To illustrate the added value of our approach, we apply it to the study of women’s employment trajectories in divided Germany (1955–1990). The leading research question for this exercise is: what conditions enabled women in East and West Germany to continue their education or employment over early- and mid-adulthood? This question is suitable for our illustrative purposes because there is extensive literature that accounts for the factors shaping women’s labor-market participation within the two contexts (Diewald et al. 2006; Rosenfeld et al. 2004). This enables us to evaluate our results against a wide range of established, substantive evidence.
During the period of division (1955–1990), the German Democratic Republic (henceforth, East Germany) and the Federal Republic of Germany (henceforth, West Germany) differed to a great extent concerning their economic and welfare systems.
The social market economy in West Germany was coupled with the promotion of a pro-traditional male breadwinner model in a corporative welfare state (Engelhardt et al. 2002; Rosenfeld et al. 2004). A highly gendered division of labor was indirectly supported by social policies that did not promote the compatibility of work and family and by a taxation system that penalized working wives (Brückner 2004; Cooke 2011; Sainsbury 1999). Female labor-market participation was around 50%—mostly part-time—and it was discouraged especially for women with children, while for male employment rates were around 80% (Diewald et al. 2006).
In the egalitarian centrally planned economy of East Germany, women’s employment was supported by an infrastructure and an ideology that affirmed the right and duty to work. Pro-natalist family policies aimed at improving compatibility of work and family: The normative pressure to have children in one’s early twenties was combined with widespread childcare, and state-controlled resources (e.g. housing or loans) were available to those who started a family (Kreyenfeld 2004). As a result, women’s employment rates paralleled men’s, reaching 90% also for women with children (Huinink et al. 1995).
When considering enabling conditions for employment, we expect gender to play a major role in the explanation of inter-individual differences along the whole life course, and especially so when specific life transitions occurred. Moreover, given the institutional differences outlined above, we expect gender to be a prominent explanatory factor in the West more than in the East. Finally, within each context, we expect some combinations of factors to be consequential for women’s employment. We focus on three drivers that the literature indicates to be relevant to female labor participation (Engelhardt et al. 2002; Kreyenfeld 2004; Rosenfeld et al. 2004): partnership status, number of children, and parental education.
To develop our empirical illustration, we analyze longitudinal-retrospective data from the Starting Cohort Six of the National Educational Panel Study (NEPS) (Blossfeld et al. 2011). We selected a subsample of individuals born in East and West Germany (N = 374 and N = 1,695 respectively) between 1944 and 1955, i.e. individuals who experienced most of their early- and mid-adulthood in divided Germany.
3.2 Empirical Analysis
In a first step, we construct individual sequences representing longitudinal employment trajectories of men and women in West and East Germany. We then apply discrepancy analysis of state sequences to estimate the proportion of the variation in employment trajectories explained by gender at each time point in the sequences. This allows us to identify the phases when gender is mostly or increasingly relevant.
In a second step, we focus on these time points and apply fuzzy-set QCA to the sample of women to identify the configurations of factors sufficient for them to be employed or pursuing education in West and East Germany.
3.2.1 Step 1: Sequence Analysis
126.96.36.199 Sequences’ Construction
We construct individual employment trajectories from ages 15 to 40 as sequences of monthly intervalsFootnote 1: each of the 300 months is encoded according to a binary definition that distinguishes being in education or employment from being out of education and out of employment (unemployment, inactivity, military service, maternity leave). We adopt this binary definition because both crisp- and fuzzy-set QCA require a two-dimensional outcome. This does not rule out the possibility of adopting more elaborate definitions of states, as SA could be combined with multi-value QCA (Cronqvist and Berg-Schlosser 2009). From a substantive point of view, being in employment or in education is often considered a “positive” outcome during early adulthood and one that is associated with greater chances of societal integration later on. We censor our observational window at age 40 because we assume that the most important steps for the establishment of one’s career have already occurred during this phase of the life course.
Figure 1 shows the state distribution plot by gender in East and West Germany. For men, periods spent out of employment or education were concentrated in the years around military service in both contexts. In contrast, women’s employment trajectories differed according to context: while women in the East exhibited very limited amounts of time spent out of employment over the whole timespan considered, in West Germany women’s likelihood of being in employment or education decreases over time.
188.8.131.52 Discrepancy Analysis
We apply discrepancy analysis of state sequences (DA) (Studer et al. 2011), which translates the ANOVA framework into sequence analysis. The resulting pseudo-R
2 values can be interpreted as the share of the total variability between sequences explained by a specific factor of interest at each point in time (for a detailed description see Struffolino et al. 2016). The input of DA is a pairwise distance matrix based on a dissimilarity measure computed by assigning a cost to each transformation needed to align the couples of sequences (insertion—deletion and substitution costs). We used the optimal matching dissimilarity measure with an insertion—deletion cost of 1 and a substitution cost of 2. Notice that in this case, the sequences are composed of only two states, and therefore any more complex specification of costs would have been pointless (Studer and Ritschard 2016). Our explanatory factor of interest is gender. Hence, the pseudo-R
2 value for between-group differences at each time point can be interpreted as the share of the total variability in the pool of sequences that is explained by gender.
Figure 2 displays the pseudo-R
2 values for gender in East and West Germany. In the East, gender explains 12% of the variation between employment trajectories around age 20: this is most probably due to men being in military service. After age 23, gender explains very little of the variation between trajectories, because employment rates were very high for both men and women. In contrast to this, in the West gender explains an increasing share of the variability between employment trajectories starting from age 22; it reaches 15% between age 30 and 36.
The peaks in the pseudo-R
2 represent phases of the life course where gender differences reach their relative maximum: These phases are of particular substantive interest because they might represent ‘turning points’ along the unfolding of employment trajectories (Abbott 2009). However, within the SA framework, change is understood as lasting over a period of time, rather than as happening at specific time points (Shanahan 2000). Divergence between sequences may then result from an extended succession of critical moments and not necessarily concentrate at single peaks. Therefore, both the peaks and the phases where gender differences display sharp increase can be considered as potential turning points. We randomly select one specific time point (month) for phases of peaks and sharp increases. To be able to compare between the two contexts, we additionally selected time points in the West and applied them to the East, and vice versa. This results in five time points that constitute the starting point for our second step of analysis: 19 years, 20 years and 9 months, 23 years, 31 years, and 35 years.
3.2.2 Step 2: Qualitative Comparative Analysis
In the second research stage, we shift the focus to women, because it is their patterns that diverge from those of men, at least in the West, and investigate which configurations of factors are systematically associated with being in employment or in education at each of the five time points identified in the first research stage and within the two contexts of East and West Germany. Our explanatory conditions refer to women’s partnership status, number of children, and family background. While many other factors could be listed as potentially explanatory, for the sake of simplicity of this empirical exercise we focus on the three identified as the most relevant according to previous literature (see Sect. 3.1). Moreover, parsimony in identifying potentially explanatory conditions is required when applying QCA, as the number of possible combinations grows exponentially with the inclusion of new conditions.
As mentioned in Sect. 2, to apply QCA, the cases under observation must be classified as members or non-members of the sets corresponding to the outcome and the explanatory conditions. While in principle researchers can attribute set membership based on their own substantive knowledge of the cases, set membership is often assigned following the more systematic procedure of calibration, which consists of applying external criteria to transform an interval-scale variable into a crisp or fuzzy set.Footnote 2
Two calibration techniques can be distinguished: Following the direct method (Ragin 2008, 94–97), researchers need to specify three values of the interval scale (also known as “source variable”) that will identify three qualitative breakpoints in the set membership: full inclusion, full exclusion, and maximum ambiguity or crossover. For fuzzy sets, full inclusion usually corresponds to a set membership of 0.99, full exclusion to 0.01, and the crossover to 0.5, while intermediate values are assigned according to a logistic function. For crisp sets, only the value corresponding to the crossover must be specified, as set membership can only assume the value of 0 or 1. Instead, when following the indirect method of calibration, one should use substantive knowledge to determine the correspondence between values of the source variable and set membership scores. The recommended set membership scores are: 1 for full inclusion, 0.8 for cases “mostly but not fully in the target set,” 0.6 for cases “more in than out of the target set,” 0.4 for cases “more out than in of the target set,” 0.2 for cases “mostly but not fully out of the target set,” and 0 for full exclusion (Ragin 2008, 95–96). For both the direct and indirect calibration methods, the threshold criteria need to be justifiable and transparent. In our empirical application, cases are constituted by individuals—or more specifically, women—in East and West Germany observed at each of the five time points selected in the SA analytical step. The criteria for the calibration of the sets corresponding to the outcome and to the explanatory conditions are detailed in the following.
Outcome: Crisp set of “women in employment or in education”. In this case no calibration is necessary because the source variable, corresponding to the two states analyzed in the first research stage, is already dichotomous (see above).
partnership: fuzzy set of “women in a stable partnership”; source variable: self-reported marital status; method of calibration: indirect; threshold criteria and set memberships: single: 0; cohabiting but unmarried: 0.6; married: 1.
children: crisp set of “women with children”; source variable: number of children; method of calibration: direct; threshold criteria and set memberships: no children: 0 for one or more children: 1.
high-paredu: fuzzy set of “women from relatively advantaged social background”Footnote 3; source variable: number of years corresponding to the highest educational qualification attained by either parent; method of calibration: direct; threshold criteria and set memberships: these are specific to the two contexts to account for the differences in the degrees of educational expansion and in the educational systems. East Germany: 15.5 years (university education): 0.99; 12.5 years (above the 12 threshold corresponding to upper-secondary education): 0.5; 11 years (less than upper-secondary education): 0.01. West Germany: 15.5 years (university education): 0.99; 11 years (above the 10 threshold corresponding to the intermediate school certificate): 0.5; 9.5 (no or low school certificate only): 0.01.
Table 1 reports descriptive information on the source variables for the outcome and the conditions for each time point and context.
184.108.40.206 Truth-Table Construction
Before proceeding to the analysis, we explore the empirical configurations displayed by the cases and their relation with the outcome for each time point and context. To this scope, we construct a so-called “truth table,” whose rows correspond to possible combinations of conditions. Based on the empirical distribution of cases, each combination is connected to either the presence or the absence of the outcome. The 10 resulting truth tables are displayed in Table 2.
The intersection of our three conditions (children, high-paredu, partnership) produces eight possible configurations. However, not all configurations display empirical instances and some rows are therefore empty (the so-called “logical remainders”). To minimize random noise, we set a frequency threshold of 20 cases, meaning that configurations with less than 20 cases are classified as logical remainders.Footnote 4 In Table 2, logical remainders are omitted for parsimony. Each row represents a combination of conditions (with 1 indicating the presence, and 0 the absence of the condition) to which a certain number of cases (N) belongs. For instance, the first row in the right part of the table indicates that, in the sample of West Germany, when they were 19 years old, 635 women did not have any children, came from highly educated families, and were not in a partnership (children = 0, high-paredu = 1, partnership = 0). Among them, the vast majority was in employment or in education (out = 1), as indicated by the consistency parameter (Cons. = 0.942). This parameter, roughly speaking, returns the proportion of women belonging to the 0-1-0 configuration who were in employment or in education.Footnote 5
Table 2 reveals that in each of the five time points, for both the East and the West, multiple configurations were associated with the outcome. In East Germany, this applies to all existing configurations (i.e. displaying at least 20 empirical instances), in line with the fact that in this context the great majority of women remained in employment (or education) throughout their whole life course (see Fig. 1).
Looking more closely at Table 2, we note that, with the exception of the second time point, there are only two configurations for East Germany. Moreover, they are constant for the last three time points: women in stable partnerships and with children, with (1-1-1) and without (1-0-1) highly educated parents. This finding is consistent with previous research underlining the standardization of individual life courses in the GDR (Fasang and Raab 2014; Struffolino et al. 2016). More diversity existed in West Germany. This is visible first of all in the number of rows that exhibit empirical instances: Women are generally grouped in four or five configurations. Second, such configurations vary considerably over time, as can be seen from the comparison of the rows across time points. Finally, some configurations are associated with the presence and some with the absence of the outcome.
220.127.116.11 Truth-Table Analysis
In order to remove the redundant elements from the configurations associated with the outcome and thus identify the “outcome-enabling” conditions, we perform the fuzzy-set minimization of the 10 truth tables.Footnote 6 Different strategies exist in the literature for dealing with the issue of limited diversity, which emerges in QCA as non-existent configurations or logical remainders (Schneider and Wagemann 2012, 160–177). Given the descriptive purpose of our analysis, we refrain from using logical remainders, meaning that configurations with less than 20 cases are not considered in the minimization process. Therefore, our solutions are to be intended as conservative (ivi: 182). Additionally, before proceeding to the analysis one must set a consistency threshold in order to exclude configurations that are not sufficient subsets of the outcome. We apply a consistency threshold of 0.75, which is generally considered acceptable in the QCA literature (ibidem), but results are generally robust even with stricter consistency levels.Footnote 7
The results are summarized in Table 3, whose columns represent the five time points and whose rows display the “prime implicants.” The prime implicants are the essential components of a configuration identified by the truth-table analysis that, read in combination with each other, constitute the logically-minimal Boolean expression sufficient for the presence of the outcome (Ragin 1987, 95–98). For example, for 19-year-old West-German women, in order to be in employment or in education, it was sufficient not to have children and not to be in a partnership, or, as an alternative, not to have children and to have highly educated parents. The resulting logically-minimal Boolean expression is therefore: “child*partnership + child*high-paredu”.Footnote 8
Table 3 thus shows the dynamic development of the combinations of factors logically sufficient for being in employment or in education. Indeed, these combinations changed over time during the phases of early- and mid-adulthood in both contexts. In both East and West Germany, not having children and not being in a partnership emerges a prime implicant for the first two time points considered, although in combination with different prime implicants (high-paredu*partnership in the East and child*high-paredu in the West), but later disappears. As women reached the stage of their life course when most entered partnerships and had children, the combinations of factors sufficient for remaining in employment or in education diverged across the two contexts: In East Germany, the only prime implicant from 24 years on is constituted by women in a partnership and with children. In West Germany, where the transition to fertility was generally delayed compared to the East (Kreyenfeld 2004), for 24-year-old women we still find the alternative combinations of not having children and having highly educated parents or or not having children and being in a partnership. However, from age 31, the only prime implicant left is that of women without children and with highly educated parents.
For both contexts, we observe a collapse over time into a single prime implicant. However, the implications are very different for East and West Germany: The prime implicant for East Germany (being in a partnership and with children) corresponds to the prevailing configuration of attributes for women aged 24 and older. Moreover, for these Eastern German women, the outcome is skewed to the right or, in other words, the overwhelming majority were in employment or in education (consistently with what shown by Huinink et al. 1995). Hence, the prime implicant and the outcome are in a relation of almost perfect set coincidence, which should not be interpreted as causal but rather as constitutive (Borgna 2013). In substantive terms, as noted earlier, this is driven by a strong standardization of individual life courses (Fasang and Raab 2014; Struffolino et al. 2016). In West Germany, in contrast, the lasting prime implicant corresponds to a limited portion of the population and can therefore properly be read as “outcome-enabling”: Among women older than 24, only those without children and with highly educated parents could systematically still be found in employment or in education. The prime implicant of women in a partnership and without children disappears, because for ages 31 and 35 it corresponds to a group that is too small to be considered an existing configuration, because the great majority of women in a partnership eventually had children, and those who did not have any originate from families with highly educated parents (see also Table 2).
Overall, while we detected a greater heterogeneity in the life courses of women in West Germany from the mere observation of the truth tables, the truth-table analyses suggest that this greater diversity does not translate into a greater variety of pathways towards employment or education. While further research would be needed for any definitive, substantial conclusions, the results of this empirical exercise are not only in line with previous evidence on women’s labor-market participation in East and West Germany but also provide some new insights into the different degree of complexity of their life courses.