Fig. 4) and the joint effect and mobility effects (Fig. 5), respectively. Among West German men, education gaps in production rates of higher-education offspring were initially larger (for the 1930–1935 cohort, the gap was .85 and .46 for West German and East German men, respectively) but decreased across cohorts. At the same time, we find a steep cohort decline in the production of low-educated offspring among West German men. Low-educated men born in prewar years produced an average of 1.5 low-educated children, whereas men born in postwar years produced slightly less than 1 low-educated child (Fig. 4). In this process, inequality in production rates of low-educated offspring converged. These patterns reflect steep fertility declines in the parent generation combined with educational expansion in the offspring generation. Similar to East German men, the impact of differential fertility on the educational reproduction of West German was small. Only for the cohorts 1930–1935 do we find statistically significant evidence that differential fertility amplified gaps in the production of low-educated offspring. The gap amounts to approximately one child, 13% of which were due to lower fertility of high-educated men.

#### Women

Differential fertility had a larger impact on women’s educational reproduction. For East German women, this impact was most obvious for the production of low-educated offspring. Differences between factual and counterfactual curves (Fig. 4) show that fertility amplified gaps in the production of low-educated offspring. Among the cohorts born 1941–1945, for example, roughly one-third of the gap is attributable to differential fertility.

The strongest role of the demographic pathway is found for West German women. In this group, a substantial part of the gap found for the production of high- and low-educated offspring is due to differential fertility. In Fig. 4, the factual and counterfactual lines show that high-educated women, endowed with the fertility of their low-educated counterparts, would have produced a substantially higher number of high-educated offspring. Conversely, low-educated women, endowed with the fertility of their high-educated counterparts, would have produced a substantially lower number of low-educated offspring. A second notable pattern is that the role of differential fertility weakened across cohorts, particularly for the production of low-educated offspring.

In Fig. 5, these patterns are summarized in terms of joint and mobility effects. We see that in the absence of educational differences in women’s fertility, the joint effect (i.e., the absolute difference in the number of high educated children) would be 22% larger for cohorts 1930–1935 (amounting to 0.98 instead of 0.80, p < .01), 21% larger for cohorts 1936–1940, 4.4% larger for cohorts 1941–1945 (nonsignificant), and 15% larger for cohorts 1946–1950 (p < .05). Differential fertility thus dampens the mobility effect on producing high-educated offspring—the expected gap in rates of reproduction if there were no fertility differences—by 18%, 17%, 4%, and 13% for the respective cohorts. Looking at the reverse outcome, the production of low-educated children in West German women, results show that fertility reinforced the mobility component. Differences in joint effects would be smaller (by roughly 20% for the first two cohorts, p < .001; and 8% for the youngest cohort, p = .051) if fertility differences between high- and low-educated women were absent. Overall, the fertility component was more relevant for West German women than for West German men. Yet, the role of fertility in educational reproduction declined over cohorts as group differences in cohort fertility converged.

In summary, our results on cohort trends show that rates of educational reproduction persisted in East Germany and converged in West Germany. The convergence is partly due to fertility declines and improved educational opportunities in smaller families, partly due to a general increase in educational opportunities across the process of educational expansion in postwar West Germany, and partly due to converging fertility rates between education groups. Importantly, changes in IEO played no major role in this convergence: origin-specific educational mobility hardly changed across offspring cohorts (see Fig. 3).

Another general finding from our models is that high-educated women reproduced their education to a smaller extent than conventional educational mobility estimates suggest. In contrast to prospective estimates, retrospective measures would suggest that educational reproduction was stronger for women in West Germany and did not differ substantially by gender in East Germany (see Tables B2 and B3, online appendix). For our study cohorts, however, lower fertility limited high-educated women in passing their educational advantage on to the next generation. This was especially true for West German women. However, our analysis of trends also reveals that fertility effects found in older cohorts of women diminished in younger cohorts.

### Consequences of Differential Fertility for Inequality in the Offspring Generation

In the final step of the analysis, we examine how differential fertility influenced the distribution of education and inequality of educational opportunities in the offspring generation. Based on our population renewal models that link educational distributions between generations, we simulate the proportion of G2 attaining higher education as well as educational inequality, indicated by the association with parents’ education. The results of the simulation are presented in Fig. 6. Detailed statistics are found in Tables B7 and B8 of the online appendix.

The data in Fig. 6 compare observed values to four hypothetical scenarios in which distributions and parameters are exchanged for educational groups in G1. The first set of scenarios (S1 and S2) swaps the fertility behavior among education groups in G1. The second set (S3 and S4) swaps the educational attainment behavior of both groups’ offspring. This scenario analysis is useful to put into context the effects of differential fertility on the one hand and IEO on the other. To calculate distributions in G2, we multiply the relative sizes of education groups in G1 with the estimated factual and counterfactual rates of educational reproduction, the latter of which link educational distributions across generations.

In our interpretation of the results, we focus mainly on West German women—the group for whom fertility differed most strongly by education. If high-educated West German women in G1 had the fertility distribution of low-educated West German women (Scenario 1 (S1) in Fig. 6), we would expect the share of high-educated persons in G2 to increase, although the effect is negligible (e.g., 0.4 percentage points for cohorts 1930–1935). Conversely, if low-educated women had the (lower) fertility of high-educated women (Scenario 2), educational attainment in G2 would increase by 2.9 percentage points among the offspring of the oldest cohorts (1930–1935) and 1 percentage point for the offspring of the youngest cohorts (1946–1950).

Although the impact of differential fertility on the distribution of education in G2 is relatively small for both scenarios, the relative size of the resulting offspring populations varies considerably (e.g., for the first cohort, 210% under Scenario 1 vs. 167% under Scenario 2). Furthermore, under both counterfactual scenarios, educational inequality measured by the log odds ratios of attaining high education for children of high- versus low-educated parents would be lower. Results are substantively the same when inspecting probability differences instead of odds ratios; see Table B8 in the online appendix. These differences emerge from fertility effects on the family level: that is, negative effects of the number of siblings on children’s educational attainment. These results of the simulation are particularly interesting when interpreted jointly. If high-educated mothers had the same fertility as low-educated mothers (Scenario 1), this would not only mean that more children would be born and a slightly higher share of children would reach higher education but also that educational inequality would be smaller. Yet, as already shown, these fertility effects largely disappeared for the younger cohorts.

In general, however, the first two scenarios show that the association between education and fertility in G1 was too weak to substantially impact the distribution of educational or educational inequality in G2. This was true even for West German women, who showed the largest educational gradient in fertility. Small differences in a two-generational model of population renewal, however, would accumulate rapidly when further extrapolated to future generations.

Scenarios 3 and 4 simulate the same quantities for counterfactual rates of mobility. As per the exchange of parameters, inequality would disappear almost entirely, although children of high-educated parents would still enjoy slight advantages due to family-level effects of differential fertility (i.e., educational advantage of having fewer siblings). Taken together, the simulation results show that the link between the educational distributions of G1 and G2 is to a large extent determined by mobility as a social pathway and only to a small extent by fertility as a demographic pathway.

## Discussion

Conventional social mobility research has examined parent-child associations in educational attainment and how these associations have changed during times of rapid educational expansion in the second half of the twentieth century. Looking backward from the perspective of children, this research is retrospective in nature, showing how social positions are inherited from parents. In the German context of the present study, previous research found this core association to have weakened somewhat across cohorts but still remaining substantial. These conclusions are limited, however, because retrospective studies are conditioned on fertility, neglecting demographic processes of intergenerational reproduction. In this study, we adopt a prospective approach that considers not only the social reproduction of education as an individual attribute (the mobility pathway) but also the demographic reproduction of individuals who carry these attributes (the fertility pathway).

We focus on the educational reproduction of East and West German men and women born between 1930 to 1950. Our aim is to quantify the role of fertility in the educational reproduction of these cohorts, who represent the engine of the second demographic transition in Germany. A comparative lens on East and West Germany allows us to examine the role of sociohistorical differences in education, mobility, and fertility.

A further key contribution is the method that we introduce to achieve these aims. Our method uses inverse-probability weighting to minimize retrospective sampling bias, circumventing the exceptionally high data demands of previous prospective models and allowing us to obtain prospective estimates from retrospective data widely available in multipurpose surveys. Furthermore, our method refines the prospective analysis of educational reproduction by a decomposition of fertility and mobility components. Prospective estimates obtained from this model consider the fertility pathway of educational reproduction in terms of childlessness, number of children, and family-level effects on educational attainment.

Based on data from the German NEPS and SOEP combined with external data on fertility, our results offer a comprehensive portrayal of educational reproduction in social, demographic, and cohort context. Three general patterns emerge from the analysis. The importance of the fertility pathway of educational reproduction was higher in West than in East Germany, higher for women than for men, and higher for earlier than for later cohorts. Accordingly, in West German women of earlier cohorts, a substantial part of the education gap found for the production of high- and low-educated offspring was due to differential fertility. Lower fertility of high-educated women tempered the gap in production of high educated offspring by 18% compared with the expectation based on the mobility effect alone. Conversely, the higher fertility of low-educated women reinforced the gap in production of low educated offspring by roughly 26% compared with the expectation based on the mobility effect. Because conventional mobility studies have ignored these processes, their results overestimate educational reproduction in high educated West German women and underestimate educational reproduction in low-educated West German women.

However, our analysis of cohort trends shows that the role of fertility in educational reproduction declined as a result of generally lowering fertility levels, a convergence in fertility rates between education groups, and overall increased educational opportunities. Again, these are important insights that retrospective analyses would have missed or misattributed to changes in origin-specific educational mobility (IEO). Our prospective analysis shows that this convergence did not reflect changes in inequality of educational opportunities among the offspring cohorts which, in line with findings from retrospective educational mobility studies, remained stable by and large.

Finally, simulations based on population renewal models reveal that differential fertility slightly lowered educational attainment and increased inequality in educational attainment in the offspring generation. Yet, the overall effect of differential fertility was very small for the cohorts under study. Based on our findings, we conclude that status transmission within families was the major mechanism in educational reproduction, although this process was also shaped by demographic pathways.

Our study contributes both in substantive and methodological ways to the literature on educational reproduction. It adds to the body of prospective social mobility studies, which is limited especially in central-European countries. For Germany, ours is the first analysis that assesses educational reproduction among men and women who grew up and had their children under radically different conditions in divided Germany. Our study is also the first to analyze cohort trends in educational reproduction prospectively. Moreover, the method introduced in this study shows that analysts of social stratification can utilize their common data sources to complement retrospective designs by prospective designs of intergenerational reproduction. In addition to the standard variables used in mobility tables, the only additional variables required for estimating a simple prospective model are the birth years of parents and the number of siblings. These variables are usually available in large-scale multipurpose surveys. This means that the method we proposed here is broadly applicable.

We close with a number of limitations and directions for future research. First, our method is of limited use for studies on the causal impact of educational degrees on educational reproduction outcomes (Breen and Ermisch 2017; Lawrence and Breen 2016). Causal estimates would require valid data on important confounders, such as academic achievement or social class background (of parents), which are usually not available in retrospective data, as well as additional assumptions on the absence of unobserved confounders. Moreover, accurate causal inference would require accounting for assortative mating as an additional demographic pathway of educational reproduction (e.g., Lawrence and Breen 2016). Further refinement could be achieved by adding mortality, migration, or the timing of births to the equation. Similar to other widely used methods in social mobility research, our approach is suitable for analyses on associations and trends in intergenerational reproduction as well as cross-national comparisons. Given that our method places few demands on the data, it opens new avenues for research along these lines.

Second, the availability of high-quality external data on fertility could limit applications. Note, however, that our approach does not rely on external data on childlessness. Two alternative strategies are possible. Researchers could estimate childlessness based on a weighted respondent sample providing truncated (i.e., positive) fertility data on parents’ number of children. Based on the assumption that decisions on whether and how many children are born are governed by one underlying process, Poisson models could estimate out-of-sample levels of childlessness conditional on education or other measures of socioeconomic status. Alternatively, researchers could estimate a target cohort’s levels of childlessness using data from the same retrospective data set, which may cover overlapping or adjacent cohorts.

Third, a general limitation of prospective models is their extensive time span. Educational reproduction can be assessed only after the fertility process in a target cohort is complete and the attainment process of their offspring is complete. In our study, we limit the analysis to school attainment because more detailed measures (e.g., tertiary education) would require many additional years before educational careers are completed. In retrospective studies, the range of study cohorts is not restricted by design. This benefit, however, comes with the disadvantage that any approach looking backward to parents ignores important mechanisms that link populations, and associated structures of inequality, to their offspring. In this regard, we consider it a promising direction for future mobility research to employ prospective models to forecast inequality in future populations.

## Authors’ Contributions

JS and TL conceived and designed the study. JS developed methodology, performed the data preparation, and ran the analyses. JS and TL wrote and revised the manuscript. Both authors read and approved the final manuscript.

## Data Availability

Replication files to this article are available at the authors’ websites: www.skopek.org and www.thomasleopold.eu. The empirical analysis in this article employed secondary data from various survey studies: (1) the German National Educational Panel Study (NEPS), (2) the German Socio-economic Panel Study (SOEP), (3) the German General Social Survey (‘Allgemeine Bevölkerungsumfrage’, ALLBUS), (4) the German Aging Survey (‘Deutscher Alterssurvey’, DEAS), and (5) the European Social Survey (ESS). All data are available for researchers based on motivated proposals. Research data centres of the respective survey studies provide more information on data access: (1) http://www.neps-data.de, (2) https://www.diw.de/en/diw_02.c.222518.en/research_data_center_of_the_soep.html, (3) https://www.gesis.org/allbus/allbus, (4) https://www.dza.de/en/fdz/german-ageing-survey.html, and (5) https://www.europeansocialsurvey.org/data/.

## Compliance With Ethical Standards

### Ethics and Consent

The authors confirm that they comply with Springer’s ethical requirements.

### Conflict of Interest

The authors declare no conflicts of interest.

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