Artículo de revista: Esping-Andersen, Gøsta; Boertien, Diederik; Giorg, Julien (2022) “Social Mobility and Partnering. The Salience of Mobility Homogamy.” Social Science Research, November, 102812. (ISSN 1096-0317) https://doi.org/10.1016/j.ssresearch.2022.102812. Social Mobility and Partnering. The Salience of Mobility Homogamy Gosta Esping-Andersen, Diederik Boertien & Julien Giorgi Abstract Does the experience of social mobility influence one’s choice of a partner? If so, are the socially mobile more likely to partner with someone from their origin or destination class? Or, if torn between the familiarity of their origin milieu and their possibly less known destination, do they opt for ‘mobility homogamy’, i.e. choosing a partner who is likewise mobile? The impact of social mobility on partner choice has received scant scholarly attention and, yet, it is an issue that should enhance our understanding of partnering dynamics. Exploiting the German SOEP panel, we find that the socially mobile are more likely to match with someone from their destination- rather than origin class. This suggests that the influence of destination-class conditions outweighs that of one’s social origin. Nonetheless, our principal finding is that once we include also the partner’s mobility history, it turns out that the upwardly mobile partner disproportionally with someone who is similarly upwardly mobile. Our analyses provide scant support for the social exchange thesis, according to which a high-status social origin is traded for the socioeconomic promises linked to upward social mobility. Instead, the dynamics we uncover are likely to be primarily driven by social networks, individuals’ resources, and a general preference for homogamy. 1 Introduction Socioeconomic homogamy, the tendency to partner with someone who is similar to oneself in terms of socioeconomic characteristics, is often used by stratification scholars as an indicator of social closure (Hout, 1982; Smits et al., 1998; Ultee & Luijkx, 1990). High levels of homogamy based on education or social class should signal the presence of significant social (and physical) distances between social strata. If society is deeply divided, this is likely to spill over to the intimate sphere of partner selection. Several studies have shown that homogamy is indeed related to a society’s degree of social mobility; i.e. when social mobility levels are high, educational homogamy is less pronounced. This suggests that both measures can help identify the extent to which a country is socially stratified (Katrňák et al., 2012; Ultee & Luijkx, 1990). However, the link between social mobility and socioeconomic homogamy is not straightforward since they may capture distinct social barriers (Katrňák et al., 2012; Ultee & Luijkx, 1990). The former indicates the extent to which social origins influence one’s life chances. In contrast, homogamy based on, for example, education level, captures a life course attainment – namely partner choice. In contrast, homogamy based on social origins might be more akin to measures of social mobility than is homogamy based on social destination attributes, be they education, income, or social class. But, most research on homogamy has focused on achieved characteristics, primarily education (De Hauw, et al., 2017; Fu & Heaton, 2008; Kalmijn, 1991; Katrňák et al., 2006; Rosenfeld, 2008; Schwartz and Mare, 2005). Our study contributes to a comparatively limited literature which focuses on the role of social origins in partner selection (Blau and Duncan, 1967; Blossfeld and Timm, 2003; Bozon, 1991; Henz & Mills, 2018; Mäenpäa and Jalovaara, 2015). But ours’ takes it one step further by identifying homogamy based on origin as well as destination, i.e. homogamy derived from the social mobility experience of both partners. We pose three main questions: How much does social origin matter for partner selection? What is its relative influence when compared to that of one’s social destination? And, under what conditions do partners select each other on both social origin and destination? In other words, do the socially mobile select similarly mobile partners? 2 Studying homogamy through the lens of intergenerational social mobility contributes to our understanding of social stratification in a variety of ways. Firstly, the extent to which a high level of homogamy based on social destination nurtures social divisions will depend on whether citizens match also on their social origins. If two partners with a similar social destination differ in terms of social origin, their partnership connects two families of a different socioeconomic standing. If the partners share a similar social origin, homogamy based on social mobility can be another mechanism which solidifies the intergenerational transmission of social class. And this may have adverse consequences for inequality (Schwartz, 2013): more couples are formed with a maximum level of socioeconomic resources when both partners represent high social destinations and high social origins (or vice versa for couples formed on the basis of meager resources). Studying the socially mobile also helps us understand better the mechanisms influencing partner selection. Homogamy is very much driven by the inclination to favour a partner who resembles oneself in terms of cultural outlook, tastes, and socioeconomic characteristics (DiMaggio & Mohr, 1985; Oppenheimer, 1977; Mare, 1991; Schwartz, 2013). We can think of this as a competing ‘risks’ scenario: is the upwardly mobile woman more likely to partner with someone from her origin class or someone from the more advantaged destination class? The upwardly mobile may very well find themselves torn between their origin and destination identities and milieu (Stacey, 1967; Tooth and Mishra, 2012; Wickrama et.al, 2016). If similarity of social identity is of significance, we might alternatively find that the upwardly (and downwardly) mobile will partner with someone from their origin class who is likewise upwardly (downwardly) mobile. To exemplify, the daughter of working-class parents who attains higher education would then partner with a working-class son who similarly makes it into a university. Social mobility may also promote non-partnering.1 Remaining single should be more likely among highly educated, upwardly mobile women and among downwardly mobile men. In the former case, this may be due to stress and anxiety (see below), or to gender asymmetries in university level educational attainment; in the latter case, downwardly mobile men are 1 King (2021) finds that upwardly mobile women (but not men) are significantly less likely to marry. 3 likely to be unattractive marriage prospects for women from their more advantaged origin class (Esping-Andersen, 2016; McLanahan, 2004). Nation-specific institutional characteristics undoubtedly influence the link between social mobility and partnering. Education systems play the double role of affecting social mobility (e.g. via tracking) while they also act as marriage markets. And societies differ in terms of the age of transition into independent living. This, in turn, may influence the likelihood that a mobile person partners with someone from one’s origin rather than destination class. And we would expect that marriage markets are less socially exclusive in high-mobility societies (such as Scandinavia) than in low-mobility ones (e.g. Italy).2 Our analyses are based on Germany, a country characterized by early educational tracking and, comparatively, rather modest levels of intergenerational social mobility (Esping-Andersen and Cimentada, 2018). Theoretical framework and hypotheses Research has shown that partners select each other based on achieved resources such as education, occupation or income (Blossfeld, 2009; Schwartz, 2013). The tendency towards socioeconomic homogamy can arise because there are benefits related to having a partner with similar resources, preferences, and lifestyles (DiMaggio & Mohr, 1985; Oppenheimer, 1977). Socioeconomic resources influence tastes and interests which, in turn, should promote spending time together and planning life as a couple. However, homogamy can also arise because individuals look for partners with abundant resources (Mare, 1991; Schwartz, 2013). In that case, homogamy ensues when resourceful individuals partner with each other, and this similarly so for those with fewer resources. Hence, if individuals match on expected or actually achieved resources, social mobility will influence partnering via attained income or social class position. Some theories argue that the influence of social origin should decline with modernization, since achievements become more important than ascribed characteristics for life outcomes (Kalmijn, 1998). And with more individualization, the influence of third parties (e.g. parents) 2 For recent evidence, see Blanden (2011) and Esping-Andersen and Cimentada (2018). Geographic mobility may also play a role; where, as in Italy, offspring typically live physically close to their parents one might expect more ‘origin partnering’. This would be an interesting topic for future research. 4 on partner selection should decline (Rosenfeld and Kim 2005). Many studies that identify increasing educational homogamy levels cite this as evidence that achieved characteristics have indeed gained more weight. However, only a few studies have investigated how homogamy based on social origin develops. These find that social origin remains important for partner selection and that its impact has changed relatively little over time (Henz & Mills, 2018; Mäenpäa & Jalovaara, 2015). Why would social origin remain important for partner selection? Firstly, the mobility experience per se can influence partner preferences. Studies of health, mortality and fertility have shown that inter-generational mobility can promote stress and anxiety, in particular among the upwardly mobile (Stacey, 1967; Tooth and Mishra, 2012; Wickrama et.al, 2016; but see Chan, 2018). Kessin (1971) identified a significant increase in anxiety among the highly upwardly and downwardly mobile. This was ascribed to becoming detached from one’s family, friends, and social milieu which, in turn, might reduce the likelihood of finding a partner, and in particular a partner with certain desired characteristics. However, the resources that higher levels of education and occupation provide, as well as the greater independence of higher educated individuals from their origin families, should increase the possibility for the upwardly mobile to partner across social statuses (Kalmijn, 1998). Secondly, the socially mobile might prefer a partner with the exact same social mobility experience because both social origin and destination influence our preferences and lifestyle. Since cultural capital (Bourdieu, 1986) can be decisive in mate selection, the socially mobile might look for someone from a similar cultural background (Schwartz, 2013; see also Mare, 1991). Thirdly, social mobility can affect the attractiveness of individuals through the resources that social origin provides. A high-status origin is a resource that may exceed one’s own career potential. Bozon (1991) shows for instance that marriage can dampen the effects of downward mobility on socioeconomic status. For instance, downwardly mobile women with parents of high social status regularly marry men of high social status. Blackwell (1998) shows that women’s likelihood of marrying highly educated men depends also on their social class origin. 5 These three arguments all predict that social origin remains important for spousal matching in today’s societies. This leads us to our first hypothesis: Hypothesis 1: Social origin matters for partner selection net of social destination. A core tenet within the vast intergenerational social mobility literature is that social origins are decisive for key outcomes in life.3 However, the studies of Kalmijn (1991; 1998) and Blossfeld and Timm (2003) emphasize that marital sorting occurs increasingly within educational institutions, and is evermore less influenced by religion or one’s cultural and family background. We can test the relative importance of social origin and destination for partnering by studying socially mobile individuals. Since their social origin differs from their destination, they provide a test-case for the relative weight of either in partner selection. Blau and Duncan (1967) showed how educational attainment was more important than social background when choosing one’s partner in the U.S. But it is unclear whether this holds in today’s Germany, the country of our study. Since we study a more recent context, we expect that: Hypothesis 2: Socially mobile individuals are more likely to select partners who match on social destination rather than on social origin. The mechanisms outlined above also provide more precise predictions regarding the kind of partner individuals select. If individuals select partners with similar life experiences or with abundant resources, we would in either case expect the socially mobile to partner with similarly mobile individuals. This expectation is further supported by studies which focus on social networks and opportunities to meet partners. Blau and Duncan’s (1967) social network hypothesis is particularly relevant for the impact of social mobility on the opportunities to 3 For recent systematic reviews of the literature, see OECD (2018) which focuses primarily on intergenerational income mobility; Bernardi and Ballarino (2016), Breen and Muller (2020), and Macmillan and Sibieta (2020) provide up-to-date and comprehensive reviews of sociological research on class mobility and on social origin effects on educational attainment. See also Bukodi and Goldthorpe (2021). 6 meet people from different social backgrounds. Socially mobile individuals are likely to be embedded in social networks from both their origin and destination class. Blossfeld and Timm (2003) present comparative evidence of how social origin influences marital choices. Their main finding is that the higher one’s parent’s education, the more one’s social networks become exclusive. And this should promote educational homogamy among the children. But if more children of low-SES origin obtain higher education, this could foster greater contact between persons of different social origin, thus lowering the socio-cultural barriers between classes. If so, the influence of parents’ social status should diminish across birth cohorts. This should especially be the case where education systems are more inclusive, and less so where tracking occurs early. Our study focuses on Germany where tracking occurs very early. We therefore expect social origin to remain relevant in our context and furthermore expect that: Hypothesis 3a: Socially mobile individuals have an increased chance of partnering other socially mobile individuals with a similar origin and destination class. However, preferences for a resourceful partner may lead to a very different prediction. One strand of social exchange theory argues that individuals look for partners whose resources are complementary to their own (Rosenfeld, 2005; Kalmijn, 2010; Sassler & Joyner, 2011; Schwartz et al., 2016). For example, a wealthy person lacking cultural capital might look for a well-educated rather than wealthy partner. There are different advantages related to social origin and destination that could spur individuals to look for such a status exchange. Having high status in-laws can provide crucial networks and resources (e.g. wealth) that individuals do not have themselves, especially at younger ages when most relationships are formed. Hence, the upwardly mobile may prefer partners with high status parents so as to gain access to resources that promote their career prospects. Existing research has not produced unequivocal evidence for the salience of social exchange in partner selection (Rosenfeld, 2005; Kalmijn, 2010; Sassler & Joyner, 2011; Schwartz et al., 2016). However, if social exchange predictions hold, we would expect that: Hypothesis 3b: Socially mobile individuals have an increased chance of partnering with individuals who differ from themselves in terms of origin and/or destination class. 7 There are a few considerations that must be considered before moving to empirical estimation. Singlehood is of course an alternative to partnering, but the likelihood of partnering per se is not the objective of our study. It can, however, influence our analyses. From a social network perspective, one would expect higher rates of singlehood among the up- and downwardly mobile if their origin networks weaken while they fail to cultivate genuine social networks within the destination status. Additionally, if mobility provokes psychological problems such as anxiety, the socially mobile may be less likely to partner. The discussion has so far been gender-neutral. Although recent studies conclude that inter- generational mobility rates are quite similar for men and women, there are some exceptions as regards partnering. Studies of partner selection have emphasized how traditional gender norms might prevent the formation of couples in cases where women command more resources than men (Bertrand et al., 2015; Esteve et al., 2012). For instance, the probability that highly mobile professional women remain single is relatively strong in some societies (like Germany) where gender-traditional norms still prevail (Bellani et.al, 2017). Neither do our hypotheses differentiate marriage from cohabitation. Research suggests that in societies where cohabitation is commonplace (as in France and Scandinavia), it approximates marriage, and a significant proportion does eventually marry, especially among the higher educated (Perelli-Harris et.al, 2014; Hiekel and Futola, 2018). Cohabitation is quite widespread also in Germany, but it is typically seen as a testing ground prior to any decision to marry (Perelli-Harris et.al, 2014). The choice of cohabitation over marriage is also positively related to parental divorce; for older cohorts, parental divorce was biased towards the higher educated; but in younger cohorts it is more likely to be biased towards less educated parents (Liefbroer and Elzinga, 2012). Opting for marriage is also influenced by factors such as religiosity and traditional gender roles. In any case, the highly educated tend to partner later, the less educated earlier; and age at partnering is a strong predictor of union stability (Billari and Liefbroer, 2010). Data and Methods Data 8 We use data from the German Socio-Economic Panel (SOEP) for the years 1984 to 2018. This is one of the very few data sources that permit us to identify the social class origin and destination of both partners. Information on current or latest occupation is collected every year, and respondents are asked to report on their parents’ occupation when they were 15 years old. We first select all individuals aged 30 to 60 with information on own and parental class who have been in a co-residential relationship during at least one wave of the observation period. Starting from the original sample, 50% of cases are excluded because they do not meet the selection criteria of age and partnership. The age restriction serves to exclude respondents for whom pursuing education or retirement are common alternatives to employment. Starting with age 30 also serves to exclude persons making their first post-education moves, and who may not yet have attained the social identities that will come to dominate their lives. The SOEP allows us to identify how social mobility relates to the probability of being partnered in any given year of the survey. For each individual, all waves with information on social class are included. From the original sample, a further 28% of cases is excluded because they were not asked about the social class of their parents or the partner’s parents during the observation period, and 11% of cases because of missing information on own social class or control variables. 4 For our main analysis, we restrict the sample to individuals in a cohabiting union or marriage. In addition, we only use the first wave with full information for each couple, and which includes controls for the duration of the relationship at the time of measurement. We exclude cohabiting unions that lasted less than 2 years to filter out partnerships that may not have had a clear long-term commitment. These selection criteria produced a final sample of 5,507 couples. Our empirical approach is conducted at the level of these couples, each of them constituting an observation unit for the econometric treatments carried out. Our main dependent variable of interest is women’s social mobility, utilizing social class measures derived from information on occupation (ISCO-88) and self-employment status. 4 Hence, the great majority of cases dropped due to missing information are derived from issues related to the design of the survey rather than selective non-response to specific questions. We replicated our analysis using sample weights provided by the SOEP. The empirical results were very similar (for details, see Online Appendix A). 9 To keep the number of combinations of own and partners’ social mobility manageable, we divide occupations into 4 broad classes, generally following the ESeC classification (Rose & Harrison, 2007): service class occupations (e.g. surgeons or executives), intermediate occupations (e.g. administrators), working-class occupations (skilled and unskilled), and the self-employed.5 The primary reason behind this limited degree of social class differentiation is that our dual-partner-mobility design would become utterly unwieldy with a more detailed, say 7- or 9-, class scheme. For the unemployed and those with missing information on current occupation, we use the status corresponding to the last reported activity. For paternal social class we use the same classification. We opt for father’s class rather than the highest of either parent given pervasive non-employment among German mothers within the cohorts studied here. We define individuals as socially mobile if their social class differs from that of their father in absolute terms, rather than relative mobility across generations. Nonetheless, our analysis will take into account the marginal distribution of own and father’s class and how this changed over time in order to compute appropriate under and over-representation indexes of partner matches. Insofar as we are analyzing the logic of partnering for individuals in our sample, our main independent variable corresponds to the social mobility of men. In other words, the construction of our sample aims to explore the statistical relationship between the mobility category of women on the one hand and the one of men on the other hand. Table 1 shows the distributions for both variables. The majority have working-class fathers. Regarding own social class, working-class occupations are still common among men whereas most women are found in the intermediate class. In addition, men are far more likely to occupy service class positions. Table 1 also includes statistics for our control variables: observation period, migration background, age, relationship duration, when the couple entered the sample, and geographical residence in 1989 (so as to distinguish those from former East and West Germany). 6 Methods 5 See Appendix A for the exact classification. 6 For migrants, we distinguish those who were born abroad (direct migration background) and those with immigrant parents born in Germany (indirect migration background). 10 Our empirical strategy consists of two main parts. In the first one, we present results that allow us to describe absolute and relative chances of couples falling into all possible combinations of intergenerational social mobility of men and women within a relationship. Results are presented in an intuitive way and allow us to finely identify the combinations of intergenerational social mobility categories with the highest prevalence among the couples in the sample, while controlling for (changes in) the occupation structure. In the second part of the analysis, we estimate log-linear models to more formally test our hypotheses. The first part is based on predictions from multinomial logistic regression models where women’s social mobility is the main dependent variable7 and men’s social mobility the independent variable. In this method, couples are the unit of observation and we model partner choice as a discrete choice problem in which each man selects a partner from a set of exhaustive and non-overlapping alternatives, namely women’s intergenerational mobility category. This method allows us to present levels of homogamy in absolute and relative terms while controlling for a larger set of characteristics than is feasible with log-linear models. The main advantage of using a multinomial model is that it makes it possible to study possible homogamy tendencies without formulating any a priori hypothesis about how people partner, but it also makes it possible to distinguish which specific mobility categories combinations have the highest over-representation. For example, couples composed of two individuals from the working class whose parents were also from the working class may not have the same over-representation as couples in which both members belong to and have parents from the service class, even though both those combinations would constitute homogamous couples. We estimate the multinomial logit model using neural networks. One of the properties of the multinomial logit model (MNL) is that it can be represented by a neural network with a much smaller number of assumptions (Bentz and Merunka, 2000). Using a feedforward neural network with Softmax output, shared weights, and no hidden layers (Bridle, 1990) it is possible to fit a MNL model through maximum likelihood using neural networks (Venables and Ripley, 2013). The use of the neural network makes it possible to 7 We also run this model using women destination class as the dependent variable to study the relationship between women's social position and men's mobility. See the first part of the result section. 11 obtain estimation results equivalent to those obtained by log-likelihood, but under a limited number of hypotheses and it enables the estimates to converge more quickly8. Table 1. Sample description Variable Men Women Decade (%) 1984-1993 0.178 1994-2003 0.285 2003-2018 0.537 Own Class (%) Working Class 0.370 0.316 Intermediate Class 0.294 0.501 Self-Employed 0.095 0.083 Service Class 0.241 0.100 Parental Class (%) Working Class 0.528 0.528 Intermediate Class 0.248 0.243 Self-Employed 0.086 0.086 Service Class 0.139 0.144 Location in 1989 (%) East Germany 0.223 0.230 West Germany 0.674 0.648 Abroad 0.096 0.116 Born after 1990 0.007 0.006 Age (Mean) 39.85 37.33 Relationship length (years) 14.7 Migration Background (%) No migration background 0.813 0.800 Direct migration background 0.141 0.157 Indirect migration background 0.046 0.043 Note. N = 5,507 relationships Using the multinomial logit model estimates, we subsequently compute the predicted probability of having a certain kind of partner while keeping control variables at the sample average. These regression-predicted estimates are presented in visual form in order to provide easily interpretable results, and to identify the absolute prevalence of couple types. To further facilitate presentation, we exclude the relatively small group of self-employed from the graphical representations. However, using predicted probabilities this way yields results whose magnitude depends on the relative size of social mobility categories for men and 8 In Online Appendix B we present the detailed multinomial logistic regression models as well as a discussion of the underlying assumptions. We also conduct robustness checks, taking men’s mobility category as the outcome variable and women’s mobility category as the explanatory one (See Online Appendix B). 12 women. Therefore, we want to produce results controlling for the relative size of the groups and highlighting the relative over/under prevalence of certain combinations of social mobility categories among couples. To this end, we utilize the predicted probabilities to identify over- and under-represented partnering categories. These estimates identify homogamy while taking into account the marginal distribution of social class and mobility categories. To compute them, we compare the predicted probabilities with a scenario in which partnering is random. In other words, we calculate the percentage of couples that would be formed with a given set of characteristics if the choice of partner were purely random. We then compare this counterfactual to the predicted occurrence of couples with these characteristics to compute an index of over- and under-representation: (𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑𝑖𝑗 − 𝑅𝑎𝑛𝑑𝑜𝑚𝑖𝑗 ) 𝑅𝑎𝑡𝑒𝑖𝑗 = × 100, ∀(𝑖, 𝑗) ∈ 𝑀 × 𝑊 (𝑅𝑎𝑛𝑑𝑜𝑚𝑖𝑗 ) with M and W being the set of social mobility classes for men and women respectively. A positive coefficient represents an over-representation of couples within any given cell. In contrast, a negative coefficient indicates under-representation of this combination of partners among all couples in the sample. This index enables us to study the prevalence of distinct categories of couples by factoring in the relative size of the groups making up the occupational distribution of men and women9. Intergenerational social mobility homogamy is observed substantial significance if, for any category i, Rateij has the highest value for i=j. The results are presented graphically. The intensity of homogamy can also be compared for different social trajectories. The multinomial models describe in detail the homogamy trends on the basis of the social class of origin, destination or social mobility trajectory. Its results allow to discuss our research hypotheses. In order to deepen and synthesize these results we apply log-linear analysis using Poisson-regressions in the second step of the analysis. These models are based on the frequency tables of partner matches on social mobility categories constructed from our sample. We estimate one set of models without accounting for time-period which absorb fewer degrees of freedom, and we estimate another set of models where frequencies are 9 We work here on all the couples in the sample, all time periods together. Since the occupation structure can evolve over time, we checked that our results were robust by time period, by reproducing the estimates by sub- sample over three time periods. The results are available in Online Appendix C. 13 calculated by time-period for each category. Our benchmark model without control of the evolution of the occupation structure over time includes two variables to control for the marginal distributions of social mobility trajectories: men’s and women’s mobility category (each category defined by a combination of origin and destination class). These models are called "independent models" and correspond to the distribution of couples that would be observed if the couples were randomly distributed across the categories corresponding to the variables incorporated in the regression. In the set of models including time-period, both variables are interacted with period to account for changes in the marginal distribution over time. Subsequently, we add different variables to these baseline models and compare model fit to test our hypotheses. We first add homogamy based on destination class and subsequently homogamy based on origin class. These variables are categorical and take on a different value for each homogamy category in order to capture homogamy for these classes more comprehensively. In other words, the strength of the homogamy effect is allowed to vary by origin/destination class. We then add two variables to test our main hypotheses: a categorical variable identifying the categories for which both partners have the exact same origin and destination (i.e. homogamy based on social mobility category); and a dummy variable indicating matches that most clearly capture a possible exchange of social origin for social destination: upwardly mobile matching with downwardly mobile individuals. Several other models are also estimated to test for robustness and context, as will be explained in the results section. Results The role of one’s destination and origin class in partner selection We begin descriptively, exploring homogamy based on social origin and destination. The graphical results presented in this section are based on the estimates of the classification models, whose regression tables are presented in Appendix B. In this first model, we slightly adapt the main classification model to explain, among couples, the social class of women as a function of the intergenerational social mobility of men. The first question we ask is: What are the most likely partnering choices among the socially mobile? Figure 1a shows the 14 destination class of women depending on their male partners’ pattern of social mobility. We control for the age of partners, survey year, migration background of both partners, duration of the relationship at the time of observation, and whether the individuals lived in East or West Germany in 1989 (underlying models and regression tables are displayed in Appendix B). 15 Figure 1a. Women’s destination class conditional on men’s social mobility Note. The models control for the age of both partners, survey year, migration background of both partners, duration of the relationship at the time of observation, and whether the individuals lived in East or West Germany in 1989. Whiskers indicate 95% confidence intervals calculated using a neural network with hidden layers. 16 Figure 1b. Over- and underrepresentation of partnering characteristics, compared to random matching Note. The models control for the age of both partners, survey year, migration background of both partners, duration of the relationship at the time of observation, and whether the individuals lived in East or West Germany in 1989. Whiskers indicate 95% confidence intervals calculated using a neural network with hidden layers. 17 The results in Figure 1a are ordered, firstly, according to men’s destination class, and, secondly, according to men’s origin class. Therefore, the first set of bars shows the values for socially immobile working-class men, i.e. with a working-class origin and destination. The following two sets of bars show how the values differ if they originated from a higher social class. The second three sets of bars show equivalent results for those with an intermediate class destination, and the last three show results for men with a service-class occupation. Overall, men are most likely to partner with women with an intermediate destination class. This is not surprising considering that 50% of women in the sample occupy this class position. The exception is immobile working-class men who are most likely to have a working-class partner. Across the groups, men are least likely to be partnered with a service- class woman, with the exception of service-class men (for whom having a working-class partner is the least common). Figure 1b presents the relative overrepresentation of partner matches as compared to random matching. What emerges is an almost “linear” pattern across social mobility categories: the “higher” the destination class of men, the more likely they are to have a service class partner. Within destination classes, service-class origins also increase the likelihood of having a service class partner. The opposite pattern, but slightly less “linear”, is observed for having a working-class partner: the “lower” a person’s destination class, the greater the likelihood of having a working-class partner. Hence, we obtain support for our first hypothesis, namely that social origin matters for partnering choices beyond the effect of destination class and that the effect of destination class dominates over the effect of origin class. Across all groups of socially mobile men, matches where their partners have the same destination class are overrepresented. On the other hand, matches where women’s destination class matches men’s origin class are underrepresented among several groups of socially mobile men. For instance, downwardly mobile men with a working-class destination but service class origin are relatively unlikely to have a service class partner. Similarly, men with a working-class origin but service class destination are unlikely to have a working-class partner. However, the probability of partnering with a working-class woman for a service class man is relatively higher for service class men whose fathers were from the working class. These results confirm that partner 18 choices are far more likely to favor the destination- rather than origin class but that social origin nevertheless influences partner selection. Social Mobility Homogamy If origin plays a role, it is therefore possible that men partner not only with women whose occupation corresponds to their social class of origin, but also with women with both the same social origin and destination. What is the probability that both partners experience a similar social mobility trajectory? We study here the statistical relationship between the social mobility of women and men among couples10. Figure 2a shows predicted probabilities of partnering outcomes for men in the working-class. As before, Figure 2b depicts the extent to which given matches are over- or underrepresented factoring in men’s and women’s occupational structure. In absolute terms, working-class men are most likely to have a working- or intermediate- class partner with a working-class origin. Interestingly, the three matches that are most clearly overrepresented (in Figure 2b) are those that reflect perfect homogamy: Immobile working- class men choose immobile working-class women. Downwardly mobile men disproportionally form unions with partners who exhibit the exact same origin and destination class. The results for downwardly mobile men are particularly interesting for our hypotheses. Next to perfect homogamy, downwardly mobile men tend to partner downwardly mobile women from a different social origin. For instance, the second most common partner for downwardly mobile men with a service class origin is a downwardly mobile woman with an intermediate class origin. Social exchange type partnerships in which a downwardly mobile partners with an upwardly mobile individual, engaging in an “exchange” of advantages linked to social origin and destination, are clearly underrepresented. 10 Results are statistically significant. See the regression tables in appendix B. 19 Figure 2a. Partners’ mobility among men with working-class occupation Figure 2b. Over-and under representation of partner combinations as compared to random partnering Figures 3a and 3b show equivalent results for men with an intermediate class destination. In relative terms, matches that reflect perfect homogamy are overrepresented among 20 intermediate class men as well. Upwardly mobile men are prone to partner intermediate class women with a similar working-class background, and downwardly mobile men are disproportionally found in unions with intermediate class women who come from a similar service class background. Figure 3a. Partners’ mobility among men with an intermediate class occupation Figure 3b. Over-and under representation of partner combinations as compared to random partnering Figure 4a and 4b display the results for service class men. In absolute terms, they are most likely to have an intermediate class partner. In relative terms, service class men are disproportionally partnered with service class women. Here too, we see an overrepresentation 21 of matches that reflect perfect homogamy in terms of both origin and destination class. It is only among the long-distance upwardly mobile, i.e. service class men with a working-class origin, that the most overrepresented match is not exactly the same: they are instead (relatively) more likely to have an upwardly mobile partner with an intermediate class origin. Perfect social mobility homogamy is particularly strong for service class men with an intermediate or service class origin. The degree of overrepresentation is by far the largest for these two partner combinations across all observed combinations (Figures 2b-4b), with a degree of overrepresentation of around two-hundred and three-hundred percent, respectively. Here again the evidence for social exchange-based matching is limited: service class men with working-class origins are relatively unlikely to partner with downwardly mobile women. Among service class men of intermediate class origins there is some overrepresentation of downwardly mobile partners from the service class, but only if their destination is an intermediate class occupation. Figure 4a. Partners’ mobility among men with a service class occupation 22 Figure 4b. Over-and under representation of partner combinations as compared to random partnering The results confirm the presence of partnering patterns that the social sciences have identified again and again: individuals seek out partners who are similar to themselves in terms of socioeconomic characteristics. However, our results show additionally that homogamy based on socioeconomic characteristics goes beyond one’s own achievements or social background: in relative terms, mobile individuals are most likely to partner someone with a similar social mobility experience. The downwardly mobile are prone to partner other downwardly mobile persons, and the same obtains for the upwardly mobile. To illustrate, in a scenario of random partnering, 17.1% of individuals would have a partner with the same origin and destination class, a number considerably lower than the 29.1% we observe in the data. Among socially mobile men, 12.6% would have a partner with the same origin and destination class, compared to 17.1% observed in our analysis. We now test this more formally using log-linear models. Log-linear models Table 2 presents the results of log-linear models predicting the frequency of partner matches. Model A1 is our benchmark model which controls for the marginal distribution of own and partner’s mobility category (i.e. the combination of origin and destination class). Model A2 adds a categorical variable for homogamy based on destination class, which improves model 23 fit considerably: the Likelihood Ratio (LR) increases whereas the Bayesian Information Criterion (BIC) and the Dissimilarity index (D) decline. In model A3 we add homogamy based on origin class to the initial model which only included the marginal distributions. Table 2. Model fit statistics of log-linear models explaining frequency of partner matches General Models LR df BIC D A1. Own mobility category + partner mobility category 5796.7 19 1978.4 0.185 A2. A1 + homogamy of destination class 6681.4 23 1112.1 0.114 A3. A1 + homogamy of origin class 6469.4 23 1324.1 0.138 A4. A1 + homogamy of origin and destination 6685.0 25 1117.8 0.115 A5. A4 + homogamy of mobility category 6792.5 34 1051.7 0.087 A6. A4 + homogamy of downwardly mobile 6685.0 26 1122.3 0.115 A7. A4 + homogamy of upwardly mobile 6685.9 26 1121.5 0.115 A8. A4 + destination versus origin exchanges 6704.1 26 1103.3 0.114 A9. A1 + homogamy of mobility category 6571.3 29 1249.8 0.102 Models with period interactions LR df BIC D B1. Own mobility*period + partner mobility*period 7098.1 57 3031.5 0.200 B2. B1 + homogamy of destination 7960.7 61 2191.7 0.131 B3. B2 + homogamy of mobility category 8064.5 70 2139.2 0.112 B4. B3 + homogamy of destination*period 8048.0 70 2155.7 0.113 B5. B4 + homogamy of mobility category*period 8117.2 96 2234.8 0.098 B6. B1 + homogamy of origin 7752.7 61 2399.7 0.155 B7. B6 + homogamy of origin * period 7781.1 69 2415.0 0.149 B8. B1 + homogamy of mobility category*period 7893.5 87 2407.1 0.113 LR = Likelihood-ratio; df = Degrees of freedom; BIC = Bayesian Information Criterion; D = Dissimilarity Index. Poisson regression models run on frequency data. General models are based on crosstabs of men’s and women’s mobility categories; Models with period interactions are based on three-way tables including three- categories of time period (1984-1993; 1994-2003; 2003-2018) Here, too, we see that model fit improves in comparison to model A1, but not as much as was observed for destination class. Model A4 adds both homogamy based on origin and 24 destination class to the initial model controlling for the marginal distributions. We see that this model performs slightly worse than the model including only homogamy of destination class (A2). In other words, individuals match on origin class but this is entirely explained by homogamy based on destination class. One reason why homogamy of origin class has no explanatory power beyond homogamy on destination class is that matches for individuals with a similar origin class include a great variety of matches. For example, it both includes an immobile working-class man partnered with an immobile working-class woman, and also an immobile working-class man partnered with an upwardly mobile woman with a working-class origin. Model A5 therefore adds a dummy variable which most directly tests our mobility homogamy hypothesis; i.e. do individuals match simultaneously on origin and destination? We see that this model has the best fit of all in Table 2. In other words, individuals are very likely to select partners with the same origin and destination class. Models A6 and A7 test whether the socially mobile partner similarly mobile individuals, but they also include matches where the origin and destination class are not exactly the same (e.g. an upwardly mobile person of working-class origins matched with an upwardly mobile individual of intermediate class origins). These do not exhibit much explanatory power, and the same holds for “social exchange” matches where upwardly mobile individuals partner downwardly mobile individuals (model A8), -- even though model fit here is slightly better than the model in A4 which only controls for marginal distributions and homogamy based on destination and origin class. Models B1 to B7 are based on a dataset where frequencies are calculated by time period. In other words, these models consider that the marginal distributions of both origin and destination classes may change over time. Models B1 to B3 suggest that our main results of significant homogamy based on destination class (B2) and social mobility trajectory (B3) also obtain in this specification. Models B4 and B5 test whether these effects changed across time, but the results suggest that is not the case. Models B6 and B7 additionally test whether homogamy based on social origin changed over time, but again we observe no significant trends over time. Robustness checks 25 Online Appendix D shows how the results change when we limit relationships to those whose duration was less than five years at the time of observation. This addresses one limitation of our study, namely that we do not observe all relationships from the date of union formation. Differences compared to our main results are generally minor with two exceptions that are underrepresented in the robustness check (but over-represented in our main results): 1) downwardly mobile males from service-to working- class partnered with women who were downwardly mobile from the intermediate- to the working- class; and 2) men with an intermediate origin and destination partnered with upwardly mobile women from the intermediate to the service class. We also reproduced the multinomial logit model results by time-period to make sure that the results obtained on our stacked sample were robust to changes of the occupational-structure over time (Online appendix C). Discussion Our study contributes to a comparatively small body of research exploring how intergenerational social mobility influences union formation. We believe that our analyses break new ground by identifying the phenomenon of mobility homogamy, of partners sharing the same social origin and destination. The issues we address stimulated a debate in the 1960s, primarily propelled by Blau and Duncan’s (1967) social networks thesis. Their argument was in contradistinction to the social exchange hypothesis. But the debate never produced any empirical study, undoubtedly because of the unusually heavy data requirements involved: very few data sources have provided information on the social mobility histories of both individuals in the partnering process. Our findings suggest a number of generalizations. First of all, mobile individuals partner primarily with someone from their destination- rather than from their origin class. Secondly, origin class does influence partner choices; a higher social origin level increases linearly the likelihood of having a service class partner. Thirdly, there is little evidence that the resources related to social origin and destination are exchanged in partnering dynamics. Instead, mobile individuals tend to match on both social origin and destination. This confirms the preference for homogamy in partnering. 26 In brief, the data suggest that the social exchange thesis has rather limited explanatory power. There is little evidence that resources provided by a high social origin are being exchanged for resources provided by a high destination class. All told, the link between social mobility and union formation appears much closer to a general tendency towards homogamy, which could be driven by a competition for resources, shared norms and lifestyles, or social networks. And this is where our ‘mobility homogamy’ concept captures a partnering logic so far not recognized in the literature. Our analyses provided some additional results relevant for research on homogamy and social stratification: we do not observe any significant trends over time in homogamy based on social class. This holds for homogamy based on social origin, social destination and social mobility trajectory. This suggests that, over time, Germany has not become less stratified in terms of the link between social class and partnering. Future research can address limitations of our study. Firstly, our analyses are confined to one country and we must be careful not to over-generalize, considering that Germany’s gender roles have for long remained quite traditional, and that its social mobility rates are comparatively quite modest (Breen & Luijkx, 2004; Cooke, 2006). Secondly, our analyses are limited to those who do end up being partnered. For reasons of space, we could not include analyses of remaining single. Social mobility can condition the opportunities to meet partners, it can influence the degree to which an individual is perceived as attractive, but also the appeal (or fate) of remaining single. In Online Appendix E, we present the average probability that an individual is partnered in any given wave of the survey. We also identify cohort effects. For women, the probability of having a partner varies little by social mobility group. For men, we observe greater chances of being partnered among the upwardly mobile, and lower ones among the downwardly mobile. This suggests that future research might explore further the role of gender-specific attractiveness variables– if such information is available. Another promising avenue for future research would be to apply similar analyses to countries that display very different social mobility rates and-or less conventional gender roles (such as in Scandinavia). 27 Returning to the social exchange versus networks debate, our study has produced scant evidence in favor of the former. The exchange of origin class ‘status’ for the economic or other advantages of partnering with an upwardly mobile individual is quite marginal. A limitation of our analysis is that we cannot say much about the precise mechanisms that make socially mobile individuals partner with individuals who are similarly mobile. Future research might investigate whether this occurs because men and women share the same networks, have similar values and lifestyles, or because they occupy similar positions in job hierarchies. In address to the longstanding debate on the equalization of life chances in advanced societies, the finding that the socially mobile disproportionally partner with someone from their destination class might suggest a substantial degree of union formation across origin classes – an indication that partnering behavior is, so to speak, ‘democratic’. But this is clearly a premature conclusion. Once we consider the mobility trajectory of both partners, the data reveal a prevalence of social mobility homogamy. The destination partner often turns out to be also a social origin partner, implying a doubly homogamous partnership. References Bellani, D, Esping-Andersen, G and Nedoluzhko, L 2017 ‘Never partnered. A multilevel analysis of lifelong singlehood’. Demographic Research, 37: 53-100 Bentz, Y, & Merunka, D 2000 ‘Neural networks and the multinomial logit for brand choice modelling: a hybrid approach.’ Journal of Forecasting, 19(3): 177-200. Bernardi, F and G. Ballarino, eds 2016 Education, Occupation and Social Origin. Cheltenham: Edward Elgar Bertrand, M, Kamenica, E, & Pan, J 2015 ‘Gender identity and relative income within households.’ The Quarterly Journal of Economics, 130(2): 571-614. Billari, F and Liefbroer, A 2010 ‘Towards a new pattern of transition to adulthood?’. Advances in Life Course Research, 15: 59-75 Blackwell, D 1998 ‘Marital homogamy in the United States: the influence of individual and paternal education’. Social Science Research, 27: 159-188 28 Blanden, J 2011 ‘Cross-county rankings in intergenerational mobility: a comparison of approaches from economics and sociology’. Journal of Economic Surveys, 27: 38-73 Blau, and Duncan, O 1967 The American Occupational Structure. New York: John Wiley & Sons. Blossfeld, HP 2009 ‘Educational assortative marriage in comparative perspective.’ Annual Review of Sociology: 513-530. Blossfeld, HP and Timm, A 2003 Who Marries Whom? Educational Systems as Marriage Markets in Modern Societies. Dordrecht: Kluwer Bourdieu, P 1986 ‘The Forms of Capital’. Pp 241-258 in J. Richardson, ed, Handbook of Theory and Research for the Sociology of Education. New York: Greenwood Bozon, M 1991 ‘Mariage et mobilité sociale en France.’ European Journal of Population/Revue Européenne de Démographie, 7(2): 171-190. Breen, R & Luijkx, R. (eds.) 2004 Social Mobility in Europe. Oxford: Oxford University Press Breen, R and Müller, W eds. 2020. Education and Intergenerational Social Mobility in Europe and the United States. Stanford, CA: Stanford University Press. Bridle, J. S. (1990). Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In Neurocomputing (pp. 227- 236). Springer, Berlin, Heidelberg. Bukodi, E, and Goldthorpe, J 2021 ‘Intergenerational Class Mobility in Industrial and Post- Industrial Societies: Towards a General Theory’. Unpublished paper, Nuffield College, Oxford University. Chan, TW 2018 ‘Social mobility and the well‐being of individuals’. The British Journal of Sociology, 69(1): 183-206 Cooke, LP 2006 “Doing” gender in context: Household bargaining and risk of divorce in Germany and the United States.’ American Journal of Sociology, 112(2), 442-472. De Hauw, Y, Grow, A, & Van Bavel, J 2017 ‘The reversed gender gap in education and assortative mating in Europe.’ European Journal of Population, 33(4): 445-474. DiMaggio, P, & Mohr, J 1985 ‘Cultural capital, educational attainment, and marital selection.’ American Journal of Sociology, 90(6): 1231-1261. Esping-Andersen, G 2016 Families in the 21st Century. Stockholm: SNS 29 Esping-Andersen, G and Cimentada, J 2018 ‘Ability and Mobility’. Social Science Research, 75: 13-31 Esteve, A, García‐Román, J, & Permanyer, I 2012 ‘The gender‐gap reversal in education and its effect on union formation: the end of hypergamy?’ Population and Development Review, 38(3): 535-546. Fu, X, & Heaton, TB 2008 ‘Racial and educational homogamy: 1980 to 2000.’ Sociological Perspectives, 51(4): 735-758. Henz, U, & Mills, C 2018 ‘Social class origin and assortative mating in Britain, 1949–2010’ Sociology, 52(6): 1217-1236. Hiekel, N and Futola, B 2018 ‘Love. Breakup. Repeat. The prevalence and stability of serial cohabitation among women and men born in the 1970s’. Demographic Research, 39: 855- 870 Hout, M 1982 ‘The association between husbands' and wives' occupations in two-earner families.’ American Journal of Sociology, 88(2): 397-409. Kalmijn, M 1991 ‘Status homogamy in the United States’. American Journal of Sociology, 97: 496-523 Kalmijn, M 1998 ‘Intermarriage and homogamy: causes, patterns, trends’. Annual Review of Sociology, 24: 395-421 Kalmijn, M 2010 ‘Educational inequality, homogamy, and status exchange in black-white intermarriage: A comment on Rosenfeld.’ American Journal of Sociology, 115(4): 1252- 1263. Katrňák, T, Fučík, P, and Luijkx, R 2012 ‘The relationship between educational homogamy and educational mobility in 29 European countries’. International Sociology, 27(4): 551- 573. Kessin, K 1971 ‘Social and psychological consequences of intergenerational occupational mobility’. American Journal of Sociology, 77: 1-18 King, M 2021 ‘College as a great equalizer? Marriage and assortative mating among first- and continuing- generation college students’. Demography, 58 (6): 2265-2289 Liefbroer, A and Elzinga, C 2012 ‘Intergenerational transmission of behavioral patterns. How similar are parents’ and children’s trajectories?’ Advances in Life Course Research, 17: 1- 10 30 Macmillan, L and Sibieta, L 2020 ‘Changing gears: understanding downward social mobility’. London: Social Mobility Commission. Mäenpää, E, & Jalovaara, M (2015). Achievement replacing ascription? Changes in homogamy in education and social class origins in Finland. Advances in Life Course Research, 26: 76-88. Mare, R (1991) ‘Five decades of educational assortative mating’. American Sociological Review, 56: 15-32 McLanahan, S 2004 ‘Diverging destinies: how children are faring under the second demographic transition’. Demography, 41: 607-627 OECD (2018), A Broken Social Elevator? How to Promote Social Mobility, OECD Publishing, Paris, https://doi.org/10.1787/9789264301085-en. Oppenheimer, VK 1977 ‘The sociology of women's economic role in the family.’ American Sociological Review: 387-406. Perelli-Harris, B, Mynarska, M, Berrrington, A, Berghammer, C, and Evans, A 2014 ‘Towards a new understanding of cohabitation’. Demographic Research 31: 1043-1078 Ripley, B., Venables, W., & Ripley, M. B. (2016). Package ‘nnet’. R package version, 7, 3- 12. Rose, D, & Harrison, E 2007 ‘The European socio-economic classification: a new social class schema for comparative European research.’ European Societies, 9(3): 459-490. Rosenfeld, MJ 2008 ‘Racial, educational and religious endogamy in the United States: A comparative historical perspective.’ Social Forces, 87(1): 1-31. Rosenfeld, MJ 2010 ‘Still weak support for status-caste exchange: A reply to critics.’ American Journal of Sociology, 115(4): 1264-1276. Rosenfeld, MJ, & Kim, BS 2005 ‘The independence of young adults and the rise of interracial and same-sex unions.’ American Sociological Review, 70: 541–562. Sassler, S, & Joyner, K 2011. ‘Social exchange and the progression of sexual relationships in emerging adulthood.’ Social forces, 90(1): 223-245. Schwartz, C. 2013 ‘Trends and variation in assortative mating’. Annual Review of Sociology, 39: 451-470. Schwartz, CR, & Mare, RD 2005. ‘Trends in educational assortative marriage from 1940 to 2003.’ Demography, 42(4): 621-646. 31 Schwartz, C, Zeng, Z and Xie, Y 2016 ‘Marrying up by marrying down. Status exchange between social origin and education in the United States’. Sociological Science, 3: 1003- 1026 Smits, J, Ultee, W, & Lammers, J 1998 ‘Educational homogamy in 65 countries: An explanation of differences in openness using country-level explanatory variables.’ American Sociological Review: 264-285. Stacey, B 1967 ‘Some psychological consequences of inter-generational mobility’. Human Relations, 20: 3-17 SOEP 2019. ‘Soep-is 2017-pgen: Person-related status and generated variables.’ Technical report, SOEP in collaboration with the German Institute for Economic Research. Tooth, L and Mishra, G 2012 ‘Intergenerational educational mobility, general mental health and depressive symptoms in young women’. Quality of Life Research, 22 (7): 1589-1602 Ultee, W and Luijkx, R 1990 'Educational Heterogamy and Father-to-Son Occupational Mobility in 23 Industrial Nations: General Societal Openness or Compensatory Strategies of Reproduction?'. European Sociological Review, 6(2): 125-149. Wickrama, K, O’Neal, C and Lee, T 2016 ‘The health impact of upward mobility. Does socioeconomic attainment make youth more vulnerable to stressful circumstances?’ Journal of Youth and Adolescence, 45: 271-285 32 Appendix A. Social class categorization Our aim was to use the ESeC class scheme using the SOEP data for both paternal class and own social class. Since the ESeC class categories were not available in the SOEP data, we recreated them using a combination of ISCO codes, EGP class, and information on self- employment: Service class: EGP 1 & 2 + Self-employed with 10 or more employees Middle class: ISCO 2230; 2320-2350;3000-4215; 5161; 5162 Working class: ISCO 4142; 7300-7399; 4216-9998 Self-employed: Self-employed with 9 or less employees 33 Appendix B. Regression tables Table B1. Multinomial logit models explaining partnered women’s destination class 34 Table B2. Multinomial logit models explaining partnered women’s mobility category 35 Table B2. Multinomial logit models explaining partnered women’s mobility category (Continued) 36 Online Appendix A. Log-linear models based on weighted frequency tables Table 2. Model fit statistics of log-linear models explaining frequency of partner matches General Models LR df BIC D A1. Own mobility category + partner mobility category 6345.0 19 1967.8 0.187 A2. A1 + homogamy of destination class 7105.1 23 1226.2 0.122 A3. A1 + homogamy of origin class 6960.7 23 1370.5 0.134 A4. A1 + homogamy of origin and destination 7114.7 25 1225.7 0.122 A5. A4 + homogamy of mobility category 7226.8 34 1154.9 0.097 A6. A4 + homogamy of downwardly mobile 7115.7 26 1229.3 0.120 A7. A4 + homogamy of upwardly mobile 7114.8 26 1230.2 0.121 A8. A4 + destination versus origin exchanges 7140.5 26 1204.5 0.118 A9. A1 + homogamy of mobility category 7069.4 29 1289.4 0.109 Models with period interactions LR df BIC D B1. Own mobility*period + partner mobility*period 6623.8 57 3031.5 0.211 B2. B1 + homogamy of destination 7368.7 61 2437.2 0.149 B3. B2 + homogamy of mobility category 7478.3 70 2378.9 0.133 B4. B3 + homogamy of destination*period 7454.9 70 2402.4 0.130 B5. B4 + homogamy of mobility category*period 7551.8 96 2453.7 0.113 B6. B1 + homogamy of origin 7228.5 61 2577.5 0.160 B7. B6 + homogamy of origin * period 7268.9 69 2582.7 0.151 B8. B1 + homogamy of mobility category*period 7393.1 87 2561.1 0.125 LR = Likelihood-ratio; df = Degrees of freedom; BIC = Bayesian Information Criterion; D = Dissimilarity Index. Poisson regression models run on frequency data. General models are based on crosstabs of men’s and women’s mobility categories; Models with period interactions are based on three-way tables including three- categories of time period (1984-1993; 1994-2003; 2003-2018) 37 Online Appendix B. Additional explanations and detailed results of multinomial logit models Multinomial Logit Modelling In our study, the question of partner choice is defined as a discrete choice problem, in which each individual selects a partner from a set of exhaustive and non-overlapping alternatives. Each couple is thus modeled as a choice procedure in which a category of partners (men or women) choose a partner belonging to a specific mobility category. In the multinomial logit model, the Additive Random Utility Model (ARUM) stipulates that the utility of choice k from a set of choices C made by the decision maker i is a random variable Uik = Vik + εik composed by the sum of an observable and a random component. The behavioral assumption is that individual i will choose the category of partner which leads to the highest utility level. Relying on three assumptions, namely that the error terms εik are independent (H1), follow a Gumbel distribution (H2) and are identically distributed (H3), the multinomial logit model is suitable for computing the unconditional probability of having a partner in each of the J mobility categories, conditional on a set of regressors. Our results are based on modeling in which the dependent categorical variable yi is the mobility category of women from the sample couples. In our model, regressors are alternative-invariant, and the regressors included are the men’s mobility category, both partners age, migration background, residence in 1989, the year of sampling, and the duration of the relationship. Formally, the unconditional probability for individual i to choose alternative k can be simplified and rewritten as a classical logit probability. These probabilities are well behaved in the sense that they lie between 0 and 1, and the sum of all probabilities across all alternatives equals one. One of the properties of the multinomial logit model (MNL) is that it can be represented by a neural network with a much smaller number of assumptions (Bentz and Merunka, 2000). The MNL model corresponds to a feedforward neural network with Softmax output, shared weights, and no hidden layers (Bridle, 1990). In this type of neural network, entropy -which is the error function- is identical to the log-likelihood function of the MNL. It is therefore possible to fit a MNL model through maximum likelihood using neural networks (Venables and Ripley, 2013). The optimization method used is the Broyden-Fletcher-Goldfarb-Shanno (BFGS) which is derived from gradient descent. The number of iterations has been arbitrarily set to 500, which is high enough for both our models to converge. Standards errors can be estimated by inverting the final Hessian matrix of the log-likelihood at the maximum likelihood estimator. Those standard errors are then used to compute confidence intervals and to assess the statistical significance of all of the model’s parameters. This estimation strategy is implemented using the R nnet package (Ripley et al., 2016). Discussing the Independence of Irrelevant Alternatives In the multinomial logit model, the assumption of uncorrelated error terms is known as independence of irrelevant alternatives (IIA). The implication of the IIA is that the problem 38 is reduced to a comparison between any pair of alternatives. This means that the relative chances of choosing one category of partner over another does not depend on the characteristics of the other available alternatives nor on the apparition of a new alternative. For example, the relative chance of being in a relationship with a working class woman rather than a service class woman, conditional on observed individual characteristics, does not depend on the class properties of intermediate class women. The relevance of the IIA hypothesis and its frequency of violation have been discussed in the theoretical and empirical econometric literature (Benson et al., 2016) ; (Latty and Beekman, 2011) ; (Koppelman and Bhat, 2006) ; (Frederick et al., 2014). In the context of partner choice in particular, preference experiments in psychology have only shown that the introduction of a third alternative could lead -under the specific conditions of asymmetric dominance- to a modification of the relative probability of choice between the two initially eligible partners (Sedikides et al., 1999). Following McFadden et al. (McFadden et al., 1977), the estimates were performed on subsamples of alternatives randomly drawn from the set of all subsets of partners’ category to assess the stability of the estimated coefficients across different subsets of alternatives. The stability of the estimated coefficients over different sets of alternatives is interpreted as a relevant indicator of compliance with the IIA in our setting. A Small-Hsiao test (Small and Hsiao, 1985) also confirmed the respect of the IIA at a 10% confidence level. Robustness tests The large majority of the results from our estimations appear to be statistically significant. Most of the coefficients associated with own social mobility are significant at the 1% level (Tables B1 and B2). In particular, for the partner mobility category (dependent variable), the own mobility categories (independent variable) corresponding to perfect homogamy or to a mobility category that is either very close or very far from the partner’s are systematically significant. A likelihood-ratio test of our model against a model containing only a slope shows that our model containing the full set of predictors represents a significant improvement in fit relative to no model, and hence that at least one population slope is non- zero. Running a likelihood-ratio test of a nested model excluding own mobility among the set of independent variables against our original model highlights the dramatic increase in fit entailed by the inclusion of the own mobility variable. In other word, own mobility is an overriding factor in explaining partner mobility. Finally, the specificity of our main equation is that it models pairing as a choice process in which the profile of the chosen partner depends on the individual characteristics of a partner that would be making the choice. In fact, the pairing process can be considered as bilateral. Thus, we also re-estimated the multinomial models by reversing the position of men and women as dependent or independent variables. These re-estimates indicate that the findings in the original model are robust to a reversal of these categories (See Figures B1 to B4). 39 Figure B1. Partners’ social destination depending on women’s mobility Figure B2. Over- and underrepresentation of partnering characteristics as compared to random matching Women’s mobility-Men’s destination Figure B3. Partners’ social mobility depending on women’s mobility 40 Figure B4. Over- and underrepresentation of partnering characteristics as compared to random matching (Women’s mobility-Men’s mobility) Appendix B References Benson, A. R., Kumar, R., and Tomkins, A. (2016). On the relevance of irrelevant alternatives. In Proceedings of the 25th International Conference on World Wide Web, pages 963–973. Bentz, Y., & Merunka, D. (2000). Neural networks and the multinomial logit for brand choice modelling: a hybrid approach. Journal of Forecasting, 19(3), 177-200. Bridle, J. S. (1990). Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In Neurocomputing (pp. 227- 236). Springer, Berlin, Heidelberg. Frederick, S., Lee, L., and Baskin, E. (2014). The limits of attraction. Journal of Marketing Research, 51(4):487–507. 41 Koppelman, F. S. and Bhat, C. (2006). A self instructing course in mode choice modeling: multinomial and nested logit models. Latty, T. and Beekman, M. (2011). Irrational decision-making in an amoeboid organism: transitivity and context-dependent preferences. Proceedings of the Royal Society B: Biological Sciences, 278(1703):307–312. McFadden, D., Tye, W. B., and Train, K. (1977). An application of diagnostic tests for the independence from irrelevant alternatives property of the multinomial logit model. Institute of Transportation Studies, University of California Berkeley, CA. Ripley, B., Venables, W., & Ripley, M. B. (2016). Package ‘nnet’. R package version, 7, 3- 12. Sedikides, C., Ariely, D., and Olsen, N. (1999). Contextual and procedural determinants of partner selection: Of asymmetric dominance and prominence. Social Cognition, 17(2):118– 139. Small, K. A. and Hsiao, C. (1985). Multinomial logit specification tests. International economic review, pages 619–627. Venables, W. N., & Ripley, B. D. (2013). Modern applied statistics with S-PLUS. Springer Science & Business Media. 42 Online Appendix C. Additional Robustness checks Results by cohort (cohort defined as first year of observation) Figure C1. Partners’ social mobility depending on men’s mobility; Cohort Pre 1985 Figure C2. Over- and underrepresentation of partnering characteristics as compared to random matching (Women’s mobility-Men’s mobility) ; Cohort Pre 1985 43 Figure C3. Partners’ social mobility depending on men’s mobility; Cohort 1986-1999 Figure C4. Over- and underrepresentation of partnering characteristics as compared to random matching (Women’s mobility-Men’s mobility); Cohort 1986-1999 44 Figure C5. Partners’ social mobility depending on men’s mobility; Cohort 2000-2016 Figure C6. Over- and underrepresentation of partnering characteristics as compared to random matching (Women’s mobility-Men’s mobility); Cohort 2000-2016 45 Online Appendix D. Additional Robustness checks Results for relationships that are intact <5 years at time of survey Figure D1. Partners’ social mobility depending on men’s mobility Figure D2. Over- and underrepresentation of partnering characteristics as compared to random matching (Women’s mobility-Men’s mobility) 46 Appendix E. Partnering probabilities One way in which social mobility can influence partnering outcomes is the opportunity of forming a union in the first place. Social mobility can condition the opportunities to meet partners, it can influence the degree to which an individual is perceived as attractive, and also the appeal of remaining single. Table E1 displays the average probability that an individual is partnered in any given wave of the survey. Tables E2-E4 display results dis-aggregated by time period. E.1: Full sample Table E1. Proportion of men and women in a relationship by own and parental social class Own/Parents Class Working Class Intermediate Class Service Class Total Working Class 84.30 80.30 77.20 83.40 Intermediate Class 86.00 81.80 80.80 83.70 Service Class 89.50 87.60 87.20 88.00 Total 85.20 83.20 82.80 84.40 N= 128,864 Table E1-1: Proportion of men in a relationship by own social class/parents’ social class combination (%) Own/Parents Class Working Class Intermediate Class Service Class Total Working Class 78.50 78.40 77.80 78.60 Intermediate Class 79.10 79.60 77.20 79.00 Service Class 79.70 77.00 78.50 78.30 Total 78.80 79.10 77.60 78.90 N= 132,988 Table E1-2: Proportion of women in a relationship by own social class/parents’ social class combination (%) On average, 84% of men and 79% of women were cohabiting or married across the observation waves. For women, we observe relatively few differences in the probability of being partnered across social mobility groups, with all percentages falling between 77% and 80%. For men, there is more variation; those with a service class destination are the most likely to be in a partnership across the waves, whereas men with a working or intermediate class occupation were partnered at roughly similar rates. As we predicted, downwardly mobile men are less likely to be in a relationship, with the lowest rates found for working 47 class men with a service class origin (77%). At the other extreme, upwardly mobile men are the most likely to be partnered, in particular those who end up in the service class (90%). In short, social mobility appears to matter somewhat less for the partnering chances of women than for men. There are different interpretations that could be given to the results for men. A first interpretation is that mobility primarily affects the attractiveness of men, with downward mobility having a negative and upward mobility a positive impact. Indeed, upwardly mobile men are even more likely to be partnered than are the immobile individuals from the same destination class (e.g. those who both originated and remained in the service class). This suggests that upward mobility either increases the opportunities for men to meet potential partners, or it increases individuals’ preferences to be in a relationship. E.2: Decomposition by decade 1984-1993 Own/Parents Class Working Intermediate Clas Service Tota Class s Class l Working Class 87,0 89,0 85,2 87,3 Intermediate Class 89,4 84,9 79,6 86,8 Service Class 93,1 91,6 85,9 90,1 Total 88,4 88,1 83,7 87,8 N= 17 ,839 Table E2-1: Proportion of men in a relationship by own social class/parents social class combination (%) – 1984-1993 waves Own/Parents Class Working Intermediate Clas Service Tota Class s Class l Working Class 86,5 88,9 87,7 86,0 Intermediate Class 85,5 84,9 71,7 82,8 Service Class 77,2 81,3 74,4 75,9 Total 85,5 85,8 76,4 83,4 N= 15 ,077 Table E2-2: Proportion of women in a relationship by own social class/parents social class combination (%) – 1984-1993 waves 1994-2003 48 Own/Parents Class Working Intermediate Clas Service Tota Class s Class l Working Class 84,4 78,2 76,0 83,1 Intermediate Class 84,9 79,6 79,2 82,5 Service Class 89,4 84,7 87,0 87,1 Total 84,9 81,0 82,1 83,8 N= 34 ,057 Table E3-1: Proportion of men in a relationship by own social class/parents’ social class combination (%) – 1994-2003 waves Own/Parents Class Working Intermediate Clas Service Tota Class s Class l Working Class 84,4 85,9 79,0 84,3 Intermediate Class 82,9 83,8 80,1 82,6 Service Class 79,1 80,5 86,1 81,3 Total 83,4 84,0 81,2 83,2 N= 31 ,889 Table E3-2: Proportion of women in a relationship by own social class/parents’ social class combination (%) – 1994-2003 waves 2004-2017 Own/Parents Class Working Intermediate Clas Service Tota Class s Class l Working Class 83,5 79,5 76,3 82,5 Intermediate Class 85,6 82,0 81,6 83,5 Service Class 88,7 88,0 87,5 88,0 Total 84,6 83,2 82,9 83,9 N= 76 ,968 Table E4-1: Proportion of men in a relationship by own social class/parents’ social class combination (%) – 2004-2017 waves Own/Parents Class Working Intermediate Clas Service Tota Class s Class l Working Class 74,6 74,0 75,3 74,7 Intermediate Class 76,5 77,5 77,0 77,1 Service Class 80,1 75,1 76,7 77,7 Total 75,9 76,5 76,7 76,4 N= 86 ,022 Table E4-2: Proportion of women in a relationship by own social class/parents’ social class combination (%) – 2004-2017 waves 49