The just gender pay gap in Germany revisited: The male breadwinner model and regional differences in gender-specific role ascriptions

Journal Pre-proof The just gender pay gap in Germany revisited: The male breadwinner model and regional differences in gender-specific role ascriptions Volker Lang, Martin Groß

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https://doi.org/10.1016/j.rssm.2020.100473

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RSSM 100473

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Research in Social Stratification and Mobility

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Please cite this article as: Lang V, Groß M, The just gender pay gap in Germany revisited: The male breadwinner model and regional differences in gender-specific role ascriptions, Research in Social Stratification and Mobility (2020), doi: https://doi.org/10.1016/j.rssm.2020.100473

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The just gender pay gap in Germany revisited: The male breadwinner model and regional differences in gender-specific role ascriptions

Volker Langa,* [email protected], Martin Großb a

Bielefeld University, Faculty of Sociology, Bielefeld, Germany

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Tübingen University, Institute of Sociology, Tübingen, Germany

Corresponding author: Volker Lang

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*

Faculty of Sociology, Bielefeld University, Postbox 100131, D-33615 Bielefeld, Germany

The male breadwinner model is critical in explaining just gender pay gaps in

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Highlights

Germany.

For childless women and men, equal earnings are considered just.

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For men with children, earnings that are approximately 8% higher than those of

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women and childless men are considered just. There is a just gender pay gap of approximately 6% in the western federal states of

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Germany, while there is no substantial just gender pay gap in the eastern federal states. Regional differences in the relevance of the male breadwinner model tend to be

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reflected in different just gender pay gaps.

Abstract Despite recent advances, women still earn less than men, and this gap is considerable. Moreover, even after accounting for differences in education, occupation, experience and 1

performance, many people think that this gap is justified, which leads to a so-called just gender pay gap (JGPG). Research thus far has not been able to explain this JGPG. In this paper, we use a factorial survey experiment conducted with a population-representative sample in Germany (SOEP-Pretest 2008, 1,066 persons, 26,650 vignette ratings) to test if the male breadwinner model (MBM)—the belief that fathers should be gainfully employed to provide for the material needs of their family while mothers attend to the unpaid family work—can account for this JGPG. Based on the MBM explanation, we expect that the JGPG

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is larger if there are children in a family. To account for the multistep rating process of the factorial survey in the SOEP-Pretest 2008, we develop and implement a new, highly flexible factorial survey model: the generalized Craggit model. Our results clearly indicate that the

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MBM is a critical factor driving the JGPG in Germany. While respondents think that childless women and men should be paid equally, they consider it just if men with children earn

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approximately 8% more than women with children or childless persons earn. Moreover, our

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analyses based on the generalized Craggit model demonstrate a lower JGPG and less relevance of the MBM in the eastern federal states than in the western federal states.

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Keywords

gender pay gap; justice attitudes; earnings; male breadwinner model; factorial survey

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experiment; Craggit model

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1. Introduction It is a well-established fact in labor market research that women earn less than men, even in similar job positions. In Germany, women’s mean hourly gross earnings were 21% lower than men’s earnings in 2016 (Statistisches Bundesamt 2017) when this gap was not adjusted for differences between job positions (which yields the “gross” gender wage gap). This gross gender pay gap is among the largest in the EU, which had an average gross gender pay gap of 16% in 2016 (Eurostat 2019). When adjustments were made for differences in education, age,

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and occupation between women and men, as well as when the influence of a firm was considered, the resulting “net” gender pay gap was 12% in 2010 (Gartner 2016). For the same year, the Federal Statistical Office calculated a net gender pay gap of 7%, adjusted for

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education, job positions and labor market experience (Statistisches Bundesamt 2017). Overall, the net gender pay gap of approximately 10% has changed little between 1993 and 2010

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other OECD countries (Ridgeway 2011).

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(Gartner 2016, Gartner and Hinz 2009, Hinz and Gartner 2005) and is comparable to that of

Less well known is the finding that the net differences in the payments of women and men are often considered just. Several general population factorial survey experiments in

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which respondents rate the justness of earnings in vignette scenarios show that gender pay gaps are reflected in people’s justice attitudes toward earnings (Jann 2003, Jasso and Webster

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1997, Sauer et al. 2014). Surprisingly, men and women do not differ in these attitudes, and

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lower earnings for women than for men in similar job positions are considered just by women and men alike. In a recent comprehensive study for Germany, Auspurg, Hinz and Sauer (2017) find a ratio of mean just earnings for women to those for men of 0.92—meaning that female as well as male respondents consider it just if women earn approximately 8% less than men in similar job positions. This so-called just gender pay gap (JGPG) roughly equals the actual net gender pay gap.

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In this paper, we ask why people consider lower earnings for women to be just. The most promising approach to explaining JGPGs is that women and men are ascribed different social roles and related responsibilities with respect to providing earnings. However, it remains unclear which value patterns lead to such gender-specific role ascriptions and how these value patterns hinge on societal contexts. To address these research gaps, we extend the analyses of Auspurg et al. (2017) in two respects. On the one hand, we provide evidence at the micro-level that gender-specific role

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ascriptions are mainly driven by a value pattern that is known as the male breadwinner model. On the other hand, we point to the origins of this value pattern by analyzing the impact of

macro-level societal contexts on earnings justice attitudes, focusing on differences in these

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evaluations between respondents from the eastern and western federal states of Germany. It is well established in the literature that large differences still exist in the gender pay gaps

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between eastern and western Germany. The gap was 18% larger in the western than in the

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eastern German federal states in 2016 (Fuchs 2018) due to differences in the occupational structure and labor market involvement of women. However, it is less clear whether these differences in the “objective” gender pay gaps are mirrored in different JGPGs. We argue that

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the more gender egalitarian structure of the labor market, as well as the stronger tradition regarding the labor market involvement of women in the eastern federal states, undermines

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the belief in the male breadwinner model.

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In the following, we develop hypotheses about the consequences of the male breadwinner model for the JGPG in general and for differences in the JGPGs between the eastern and western federal states of Germany. Then, we test these hypotheses with the population representative sample of the SOEP-Pretest 2008 (Sauer et al. 2009). To account for the three-step rating process implemented in the SOEP-Pretest 2008 and to capture related heaps in the rating distribution, we developed a so-called generalized Craggit model based on prior models we used to analyze distributions of vignette ratings with heaps, censoring points 4

and different scaling levels of responses (Groß and Lang 2018, Lang 2018). Such a model is of value for factorial survey research in general, since these types of rating distributions are quite common. As we view these analyses as an extension of Auspurg et al. (2017), with a population-representative sample and different models, we first replicate the JGPG found in their study to establish baseline comparability between the two studies. 2. Theory and hypotheses 2.1. Previous explanations for just gender pay gaps

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In previous research, three types of theoretical explanations of the JGPG have been proposed: 1) statistical discrimination, 2) labor market involvement, and 3) gender-specific status

beliefs. In the statistical discrimination explanation, gender is a proxy for missing information

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about scenarios or persons to evaluate (Gangl and Ziefle 2009). Being a woman is associated

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with having less labor market experience, having more family responsibilities and sometimes performing more poorly on the job for various reasons compared to men (Bielby and Baron

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1986). These gender-related connotations are projected onto women and lead to a JGPG if no information on these characteristics is given to respondents. However, the analyses of

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Augspurg et al. (2017) show that the addition of relevant information with respect to gender stereotypes, such as tenure, to vignette scenarios of factorial surveys has no substantial effect

JGPG.

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on the JGPG, ruling out the statistical discrimination thesis as a sound explanation of the

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The labor market involvement explanation starts from the assumption that justice attitudes are framed by respondents’ social comparisons, with similar others functioning as reference groups (Major and Testa 1989). Since labor market participation and the occupational and sectoral structure of the labor market are segregated by gender (Charles and Grusky 2004), the social comparison groups of women and men tend to be different (Major and Konar 1984, Gibson and Lawrence 2010). Therefore, women who work in less gender5

segregated (i.e., more equally paid by gender) job positions should less often consider a gender pay gap to be justified than should women working in more gender-segregated jobs, women not involved in the labor market or men. Hence, we would expect that a respondent’s gender or combinations of a respondent’s gender and employment characteristics would influence the JGPG. Previous research found no effects of related indicators on the JGPG in their analyses (Auspurg et al. 2017, Sauer et al. 2009). In contrast, the gender-specific status belief explanation is based on the assumption

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that social contexts and practices shape the formation of attitudes towards the status and value of certain groups, especially during socialization (Berger et al. 1977, Ridgeway and Correll 2004). These status beliefs are typically related to specific, easily observable general

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characteristics such as gender or race (Correll 2004). Such status characteristics are not a proxy for missing information in specific situations (as the statistical discrimination

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explanation assumes), and they are not tied to social comparisons with similar others; rather,

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they are an expression of cultural sentiments or stereotypes (Berger and Fişek 2006). Thus, if the status beliefs explanation for the JGPG is true, one would expect that all people sharing a cultural background in which women are considered to have lower status would consider

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lower earnings for women to be just (Auspurg et al. 2017, Thébaud 2015). In particular, male and female respondents should be alike in this regard. In line with this expectation, previous

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vignette experiments found a rather robust JGPG that was shared by male and female raters

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and that could not be explained by an extensive set of control variables (Auspurg et al. 2017, Jasso and Webster 1997). However, while a robust JGPG is compatible with the gender-specific status belief

explanation, it remains unclear what these beliefs consist of and where they come from. Moreover, the status belief approach might not explain the JGPG at all. If women are considered to be lower in status because they typically earn less, then lower earnings are the

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cause—and not the consequence—of gender-specific status beliefs.1 Thus, without a more “substantial” theory about the status characteristics and motives involved, gender-specific status beliefs are an insufficient explanation for the effect that vignette gender has on earnings justice attitudes. 2.2. Gender-specific role ascriptions and the male breadwinner model Here, we propose a more substantial alternative to address the shortcomings of the genderspecific status beliefs explanation of JGPGs thus far. We expect that justice attitudes toward

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earnings derive mainly from a value pattern known as the male breadwinner model (MBM) and are formed by social structure and socialization processes. The MBM explanation starts

with different social roles ascribed to women and men, which are, similar to gender-specific

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status beliefs, grounded in cultural sentiments and socialization processes (Cunningham 2008, Gillian 2010). According to the MBM, men are predominantly responsible for the economic

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welfare of their family. Men are in the “material provider role” and have “to make the

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money”, while women take care of domestic work and children. On the other hand, based on the MBM, women work only if their husbands cannot perform their provider role or if women seek to advance their own self-fulfillment. Consequently, women’s labor contribution—

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mostly part-time—is considered to be an “add-on” to the basic household income—provided by their husbands—which does not necessarily have to result in similar pay.

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We see two possible theoretical mechanisms by which these gender-specific social

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role ascriptions could lead to JGPGs. First, we would expect a JGPG as a result of different incentives to work (Bowles et al. 2001). If women’s labor contribution is considered an “addon” to the basic household income, and, in particular, if women’s work is considered a means to self-fulfillment, people (men and women alike) would evaluate this self-fulfillment as part

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These objections against the gender status beliefs explanation of the JGPG were brought up by two anonymous reviewers, whom we thank for these suggestions.

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of their compensation for their work, and they would consequently deem lower wages appropriate. Second, a lower wage could be justified by social justice theories of earnings (Wegener 1999). Surely, the so-called “meritocratic principle” dominates the justice evaluation of the income distribution generated in the labor market. According to this principle, wages should strictly reflect workers’ productivity, precluding any gender differences in pay. However, the “need principle” of justice is also a widely accepted standard

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for evaluating the justice of earnings. For instance, people often support minimum wages that do not primarily reflect productivity but rather help to satisfy workers’ basic needs to live

with dignity. In a similar way, we can expect that respondents would consider higher pay for

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men to be justified if it is deemed necessary to feed their family.

The shares of couples and families with labor division patterns matching the MBM

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have been declining over recent decades in many OECD countries (Blossfeld and Drobnic

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2001). Accordingly, analyses for the United States report declines in attitudes involved in the MBM, mainly for the more highly educated population during the 1970s and 1980s (Cunningham 2008). A study from the Netherlands shows similar declines until the early

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2000s, at least for some attitudes regarding the MBM, while other relevant attitudes did not change (Kraaykamp 2012). Given this state of research, we consider it plausible to assume

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that the ascriptions of gender-specific social roles change slowly, and despite growing

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commitment to egalitarian partnership patterns, especially among youth, the MBM is still lively in the minds of many people. If JGPGs are grounded in the MBM, we would expect that people do not consider

higher earnings to be just for men than for women in general, rather only for men who are responsible for a family. Possible indicators of such responsibilities are the presence of children in the household and a person’s marital status. If the effects of such family-related indicators do not differ by gender of the wage-earners, people express a general valuation of 8

family obligations, but if these effects differ by gender, they express gender-specific role ascriptions in line with the MBM, which can lead to a JGPG. Thus, according to the MBM explanation, married single-earning men are expected to provide a living for their family. Moreover, this responsibility sharply increases with the number of children for whom these single-earners must provide. Consequently, assuming that the MBM explanation for JGPGs is true, we would expect that the marital status and the number of children of male vignette persons affects respondent’s earnings justice ratings,

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while we would expect no such effects for female vignette persons. These different evaluations of the number of children and marital status by the gender of vignette persons translate into differences in JGPGs which lead us to our first hypothesis:

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Hypothesis 1a (H1a). The JGPG will increase with the number of children of those whose earnings are evaluated.

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Hypothesis 1b (H1b). The JGPG will be larger for married single-earners than for unmarried

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persons.

2.3. How the male breadwinner model is shaped by social structures Thus far, we have developed a clearer idea of the social role ascriptions constituting the MBM

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that lead to JGPGs. However, how are these role ascriptions formed by social contexts? We expect that the relevance of the MBM depends on structural features of the labor market.

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Personal experiences in the labor market could undermine the social role ascription associated

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with the MBM—the belief that only men are responsible for the economic well-being of the family. For example, knowing that female coworkers have earnings that are comparable to those of male coworkers could lead to fewer salient gender-specific role ascriptions and could be associated with a more egalitarian approach with respect to gender differences in earnings. Some findings support this hypothesis. Using nonexperimental data, Valet (2018) finds similar earnings justice attitudes among women and men working in male-dominated occupations, while women working in female-dominated occupations more often consider 9

their lower earnings compared to those of men to be just. Auspurg et al. (2017) show that working in occupations with a lower “objective” gender pay gap is associated with a lower JGPG for male and female respondents. Although these differences in earnings justice attitudes, which reflect the occupational backgrounds of respondents, could not explain the overall JGPG found in the study, they indicate that labor market experiences affect justice ratings of earnings. Moreover, as mentioned above, the values associated with the MBM change slowly

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(Cunningham 2008). Consequently, it can be expected that a long-lasting exposure of a large fraction of the workforce to a more gender egalitarian structured labor market will affect the

prevalence of the MBM more strongly than will shorter exposures to more gender egalitarian

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structures at specific workplaces. In Germany, the labor market strongly differs between the eastern and western federal states with respect to women’s labor market participation and

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gender-related pay regimes (Trappe et al. 2015), facilitating a test of this expectation.

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In the former German Democratic Republic (GDR), the labor market involvement of women was considered a public goal in line with the egalitarian ideology of the state. While reconciling work and family life for women was far from easy, institutions such as day care

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facilities for children were much more common than in the Federal Republic of Germany (FRG) (Bredtmann et al. 2013, Trappe and Rosenfeld 2004). Consequently, labor

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participation and full-time employment rates for women were much higher than in the FRG.

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In addition, not only was female labor force participation more often considered “normal”, but enabling it was also regarded as a public concern much earlier than in the FRG (Trappe and Rosenfeld 2000). Thus, at least in public debate, women and men were considered equal as workers, and therefore, discrimination in payment was not considered legitimate. In contrast, in the FRG, female labor market involvement was seen for a long time as sometimes necessary but unwanted, as it deviated from the norms of the MBM (Rosenfeld et al. 2004, Trappe et al. 2015). The more gender-egalitarian ideology with respect to labor market 10

involvement in the GDR is expected to be consistent with less gendered ascriptions of social roles and smaller JGPGs. Differences in the occupational structure and labor market involvement of women between the eastern and western German federal states still persist (Adler 2004, Kreyenfeld and Geisler 2006, Matysiak and Steinmetz 2008, Trappe and Sørensen 2006).2 The sectoral structure of the western German federal states—especially in the southern part—is strongly focused on private industrial production, including many male-dominated occupations. In

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contrast, the sectoral structure in the eastern German federal states is more characterized by public administration and service industries, which have a less gendered occupational

structure (Fuchs 2018). To the present day, these differences are reflected in gender pay gaps

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(Smolny and Kirbach 2011). Based on the median daily gross earnings of full-time

employees, Fuchs (2018) finds an average gender pay gap of 16% and –2% for, respectively,

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the western and eastern German federal states in 2016. At the level of the federal states, the

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gender pay gap varies between 21% in Baden-Württemberg and –5% in Brandenburg. We assume that these larger gender differences regarding labor market involvement and payment in the western federal states, together with the less gender egalitarian cultural

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tradition of the FRG mentioned above, bring about more strongly gendered social roles. Consequently, this would lead to a lower prevalence of the MBM in the eastern than in the

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western federal states. Since we further presume that the MBM drives JGPGs, we hypothesize

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the following:

Hypothesis 2 (H2). The JGPG will be larger for respondents residing in the western federal states than for respondents residing in the eastern federal states.3

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After reunification, the labor market involvement patterns of women in the eastern German federal states became more similar to those in the western German federal states (Rosenfeld et al. 2004). Please note that our empirical analyses use data from 2008, when differences between the eastern and western states were more marked than at present. 3 Regarding H2, Auspurg et al. (2017), as well as Auspurg et al. (2013), reported lower JGPGs in the eastern than in the western German federal states. However, these differences were not statistically significant, which the authors attributed to problems with the sample size and structure.

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Furthermore, if the MBM is more prevalent in the eastern part of the country, we would not only expect a lower JGPG in the eastern federal states overall but also smaller effects of children in the household and marital status on the JGPG. That is, marital status and number of children might be relevant for earnings justice attitudes in the eastern part of the country, but the presence of children or responsibility for a married partner should not lead to different evaluations of men’s wages compared to women’s wages. This conclusion regarding regional differences in the effects of MBM-related indicators leads to our third hypothesis:

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Hypothesis 3a (H3a). The effect of the vignette dimension number of children on the JGPG will be larger for respondents residing in the western federal states than in the eastern federal states.

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Hypothesis 3b (H3b). The effect of the vignette dimension marital status on the JGPG will be

3. Experimental design and data

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larger for respondents residing in the western federal states than in the eastern federal states.

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For our analyses, we use the SOEP-Pretest 2008. This survey was conducted with a general population household sample. Within sampled households, a person aged 16 or older is

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interviewed (Siegel et al. 2009). The interview comprised a factorial survey experiment on earnings justice attitudes, which can be used to test the hypotheses developed above. In such

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experiments, respondents evaluate a topic of interest that is presented by vignettes that describe hypothetical situations that are assumed to influence this evaluation. In the present

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study, respondents had to rate the fairness of the wages of employed workers. Each respondent rated 25 vignettes that varied along ten different characteristics of hypothetical wage earners. The effects of these vignette characteristics on the ratings reveal the justice principles that are used by the respondents; e.g., respondents who adhere to the MBM will concede higher wages (i.e., will rate higher wages as just) to male respondents with children

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than to male respondents without children (net of the influence of the other characteristics of vignette scenarios). An example vignette is presented in Figure A1 in the appendix. It shows that the response instrument used implements a three-step rating process. First, respondents classify a vignette as either “just” or “unjust”. Second, if they classify it as “unjust”, they categorize it as “unjustly too high” or “unjustly too low”. Third, they are instructed to fill in a number between 1 and 100 expressing the degree of injustice. After a zero is assigned to vignettes

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rated as “just” and the signs are changed for ratings classifying vignettes as “unjustly too low”, all ratings can be expressed on a joint scale ranging from -100 to 100.

The 10 dimensions of the vignettes (Sauer et al. 2009, see Table A1 in the appendix)

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were chosen based on their importance in previous factorial surveys (Alves and Rossi 1978, Jasso 1978, Jasso and Rossi 1977) and other studies (Liebig and Schupp 2005, Hinz and

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Abraham 2005) of justice attitudes regarding earnings. Some implausible combinations of

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levels for the dimensions education, occupation and earnings were excluded from the vignette universe consisting of all combinations of dimensions and levels. Afterwards, a so-called Defficient sample (Dülmer 2007) of 240 vignettes based on algorithms that simultaneously

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maximize orthogonality (low correlation between vignette dimensions) and balance (high variance of levels within vignette dimensions) was drawn. The D-efficiency of the sample

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was larger than 90, which is considered good. The sample was fractionalized into 10 vignette

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decks with 24 vignettes each, and the decks were randomly assigned to respondents.4 The random assignment of the vignette decks to respondents ensures that vignette and

respondent characteristics are independent. The correlations of the vignette dimensions in the sample are shown in Table A2 in the appendix. Overall, these correlations are low. The maximum correlation of the dimensions not affected by the exclusion of implausible

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An additional vignette with two dimensions on migration background was assigned to each deck. 13

combinations is -0.06. These low correlations indicate that the multifactorial design of the experiment worked properly, and consequently, the vignette dimensions are independent of each other. Given this independence and the independence with respect to respondent characteristics, we can identify the causal effects of the vignette dimensions on the respondent’s justice attitudes. For our study, we use all 25 vignettes, rated by 1,066 respondents, but do not analyze the two additional dimensions in the last vignette. Thus, our analysis sample consists of

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26,650 vignette ratings. At the start of the factorial survey module, participants were instructed that the monthly gross earnings stated in the vignettes relate to jobs with a working time of 40 hours per week and had to complete a training vignette together with the

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interviewer. Similar to previous studies, we coded the vignette occupations using the Standard International Occupational Prestige Scale (SIOPS) for our analyses. We employ weights that

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are provided with the data that make the sample representative of the German population aged

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16 and older. Of the respondents, 53% are women, the mean age of respondents is 52 years, and 19% of the respondents live in an eastern federal state. A total of 45% of the men and 43% of the women are currently employed.

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In our study we focus on the dimension vignette gender, which indicates JGPGs, and the two dimensions of the vignettes related to characteristics involved in the MBM. These

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dimensions are number of children, which ranges from zero to four, and marital status, which

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consists of the following three categories: single, married single-earners and married doubleearners. We operationalize the number of children using four indicator variables for one to four children, with zero children as the reference category. Analogously, we operationalize marital status using indicator variables for married single-earners and married double-earners, with singles as the reference category. The person-level explanatory variable we focus on in our analysis is a dichotomous indicator for raters residing in an eastern federal state at the time of the interview. This variable contains no missing values. We test H1a and H1b with 14

two-way interactions between vignette gender and vignette number of children as well as between vignette gender and vignette marital status. H2 is assessed by a two-way interaction between vignette gender and an indicator for respondents living in an eastern federal state. H3a and H3b are tested with three-way interactions among the indicator for respondents residing in an eastern federal state and the variables involved in testing H1a and H1b. < Figure 1 about here > Figure 1 displays the realized vignette rating distribution. The distribution shows three

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major heaps at 0 (vignettes rated as “just”; 34.8% of the ratings), -100 (vignettes rated as “unjustly much too low”; 11.7% of the ratings), and 100 (vignettes rated as “unjustly much too high”; 7.9% of the ratings), as well as several minor heaps (for example, at 50; 5.0% of

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the ratings). Sauer et al. (2014) conduct analyses that show that the less fine-grained vignette ratings causing these heaps are related neither to specific parts of the experiment (for

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example, the beginning or the end) nor to the age or education of respondents. They conclude

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that it is not necessary to implement stepwise or more fine-grained rating instruments in factorial survey experiments, since in most cases, attitudes are not expressed in such detailed ratings. However, contrary to this conclusion, the findings of Sauer et al. (2014) can also be

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interpreted to show that most respondents adapt the granularity of their ratings in a way that matches a stepwise rating process, starting coarsely (which causes the heaps) and adding more

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detail if possible and deemed necessary. The standard tool to analyze factorial surveys—a

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hierarchical linear regression model (Hox et al. 1991)—cannot be used to adequately analyze a multistep rating process that results in a rating distribution with heaps and censoring points.5 4. Methods

Instead, to take into account the three-step rating process and the related heaps in the rating distribution, we analyze these data using a combination of a Craggit model (Cragg 1971) and 5

Alternatively, Sauer et al. (2009) use a multinomial logit model to analyze the earnings justice attitudes in the SOEP-Pretest 2008 data, focusing on the differentiation among “unjustly too low”, “just” and “unjustly too high”. However, such an approach neglects the additional information of the more fine-grained ratings.

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a generalized ordered probit model (Maddala 1983, Williams 2009), which we call the generalized Craggit model.6 < Table 1 about here > In combination, the first and second rating steps classify the justice evaluations into three rather crude categories: earnings rated as “unjustly too low” (< 0), “just” (0) or “unjustly too high” (> 0). To estimate the effects of explanatory variables on this classification, we use a generalized ordered probit model consisting of two probit equations: one differentiating

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between < 0 and ≥ 0 and the other between ≤ 0 and > 0.7 This first ordered categorical part of the generalized Craggit model addresses the heap of “just”-rated (0) vignette scenarios. It facilitates adequate modeling of the latent variance in the “just” category of ratings.

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The third rating step involves more fined-grained ratings. However, our model needs to address the heaps of “unjustly much too low” (-100) and “unjustly much too high” (100)

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ratings in the rating distribution. These heaps represent censoring points: people choose these

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extreme values if they think that the provided scale is not useful to express a gradation of injustice. These vignette scenarios are evaluated as extremely unjust. Consequently, a linear regression of explanatory variables on the gradation of unjustness is only sensible if these

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extreme evaluations are not included. To model this censored rating process, we implement two Craggit models. Each Craggit model consists of two equations: first, a probit equation

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expressing the probability of a rating not being censored (i.e., not being rated -100 or 100);

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and second, a truncated regression equation to analyze the observed variance in the detailed ratings that are not censored (i.e., ratings in ranges ℕ[-99;-1] or ℕ[1;99]). Each of the six equations in the generalized Craggit model has a respondent-level

random intercept; additionally, the model contains the covariances between these random

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Prior research has already used standard Craggit models to analyze factorial surveys with censored vignette rating distributions (Auspurg and Gundert 2015, Groß and Lang 2018). 7 Using such a generalized instead of a standard ordered probit model enables a more flexible specification in which coefficients can differ between thresholds for the different ordered categories (Williams 2009).

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level intercepts.8 Thus, our generalized Craggit model is a specific form of a generalized multilevel structural equation model (GSEM, Rabe-Hesketh et al. 2004), building on earlier GSEMs used to analyze factorial surveys (Lang 2018). Like all GSEMs, the generalized Craggit models support the specification of constraints between parameters. We estimate the six equations and the variance-covariance matrix (COV) of respondent-level intercepts jointly using maximum likelihood. The most parsimonious specification for the COV of our model contains four respondent-level random effects and three significant covariances between these

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effects. More details on the formalities, the parameterization and the estimation of the generalized Craggit model are documented in the method paper accompanying this article (Lang and Groß in press).

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We use two parameterizations of the generalized Craggit model in the remainder of this article. One parameterization implements the parsimonious specification of the COV

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described above and constrains all other parameters except fixed intercepts to be equal across

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equations. We call this parameterization the “constrained generalized Craggit model”. The other parameterization removes the constraints across some equations for the parameters of the vignette dimensions log earnings and the SIOPS. Dropping the constraints on these

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parameters optimizes the fit of the model. Thus, we call this parameterization “optimized generalized Craggit model”.

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Based on the justice evaluation function developed by Jasso (1978, 1996, Jasso and

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Wegener 1997), we convert all coefficients reported in our study to a log-earnings scale using the coefficient of the vignette dimension log earnings as the denominator. Such log earningsscaled coefficients can be used to compare results between experiments with different response instruments and response scales. Moreover, since small differences on a natural-log scale approximate rates (ln(a) – ln(b) ≈ a/b – 1), coefficients can be interpreted as rates or

8

The covariances between respondent-level random intercepts and vignette-level error terms are zero due to the random assignment of vignette decks to respondents (see section 3. Experimental design and data).

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changes in percent (i.e., rates * 100) if the coefficient is not too large (e.g., < 0.2 or smaller than 20%). Consequently, the coefficient of the vignette dimension gender can be interpreted as a percentage estimate of the JGPG, and coefficients of interaction terms involving the vignette dimension gender indicate the percent difference in the JGPG.9 Positive coefficients in our models indicate that respondents consider lower earnings for the respective vignette dimension or respondent characteristic just (i.e., the earnings are rated as unjustly high), while negative coefficients show that they think higher earnings would be justified. Since the effects

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of different vignette dimensions and levels are independent of the experimental design (see section 3. Experimental design and data) we dispense with presenting models that include

different vignette dimensions and levels in a stepwise manner. Instead, we directly show the

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results of models including fixed effects for all vignette dimensions included in the SOEP-

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Pretest 2008. 5. Results

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We present our analysis in three steps. First, we replicate the analysis of Auspurg et al. (2017) and the JGPG in Germany based on the SOEP-Pretest 2008 using our generalized Craggit

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model as well as a standard hierarchical linear model. Second, we test whether indicators related to the MBM—the vignette dimensions number of children and marital status—can

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explain the JGPG in Germany. Third, we assess whether we find differences in JGPGs and in the effects of the indicators related to the MBM on the JGPGs between the eastern and

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western federal states.

5.1. Replication of Auspurg, Hinz and Sauer (2017) and the JGPG in Germany First, Table 2 presents the results of our replication of the analysis of Auspurg et al. (2017) and related estimates of the JGPG in Germany. Comparing the JGPG estimates—the effects associated with the vignette dimension gender—between the columns, we see that the results More sophisticated transformations to express “just gender pay ratios” (Auspurg et al. 2017) or expected fair earnings (Jasso 1996) are also possible in the framework of the justice evaluation function. 9

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we obtained are quite similar to the 8% reported by Auspurg et al. (2017) (see Table 3, column 1). This finding holds regardless of the model specification we used to analyze our data. Using a hierarchical linear model, our estimated JGPG is approximately 7% (≈ 0.074*100; see Table 3, column 3). Based on our generalized Craggit model, it is 6% using the constraint and 5% using the optimized specification (see Table 3, columns 4 and 5).10 < Table 2 about here > Furthermore, also similar to Auspurg et al. (2017), we found no effects of respondent

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gender on the ratings. The effects of the vignette dimension education are weaker than in the base model, with fewer vignette dimensions reported by Auspurg et al. (2017) (see Table 3, column 1). However, these differences largely vanish if we compare our results to a model

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with a similar number of vignette dimensions (see Table 3, column 2). Overall, our analyses

replicated the results of Auspurg et al. (2017) quite well based on a population-representative

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sample. Consequently, we are able to use the robust finding of a JGPG in Germany as a

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starting point to investigate the roles of the MBM in explaining this gap. 5.2. Test of the male breadwinner model explanation Next, Table 3 presents the results of the optimized generalized Craggit model specifications

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testing the influence of the MBM on the JGPG in Germany.11 Model I in Table 3 again shows the JGPG (approximately 5%), as well as the main effects of the family-related vignette

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dimensions number of children and marital status. The results show that respondents consider

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approximately 3% higher earnings to be just for vignette persons with two children compared to childless vignette persons. For vignette persons with four children, this difference

10

In the optimized generalized Craggit model, the effect of the vignette dimension log earnings in the Craggit selection components of the model is about two-thirds as strong (0.676; see Table 3, column 5) as the effect of the vignette dimension log earnings in the generalized ordered probit components, and in the Craggit truncated regression components, it is about two-fifths as strong (0.391; see Table 3, column 5). Also, the effect of the vignette dimension SIOPS is about half as strong in the Craggit components of the model as in the generalized ordered probit components (-0.129 vs. -0.057; see Table 3, column 5). 11 Similar analyses based on standard hierarchical linear models are reported in Table A3 in the appendix. We only refer to those latter estimates in cases of relevant differences compared to the results of the optimized generalized Craggit models.

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compared to vignette persons without children is as large as 7%. Furthermore, respondents prefer approximately 4% higher earnings for married single-earners compared to singles and approximately 5% lower earnings for married double-earners compared to singles. Taken together, these results indicate that the family situation of an employee is relevant for a respondent’s earnings justice attitudes over and above job- and career-related characteristics. The effects of these family-related effects are large enough to potentially account for the JGPG.

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< Table 3 about here > To test for differences in the JGPG by these family-related indicators, Model II in

Table 3 presents estimates of interaction effects between the vignette dimensions gender and

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number of children as well as marital status; a significant interaction effect was found

between gender and number of children. Respondents consider approximately 7% higher

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earnings for male vignette persons with two children—and approximately 13% higher

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earnings for male vignette persons with four children—than for male vignette persons without children to be just. For female vignette persons, the effects of the vignette dimension on children’s earnings justice attitudes are much closer to zero and are nonsignificant. These

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differences in the valuation of vignette children by vignette gender translate into a JGPG of approximately 8% for vignette persons with children, while there is no JGPG for childless

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vignette persons. Thus, only men who are responsible for children should earn more than

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women. Moreover, the effect of being a married single-earner compared to a single person on earnings justice attitudes is slightly weaker for female compared to male vignette persons, while the effect associated with being a married double-earner is slightly stronger. However, both of these differences are not significant. The finding indicates that married single-earners should earn more to provide for their partners and families, irrespective of their gender. In sum, the results of Model II in Table 3 clearly support H1a: The JGPG is larger for vignette scenarios with more as opposed to fewer or no children, and this difference is large 20

enough to account for the overall JGPG in Germany. H1b, on the other hand, is rejected. There are no substantial differences in the JGPG by marital status. However, the large differences in the JGPG by the number of children indicate that the MBM explanation is highly relevant for the JGPG in Germany. Respondents consider higher earnings for men with children to be just, since children are indicative of their role as the material provider for their family. For women, we find no comparable effect because women are not considered material providers in the context of the MBM.12

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5.3. Regional differences in the just gender pay gap and the male breadwinner model We start this section with estimates of the overall difference in earnings justice attitudes

between respondents living in the eastern and western federal states of Germany. All models

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in Table 3 indicate that respondents from the eastern federal states consider lower earnings to be just, specifically, approximately 7% lower earnings according to Models I and II and

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approximately 12% lower earnings based on Model III. This difference in earnings justice

eastern federal states.

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attitudes can be rationalized by the average lower wage levels and lower costs of living in the

Next, we assess how far the JGPG and the effects of the family-related vignette

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dimensions number of children and marital status differ between the eastern and western federal states (see Model III in Table 3). The results show a significant difference in the effect

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of the vignette dimension gender between respondents in the eastern and western federal

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states. While there is a JGPG of approximately 6% for raters living in the western federal states, there is no relevant JGPG for raters living in the eastern federal states.13 This result indicates support for H2: The JGPG tends to be larger for respondents residing in the western

12

These conclusions about the relevance of the MBM-explanation are not dependent on the type of model we use. The findings are similar using standard hierarchical linear models (see Model II in Table A1 in the appendix). 13 Based on a standard hierarchical linear model (see Model II in Table A3 in the appendix), the JGPG is approximately 8% and significant for the western federal states and approximately 3% and not significant for the eastern federal states. In contrast to the optimized generalized Craggit model, this regional difference in the JGPG is not significant.

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federal states than for those residing in eastern federal states. Furthermore, we find no significant regional differences in the effects of the vignette dimensions number of children and marital status on earnings justice attitudes. < Table 4 about here > The larger JGPG in the western than in the eastern federal states indicates potential regional differences in the relevance of the MBM for the JGPG in Germany (see H3a and H3b). We test the related hypotheses using three-way interaction terms between an indicator

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for respondents living in the eastern federal states, the vignette dimension gender and the family-related vignette dimensions number of children and marital status. The results of this analysis are presented in Table 4.14

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The findings for respondents residing in the western federal states are similar to those of the model without regional differentiation (see Model II in Table 3). While there is a JGPG

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of approximately 8% for vignette persons with children, there is no JGPG for childless

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vignette persons. In contrast, we find less pronounced differences by vignette gender in the effects of the vignette dimension number of children for respondents living in the eastern federal states. Here, the results show that raters prefer higher earnings for both male and

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female vignette persons with children compared to vignette persons without children. The effects of the vignette dimension number of children tend to be slightly larger for male

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vignette persons (also in comparison to raters residing in the western federal states). However,

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in contrast to the findings for the western federal states, these differences are not significant and do not indicate a substantial JGPG.15 This result is in line with H3a: Differences in the JGPG by the vignette dimension

number of children are larger for respondents residing in the western federal states. This 14

An additional analysis based on a standard hierarchical linear model is show in Table A4 in the appendix. We only refer to those latter estimates in cases of relevant differences compared to the results of the optimized generalized Craggit model. 15 These nonsignificant differences in the JGPG are not only due to the larger standard errors based on the smaller number of respondents from the eastern than from the western federal states, but the point estimates of these differences are also much smaller for the eastern federal states (see Table 4).

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finding indicates that the MBM is of larger relevance in the western federal states and further supports the conclusion that the MBM is the critical factor explaining the JGPG in Germany. However, we cannot replicate this finding using a standard hierarchical linear model (see Table A4 in the appendix). Using this model, which ignores the heaps in the vignette rating distribution, we find substantial and significant differences in the JGPG by the vignette dimension number of children not only for respondents living in the western federal states but also for respondents living in the eastern federal states. Consequently, our conclusion about

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regional differences in the relevance of the MBM depends on the use of the generalized Craggit model, which takes the three-step rating process in the SOEP-Pretest 2008 into account.

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Furthermore, like H1b, H3b is also rejected. In contrast, we find that raters living in

the eastern federal states consider higher earnings for married single women to be just, but not

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for married single men (see Table 4). However, we cannot replicate this result using a

the appendix).

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6. Conclusion and discussion

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standard hierarchical linear model instead of the generalized Craggit model (see Table A4 in

In this paper, we analyzed how far the MBM—the belief that men should provide for the

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material needs of their family while women should take care of the household and children— can account for the JGPG in Germany. We test this idea with the factorial survey

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implemented in the population-representative sample of the SOEP-Pretest 2008 using the family-related vignette dimensions number of children and marital status as indicators. Our findings clearly show that the JGPG in Germany can be explained by the MBM. While respondents support a JGPG of approximately 8% for vignette persons with children, there is no JGPG for childless persons. In contrast to previous studies that used gender-specific status

23

beliefs as a “residual explanation” for a persistent JGPG, our study is the first to demonstrate the relevance of the MBM for the JGPG in Germany. It could be argued that the gendered social role ascriptions involved in the MBM might be accompanied by attributing a lower status to women. In general, our results do not support such a conclusion, since respondents do not consider lower earnings for childless women to be just. However, to more specifically assess how far the role ascriptions of the MBM are associated with gender-specific status beliefs, more direct measures of the attitudes

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involved in both constructs are needed. Moreover, only scenarios with full-time employment (40 hours per week) are considered in the vignette experiment we analyze. Consequently, we cannot test whether the effects of labor market involvement on earnings justice attitudes differ

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by vignette gender in this study. Since the gendered expectations regarding labor market involvement are an important component of the MBM, an extension including a related

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indicator would surely be useful to capture possible influences of the MBM on JGPGs more

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comprehensively.

Furthermore, we looked at the influence of macro-level societal contexts on the relevance of the MBM explanation. Specifically, we tested whether we find a smaller JGPG

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in the eastern federal states than in the western federal states of Germany. This part of the study was motivated by the assumption that a more gender-egalitarian structure of the labor

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market, as well as a stronger labor market involvement of women in the eastern part of

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Germany, would undermine the power of the MBM, thus diminishing the JGPG. Indeed, our analyses show a JGPG of approximately 6% in the western federal states, while there is no substantial JGPG in the eastern federal states. Moreover, our results indicate a lower relevance of the MBM for earnings justice attitudes in the eastern federal states, as the JGPG for vignette persons with children is smaller compared to western federal states. However, we cannot replicate this finding using a standard hierarchical linear model instead of the

24

generalized Craggit model that we developed and implemented to account for the heaps and censoring in the vignette rating distribution of the SOEP-Pretest 2008. Previous studies have shown that the effects of explanatory variables related to vignette dimensions, which are set by the experimental design, are often robust even if a rating distribution does not match the assumption of a linear regression (Auspurg and Hinz 2015, Lang 2018). In contrast, respondent-related explanatory variables—which are not set by the experimental design—are more susceptible to bias. This also seems to be the case in our

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study. While the effects involving only vignette gender, vignette number of children and vignette marital status are similar using both models, conclusions about effects involving the indicator for respondents living in Eastern federal states depend on the type of model used.

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However, given the vignette rating distribution of the SOEP-Pretest 2008, the generalized

Craggit model is clearly fitting the data better (Lang and Groß in press), and our conclusions

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about the overall relevance of the MBM explanation do not depend on the model used.

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A further limitation of our study with respect to the comparison between the eastern and western federal states is the relatively low number of respondents from the eastern federal states (205 persons). The small sample implies less precise estimates, especially for the part of

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the study that additionally differentiates by vignette gender (see Table 4 and Table A4 in the appendix). While the sample is representative of the German population, an oversampling of

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respondents living in the eastern federal states would have been better for this specific

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analysis. In addition, we cannot definitely preclude that the different JGPGs in the eastern and western federal states result from differences in labor market involvement and structures. As reported above, previous studies show that earnings justice attitudes differ by occupational characteristics (Auspurg et al. 2017, Valet 2018). However, other than that, previous research does not find that respondent’s labor market involvement affects JGPGs (Auspurg et al. 2017, Sauer et al. 2009). Moreover, in our opinion, different labor market involvement or structures cannot account for the differential effects of the family-related vignette dimensions in the 25

eastern and western federal states. Finally, to assess the influence of labor market involvement or structures on the prevalence or relevance of the MBM, future studies that include direct measures of the attitudes involved in the MBM are needed. Despite these limitations, our study still clearly demonstrates the relevance of the MBM for earnings justice attitudes and the JGPG in Germany. With respect to policy implications, these findings indicate that efforts focusing on workplaces and related equal pay might not be sufficient to close the gender pay gap, which partly is due to different earnings

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justice attitudes.16 If the aim is to also address this part of the gender pay gap, we must also examine family policies. Specifically, related policies must take into account how financial or other incentives offered foster or undermine the gendered social role ascriptions of the MBM.

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Our study notes that policies that undermine gender-specific role ascriptions with respect to

labor market involvement and family responsibilities can sustainably affect gender pay gaps.

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Finally, social role ascriptions change slowly and partly only over generations

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(Cunningham 2008). Therefore, the effects of policies aimed at changing those ascriptions can only be seen after longer periods of time. This must be taken into account in evaluations of related policy measures. Moreover, thus far the MBM is grounded in macro-level societal

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contexts single or limited policy measures might be ineffective. In this context, it should be noted that our analyses are based on data from 2008. It would be interesting to see if and how

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generational change and related policy measures over the last decade have influenced

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attitudes related to the MBM and the JGPG. Moreover, it would be fruitful to compare the German case analyzed in this study with other countries.

Declarations of interest None.

If and how JGPGs affect “objective” gender pay gaps is an area of ongoing research. However, Auspurg et al. 2017 have already shown that “objective” gender pay gaps have an effect on JGPGs. 16

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Acknowledgements We like to thank two anonymous reviewer, the participants of the ISA RC28 Spring Meeting 2019 in Frankfurt a. M. (Germany), especially Katrin Auspurg and Carlo Barone, and the participants of the workshop „Educational policies, processes and social inequalities“ in 2017 at Tübingen University (Germany), especially Herman van de Werfhorst, for very helpful comments on earlier versions of this paper. Furthermore, we are very grateful to all

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researchers and other persons involved in developing and implementing the factorial survey

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module in the SOEP-Pretest 2008.

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breadwinner model: Institutional underpinnings and future expectations. European Sociological Review 31(2):230–242. Trappe, H. & Rosenfeld, R. A. (2000). How do children matter? A comparison of gender earnings inequality for young adults in the former East Germany and the former West Germany. Journal of Marriage and Family 62:469–507.

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Trappe, H. & Sørensen, A. (2006). Economic relations between women and their partners: An East and West German comparison after reunification. Feminist Economics 12(4):643–665. Valet, P. (2018). Social structure and the paradox of the contented female worker: How occupational gender segregation biases justice perceptions of wages. Work and Occupations 45(2):168–193. Wegener, B. (1999). Belohnungs- und Prinzipiengerechtigkeit: Die zwei Wege der

Druwe, U. & Kunz, V. Opladen: Leske & Budrich-Verlag.

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empirischen Gerechtigkeitsforschung. Pp. 167–214 in Politische Gerechtigkeit, edited by

Williams, R. (2009). Using heterogeneous choice models to compare logit and probit

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coefficients across groups. Sociological Methods and Research 37(4):531–559.

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Figures

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Figure 1. Distribution of vignette ratings in the SOEP-Pretest 2008

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Tables

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Table 1. Translation of rating steps in SOEP-Pretest 2008 into a generalized Craggit model 1st and 2nd rating step: “unjustly too low” (< 0) vs. “just” (0) vs. “unjustly too high” (> 0) → Generalized ordered probit model: Equation 1 (Probit model): “unjustly too low” (< 0) vs. “just or unjustly too high” (≥ 0) Equation 2 (Probit model): “unjustly too low or just” (≤ 0) vs. “unjustly too high” (> 0) 3rd rating step given that rating after 2nd rating step was “unjustly too low” (< 0) → 1st Craggit model: Equation 3 (Probit model): “unjustly much too low” (-100) vs. “unjustly too low” (ℕ[-99;-1]) Equation 4 (Truncated regression model): Detailed ratings in range ℕ[-99;-1] 3rd rating step given that rating after 2nd rating step was “unjustly too high” (> 0) → 2nd Craggit model: Equation 5 (Probit model): “unjustly much too high” (100) vs. “unjustly too high” (ℕ[1;99]) Equation 6 (Truncated regression model): Detailed ratings in range ℕ[1;99]

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Constrained generalized Craggitc

Optimized generalized Craggitc

b / c.s.e.

b / c.s.e.

0.064*** (0.011) 1 (scale anchor) . . . . -0.025*** (0.004) -0.094*** (0.014) -0.148*** (0.014) -0.124*** (0.004) . . -0.020*** (0.003) 0.129*** (0.013) -0.092*** (0.012) -0.026* (0.012) -0.037** (0.013) -0.050*** (0.014) -0.065*** (0.013)

0.047*** (0.009) 1 (scale anchor)d 0.676*** (0.029) 0.391*** (0.018) -0.020*** (0.003) -0.068*** (0.011) -0.115*** (0.011) -0.129*** (0.004) -0.057*** (0.004) -0.017*** (0.003) 0.098*** (0.011) -0.070*** (0.010) -0.020* (0.010) -0.025* (0.011) -0.048*** (0.011) -0.059*** (0.010)

-0.003 (0.019) 26,650 1,066

-0.004 (0.015) 26,650 1,066

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Table 2. Replication of analyses of earnings justice attitudes.a Auspurg et Auspurg et Hieraral. (2017), al. (2017), chical Table 3, Table 5, linearc column 1 column 1b b / c.s.e. b / c.s.e. b / c.s.e. Vignette level: women 0.081*** 0.096*** 0.074*** (0.007) (0.022) (0.012) (€-)log-earnings 1 (scale 1 (scale 1 (scale anchor) anchor) anchor) Craggit selection . . . . . . Craggit truncated . . . regression . . . age (in 10 years) -0.024*** -0.018*** -0.025*** (0.003) (0.007) (0.004) vocational traininge -0.139*** -0.098*** -0.084*** (0.009) (0.015) (0.014) university degreee -0.220*** -0.165*** -0.140*** (0.009) (0.016) (0.014) SIOPS (in 10 points) -0.158*** -0.132*** -0.119*** (0.002) (0.004) (0.004) Craggit . . . . . . number of children . -0.031*** -0.020*** (0 to 4) . (0.004) (0.003) below average . 0.135*** 0.137*** f performance . (0.022) (0.014) above average . -0.136*** -0.073*** f performance . (0.022) (0.013) medium sized . -0.021 -0.034* g employer . (0.015) (0.014) g big employer . -0.021 -0.037** . (0.015) (0.014) solid economic . -0.076*** -0.052*** situationh . (0.015) (0.014) h high profit situation . -0.097*** -0.061*** . (0.015) (0.013) Respondent level: women ~0 . -0.007 (0.029) . (0.017) Nvignettes 26,207 8,792 26,650 Nrespondents 1,604 545 1,066

All coefficients are scaled in (€-)log-earnings and standard errors are clustered on respondent level. Interaction terms between vignette gender and vignette performance not presented. c Model includes fixed effects for all vignette dimensions and differences between vignette decks. d Vignette log-earnings effect of the generalized ordered probit-part of the model used as scale anchor. Reference categories: e no degree, f average performance, g small employer, h threatened by bankruptcy Sources: Auspurg, Hinz, and Sauer (2017) and own calculations based on SOEP-Pretest 2008 † p < 0.10; * p < 0.05; ** p < 0.01; *** p < 0.001 a

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Table 3. Optimized generalized Craggit models of earnings justice attitudes.a Model I Model II Model III Vignette gender: Person federal state: men women JGPG western eastern b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. Vignette level: women 0.051*** . . . 0.063*** -0.009 (0.010) . . . (0.010) (0.028) no children . . -0.018 0.018 . . and single . . (0.021) (0.021) . . b one child -0.016 -0.053** 0.020 0.074** -0.014 -0.027 (0.012) (0.017) (0.019) (0.025) (0.014) (0.025) b two children -0.025* -0.066*** 0.014 0.080** -0.018 -0.060* (0.012) (0.017) (0.019) (0.027) (0.013) (0.029) b three children -0.049*** -0.085*** -0.015 0.070* -0.041** -0.092** (0.012) (0.018) (0.018) (0.028) (0.013) (0.030) four childrenb -0.073*** -0.125*** -0.024 0.101*** -0.072*** -0.083* (0.014) (0.018) (0.020) (0.026) (0.015) (0.041) married, -0.040*** -0.055*** -0.028* 0.027 -0.41*** -0.033 c single earner (0.009) (0.013) (0.014) (0.019) (0.010) (0.026) married, 0.045*** 0.035* 0.053** 0.018 0.045** 0.045† c double earner (0.012) (0.016) (0.016) (0.021) (0.013) (0.024) Person level: eastern federal 0.065** 0.065** . . 0.118** state (0.023) (0.023) . . (0.039) All coefficients are scaled in (€-)log-earnings, standard errors are clustered on respondent level and models include fixed effects for all vignette dimensions and differences between vignette decks. Reference categories: b no children, c single Sources: Own calculations based on SOEP-Pretest 2008 (Nvignettes = 26,650; Nrespondents = 1,066) † p < 0.10; * p < 0.05; ** p < 0.01; *** p < 0.001

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Table 4. Optimized generalized Craggit models of earnings justice attitudes (continued).a Person western federal state Person eastern federal state Vignette gender Vignette gender men women JGPG men women JGPG b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. Vignette level: no children . -0.003 0.003 . -0.085 0.085 and single . (0.024) (0.024) . (0.052) (0.052) b one child -0.048* 0.014 0.062* -0.090* -0.057 0.034 (0.019) (0.024) (0.026) (0.038) (0.054) (0.052) b two children -0.058** 0.015 0.073** -0.126*** -0.095† 0.031 (0.020) (0.023) (0.025) (0.032) (0.055) (0.063) b three children -0.072*** -0.018 0.054† -0.161*** -0.121† 0.041 (0.021) (0.025) (0.025) (0.045) (0.062) (0.071) b four children -0.124*** -0.031 0.93*** -0.154** -0.104 0.051 (0.020) (0.026) (0.026) (0.048) (0.089) (0.083) married, -0.060*** -0.027 0.033 -0.031 -0.126** -0.095* c single earner (0.014) (0.023) (0.023) (0.035) (0.048) (0.039) married, 0.035† 0.058* 0.022 0.057† -0.044 -0.100† c double earner (0.019) (0.024) (0.025) (0.033) (0.042) (0.055) Person level: eastern federal . . 0.129*** . state . . (0.042) . All coefficients are scaled in (€-)log-earnings, standard errors are clustered on respondent level and models include fixed effects for all vignette dimensions and differences between vignette decks. Reference categories: b no children, c single Sources: Own calculations based on SOEP-Pretest 2008 (Nvignettes = 26,650; Nrespondents = 1,066) † p < 0.10; * p < 0.05; ** p < 0.01; *** p < 0.001

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Appendix

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Source: Sauer, Liebig, Auspurg, Hinz, Donaubauer, and Schupp (2009)

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Table A1. Dimensions and levels of the factorial survey in the SOEP-Pretest 2008.

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Table A2. Correlations of the dimensions of the factorial survey in the SOEP-Pretest 2008.

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MPS: Magnitude Prestige Score as measure of occupational prestige. Source: Sauer, Auspurg, Hinz, Liebig, and Schupp (2014)

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Figure A1. Translation of an example vignette from the SOEP-Pretest 2008.

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Model III Person federal state: western eastern b / c.s.e. b / c.s.e. 0.082*** (0.013) . . -0.039* (0.017) -0.033* (0.016) -0.043** (0.015) -0.091*** (0.018) -0.45** (0.013) 0.065*** (0.018)

0.034 (0.027) . . -0.038 (0.033) -0.084* (0.033) -0.102** (0.035) -0.076† (0.041) -0.043 (0.028) 0.045 (0.032)

. .

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Table A3. Hierarchical linear models of earnings justice attitudes.a Model I Model II Vignette gender: men women JGPG b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. Vignette level: women 0.074*** . . . (0.012) . . . no children . . 0.022 -0.022 and single . . (0.024) (0.024) b one child -0.039* -0.072** -0.006 0.066* (0.015) (0.021) (0.022) (0.030) b two children -0.042** -0.098*** 0.012 0.110** (0.014) (0.021) (0.023) (0.034) b three children -0.053*** -0.083*** -0.023 0.060* (0.014) (0.022) (0.019) (0.030) b four children -0.088*** -0.128*** -0.049* 0.079* (0.017) (0.022) (0.024) (0.033) married, -0.045*** -0.049** -0.043* 0.006 c single earner (0.012) (0.017) (0.017) (0.024) married, 0.062*** 0.065** 0.057** -0.009 c double earner (0.016) (0.021) (0.021) (0.027) Person level: eastern federal 0.090*** 0.090*** . state (0.023) (0.024) .

All coefficients are scaled in (€-)log-earnings, standard errors are clustered on respondent level and models include fixed effects for all vignette dimensions and differences between vignette decks. Reference categories: b no children, c single Sources: Own calculations based on SOEP-Pretest 2008 (Nvignettes = 26,650; Nrespondents = 1,066) † p < 0.10; * p < 0.05; ** p < 0.01; *** p < 0.001

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Table A4. Hierarchical linear models of earnings justice attitudes (continued).a Person western federal state Person eastern federal state Vignette gender Vignette gender men women JGPG men women JGPG b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. b / c.s.e. Vignette level: no children . 0.024 -0.024 . 0.007 -0.007 and single . (0.027) (0.027) . (0.046) (0.046) b one child -0.073** 0.019 0.092** -0.071† -0.003 0.068 (0.024) (0.028) (0.031) (0.042) (0.066) (0.073) b two children -0.085*** 0.040 0.125*** -0.161*** -0.002 0.159* (0.024) (0.028) (0.032) (0.043) (0.056) (0.075) b three children -0.066** 0.005 0.071* -0.165*** -0.033 0.132* (0.024) (0.028) (0.035) (0.047) (0.055) (0.059) b four children -0.127*** -0.031 0.096** -0.137* -0.010 0.127 (0.023) (0.032) (0.035) (0.059) (0.066) (0.080) married, -0.055** -0.012 0.043† -0.016 -0.064 -0.048 single earnerc (0.018) (0.026) (0.026) (0.043) (0.042) (0.051) married, 0.059* 0.094** 0.035 0.094** 0.001 -0.092† c double earner (0.024) (0.029) (0.030) (0.035) (0.052) (0.056) Person level: eastern federal . . 0.121** . state . . (0.040) . All coefficients are scaled in (€-)log-earnings, standard errors are clustered on respondent level and models include fixed effects for all vignette dimensions and differences between vignette decks. Reference categories: b no children, c single Sources: Own calculations based on SOEP-Pretest 2008 (Nvignettes = 26,650; Nrespondents = 1,066) † p < 0.10; * p < 0.05; ** p < 0.01; *** p < 0.001

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