Assortative Mating and Wealth Inequalities Between and Within Households

Abstract:Positive assortative mating may be a driver of wealth inequalities, but this relationship has not yet been examined. We investigate the association between assortative mating and wealth inequality within and between households drawing on data from the United States Survey of Income and Program Participation and measuring current, individual-level wealth for newly formed couples (N = 3936 couples). We find that partners positively sort according to wealth over and above sorting by age, race, education, and income. In the absence of assortative mating according to wealth, the Gini coefficient for between-household wealth inequality would be 7 percent lower. Wealth inequalities would thus remain high if couples did not match by wealth. We find a within-household wealth gap of about USD 23,000 to the disadvantage of women. Whereas the within-household wealth gap would be markedly greater for women at the bottom and in the middle of the female wealth distribution without assortative mating, we also find that women would have a substantial wealth advantage under random matching at the top of the female wealth distribution.


Introduction
Social mobility and social inequality are two of the most central concepts in sociology (Mare 2001).The former relates to the openness of societies.How mobile are individuals in the social hierarchy?How easily do they interact with others across the hierarchy?The latter relates to the distribution of valued resources between individuals and households.How unequal and distant are positions in the social hierarchy?Although social mobility and social inequality are distinct concepts and often examined separately, they "go together intuitively" (Hout 2004: 969) and interas well as intra-generational social mobility can be directly related to dynamics in inequality (Mare 2001) and vice versa (Hertel and Groh-Samberg 2019).The joint study of mobility and inequality therefore advances our understanding of how social inequality emerges and changes.
Assortative mating, the systematic sorting of partners into unions to form households, is one type of intragenerational social mobility that can have a powerful effect on social inequality (Breen and Salazar 2011;Schwartz 2013).If partners from different positions in the social hierarchy are able to mate across social boundaries, this ref lects a mobile and open society in which inequality between households will generally be reduced after household formation. 1In contrast, if partners from similar positions in the social hierarchy mate within social boundaries, this ref lects a closed and rigid society in which inequalities between households will generally increase, as resources will be more concentrated within households.Importantly, these inequalities will determine the family context of the next generation (Torche 2010).
Inequalities in economic wealth are an increasing concern in sociology (Killewald, Pfeffer, and Schachner 2017) and in the broader public.By historical comparison, wealth inequality is immense in many rich democracies.There is approximately twice as much wealth inequality as income inequality in most OECD countries (Balestra and Tonkin 2018).In the United States, between-household wealth inequality, as measured with the Gini coefficient, was about 0.86 in 2016 (Kuhn et al. 2020).
Wealth inequalities can create salient social boundaries, and can be an important factor in partner selection, because wealth has profound consequences for the life chances of individuals (Spilerman 2000).In line with the economic inequality hypothesis, which states that large inequality in resources should lead to strong sorting on these resources because stakes in the search for partners are high (Schwartz 2013), we would, therefore, expect that assortative mating in wealth is substantial.This would indicate that the social structure is even more rigid than previously believed.In turn, assortative mating may facilitate the concentration of wealth in particular households.
Assessing the distribution of valued resources such as wealth at the level of households is common in the literature, but inadequate, because it ignores potential inequalities within households, which may affect individuals' well-being, independent of their absolute levels of resources (Bennett 2013;Bloome, Burk and McCall 2019).Moreover, although social mobility in the partner market may lead to lower between-household inequality, it may reinforce within-household inequality (Jasso 2018).Even if strong positive assortative mating leads relatively advantaged men to partner with relatively advantaged women, gender differences in the distributions of resources may still cause men to control more resources than women within these households.The disadvantaged position of women compared with their partners can contribute to their inferior status and lower power within households, with negative consequences for their wellbeing (Bennett 2013).In order to fully understand how assortative mating shapes social inequality, it is thus indispensable to study between-and within-household inequalities together and to take the gender-specific distribution of (individual) wealth into account.
Despite the importance of wealth as a unique dimension of social inequality, we know little about its role in mate selection and even less about how patterns of assortative mating impact between-and within-household inequality.The focus of previous studies on assortative mating has been on education and income (Breen and Salazar 2011;Kalmijn 1991;Schwartz 2013), which may be explained, at least in part, by data availability: although information on education and personal income are readily available, reliable data on personal wealth in couples is scarce.Not considering wealth as an independent dimension in assortative mating may result in an inadequate understanding of mating processes and in misestimating the importance of other dimensions, in particular education and income, since both are related to wealth.
Therefore, the current study examines the relationship between assortative mating and wealth inequalities in the United States.More specifically, we investigate (i) the extent to which oppositesex individuals mate assortatively according to wealth; (ii) whether assortative mating by wealth is related to substantially different between-household wealth inequality compared with random matching and conditional matching by age, race, education, and earnings; and (iii) the extent to which assortative mating is related to within-household inequality.We draw on high-quality data from the Survey of Income and Program Participation (SIPP, 2008(SIPP, -2017)).We examine the current personal wealth of both partners recorded at the individual level in newly formed couples, i.e. the prorated sum of all assets for which individuals have sole or joint legal ownership rights, less their debts.
Thereby, we make three contributions to the literature on assortative mating and economic inequality.First, we examine assortative mating by individual wealth, which may comprise salient social boundaries for partner selection in the context of high wealth inequality in many rich democracies.Second, we empirically quantify the potential effect of assortative mating on wealth inequality by studying empirical and hypothetical mating regimes.By considering the increasingly relevant dimension of stratification, we contribute to the ongoing debate about when we can expect assortative mating to increase inequality.Third, we bridge the literature on assortative mating and within-household inequality by examining the within-household gender gap in wealth at union formation and the degree to which this gap is shaped by assortative mating.

The Partner Market and Assortative Mating
In the theoretical framework of the partner market (Becker 1973), positive assortative mating may result from two processes: competition and matching.Competition may lead to assortative mating if individuals prefer partners with more resources, and neither party is willing to accept a partner with fewer resources.Assortative mating may also result from preferences for similar traits (such as tastes and values) in partners, that is, cultural matching (Kalmijn 1998;Torche 2010).In both processes, individuals may actively choose partners, but they are also constrained by the structure of the partner market.This structure can manifest itself in segmented, locally or institutionally limited submarkets, which reduces the number of available partners.Although assortative mating and homogamy-at least for education-are increasingly dominant patterns in union formation, heterogamous couples remain prevalent (Schwartz 2013).Systematic gender inequality can make homogamy in socioeconomic resources unachievable for some (Edwards 1969;Fu and Heaton 2000).

Wealth in the Partner Market
To our knowledge, Fagereng et al. (2022) is the only study of assortative mating by individual wealth.They find a Spearman rank correlation coefficient of 0.19 between opposite-sex partners' wealth four years before marriage or joint custody of a child is observed in Norwegian register data.They are not able to observe assortative mating among childless cohabiters.
Because wealth inequalities may comprise salient social boundaries, such positive assortative mating by wealth is likely to arise through both competition and matching.First, wealth can be an important economic resource, independent of income, for which partners compete in the partner market.Wealth provides consumption potential on top of current income.Wealth also has additional benefits that income cannot offer (Killewald et al. 2017), as it provides an important safety net and use value (e.g. home ownership) and can be easily transferred across generations (Spilerman 2000).Because wealth is a stock rather than a f low of economic resources, it can also be a strong signal for the long-term ability to support a family and maintain social status, which may be attractive on the partner market, particularly since income and wealth are only moderately correlated (Killewald et al. 2017).
Wealth may also signal traits in which partners culturally match, such as preferences, tastes, and values (Bourdieu 1984: 195ff;Lamont and Molnár 2002).For instance, wealth is related to political preferences, independent of income and education, where the wealthier identify with more conservative political positions, whereas, for example, more education is related to more leftist positions (Arndt 2020).Arguably, cultural matching may be stronger for inherited parental wealth than for self-earned wealth because parental wealth is probably associated with particular socialization during childhood that increases shared understanding between partners (Fremeaux 2014).
Next to the direct sorting of partners by wealth, a correlation between the wealth of each partner may also be the result of sorting according to other characteristics, such as age, race, education, and income, which may themselves be associated with wealth.At the same time, assortative mating by education and income may be misestimated without considering wealth.Whether there is assortative mating by wealth beyond these other aspects of partner selection is thus an empirical question.

The Role of Parental Wealth
Instead of considering individual wealth, previous work has mostly studied sorting by both partners' parental wealth in marriage.Charles et al. (2013) showed a strong positive correlation (about r = 0.40) in log parental wealth between spouses in the United States after adjusting for age and race.Only about a quarter of this correlation could be explained by the educational matching of spouses (see also Fremeaux 2014 for evidence from France).Wagner et al. (2020) show that in Denmark, assortative mating in marriage and cohabitation by parental wealth is particularly strong at the top of the wealth distribution, where individuals with rich parents seem to avoid partnering down.Drawing on high-quality register data, they show that assortative mating in the rest of the wealth distribution is much weaker.Overall, they find correlations in both partners' parental wealth between r = 0.04 and 0.19, depending on empirical specifications (Wagner et al. 2020).
Although parental wealth is important in the study of partner choice, examining sorting only on parental wealth provides an incomplete picture at best, not only because parental wealth is most relevant at the top of the distribution but also because union formation occurs early in the life course, long before large intergenerational transfers will take place.In the United States, for example, the average age of receiving a bequest is about 50 years (Zagheni and Wagner 2015).Studying the wealth that individuals bring into the union is thus necessary in order to more fully understand the sorting process and the resulting inequalities.In line with this argument, Fagereng et al. (2022) finds that parental wealth explains little of the positive sorting on personal wealth in Norway.Nevertheless, current individual wealth at partnership formation, which mostly occurs at young ages, may not fully ref lect the future wealth potential of individuals, which substantially depends on their own savings from lifetime earnings and transfers from their parents' wealth.

Assortative Mating and Economic Inequality between Households
Economic inequality in wealth or income between households is shaped by two conditions: the distribution of economic resources between individuals and the grouping of individuals within households (Breen and Salazar 2011).Here, we focus on the grouping of individuals within households, studying how assortative mating contributes to social inequality (Gonalons-Pons and Schwartz 2017).If resource-rich individuals are more likely to sort into households with resource-rich partners than with resource-poor partners-a scenario of low social intermarriage-inequality between households is expected to be larger compared with a scenario with high social mobility in which individuals mate independent of resources across social boundaries.

Assortative Mating and Within-Household Inequality
Assessing the distribution of resources such as wealth at the level of households is common in the literature-often for practical reasons-and rests on the strong assumption that resources are fully pooled within households and are equally accessible to all household members.From this perspective, within-household inequality is irrelevant.However, a large and growing literature contests the assumption of complete pooling (for an overview, see Bennett 2013).Therefore, we move from a household-level perspective to an individual-level perspective to push beyond questionable assumption that all assets observed and measured for a household provide an equally good measure of wealth for each partner in a household.
Individual property rights and personal wealth are relevant even in married couples.For those married, in most US states, the default marital property regime maintains the separation of personal property during a marriage.The property regime only enforces a redistribution of accrued property in the event of divorce or the death of a spouse.In just nine states (and optionally in Alaska), the default marital property regime is a community of property, but this pertains only to (part of the) property acquired during the marriage.All pre-marital property remains individual property at the end of a marriage.The separation of property within marriage is only legally limited by the financial obligation to support the other spouse.Spouses may agree to nuptial agreements modifying the property regime (Deere and Doss 2006;Katz 2011).Ownership rights convey access and control of assets within marriage (Lee 2022).Individual ownership is even more consequential in non-married, cohabiting couples, which comprise about 47 percent of our sample (see below).In the United States, as a rule, the property rights of cohabiting partners are not explicitly legally regulated.
Even if individuals have legal property rights, do these legal rights matter subjectively for individuals within marriage or do they assume that everything belongs to them jointly?A large body of evidence from qualitative (e.g., Burgoyne et al. 2007;Joseph and Rowlingson 2012) and more recently also quantitative studies (Cesarini et al. 2017;Lersch 2017) shows that partners do not pool all assets or subjectively treat them as joint property, calling a unitary household model (Becker 1973) into question.
Such within-household inequality is of relevance for two reasons.First, in general, ignoring within-household inequality by assuming that household members have the same resources will lead to missing an important aspect of inequality.Inequality between individuals (and, therefore, gender inequality) will be underestimated if resources are assumed to be equally divided in the household while individuals have systematically unequal access to these resources.Second, within-household inequality itself may have numerous negative consequences for the partner who has fewer resources.These consequences can range from the distribution of other resources and power within marriage (Fafchamps and Quisumbing 2005) to an increased risk of intimate partner violence (Oduro et al. 2015). 2  It is therefore important to consider how disparities at the individual level translate into within-household inequality through patterns of assortative mating.All else being equal, positive assortative mating will lead to less within-household inequality.However, even under positive assortative mating, substantial within-household inequality may persist if the gender-specific distributions of resources do not fully overlap (Kalmijn 1998).If rich women mate with rich men, but rich men have more wealth than rich women, within-household inequality will persist despite assortative mating.How the structure of gender inequality in a society translates into withinhousehold inequality through assortative mating is thus a question that depends on the wealth distribution for women and men.
Women are generally expected to bring less wealth into a union than men because women are typically younger at union formation and have thus accumulated wealth for a shorter period (Grabka et al. 2015).Wealth inequalities between women and men are expected to further increase over the course of the partnership because earning inequalities between women and men will feed into wealth inequalities (Chang 2010: 72ff)-the former being greater when unions last longer and children are present.Consistent with this argument, research has shown that wealth inequalities between never-married single women and men are relatively small and statistically non-significant compared with marked inequalities between married women and men (Sierminska et al. 2010; but see Kapelle and Lersch 2020).

The Present Study
We address three research questions: Do individuals mate with partners who have wealth levels similar to their own?To what extent is assortative mating by wealth related to between-household wealth inequalities?To what extent is assortative mating by wealth related to within-household inequalities?To answer our research questions, we first describe the observed wealth distribution among newly formed couples.Second, we estimate the association in personal wealth between both partners in newly formed couples and estimate this association net of sorting by age, race, education, and income.Third, we simulate counterfactual distributions of wealth in which partners are assumed to mate (i) randomly; (ii) conditionally on age, race, education, and income; (iii) with partners equally ranked in the gender-specific wealth distributions; and (iv) with partners on opposite ranks.We use these simulations to determine the extent to which the counterfactual household-level wealth inequality differs from the observed wealth distribution.Fourth, we examine how within-household inequality in wealth differs across these simulated scenarios.
Note that we aim to quantify counterfactual changes in wealth inequality in order to understand the potential effect of assortative mating by wealth.Because our data cover only a relatively short time period, we cannot examine the contribution of assortative mating to historical trends in wealth inequality, and thus, our analysis cannot establish whether changes in assortative mating in recent decades have contributed to changes in wealth inequality.Notwithstanding this limitation, our data are unique in allowing the differentiation of individual wealth within households, which is essential for examining sorting by wealth.

Data
The lack of previous studies on assortative mating and wealth inequality can be explained, at least in part, by data limitations.Because wealth is often conceptualized and measured at the household level, assortative mating by wealth can be examined only if both partners have been surveyed in separate households before union formation.With the exception of register data (Fagereng et al. 2022), most longitudinal surveys examine only one partner before union formation.In the present study, we draw on unique data that allow this problem to be circumvented by differentiating the wealth of both partners, even within the same household: the US Survey of Income and Program Participation (SIPP).
The SIPP is a nationally representative longitudinal household survey that began in 1983.The survey collects a wide range of information on all adult household members in rotating panels.Respondents are interviewed every four months.We draw on data from the SIPP 2008 panel, in which the same respondents were interviewed from 2008 to 2013, and from the SIPP 2014 panel, in which the same respondents were interviewed from 2014 until 2017. 3Detailed wealth data were collected for 2009 to 2011 and 2013 to 2016 (wealth is measured retrospectively for the last calendar year in SIPP 2014).Missing data in SIPP are imputed using a single hot-deck imputation carried out by the data provider.
Compared with the Survey of Consumer Finance (SCF), which is considered the "gold standard" for wealth data in the United States (Eggleston and Klee 2016), the SIPP substantially underreports wealth.We nevertheless use the SIPP data because, in contrast to the SCF, wealth can be assigned to individual household members, and we are not concerned with estimating population-wide wealth inequality in the present study.Similarly, we prefer the SIPP over the Panel Study of Income Dynamics (PSID) because the latter also does not allow to measure wealth at the individual level.

Sample
We restricted the analytic sample to respondents aged 18 and older who had formed a new coresiding couple (cohabitation or marriage) in the last year to examine initial sorting.We selected a sample of newly formed couples because this helps to identify the personal wealth of both partners and their initial assortative mating.Married and cohabiting couples can be expected to increasingly integrate their resources and converge in their characteristics over time.Overall, we observed 3936 newly formed couples in SIPP.About 53 percent of couples are married at the time of interview. 4Our restriction in analyzing newly formed couples means that our analytic sample is quite young with a median age of 32 for women and 90 percent of the sample being 57 years old or younger (median is 34 and 90 percent of sample younger than 59 for men).We do not intend to generalize to the entire partnered population in the United States.

Measurement
We measure the current wealth at the individual level in newly formed couples.We have to assume that this accurately ref lects the earlier wealth relevant for partner selection.Personal net wealth is the sum of all wealth personally owned by an individual.Real and financial assets, life insurances, private pension plans, business assets, and other assets are included.Personal debts and loans are subtracted from these assets. 5Respondents may have negative net wealth.Wealth is top-coded at the 99.5 percentiles of the full sample in the SIPP.We aggregate personal wealth to the household level to analyze between-household inequalities.Net wealth is in constant 2015 prices.
In SIPP, a number of major wealth components (owner-occupied homes, other real estate, and vehicles) are not fully recorded at the individual level.Instead, the values of these components are measured at the household level.Because the individual owners of assets (but not their exact share of ownership) are recorded, the value of assets can be assigned equally to individual owners in the next step (Eads and Tach 2016; US Census Bureau 2019).Ignoring potential inequality in the shares of ownership within households probably leads to an underestimation of withinhousehold inequality.
SIPP enables the direct individual-level measurement of wealth held in businesses, stocks and mutual funds, bonds and securities, saving accounts, retirement accounts, and life insurance.Credit card debt, store debt, loans, and other debt are also recorded at the individual level.For the main analysis, we sum all wealth components in SIPP for our measure of personal wealth, but in a supplementary analysis, we focus on wealth components that are measured at the individual level only, and the results are generally consistent (see the online supplementary material for Tables C1 and C2, Online Appendix C).In this alternative measure, however, we observe more negative wealth and more overall inequality.In order to estimate the degree of assortative mating net of other variables, we include additional variables: age, a binary indicator of being Black (1 = yes; 0 = no), a binary indicator for university/college degree (1 = yes; 0 = no), and annual labor earnings (def lated to 2015 prices).These variables are measured separately for both partners in a couple.We also add survey year dummies.The descriptive statistics for all variables are presented; see the online supplementary material for Table A1 (Online Appendix A).

Estimating the Degree of Assortative Mating by Wealth
In order to examine the magnitude of assortative mating by wealth, to make full use of the information in the continuous wealth variables, and to obtain a direct estimate of the degree and direction of assortative mating, we estimate simple ordinary least squares (OLS) regression models of the following form: where W w is the wealth of the woman and W m is the wealth of the man (see, similarly, Charles et al. 2013); γ is the coefficient of main interest.Our estimate of γ is biased if there are additional, unobserved dimensions of assortative mating that are also related to personal wealth.We thus adjust for a range of partners' characteristic (vector X), as discussed above.Since we cannot rule out that there are additional unobserved confounders, we must be cautious in interpreting our results as evidence for direct assortative mating by wealth.We assume that the idiosyncratic error, , is normally distributed.We also estimate log-linear models, which lead to similar conclusions (see the online supplementary material for Table B.1-B.6 in Online Appendix B).

Counterfactual Matching in Couples
In order to examine the potential relevance of assortative mating for inequality, we compare the observed distributions of wealth in our data to counterfactual distributions that are based on specific assumptions about how individuals mate.These counterfactual matchings are based on the observed data so that all scenarios are permutations of the empirical matching.We use random draws without replacement to mimic restrictions in the partner market.Betweenand within-household inequality will differ compared with the observed distribution in the counterfactual scenarios because women and men are organized differently into households.Inequality within the groups of women and men and across all individuals does not change in these counterfactual matchings.
First, we simulate a random match in which women and men are grouped purely by chance.Second, we condition the random matching to occur (i) within age bands of −one to +4 years around women's ages, (ii) within race, (iii) within educational groups defined by having a university/college degree, and (iv) within gender-specific income tertiles.Compared with any scenario with positive assortative mating, (un-)conditional random matching should increase withinhousehold inequality and reduce between-household inequality.Third, we simulate a matching process, where women and men are matched to partners who are in the same rank in the empirically observed gender-specific wealth distributions.This matching should reduce withinhousehold inequality but will not eliminate within-household inequality if women and men differ in their average wealth levels.Fourth, we simulate a matching process, where women and men are matched to partners of opposite rank, e.g. the wealthiest woman is matched to the poorest man.This scenario should maximize within-household inequality and minimize between-household inequality, but between-household inequality may not be eliminated if women and men differ in their average wealth levels.The third and fourth are extreme scenarios that will not be observed empirically.They represent ideal-typical mechanisms intended to provide benchmarks to compare the other matching scenarios.In each of these scenarios, we repeat the simulation 1000 times and average results across these repetitions to capture the uncertainty of the random draws.

Analyzing Inequality Between and Within Households and the Contribution of Assortative Mating
We mainly use two indices of inequality to capture distinct aspects of wealth inequality.First, we use the Gini coefficient to measure between-household inequality.The Gini coefficient is usually bounded between 0 and 1, where higher values indicate more inequality.However, in our case, because of negative wealth values, the Gini is not bounded by 1 (Cowell and van Kerm 2015).
As a second index, we use half the squared coefficient of variation GE(2), which is defined as where σ is the standard deviation and μ is the mean.GE(2) is more sensitive at the upper end of the wealth distribution than the commonly used Theil index, GE(1), which is not defined for negative wealth values (Cowell 2011: 169-170).The generalized entropy inequality indices GE(a) are mathematically more tractable than the Gini coefficient and have desirable properties for decomposition (Jenkins 1995), which makes this family of inequality indices attractive for the present study.Wealth inequality at the household level can be decomposed into inequality among women and men (measured with the coefficient of variation [CV]) and the correlation ρ mw between partners' wealth (Lam 1997): where subscript m indicates male partners, and w indicates female partners.The share of a couple's wealth accounted for by the male partner's wealth is denoted by a; b denotes the share accounted for by women's wealth.This decomposition means that the effect of ρ mw on betweenhousehold inequality can be examined analytically.
As these inequality measures are agnostic to the potentially gendered nature of inequality within households, we also consider a measure of the absolute within-household gender gap in wealth, where we subtract the man's wealth from the woman's wealth within each household.We then order households by women's (and men's) wealth and take the average of the gender gap at different points in the wealth distribution: for the bottom 20 percent, for the middle 20 percent, and for the top 20 percent.For those households in which both partners have 0 or positive net wealth, we also compute the relative share of the couples' wealth owned by women.This is not possible for the bottom 20 percent because of negative net wealth.
Finally, to examine the inf luence of the overall gender gap in wealth on the relationship between assortative mating and within-household inequality, we create a hypothetical female wealth distribution in which women's ranks do not change but their levels of wealth are uprated to the levels of wealth observed in the male wealth distribution using an inverse cumulative distribution function.With this uprated female wealth distribution, the average gender wealth gap is 0. Inference for all inequality indices and other quantities of interest is based on bootstrapped standard errors with 1000 replications.All analyses were carried out using Stata 16.1.

Observed Wealth Distributions
Table 1 reports characteristics of the observed wealth distribution of men and women within newly formed couples. 6There is considerable inequality in women's and men's wealth, with a Gini coefficient of 1.10 for women's personal wealth and 0.97 for men's wealth.Remember that the Gini is not bounded above by 1 if negative values are included.Similarly, Sierminska et al. (2010) found higher inequality among cohabiting women than men.We also report inequality measures at the couple level (i.e.aggregating women's and men's personal wealth in the household) and at the individual level (i.e.pooling women and men).At the couple level, inequality in wealth is lower (Gini coefficient of 0.95), which provides prima facie evidence that mating reduces inequality in household wealth compared with remaining single.Overall, inequality between newly formed couples is greater than that previously found for the whole population in the United States, which is probably due to the larger share of individuals with no wealth at young ages in our sample.Previous research has found wealth inequality to be higher at younger ages (Cowell et al. 2016).

Magnitude of Assortative Mating by Wealth
We now tackle the first research question and examine the degree to which individuals choose romantic partners with wealth levels similar to their own.Figure 1 shows a scatterplot of women's and men's absolute net wealth, showing a positive but far-from-perfect association. Figure 2 additionally shows the rank-rank relationship, where the ranks refer to the gender-specific wealth distributions.Again, a positive association is apparent, but the relationship is much smaller in the female wealth distribution's lower half than in the upper half.Interestingly, women tend to mate with men lower ranked than themselves in the upper half of the female wealth distribution.Note that men tend to have more absolute wealth than women at the same rank (Table 1).If assortative mating would only be driven by competition for wealth (Kalmijn 1998), we would expect a stronger tendency to mate with equally ranked partners.Such matching on equal rank, however, would also imply more within-household inequality.
Table 2 reports the results from OLS regression models to further examine the relationship visible in Figure 1 (left panel).In Model 1, we include only men's wealth to predict women's wealth.The variables are standardized, so the coefficient indicates that a standard deviation increase in man's wealth (USD 254,466.27,see the online supplementary material for Online Appendix A, Table A1) is associated with an increase of 0.30 standard deviations in woman's wealth (USD 183,512.85),which is about USD 55,000.The association is statistically significantly  different from zero at the 95 percent confidence level.The association remains statistically significant after adjusting for the other observed dimensions of assortative mating.Including woman's and man's age as well as their race reduces the association between spousal wealth slightly by 13 percent to 0.26 (Table 2, Model 2).When additionally adjusting for woman's and  man's education and labor incomes, the association in wealth is estimated at 0.22 (Table 2, Model 3).Notably, if we are concerned about the inf luence of assortative mating on wealth inequality, the unconditional association between partners' wealth may be more informative, whereas the conditional association is more relevant to understand how wealth drives assortative mating.
Re-estimating the models in which both wealth variables and labor incomes are transformed using an inverse hyperbolic sine transformation (see the online supplementary material for results in Table A2, Online Appendix A) shows substantially higher estimated associations compared with the untransformed wealth reported in Table 2 but does not change the conclusions.Alternative log-linear models lead to similar conclusions (see the online supplementary material for Online Appendix B).This is tentative evidence that wealth is a unique and relevant dimension of assortative mating, although we cannot rule out that additional, unobserved dimension of assortative mating, which is also related to wealth, biases our estimates.

Observed Between-Household Inequality Compared With Counterfactual Distributions
We now turn to the second research question by investigating the extent to which assortative mating on wealth shapes between-household wealth inequalities compared with random matching.
To this end, we compare the observed wealth distribution to the four counterfactual distributions.
We consider household-level wealth in this step.Under random matching, where the correlation between both partners' personal wealth is naturally zero, wealth is more equally distributed across households (Table 3).We find a decrease in the Gini coefficient of about seven percent from empirically observed 0.95-0.88under random matching.Between-household inequality remains high, but the confidence intervals of the observed Gini coefficient and the Gini under random matching do not overlap.The changes in the counterfactual distribution are small when we restrict random matching to occur conditionally on age bands, race, educational groups, and income tertiles.Because the correlation between partners' wealth increases in this scenario, the results become more similar to the observed distribution, but the Gini coefficient under conditional random matching (.90) is still statistically significantly different from the observed Gini coefficient (.95).
If couples are matched by rank, the Gini increases to 1.02, which is statistically significantly different from the other scenarios as indicated by the confidence intervals.We find a decrease in the Gini of about 27% to 0.69 under the matching of opposite ranks.Despite this substantial reduction, inequality remains high even under this extreme condition because of the gender inequality in empirically observed wealth distributions (see Table 1 and see the online supplementary material for Figure A1, Online Appendix A).
Overall, our conclusions are similar when GE(2) rather than the Gini coefficient is used to evaluate between-household inequality, but the changes in inequality are more pronounced (Table 3).Using GE(2) and the analytical decomposition outlined in Equation 3 allows us to examine the hypothetical between-household inequality when various parameters, such as the correlation between partners' wealth, the share of women's wealth, the inequality in women's wealth, and the inequality in men's wealth are manipulated (Figure 3).Again, we find that without assortative mating (correlation of 0), between-household wealth inequality would remain high (Figure 3, upper right panel).We find that, in the extreme case of perfect negative assortative mating (correlation of −1), between-household inequality would approach 0. Note that this does not contradict the results from the counterfactual opposite rank matching scenario above.The difference in the empirically observed wealth distributions for women and men prohibit a correlation of −1, even if spouses are matched by opposite ranks.The within-couple correlation in wealth under this matching regime is −0.28 (Table 3), which would lead to a GE(2) of 2.74 (see Table 2 and Figure 3).
Figure 3 also illustrates the hypothetical consequences of changes in inequality in the genderspecific wealth distributions.Although this is not the focus of the present study, it is evident that inequality in men's wealth is strongly linked to between-household inequality-more so than inequality among women, which mirrors the findings from counterfactual matching scenarios.For instance, to achieve a reduction in between-household inequality similar to that achieved by switching off assortative mating (from GE(2) = 4.77 to 3.72), men's wealth inequality would have to be reduced by about 19 percent (from a coefficient of variation of about 3.67 to only about 2.97-Figure 3, lower left panel), all else being equal.In contrast, to achieve the same reduction, women's wealth inequality would have to be reduced by 33 percent (from a coefficient of variation of 4.00 to 2.68).Finally, Figure 3 illustrates the importance of gender inequality for between-household inequality by considering the effect of women's share of wealth.Women own about 40 percent of the wealth.With a more equal division of wealth between women and men, inequality between households would be reduced, holding constant the observed matching patterns.More generally, the matching of individuals from two identical distributions tends to result in a more equal distribution if pairing is not perfectly rank-correlated (Lam 1997).However, it is important to keep in mind that this counterfactual simulation ignores how the distinct parameters are related, where, for instance, a change in women's share of wealth is likely to coincide with a change in the correlation between partners' wealth.

Observed Within-Household Inequality Compared With Counterfactual Distributions
We now address the final research question about within-household inequalities by investigating how these inequalities would change under the different counterfactual matching regimes.We analyze this within-household inequality with gender-sensitive measures of the absolute wealth gap (in USD 1000) between women and men, where a negative sign indicates disadvantage for women and the relative share owned by women (Figure 4).We present the results both from the perspective of women's wealth distribution (Figure 4, left panels) and men's wealth distribution (Figure 4, right panels).
Overall, we observe a mean within-household gender wealth gap of about USD −23,000 to the disadvantage of women in the United States. 7We find the average gender gap in wealth to be USD −56,000 for women in the lowest 20 percent of the female wealth distribution (Figure 4, left top panel).Among women in the middle 20 percent of the female wealth distribution, the gender gap is clearly smaller (USD −23,000).The wealth gap in the top 20 percent of the female wealth distribution is USD 39,000 to the advantage of women.In other words, the wealthiest women mate with men who are less wealthy, on average, resulting in considerable hypogamy in the top 20 percent.Given their position at the top of the female wealth distribution, by chance, these women could be expected to mate with less wealthy men unless strong positive sorting would limit their partner search to the upper end of the male wealth distribution.
When we consider the counterfactual distribution under random matching, we find an increase in the gender wealth gap at the bottom and in the middle of the female wealth distribution.In other words, women at the bottom and in the middle of the female wealth distribution have partners with less wealth than would be expected if women mated randomly.Under random matching, women in the top 20 percent would have, on average, USD 167,000 more wealth than their partners.Thus, women at the top of the female wealth distribution have partners with more wealth than would be expected by chance.This pattern is similar but less pronounced for random matching restricted by age, race, education, and income indicating that sorting on these additional dimensions partly explains why we see less hypogamy than would be expected by chance.Using relative wealth shares (Figure 4, bottom left panel), which indicate the share of couples' wealth owned by women, we also come to similar conclusions.For instance, in the top 20 percent, women would own 78 percent of couples' wealth under random matching compared with 59 percent in the observed distribution.The relatively small absolute gap in the equal rank counterfactual translates into large relative gaps because couples' average joined wealth is low in this scenario.
We consider two additional matching scenarios for illustration and to benchmark the other results: matching on equal ranks and matching on opposite ranks (Figure 4, top left panel).Under matching on equal ranks in the observed wealth distributions, there would be almost no gender wealth gap for women in the lowest and the middle 20 percent of the female wealth distribution.However, the wealth gap in the top 20 percent of the female wealth distribution would be USD −91,000 ref lecting the higher wealth levels of men at the top of the distribution (Table 1).Generally, our observed gender gap falls between the counterfactual gaps of equal rank and conditional matching.Not surprisingly, under a opposite rank matching regime, where the wealthiest (poorest) woman is matched with the poorest (wealthiest) man, the gender wealth gap would be very pronounced at the lower end of the female distribution (USD −356,000), almost non-existent in the middle, and large and to the advantage of women at the top (USD 261,000).
The results from the perspective of men's wealth distribution mirrors those just described.Among men in the top 20 percent of men's wealth distribution, the within-household gender gap is USD −179,000.The wealth gap would be even more pronounced under random matching (USD −280,000).Again, this suggests that men at the top of the distribution mate with richer women than would be expected by chance.The gender gap is small but positive in the middle and bottom 20 percent of the male wealth distribution and would increase under random matching.
Finally, we consider a hypothetical scenario in which women's wealth is uprated to the level of wealth observed in the male wealth distribution, whereas they would still match with the same men (Figure 5).In other words, and in contrast to what we observe in our data, the female and male wealth distributions completely overlap and, on average, no general gender wealth gap exists in this hypothetical scenario.This gender equality is ref lected in a wealth gap of 0 for the equal rank counterfactual.In this scenario compared with results from Figure 4, the within-household wealth gap most pronouncedly changes at the top of the distribution, where women would now have USD 129,000 (compared with USD 39,000 in the original distribution) more wealth than their partners, on average.The gender wealth gap in the middle and at the bottom of the female wealth distribution would hardly change ref lecting the small absolute changes in the female wealth distribution due to uprating in this part of the distribution (cf.Table 1).

Discussion
Questions about how partnerships form and the societal consequences of partnership formation are central to sociology and neighboring disciplines.From the perspective of inequality research, assortative mating can be seen as one type of intragenerational social mobility with a powerful impact on social inequality.Although assortative mating may be linked to wealth inequalities between and within households, this relationship has not been examined previously.We addressed this gap by investigating the links between assortative mating and wealth inequality in the United States.Our study departs from previous research in important ways.First, we used data from SIPP to identify individuals' wealth in newly formed couples, which enabled us to examine assortative mating by individual wealth rather than by parental wealth.This allowed us, second, to construct counterfactual wealth distributions to assess the potential effect of assortative mating on between-household wealth inequality.Third, we analyzed how the withinhousehold gender wealth gap is affected by assortative mating.This allowed us to produce a number of original and useful results.
First, we find considerable positive assortative mating in individual wealth across various model specifications in the United States, complementing previous findings on mating by parental wealth (Charles et al. 2013).This association remains if we consider other important drivers of assortative mating-age, race, education, and labor income.Our estimates (standardized regression coefficients between 0.30 and 0.22 when other dimensions are controlled for) are similar in size to the estimated correlation in parents' wealth for the United States (Charles et al. 2013) and in line with results for Norway (Fagereng et al. 2022).These findings suggest that individuals mate assortatively according to their wealth early in the life course, even before most people have received inheritances from their parents.
Second, we quantify the potential effect of positive assortative mating on between-household wealth inequality.Our counterfactual results show that, in the absence of positive assortative mating by wealth, between-household inequality measured with the Gini would be about seven percent lower in the United States.It is important to note that comparisons with counterfactual distributions cannot establish causality because unobserved third factors may be related to assortative mating and inequality.Nevertheless, the present findings suggest that assortative mating is a potentially relevant mechanism modestly contributing to between-household wealth inequality when compared with the increases in wealth inequality in recent decades in the United States (about 13 percent higher Gini from 1977 to 2016 in the United States; Kuhn et al. 2020).
Third, we show that there exists considerable within-household wealth inequality between partnered women and men living in the same household.The within-household gender gap in wealth is not uniform across the wealth distribution.We find considerable hypogamy at the top of the female wealth distribution, where the wealthiest 20 percent of women have more wealth than their partners, on average.If women would sort perfectly on rank, we would expect hypergamy given men's higher absolute wealth levels at the top of the distribution.Instead, the results suggest that wealthy women sort into households in which they are relatively advantaged because they mate with men that are less wealthy than would be expected by perfect rank matching.In addition, compared with random matching, the results suggest that wealthy women sort into households in which they are relatively disadvantaged because they mate with men that are wealthier than would be expected by chance.Conditional matching on other dimensions such as age, race, education, and income can partly explain this difference.Further down the female wealth distribution, we find women to have less wealth than their partners in the middle and at the bottom of the distribution.Here, the gender gap would be amplified at the bottom and in the middle of the distribution under random matching.
We acknowledge two main limitations of our study.First, because we observed only the wealth of newly formed couples between 2009 and 2016, and because the year-specific case numbers are low, we could not thoroughly examine trends in the associations under study.We therefore cannot determine whether an increase in within-couple wealth correlation over time contributed to an increase in between-household inequality.To answer this question, future research would have to examine longer observation periods.Preliminary analysis (see footnote 3) shows that withincouple wealth correlation may have decreased in the United States between 2004 and 2005 and 2009 and 2016.
Second, we may have underestimated within-household inequality because some major wealth components such as housing equity cannot be fully assigned to individuals in the SIPP.Instead, it needs to be assumed that these assets are owned equally by both partners.Furthermore, partners may report perceived rather than legal ownership of assets.For instance, two partners may report an equally shared ownership of their home, whereas, legally, one partner owns a larger share in the house.However, based on qualitative evidence (Joseph and Rowlingson 2012), cases seem more likely in which partners report an equally shared ownership despite unequal legal titles than cases in which partners report unequal ownership despite equal legal titles.Nevertheless, the SIPP provides the most appropriate data for our study in the United States because other surveys measure wealth only at the household level.
Our study has important implications for the study of assortative mating and economic inequality and for the question of when we can expect assortative mating to contribute to inequality.First, in line with recent literature on wealth as an independent dimension of stratification (Killewald et al. 2017), we emphasized the distinct role of wealth in assortative mating by building on the ideas of competition and matching in partner markets.Our results regarding substantial positive assortative mating by wealth are in line with this theoretical conjecture.Our findings extend previous work on assortative mating on earnings (Schwartz 2010) by furnishing evidence for an additional and independent economic dimension of assortative mating.Without considering mating according to wealth, estimates of mating by earnings and education may be misestimated.Furthermore, taking the openness of the partner market as an indicator of the f luidity of a society (Blau 1977), our results suggest overall that the social structure in the United States is even more rigid in the economic dimension than previously believed.
Second, assortative mating necessarily comes with a trade-off between within-and betweenhousehold inequality that is often overlooked in this area of research (Jasso 2018).Everything else equal, more assortative mating will increase between-household inequality, whereas it reduces within-household inequality.Lower between-household economic inequality due to social mobility may come at the cost of higher within-household economic inequality, often to the disadvantage of women, which can have negative consequences for their well-being (Bennett 2013).Thus, only considering between-household inequality ignores important implications of assortative mating and disguises how women's life chances are affected by assortative mating.Concerns about growing between-household economic inequality due to assortative mating need to be balanced with related advances in women's relative standing within households.The weight that one gives to these two dimensions of inequality will ultimately guide the judgment whether increasing assortative mating is good or bad in terms of inequality.
Third, we find that even in the absence of assortative mating, however, wealth inequality remains high, and wealth inequalities are fairly stable even under extreme matching scenarios.This indicates that the individual wealth distributions-and changes therein-for women and men (including the share of wealth held by both groups), which we treated mostly as fixed in the present study, arguably have a greater effect on household-level inequalities than does the matching of partners.Uprating women's wealth to match the observed distribution for men would naturally eliminate average gender inequality in wealth, but within-household inequality would remain to the advantage of women at the top of the female wealth distribution and to the disadvantage of women in the rest of the female wealth distribution.This shows that assortative mating processes can lead to systematic within-household inequality for subgroups even in the absence of general gender inequality in resources.
Our study has several implications for future research.It would be important to jointly examine parental wealth and individual wealth in processes of assortative mating following Fagereng et al. (2022).As we argued in our study, the wealth of both generations' is expected to be inf luential in assortative mating, and both generations' wealth is closely related (Wagner et al. 2020).The joint study would allow this relatedness and the lasting inf luence of social origin to be considered and aim to disentangle the unique contribution of both types of wealth to assortative mating.Data demands are high, however, because the wealth of both generations needs to be examined.Wealth register data would allow for this kind of analyses (Fagereng et al. 2022), whereas, even in long-running panel studies such as the PSID, the parents of at least one partner will not usually be included in the data.Here, it would also be important to pay attention to variation in assortative mating across the wealth distribution as our analysis suggests unique mating patterns in different parts of the distribution (see also Wagner et al. 2020).
A crucial open question is how partnership dynamics affect homogamy in wealth and inequality.As Gonalons-Pons and Schwartz (2017) show for assortative mating and income, the labor force adjustments after partnership formation are central for inequality outcomes.Similarly, the consumption, saving, and investment decisions of both partners after partnership formation will have a profound effect on the outcomes under study.Although increasing resource integration seems likely, there is also evidence for stable gaps in wealth between partners throughout the partnership duration (Kapelle and Lersch 2020).Moving beyond newly formed couples to study similarity in wealth between partners more generally would improve our understanding of how household sorting affects inequality.

Endnotes
1.Because we focus on couple households with and without children, we use the terms "couple" and "household" interchangeably in the following.2. Although the empirical evidence for within-household wealth inequality in this direction until now comes from poor countries, results regarding income inequality from aff luent countries (e.g., Aizer 2010) suggest that within-household wealth inequality may also matter in these countries.3. We re-run the analysis with data from the SIPP 2004 panel for the years 2004 and 2005.
Overall, results are consistent (see the online supplementary material for Tables C1 and C2, Online Appendix C).However, the correlation between women's and men's wealth is found to be somewhat larger.The results are consistent if we only consider SIPP 2008 and exclude SIPP 2014.4. For cohabiting couples, we find a slightly lower degree of positive assortative mating than for married couples.Excluding separated, divorced and widowed respondents (based on current marital status) does not change results (see the online supplementary material for Table C1, Online Appendix C). 5. We also find positive assortative mating on debts and loans (see the online supplementary material for Table C1, Online Appendix C). 6. See the online supplementary material for Figure A1 in Online Appendix A for density plots of the gender-specific wealth distributions and a comparison with the distribution in unrestricted samples (including singles and couples who had lived together for more than two years).In the unrestricted samples, more extreme wealth values are included, but overall inequality is lower than in our analytical samples (Gini coefficient of 0.81 in unrestricted samples).7.Because we do not include singles in our data, the within-household gender gap is identical to the general gender gap in our data.

About the authors
Philipp M. Lersch is an associate professor in the Department of Social Sciences at Humboldt-Universität zu Berlin and Senior Research Fellow at the German Institute for Economic Research (DIW Berlin/SOEP).His main research interests are in dynamics in social inequalities over and between life courses in divergent institutional contexts focusing on family, wealth, and employment.His recent work has been published in the American Sociological Review, Acta Sociologica, and European Journal of Population.Reinhard Schunck is a professor of sociology at the University of Wuppertal.He works primarily in the field of social stratification and inequality, examining how migration and family-related processes relate to patterns of social inequality.In addition to that, he has a focus on quantitative methods.

Figure 1 .
Figure 1.Scatter plot of the observed wealth distributions among women and men in newly formed couples.Note: Data from SIPP 2008/2014 (unweighted).All figures use a graph scheme by Bischof (2017).

Figure 2 .
Figure 2. Rank-rank relationship of the observed wealth distributions among women and men in newly formed couples.Note: Data from SIPP 2008/2014 (unweighted).CDF = cumulative distribution function.

Figure 4 .
Figure 4. Absolute and relative within-household gender gap in wealth across women's and men's wealth distributions.Note: Data from SIPP 2008/2014.Lines indicate 95 percent confidence intervals.For relative share, only couples are included in which no partner has negative net wealth (therefore, lowest quintile and opposite rank counterfactual are excluded).This figure and Figure 5 use a Stata package by Jann (2014).

Figure 5 .
Figure 5. Absolute and relative within-household gender gap in wealth across women's and men's wealth distributions with adjusted women's wealth distribution.Note: Data from SIPP 2008/2014.Lines indicate 95 percent confidence intervals.For relative share, only couples are included in which no partner has negative net wealth.Therefore, lowest quintile and opposite rank counterfactual are excluded.

Table 1 .
Inequality Measures for Personal Wealth of Women and Men and Household Wealth

Table 2 .
OLS Regression Model of Women's Wealth with Men's Wealth