Abstract

Exchange of racial for educational status has been documented for black/white marriages in the United States. Exchange may be an idiosyncratic feature of U.S. society, resulting from unusually strong racial boundaries historically developed there. We examine status exchange across racial lines in Brazil. In contrast to the United States, Brazil features greater fluidity of racial boundaries and a middle tier of “brown” individuals. If exchange is contingent on strong racial boundaries, it should be weak or non-existent in Brazilian society. Contrary to this expectation, we find strong evidence of status exchange. However, this pattern results from a generalized penalty for darkness, which induces a negative association between higher education and marrying darker spouses (“market exchange”) rather than from a direct trading of resources by partners (“dyadic exchange”). The substantive and methodological distinction between market and dyadic exchange helps clarify and integrate prior findings in the status exchange literature.

Introduction

Status exchange is the hypothesis that individuals trade status characteristics when they establish heterogamous marriages. Status exchange has received much attention by social scientists. The reason is not its prevalence. Heterogamous marriages—that is, those that cross educational, racial, or other status boundaries—are scarce. Rather, status exchange is an interesting object of study because it provides information about the social valuation of different status attributes that make a partner desirable. Thus, status exchange tells us about the systems of racial and socioeconomic stratification within a particular society and how these systems of stratification affect individuals in one of the most intimate realms of life. To date, the study of exchange has been largely confined to black/white unions in the United States. Some studies have found evidence consistent with both status exchange between blacks and whites and isolation of less-educated blacks from the interracial marriage market (Fu 2001; Gullickson 2006; Qian 1997; Schoen and Cheng 2006; Schoen and Wooldredge 1989). Significant debate exists, however, about the correct methodological approach to measure status exchange as well as the generalizability of the exchange hypothesis outside the U.S. white/black context.

Within the United States, tests of status exchange for interracial marriages other than black/white unions have been inconclusive. Weak indication of status exchange between Hispanics and non-Hispanic whites exists (Fu 2001; Qian 1997), and results are mixed for Asians and whites (Fu 2001; Hwang et al. 1995; Qian 1997). These findings suggest a more tenuous racial hierarchy between these groups than the distinction between blacks and whites. Furthermore, very few studies have extended the question about status exchange to other national contexts. The studies that exist have not found evidence of exchange in Canada (Hou and Myles 2013) or the Netherlands (Kalmijn and van Tubergen 2006). These null findings suggest that status exchange may be an idiosyncratic feature of black/white marriage in the United States, stemming from the unusually strong racial boundaries historically developed in that country (Kalmijn 2010). Testing this hypothesis requires examining status exchange in other countries, particularly those with a large black population.

Scholars also debate as to how status exchange should be measured. This debate reflects not only methodological disagreement but also substantively different understandings of the process. Most commonly, status exchange is seen as a direct barter between spouses in which blacks trade their high educational status in exchange for the racial advantages of the white partner. Conversely, white partners trade their racial advantage in exchange for the socioeconomic status associated with higher levels of education, such that the union is advantageous for both parties.

However, Fu (2001) instead conceptualized status exchange as emerging from the preference, in racially stratified societies, for more-educated and lighter spouses, with no direct exchange necessary. Gullickson (2006) developed a comprehensive model of the relationship between education and interracial marriage that includes both the more common understanding of status exchange as a direct trade and Fu’s approach, but did not interpret the parameters derived from Fu as representing exchange. Rosenfeld (2005) criticized prior studies on methodological and substantive grounds and argued that when models are properly constructed, there is little evidence of status exchange in the United States. However, as we will show, some of the parameters that Rosenfeld “controls for” are precisely the terms that Fu argued represent exchange.

In this article, we examine interracial marriage in Brazil to address two questions. First, what is the correct way to conceptualize and measure racial disadvantage and privilege in the marriage market? Second, is status exchange on the marriage market restricted to black/white unions in the United States, or does it have applicability to other racially diverse societies? In terms of conceptualizing how race and education interact on the marriage market, we integrate prior literature to offer a key analytical distinction between dyadic exchange and market exchange. Although most research to date has focused on dyadic exchange, we argue that market exchange is a broader, more pervasive manifestation of racial stratification. Brazil is a particularly useful context for illustrating this distinction because the relatively high frequency of interracial marriage leads to a large sample size that allows us to adjudicate between models of exchange.

Furthermore, the study of Brazil provides substantive insights into race relations that would not emerge in other contexts. Like the United States, Brazil has a large Afro-descendant population and is marked by sharp educational and socioeconomic inequalities by race (Arias et al. 2004; Reichmann 1999). However, in contrast with the United States, sociability across racial boundaries—both casual and intimate—is frequent (Telles 2004).1 Furthermore, racial identification in Brazil is based on phenotype rather than ancestry, and racial boundaries are more porous and fluid (Lovell 1999). As a result, Brazil features a color gradient, with a large and fluid tier of “browns” in the middle of the racial hierarchy (Bailey 2009; Degler 1971; Telles 2004).

We ask whether status exchange exists in a context that combines high inequality with high sociability and fluid boundaries between racial groups. We also examine whether the strength of exchange between blacks, browns, and whites matches the socioeconomic distances between these groups. Examining status exchange in Brazil is useful in several respects. First, it enriches our understanding of the differences in race relations in the United States and Brazil. Second, it helps us move toward a more general understanding of racial disadvantage in the marriage market that transcends the probably idiosyncratic U.S. case. Third, this analysis informs us about the future possibilities for race relations and interracial marriage in the United States itself. Some have argued that the United States is beginning to move toward a more Latin American style of race relations, in which greater sociability, the growing acceptance of a mixed-race group, and the greater fluidity of race serve to mask continuing racial inequality (Bonilla-Silva 2004).

Status Exchange in Interracial Marriage

The theory of status exchange, developed independently by Merton (1941) and Davis (1941), argues that interracial unions would often involve an exchange of status in which the dominant group member exchanges a higher racial status for a higher status on some other characteristic, generally operationalized as education. Unions formed from such exchanges would deviate from educational homogamy (in which partners have a similar level of education) and instead would feature a minority spouse who was more educated than the dominant group spouse. Merton and Davis developed this theory for the particular case of black/white interracial marriage. Given the traditional gender division of labor in society, education is claimed to be a more valuable attribute on the marriage market for a man than for a woman. As a result, the most prevalent form of exchange should be the case in which the male partner trades his educational status for the racial status of the female partner.

Both Merton and Davis defined exchange as a dyadic phenomenon in which there is a direct trading of resources between partners. Merton (1941:372) conceptualized “a reciprocal compensatory situation in which the black male ‘exchanges’ his higher economic position for the white female’s higher caste status,” and Davis (1941:389) indicated that “the class achievements of certain Negro males enable them to bargain for females of the white caste who stand low in the class hierarchy.” Guided by this original definition, early attempts to test status exchange theory for black/white intermarriage in the United States assumed that the educationally asymmetric pairings predicted by the theory—those characterized by white educational hypergamy, in which the black spouse has more education than the white spouse—would be the most common form of interracial union. These studies found little support for the theory because educationally homogamous marriages were found to be the most common form of union in black/white intermarriage, just as they are for other types of marriage (Bernard 1966; Heer 1974; Monahan 1976). However, this test is overly stringent. The key test of dyadic status exchange lies in the comparison between interracial and intraracial couples. Specifically, white partners in interracial marriages are expected to be more educationally hypergamous (marry up) and less educationally hypogamous (marry down) than their respective sexes in intraracial unions. Conversely, black partners in interracial unions should be more educationally hypogamous and less educationally hypergamous than their respective sexes in intraracial unions. Such educational asymmetry in interracial marriages is the crucial test of dyadic exchange.

Several approaches have been used to measure dyadic exchange, including harmonic means (Schoen and Wooldredge 1989), hypergamy ratios (Kalmijn 1993, 2010; Qian 1997), log-linear modeling (Gullickson 2006; Rosenfeld 2005), and multinomial logit modeling (Hou and Myles 2013). Most empirical studies have found evidence of status exchange in marriages between black men and white women in the United States but mixed results in marriages between black women and white men. Other studies find no evidence of exchange (Rosenfeld 2005), and dissent exists regarding the correct method of measuring the phenomenon (Gullickson and Fu 2010; Kalmijn 2010; Rosenfeld 2010).

Although the dyadic approach to exchange is predominant in the literature, an alternative definition of exchange emerges from a market rather than a dyadic perspective. This approach assumes that in racially stratified societies, darkness operates as a generalized penalty on the marriage market that can be compensated for by education.2 If both education and whiteness are considered valuable resources in the marriage market, and if these resources are at least partially fungible, then individuals with higher education will have better access to lighter partners and lighter individuals will have better access to more educated partners (Fu 2001). As a result, both blacks and whites will be increasingly likely to marry whites as their education increases. Thus, educational attainment will have different effects on the probability of interracial marriage for blacks and whites: educational attainment will increase the odds of interracial marriage for blacks but decrease those same odds for whites. This differential effect of educational attainment on interracial marriage is distinct and separable from overall educational assortative mating—the patterns of educational sorting and matching between spouses’ education—that apply to all spouses.

This market exchange perspective shares the underlying rationale of dyadic exchange that racial stratification shapes marriage choices, but it does not require or predict a direct dyadic transaction of status between the spouses themselves. Instead of seeking equality through the exchange of different forms of status, each person on the marriage market seeks the “best” potential partner on these two dimensions, and race and education have some exchangeability as desired resources. In methodological terms, market and dyadic exchange can be distinguished by the fact that market exchange makes a prediction about how the odds of interracial marriage change based on each spouse’s education separately, whereas dyadic exchange makes a prediction about how the odds of interracial marriage change depending on particular asymmetric combinations of both spouses’ education. As a result, market exchange applies not simply to the small number of educationally asymmetric interracial couples but rather to all interracial couples.

Although market exchange is not defined by the educational asymmetry of spouses in interracial marriage, it indirectly produces the same expectation as dyadic exchange about the relative frequency of white hypergamy. Because lightness is a valued resource in racially stratified societies, blacks who marry across racial lines will be less able to compete with whites of the same educational level for highly educated spouses and therefore will be more likely to marry down in education (black hypogamy). Analogously, whites who marry across racial lines will be better able to compete for highly educated spouses than blacks who marry fellow blacks and therefore will be more likely to marry up in education (white hypergamy). Under market exchange, this asymmetry is a by-product of the competition for “desirable” spouses along educational and racial lines; in dyadic exchange, it is a result of a trade between spouses. If market exchange is not properly modeled, it will appear as dyadic exchange—a limitation affecting most analyses of exchange to date.

Some prior work has examined the association between an individual’s education and the odds of interracial marriage, but it has not included it in a conceptual framework that distinguishes market from dyadic exchange. The theoretical concept of exchange as resulting from a generalized penalty for darkness was initially developed by Fu (2001), although he did not distinguish between market and dyadic exchange. Gullickson (2006) included terms capturing market exchange and dyadic exchange in a model for black/white marriage in the United States, although he used them to test several theories about the effect of education on the probability of crossing racial barriers in marriage. Hou and Myles (2013) applied a similar model using a multinomial rather than log-linear formulation to compare the United States and Canada. These last two analyses, however, were hampered by the relatively small number of intermarriages in the United States and the resulting difficulty in choosing a best-fitting model. Because market and dyadic exchange parameters partially overlap, the collinearity between them limits the researcher’s ability to select an appropriate model.

Beyond these debates over conceptualization and methodology, Kalmijn (2010) argued for the need of comparative work to determine whether status exchange is a general feature of racially divided societies or is a historically specific feature emerging from particular race relations in the United States. Based on his own work in the Netherlands that showed weak evidence of status exchange between black Caribbean immigrants and whites (Kalmijn and van Tubergen 2006), Kalmijn (2010) suggested that status exchange may be stronger in societies with strong racial boundaries, such as the United States. Hou and Myles (2013) found little evidence of status exchange between blacks and whites in Canada, providing support for this hypothesis. Although research on interracial and interethnic marriage outside the United States is growing (Choi et al. 2012; Model and Fisher 2002; Model et al. 1999), these studies of Canada and the Netherlands remain the only analyses of race-by-education exchange outside the United States.

Moving Beyond the United States: The Brazilian Case

Brazil offers an important case for status exchange theory because of the clear contrasts between race relations there and in the United States. The primary racial division in both countries lies along a black/white axis that emerged from a system of African slavery. However, although this divide is binary in the United States with relatively rigid boundaries between black and white, the boundaries in Brazil are fluid and conform more to a continuous color gradient that has not given rise to a strong sense of group identity (Bailey 2009; Reichmann 1999).

Perhaps the most important difference between the two countries is the treatment of race mixing. Historically, mixed-race black/white individuals in the United States have been treated as exclusively black, according to the rule of hypodescent, which classifies all individuals with identifiable African ancestry as black regardless of other ancestries they might possess (Davis 1991; Williamson 1980). Thus, no distinction was made for a middle tier between black and white, and “blackness” came to be defined by ancestry rather than appearance. In Brazil, on the other hand, race mixing has been embraced as part of the national identity, and a middle tier of mixed-race “browns” exists between black and white (Degler 1971; Telles 2004; Wolfe 2001). Because of the weakness of group identity, however, one should not think of Brazil as possessing three distinct groups. Rather, the existence of a color continuum in Brazil allows for a highly fluid middle position that is defined more by phenotype than by ancestry.

An apparent paradox of race relations in Brazil is the coexistence of pronounced racial inequality with fluid sociability across racial boundaries. Residential segregation is much lower in Brazil than in the United States, friendships crossing racial boundaries are more common, and interracial marriage is much more prevalent (Ribeiro and Silva 2009; Telles 1995, 2004). Figure 1 shows the odds ratio of exogamous marriages, which adjusts for differences in group size, among younger married couples in the 2000 Brazilian census, and compares it with the 2000 U.S. census.3 The odds ratio is highest for brown/black unions and lowest for white/black unions, and white/brown unions are slightly more common than white/black unions. All three types of exogamous unions in Brazil are far more prevalent than white/black unions in the United States.

Telles (2004) attempted to resolve this seeming paradox of coexisting racial inequality and interracial sociability in Brazil by separating race relations into two relatively orthogonal dimensions: one dimension measuring a horizontal axis of sociability and another dimension measuring a vertical axis of inequality. From this perspective, the importance of Brazil is that it demonstrates that racial inequality is compatible with racial sociability. High levels of racial sociability may in fact reinforce inequality by emphasizing the view that “race is not a problem here” and thus deflecting any critique of the status quo (Bonilla-Silva 2004; Telles and Sue 2009).

Historically, this greater sociability has helped to promote the notion that Brazil possesses a “racial democracy” in which racial relations are harmonious and any observed inequality by race merely reflects class disparities, the inheritance of privilege, and the lingering effects of slavery. Nonetheless, high levels of inequality persist between whites and nonwhites, and this inequality is not explainable simply by differences in class origin (Lovell 1999; Marteleto 2012; Silva 1985; Telles and Lim 1998).

There is considerable debate, however, about whether the life chances of blacks and browns differ. Some scholars have found evidence of a brown-black socioeconomic gradient, although the differences are much smaller than the gap between whites and browns (Bailey et al. 2013; Telles and Lim 1998). Other research, however, has found little evidence of a gradient in income and other socioeconomic indicators between blacks and browns (Lovell 1999; Silva 1985; Silva and Hasenbalg 1999). Furthermore, black/brown socioeconomic differences appear to have been closing in the recent past (Marteleto 2012; Telles 2004:123).

A corollary of racial fluidity in Brazil is that racial categories are not rigid and immutable but rather can be altered within the individual life cycle and across generations. In the United States, racial classifications are largely stable across the life cycle (but see, e.g., Noymer et al. 2011; Saperstein and Penner 2012). In contrast, Brazil has historically held a widespread belief in a “whitening” process by which the mixing of white and nonwhite members would gradually whiten the population and lead to the extinction of the black influence—an objective explicitly promoted by the Brazilian state in the early twentieth century (Loveman 2009; Nobles 2000; Skidmore 1974).

Even if the explicit preference for “whitening” gave way to notions of “racial democracy” by the mid-twentieth century, whitening still remains an implicit component of discourse on miscegenation (Schwartzman 2007; Telles 2004; Twine 1998; Wolfe 2001). “Whitening” is a widespread aspiration, which can be accomplished by marrying a lighter partner or by economic success, as expressed in the “money whitens” formulation (Harris 1956; Ianni 1960; Loveman et al. 2012; Telles 2004). Researchers have also found that “whitening” (and “darkening”) is particularly common across the brown-black boundary, whereas the white category is more stable and impervious to modification through upward mobility or intermarriage (Lovell and Wood 1998; Schwartzman 2007).

Because racial classification in Brazil depends more on appearance than ancestry, this preference for lightness creates the possibility for intergenerational upward mobility within the racial hierarchy unfamiliar in the United States—namely, that one can improve the lives of one’s children by marrying someone of lighter skin (Burdick 1998; Degler 1971; Telles 2004). Such potential intergenerational mobility would provide a motivation for status exchange virtually unknown in the U.S. context.

In sum, Brazil provides a unique test case for the status exchange hypothesis beyond the United States. If, as suggested by past literature, exchange is a uniquely American phenomenon stemming from unusually strong black/white boundaries, then we should find weak or nonexistent exchange in the Brazilian context. On the other hand, fluid sociability among racial groups in Brazil means that a large proportion of nonwhites and whites cross racial boundaries in intermarriage. Furthermore, socioeconomic inequality across racial groups and the preference for “whitening” provides a strong incentive to choose a lighter partner. In contrast to the hypothesis that exchange depends on the unusually strong racial boundaries existing in the United States, Brazil could then provide a particularly powerful case of status exchange.

We address the following questions about the nature of interracial marriage in Brazil. First, do we observe a process of status exchange? Second, is this process better captured by market or dyadic exchange? Third, in a context with a gradational sense of race, is the exchange process isomorphic with the relative socioeconomic gradient between groups in the racial hierarchy? That is, do we expect that status exchange will be greater between whites and blacks than between whites and browns?

To date, empirical evidence about status exchange in Brazil is limited. Burdick (1998), in an ethnographic study in Rio de Janeiro, found evidence of processes of status exchange in which nonwhite partners exchange other resources for access to white partners, although he did not examine class resources, such as education. Burdick found that lighter women and men who married darker partners claimed to receive greater devotion than they would have received from lighter spouses. Ribeiro and Silva (2009) reported a decline in both racial and educational barriers to intermarriage between 1960 and 2000 but did not analyze the exchange between these two resources. Telles provided the only statistical test of status exchange in Brazil using education as the status characteristic. He found some evidence of dyadic exchange among white/black and brown/black marriage partners but none between white/brown partners (2004:289–291). However, he used only cross tabulations of education by marriage type, which do not account for the various marginal distributions of each spouse’s education as well as the general pattern of educational assortative mating. In the analysis that follows, we build on Telles’ research by using a formal approach to identify the role of both dyadic and market exchange in interracial marriage in Brazil.

Data and Variables

Data come from the 6 % random sample from the Brazilian 2000 National Census, harmonized by the Integrated Public Use Microdata Series, International (IPUMS-I) project. We select prevailing married couples. Prevailing unions may be subject to bias resulting from selective union dissolution, educational upgrading after marriage, and remarriage (Schwartz and Mare 2005). We examine prevailing unions because it is the only type of data available that would provide a sufficiently large sample size for Brazil. We restrict our sample to marriages in which the male partner is age 25 to 35 to reduce the chances of union dissolution and remarriage. We exclude couples in which the female is younger than age 15 or older than 60, which is less than 0.2 % of couples.

Table 1 shows the distribution of race and education for the husbands and wives in our sample. We distinguish five levels of educational attainment: less than complete primary education, primary graduate (eight years of schooling), lower secondary, upper secondary, and some college or more. Information about spouses’ race is based on the following census question: “What is your race or color?,” which offers respondents a choice between branco (white), pardo (brown), preto (black), amarelo (yellow), and indígena (indigenous). We restrict the sample to individuals self-identifying as black, brown, or white (99.3 % of our sample).

This article follows the standard approach to assortative mating of focusing on spousal resemblance conditional on the existence of a marriage; we exclude individuals who have never married or are currently not living with a partner (32.8 % of males in the selected age range). A comprehensive model of assortative mating would consider the entire population at risk to marry. Unfortunately, we cannot expand our analysis to the single population because there is no plausible counterfactual about their status exchange pattern if they were married.

We focus only on married couples in order to present results that are comparable with prior research on status exchange. This means that we exclude cohabitations, which are common in Brazil, with 24.6 % of males in the age range in a consensual union. In order to evaluate whether patterns of status exchange vary by union type, we conducted an ancillary analysis comparing marriages and cohabitations. Results (presented in Online Resource 1) show that patterns of exchange are substantively identical across union type in Brazil.

Racial fluidity and the potential of “whitening” related to socioeconomic attainment poses challenges for our analysis if nonwhite individuals with high levels of education are more likely to experience “whitening” than nonwhite individuals with lower levels of education. Another potential source of bias is that partners might be more likely to report the same race when they are married than they would independent of one another. The consequences of this sort of racial switching will depend on where, in both the educational and race distribution, such switching is most likely to occur and which partner is more likely to switch. At the moment, we do not have data that can directly address this potential source of bias. However, prior research indicates that crossing the boundary separating whites from browns is much less likely than crossing the one separating browns from blacks (Lovell and Wood 1998; Schwartzman 2007). Therefore, patterns of intermarriage involving whites are much less likely to be affected by switching than those involving browns and blacks.

Modeling Status Exchange

In this section, we outline models for estimating both dyadic and market exchange. We also address methodological debates about how to measure status exchange. We apply a series of log-linear models to a table cross-classifying husband’s race (i), wife’s race (j), husband’s education (k), and wife’s education (l). For illustrative purposes, we treat race as having two categories (0 = white, 1 = black), but as described later, we expand this to three categories to include browns in some of the analyses that follow.

We begin with a baseline model as follows:
logFijkl=λ+λi+λj+λk+λl+λij+λik+λjl+λkl.
(1)

This model assumes that there is nothing special about racially exogamous couples that is not accounted for by a general pattern of racial endogamy (λij), different marginal distributions of education by husband’s race (λik) and wife’s race (λjl), and a single pattern of educational assortative mating across all interracial and intraracial couples (λkl). Our parameters for status exchange will be built on this baseline model. For brevity, we present parameters that estimate the same effects for black male/white female (BM/WF) couples and white male/black female couples (WM/BF). In the actual analysis, we estimate separate parameters for these two couple types.

Measuring Dyadic Exchange

A model that captures dyadic status exchange needs to compare the pattern of educational assortative mating (EAM) among interracial couples to this same pattern among racially endogamous couples. Among interracial couples, three types of educational relationships can exist between spouses: (1) the black partner has more education than the white partner (white educational hypergamy), (2) both partners have the same level of education (educational homogamy), or (3) the black partner has less education than the white partner (white hypogamy). We capture these patterns in our second model, based on Gullickson (2006), as follows:
logFijkl=λ+λi+λj+λk+λl+λij+λik+λjl+λkl+τxijkl+γyijkl,
(2)
where xijkl and yijkl are given by
xijkl=1ifk>landBM/WFor(l<kandWM/BF)0elseyijkl=1ifl>kandBM/WFor(k<landWM/BF)0else.

xijkl identifies white hypergamy, and yijkl identifies white hypogamy. Because the parameters apply only to interracial couples, racially endogamous couples are used as a baseline for comparison. These parameters capture how the likelihood of observing an interracial marriage changes as the educational pairing of spouses moves from homogamy to either hypergamy (τ) or hypogamy (γ). According to the dyadic approach to status exchange theory, τ (white hypergamy) should be positive, and γ (white hypogamy) should be negative.

Measuring Market Exchange

Under the market exchange approach, the central argument is that as the education of all potential partners increases, they are more likely to attract white spouses. Therefore, with regard to interracial marriage, the expectation is that the chances of intermarrying decrease for whites as their education increases but increase for blacks as their education increases, regardless of the educational level of their partners. To test this expectation, we follow Gullickson’s (2006) modeling strategy and add race-specific associations between education and the probability of interracial marriage, which we call “educational barriers to intermarriage.”

Educational barrier parameters can be added to the baseline Model 1 as follows:
logFijkl=λ+λi+λj+λk+λl+λij+λik+λjl+λkl+p=14ηpupij+q=14δqwqij.
(3)
where p and q index levels of education, and upij and wqij are defined as
upij=1ifk>pandBM/WFor(l>pandWM/BF)0elsewqij=1ifl>qandBM/WFor(k>qandWM/BF)0else.

Each of the terms ηp and δq indicate how the log-odds of interracial marriage change for blacks and whites, respectively, when moving up one level of education from either p or q (e.g., from upper secondary to college).4 When we add these terms, separately by gender, they exactly fit the three-way interactions of husband’s race by wife’s race by husband’s education (λijk) and husband’s race by wife’s race by wife’s education (λijk) as well as the lower order two-way tables of husband’s race by wife’s education and wife’s race by husband’s education (λil and λjk).

The market exchange approach expects all the ηp terms to be positive, indicating that the odds of interracial marriage increase with the education of black spouses. Likewise, all the δq terms are expected to be negative, indicating that the odds of interracial marriage decrease with the education of white spouses. Because these parameters depend on each spouse’s education separately, the model assumes that the general pattern of EAM, as modeled by λkl, is the same between interracial and intraracial couples. In contrast, dyadic exchange assumes a particular pattern of EAM for interracial couples, characterized by white hypergamy and black hypogamy. This is the key methodological distinction between dyadic and market exchange.

Addressing Criticism of the Log-Linear Approach to Status Exchange

There has been considerable recent debate about the appropriate structure for log-linear models that estimate status exchange. Rosenfeld (2005) defined status exchange as dyadic. He argued that the key exchange parameter is a four-way interaction term involving the race and education of both spouses, and that it is necessary to fit all the lower-ordered interaction terms in a log-linear model. His preferred model fits saturated tables for all six two-way interactions and all four three-way interactions, and he found that the dyadic status exchange parameter is negligible in size and statistically insignificant after adding in these lower-ordered terms. He criticized other scholars for not following the practice of including lower-ordered terms along with interaction terms when estimating log-linear models (Rosenfeld 2005:1308–1309).

Rosenfeld presented his critique as largely a technical point and did not elaborate the implications on the substantive difference between his preferred model and other models. However, these model selection issues have substantive implications that are intuitive to understand. As noted earlier, the market exchange parameters used in Model 3 are equivalent to the two-way interaction terms λil and λjk and the three-way interaction terms λijk and λijk that are missing from Model 2. Rosenfeld’s model used these terms as controls but failed to recognize that they themselves contain important information about how the marriage market is structured by racial disadvantage. Market exchange provides a substantive rationale for including and interpreting these terms.

Rosenfeld also controlled for the three-way interaction terms capturing the association between husband’s race and husband’s education and wife’s education (λikl) and between wife’s race and husband’s education and wife’s education (λjkl) that allow the EAM of couples with at least one black spouse to vary regardless of the race of partner. This approach is incorrect because it relies on the argument that the dyadic exchange parameter is itself a four-way interaction term. Although it is true that the status exchange parameter depends on information regarding all four characteristics of spouses, it is not correct that the dyadic exchange parameter is a four-way interaction term within the log-linear model framework. (See also Gullickson and Fu (2010) and Kalmijn (2010)). Treating whites as the reference group (i.e., given value 0 in a 0/1 dummy variable coding), the saturated four-way interaction term (λijkl) actually measures how different EAM is for black endogamous couples relative to other types of couples rather than the EAM of racially exogamous couples. It is the two three-way interaction terms that Rosenfeld controlled for (λikl and λjkl) that measure how the EAM of racially exogamous couples is different from other couples. Thus, the terms λikl and λjkl overlap with the dyadic exchange parameters themselves. In fact, including these three-way interaction terms in Models 2 or 3 would induce perfect collinearity with the dyadic exchange terms, forcing some terms to be dropped from the model. We provide methodological details in Online Resource 2.

Despite these issues, Rosenfeld’s critique addressed an important potential shortcoming of the preceding models. In both Models 2 and 3, the patterns of hypergamy and hypogamy of racially exogamous unions are implicitly compared with a reference group that consists of both white and black endogamous unions collectively (as captured by the λkl term). But what if white and black endogamous couples have different patterns of EAM? As Rosenfeld (2005) showed, models assuming one single pattern of EAM across white and black endogamous couples fit poorly to U.S. data because patterns of EAM are different between these two types of couples. If this is the case, we might obtain different results based on the type of endogamous couples we use as the reference group.

To address this issue, we conducted a sensitivity analysis that uses different specifications of the baseline EAM for racially endogamous couples. We used two alternative approaches to that of pooling all racially endogamous couples together, as we have done in Models 2 and 3. In the first approach, we followed the technique of Kalmijn (1993, 2010) and used the geometric mean of the EAM terms for white and black endogamous couples as a baseline. In the second approach, we set the baseline alternatively to white endogamous couples and black endogamous couples (results in Online Resource 2). The results were highly robust to these different specifications, and our substantive conclusions would be identical regardless of which approach we used. Therefore, we decided to use the simpler formulation that pools all racially endogamous couples and models a single baseline EAM pattern, as presented in Model 2 and Model 3 in the Results.

Analytic Approach

We evaluate the status exchange process in Brazil by estimating two models. The first model follows most prior literature and includes dyadic exchange parameters only. Secondly, we add market exchange parameters. If dyadic exchange parameters remain significant even after adding in market exchange terms, then we have evidence of a process of direct exchange within interracial unions. If dyadic exchange parameters drop to zero after including market exchange terms, we will conclude that the observed pattern of status exchange was instead driven by a generalized penalty associated with darkness on the marriage market affecting all interracial couples and not only those that are educationally asymmetric.

We also explore the role that the large intermediate category of browns plays in organizing exchange. To accomplish this, we first examine interracial marriages between whites and nonwhites, drawing a binary distinction similar to the U.S. formulation, where nonwhite includes both blacks and browns. We then use the more gradational formulation of race to separately examine white/black couples, white/brown couples, and brown/black couples.

Results

Figure 2 shows Bayesian information criterion (BIC) goodness-of-fit statistics for each model that we estimated. We rely exclusively on the BIC statistic because our sample size is so large that it is difficult to not prefer models with more terms using standard hypothesis tests. In addition, BIC can be compared across nonnested models. We use it here as a guide for model selection rather than as a strict test of the “correct” model. We are more interested in examining the consistency of parameter values across specifications than in selecting a single best model.

The baseline model is not preferred to the saturated model for either the white/nonwhite or the white/brown/black case. Dyadic exchange parameters are strongly preferred to the baseline model but not the saturated model. The largest gains in BIC come from the market exchange terms. Models with these terms are also strongly preferred to the saturated model. In both cases, BIC is fairly indifferent between a model with just market exchange terms and a model with both dyadic and market exchange terms. This is the first indication that interracial marriage dynamics are largely accounted for by a market-level phenomenon expressing a generalized penalty associated with darkness, rather than by a direct transaction between spouses. To understand what is driving these results, we turn to an examination of the parameter values in these various models.

White and Nonwhite Comparison

Figure 3 shows the estimated dyadic exchange parameters for nonwhite male/white female and white male/nonwhite female couples separately. The upper panels show these parameters without market exchange terms, and the lower panels show how these parameters change when we add market exchange terms.

Looking first at the upper panels, we find that the odds of interracial marriage increase when white men and women are in an educationally hypergamous union relative to an educationally homogamous union and that the odds decrease when white men and women are in an educationally hypogamous union. All estimated parameters are distinguishable from zero, and the results are consistent across both gender combinations. At a first glance, these results provide strong support for dyadic exchange.

However, these values change dramatically in the lower panels. After we account for market exchange, we no longer see evidence of dyadic exchange. The white hypergamy terms are significantly reduced although still positive. However, the white hypogamy terms are also positive. Thus, the results indicate that racially exogamous couples are somewhat more likely to be educationally heterogamous than racially endogamous couples but not in a particular direction that favors white hypergamy. This questions the hypothesis about a direct transaction of resources within couples, which is the conventional understanding of exchange.

To better understand this change across models, we turn to an examination of the educational barrier terms capturing market exchange in Fig. 4. Each term shows how the odds of interracial marriage change across adjacent educational categories. In general, the effects are positive for nonwhites, indicating that as the education of nonwhites increases, they are more likely to be in an interracial marriage. The effects are negative for whites, indicating that as their education increases, they are less likely to be in an interracial marriage. For all spouses, the change in the odds of interracial marriage is greatest at the extremes of the educational distribution rather than the middle, particularly for the barrier separating those with college education from the rest. This means that gaining access to a college education substantially increases the chances that a nonwhite person marries a white spouse, but it also decreases the chances that a white person marries a nonwhite spouse.

The results suggest that there is a penalty associated with darkness that can be compensated for by educational advantage for both men and women. As both whites and nonwhites gain education, they are less likely to acquire a nonwhite spouse. Furthermore, these findings indicate that the greater prevalence of white hypergamy and lower prevalence of white hypogamy apparently supporting the notion that dyadic exchange is a by-product of market exchange. The findings also question the role of education as a force that would dissolve group barriers by promoting intergroup social interaction and universalistic values (Gordon 1964; Kalmijn 1998; Lieberson and Waters 1988; Rosenfeld 2008).

White, Brown, and Black Comparison

Do our results hold when we allow for a “middle” category of brown between white and black? Does the extent of exchange across racial groups replicate the socioeconomic distances between them: blacks at the bottom, closely followed by browns and then by whites at a far distance? We now must examine parameters for three types of interracial marriage: white/black, white/brown, and brown/black. Because we estimate different parameters by gender combinations, this gives us six sets of parameters to estimate for each model.

Figure 5 shows the dyadic exchange parameters across these six sets of interracial couples. As in Fig. 1, the upper panels show the dyadic exchange parameters without market exchange terms, and the lower panels show the dyadic exchange parameters with market exchange terms. Looking first at the upper panel, we see evidence of dyadic exchange in all six couple types, although exchange between brown and black spouses fails to reach statistical significance for the hypogamy term. Weak indication of dyadic exchange between browns and blacks is consistent with the small socioeconomic differences between these two racial groups. For both gender combinations, dyadic exchange appears to be strongest for white/black marriages, intermediate for white/brown marriages, and smallest for black/brown unions. We test this gradient formally by running models with a single hypergamy and hypogamy term for each gender combination but with different uniform scale effects across the three racial combinations. The results are shown in the upper half of Table 2. Overall, the preferred model is the one that strictly replicates the socioeconomic distances between racial groups, in which the dyadic exchange effects are largest for white/black couples and lowest for brown/black couples, with white/brown couples falling in-between. This model is preferred to a model in which white/brown and white/black couples are treated similarly. These results suggest a close similarity between the socioeconomic distances separating racial groups and their distance in terms of intermarriage.

However, these results do not distinguish between market and dyadic components of exchange. When we turn to the lower panels of Fig. 5, a similar pattern as for the white/nonwhite models emerges. The dyadic exchange parameters are substantially reduced by the inclusion of the market exchange terms. In general, the results suggest either no effects or minor positive effects for both hypergamy and hypogamy of the lighter partner. In other words, interracial couples are less likely to be educationally homogamous than racially endogamous couples, but such departure from homogamy is not biased toward white hypergamy, as predicted by dyadic exchange. The lone exception to this pattern is for black man/brown woman couples, for whom the dyadic exchange expectation holds after accounting for market exchange.

Figure 6 confirms the important role played by market exchange. In general, the results for white/black and white/brown unions are consistent with those shown for white/nonwhite unions in Fig. 4 but also reveal some new insights. As in Fig. 4, the darker member’s odds of marrying exogamously increase with education, whereas the lighter spouse’s odds of marrying exogamously decrease with education. However, market exchange terms separating browns from blacks are largely insignificant, suggesting that education does not affect the likelihood of these groups intermarrying. Furthermore, we find that the educational barrier terms separating whites from blacks tend to be larger than the barriers separating whites from browns, indicating that from the perspective of whites, being black is seen as more disadvantageous in terms of racial status than being brown. To test this pattern formally, we use a scaling technique similar to that used earlier. The results, shown in the bottom half of Table 2, indicate that the best fitting model allows for the negative effect of education on interracial marriage for whites to be larger for white/black unions than for white/brown unions, while the educational barriers separating browns from blacks are not significantly different from zero.

This finding extends Telles’ (2004) analysis that found the black-nonblack distinction to be crucial in the marriage market, and suggests that the question of whether browns and blacks are distinguishable within the Brazilian racial hierarchy depends on who is making the comparison between them—whites or nonwhites. There appears to be little evidence of dyadic or market exchange in marriages between browns and blacks, but the educational barriers between whites and blacks are stronger than the same barriers between whites and browns. In other words, important hierarchical differences exist between blacks and browns as potential partners from the perspective of whites, but no hierarchical differences from their own pattern of intermarriage. This conclusion is only suggestive, however, because at the moment we cannot correct for the potential “whitening” of highly educated black partners, which would result in their identification as brown.

Conclusion

Race and education interact in important ways on the Brazilian marriage market. Our findings refute the hypothesis that exchange is an idiosyncratic attribute of black/white marriages in the United States, emerging from historically strong barriers between these groups. In spite of easy sociability between racial groups, racial disadvantage is pervasive in Brazil and expresses itself in marked educational asymmetries between darker and lighter spouses in interracial marriages. However, these asymmetries are not a product of the direct trading of resources between spouses predicted by dyadic exchange theory, as formulated by Merton (1941) and Davis (1941) and usually tested by empirical research. Rather, they are produced by contrasting educational barriers to intermarriage resulting from a preference for lightness in racially stratified societies. Darkness can be compensated for by achieving higher education; but education is not regulated by a direct transaction between spouses. Whites are less likely to marry a darker partner as their education increases, and nonwhites are more likely to marry a lighter partner as their education increases. As a result, interracial marriages are more likely to be formed by a less-educated white spouse and a more-educated black spouse than the educational distributions of equivalent-sex spouses in same-race couples. This result appears as a dyadic transaction within couples if the different likelihood of interracial marriage across educational levels by race is not accounted for.

The distinction between market and dyadic exchange has important implications. Our findings suggest a broader pattern of racial disadvantage than the one traditionally captured by dyadic exchange. Although dyadic exchange applies only to interracial couples that are educationally heterogamous, market exchange terms apply to all interracial couples, including the large majority of educationally homogamous unions. To the extent that apparent dyadic exchange is largely a by-product of market exchange, our results suggest that researchers should broaden the notion of exchange, moving away from Merton’s and Davis’ original formulation and considering darkness as a “generalized penalty” in the marriage market.

The strong educational barriers to intermarriage that we find in Brazilian society likely result from both individual preferences for partner’s race as well as constrained access to potential partners of a different race—driven, for example, by residential segregation and racially segregated friendship networks. Given that these constraints are much weaker in Brazil than in the United States, we speculate that individual preferences play an important role in defining racial disadvantage in Brazil. This finding also strongly questions the expectation that education will promote universalistic values that would do away with racial barriers.

Finally, we find qualified evidence about a racial gradient that places browns in an intermediate location between blacks and whites. On the one hand, educational barriers for whites are stronger in white/black intermarriage than in white/brown intermarriage, suggesting that darkness is associated with a heavier penalty in the Brazilian marriage market. On the other hand, patterns of intermarriage between blacks and browns show no evidence of market or dyadic exchange. Combined, these findings highlight that the strength of the racial differences depends on who is making the distinction, and perspectives from different racial groups should be considered to obtain a comprehensive assessment of racial disadvantage in the marriage market.

Our results indicate that status exchange is not a U.S. idiosyncrasy. They also show that the substantial interracial sociability characteristic of Brazilian society does not necessarily lead to the elimination of racial disadvantage in the marriage market. On the contrary, interracial sociability may facilitate the expression of racial disadvantage by making interracial unions less exceptional, the gains associated with marrying lighter persons more valuable, and the generalized penalty associated with darkness more acceptable. We trust that more comparative research will further expand our understanding of the connection between macro-structural contexts and racial disadvantage in the marriage market.

Acknowledgments

This article uses data from the Integrated Public Use Microdata Series, International (IPUMS-I). We thank the Minnesota Population Center and the Brazilian Institute of Geography and Statistics for making the data available. We are grateful to Matthijs Kalmijn for generously providing us with the code to replicate his model of status exchange. We thank Demography anonymous reviewers, Patricia Gwartney, Jill Harrison, Ryan Light, Matthew Norton, Eileen Otis, Jiannbin Shiao, Jessica Vasquez, and especially Paula England for helpful comments and suggestions.

Notes

1

Following Telles (2004), we define interracial sociability as the ease and frequency of social interaction across racial boundaries.

2

We use the terms lightness and darkness to indicate positioning on a graduated scale of racial categories that separate white from black at the extremes, not as a direct reference to skin tone, for which we have no direct data.

3

For two groups B and W, where Fij gives the number of married couples where the husband belongs to group i and the wife belongs to group j, the odds ratio of exogamy is calculated as FBW × FWB  / (FBB × FWW).

4

Our approach uses difference coding, in which the estimated parameters give the differences between adjacent pairs on an ordinal scale variable. This approach differs from the more common dummy variable coding, which sets one category as the reference for all comparisons. Difference coding is preferred because it allows direct evaluation of the effects of a one-level increase in education for each particular level. There is no difference between the coding schemes in terms of model fit because the estimated parameters of one technique can easily be derived from the other.

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