## Abstract

Past research has indicated that mixed-race couples with children appear to possess a heightened preference for neighborhoods that are racially and ethnically diverse and relatively affluent so as to reside in areas that are requisitely accepting of, and safe for, their children. However, neighborhoods with higher racial and ethnic diversity tend to be lower in socioeconomic status, implying that some residentially mobile mixed-race couples with children encounter trade-offs between neighborhood diversity and neighborhood affluence in their residential search processes. To investigate this, we apply discrete-choice models to longitudinal data from the Panel Study of Income Dynamics linked to neighborhood-level data from multiple population censuses to compare the neighborhood choices of mixed-race couples with children to those of monoracial couples with children, while assessing how these choices are simultaneously driven by neighborhood diversity and neighborhood affluence. We observe that mixed-race couples with children tend to be more likely to choose higher-diversity neighborhoods than white couples with children, even when neighborhood affluence is allowed to determine the residential choices for these couples. Some higher-income mixed-race couples with children seemingly translate their resources into neighborhoods that are both diverse and affluent.

## Introduction

Recently, scholars of locational attainment have begun to study the residential patterns of mixed-race couples. This has been partially driven by their increasing representation of all couples: mixed-race couples accounted for approximately 17 % of all new marriages in the United States in 2015, more than a fivefold increase since 1967 (Bialik 2017). Moreover, the increase in mixed-race coupling has led to a substantial number of multiracial children. In 1970, 1 % of all newborns were multiracial. Comparatively, in 2013, 10 % of all newborns were born to parents of different races and ethnicities (Parker et al. 2015).1 These increases in mixed-race coupling and the multiracial children from these unions have coincided with research observing that mixed-race couples with children appear to possess a heightened preference for neighborhoods that are racially and ethnically diverse and relatively affluent so as to reside in areas that are requisitely accepting of, and safe for, their children (Dalmage 2000:96). In conjunction with this finding is research on the socioeconomic status of neighborhoods with larger shares of racial and ethnic minorities that highlights that these areas are often less affluent than predominately white neighborhoods (Jargowsky 2014; Logan 2011). The implication of these findings is that some residentially mobile mixed-race couples with children may encounter trade-offs between neighborhood diversity and neighborhood affluence in their residential choices.

The residential choices of mixed-race couples with children have several broad implications. If mixed-race couples with children are prioritizing neighborhood diversity in their residential search processes, their choices have the potential to enhance neighborhood diversity for the foreseeable future because families with children are less likely to migrate out of their neighborhoods compared with their counterparts without children (South and Crowder 1998). The resultant growth of diverse neighborhoods through these families choosing diverse areas has the potential to help disrupt the long history of persistent racial segregation in the United States (Massey and Denton 1993; Rothstein 2017). At the same time, because neighborhoods with larger shares of racial and ethnic minorities tend to have lower socioeconomic status compared with neighborhoods with lower concentrations of minorities (Jargowsky 2014; Logan 2011), mixed-race couples with children may sacrifice some amount of neighborhood affluence to live in diverse settings. If so, these families may also forgo amenities correlated with affluent neighborhoods, such as high-quality schools, better public services, high property values, and low crime rates (Peterson and Krivo 2009; Solari 2012; Swanstrom et al. 2002). However, because of an increase in the number of diverse neighborhoods (Zhang and Logan 2016), a cross-section of neighborhoods are potentially both relatively diverse and affluent, possibly allowing higher-income mixed-race couples with children the opportunity to convert their advantaged economic position into these neighborhoods, effectively minimizing the trade-offs between the cosmopolitanism of diverse neighborhoods and the amenities associated with neighborhood affluence.

However, it remains unclear the extent to which neighborhood diversity itself drives the residential trends among mixed-race couples with children and the extent to which neighborhood diversity comes at the expense of neighborhood affluence. Prior studies have frequently used traditional locational attainment models, making it unfeasible to simultaneously assess the relative attractiveness of neighborhoods characterized by higher racial and ethnic diversity versus those with higher socioeconomic status (Ellis et al. 2006; Gabriel 2016; Iceland and Nelson 2010; Wright et al. 2011, 2013). Prior studies have also not fully accounted for the issue of neighborhood availability. Thus, investigating the neighborhood choice of mixed-race couples with children requires an alternative approach that is better positioned to assess the potential trade-offs these families encounter when searching for their ideal neighborhood.

In this study, we aim to clarify patterns of locational attainment among mixed-race couples with children with our application of discrete-choice models. We use data drawn from almost a quarter-century of data from the Panel Study of Income Dynamics (PSID) linked to neighborhood-level data from multiple population censuses. With these data, we compare the neighborhood choices of several categories of mixed-race couples with children against monoracial couples with children and assess how these choices are simultaneously driven by the racial and ethnic diversity and socioeconomic affluence of neighborhoods. The results of our analysis highlight the implications of locational attainment among a population that may play an increasingly important role in diversifying U.S. neighborhoods (Ellis et al. 2012) while furthering traditional theories of location attainment into new areas as it relates to this burgeoning population.

## Background and Theory

Theories of locational attainment can provide insight into why mixed-race couples with children are likely to migrate to diverse neighborhoods. The first theory—spatial assimilation—is related to economic resources. The spatial assimilation theory developed from early theories of locational attainment that focused on an ecological framework asserting that racial and ethnic groups were sorted into neighborhoods matching their economic resources and stage in the life course (Park et al. 1925). This broad theory of human capital for residential sorting became further specialized by scholars who argued that racial and ethnic minorities, as well as white households, use their economic resources to gain access to neighborhoods with higher levels of affluence and with more whites that tend to offer enhanced amenities (Logan and Alba 1993), from higher-quality public services (Sharkey and Faber 2014) to increased safety (Peterson and Krivo 2009). Thus, scholars predicted that as racial and ethnic groups increase in economic status, they would upgrade to more affluent neighborhoods with higher shares of whites, effectively spatially assimilating with the dominant group. As a consequence, racial and ethnic group differences in the attainment of affluent neighborhoods would be predicted to disappear after racial and ethnic group differences in economic status are accounted for. Extending this argument to mixed-race couples with children would imply that because of limited economic resources, they end up in neighborhoods that are more diverse but less affluent than monoracial white couples, and that given more resources, these mixed-race couples would reside in neighborhoods with levels of affluence and diversity that are similar to neighborhoods where whites reside.

The small amount of available evidence on the locational attainment of mixed-race couples in general suggests that their residential outcomes might diverge from the assumptions of the spatial assimilation model because these couples are typically found in more diverse neighborhoods than whites. For instance, Wright et al. (2011) observed that black-white couples were likely to live in diverse neighborhoods, no matter which racial and ethnic group made up the majority. In a separate study, Holloway et al. (2005) found that mixed-race couples—and especially black-white couples—were more likely to reside in areas of greater diversity than white couples. In a separate analysis, Gabriel (2016) observed, when controlling for socioeconomic status, that mixed-race couples were more likely to migrate to diverse neighborhoods than white couples and that mixed-race couples with black partners were more likely to be found in diverse areas than mixed-race couples without black partners. The sum of these findings points to the fact that mixed-race couples seem not to be assimilating into predominantly white neighborhoods that are frequently more affluent, pointing to the need to explore other theoretical arguments to explain the locational attainment of these families.

A second theoretical perspective is that mixed-race couples with children might have heightened preferences for areas with substantial levels of racial and ethnic diversity (Dalmage 2000; Datzman and Gardner 2000; Holloway et al. 2005). Research on the racial and ethnic group preferences for neighborhoods of varying racial and ethnic composition can provide understanding regarding the potential preferences of mixed-race couples, given that couples’ preferences are shaped by each individual members’ preferences. Prior research has found that blacks, more than other racial groups, rate neighborhoods that have relatively even distributions of racial and ethnic minorities as highly attractive (Krysan and Bader 2007). Studies have chronicled the multiple reasons that blacks have provided for their desire to reside in diverse neighborhoods, from the positive effects of integration to having improved neighborhood attributes (Krysan and Farley 2002). Latinos and Asians tend to demonstrate a greater openness to sharing neighborhoods with racial and ethnic minorities than whites but appear to be partially resistant to neighborhoods with higher shares of blacks (Charles 2000). Whites, on the other hand, appear to be resistant to neighborhoods with nontrivial numbers of racial and ethnic minorities. In experiments, when whites are asked about their comfort in neighborhoods with varying degrees of racial and ethnic minorities, they typically state that neighborhoods with little racial and ethnic diversity are most attractive (Charles 2003).

Although much of the research on preferences is limited to monoracial couples, a few qualitative studies have illuminated why mixed-race couples might be drawn to diverse neighborhoods. In her extensive ethnographic analysis of black-white couples, Dalmage (2000) observed that these couples sometimes encountered discrimination in both predominantly black and predominantly white neighborhoods. Although predominantly black neighborhoods have typically been more accepting of mixed-race couples than predominantly white neighborhoods, some black-white households have encountered a guarded acceptance in these areas with large black concentrations (Dalmage 2000:83–84). Conversely, Dalmage reported that a number of black-white couples in her analysis stated that residing in highly white neighborhoods led to a feeling of being “scared or uncomfortable,” while others recounted being “downright terrified at the possibility of racist retaliation” (2000:87). These findings from Dalmage confirm what many black-white couples stated in her analysis—that diverse neighborhoods were a reprieve from the isolation and discrimination they might face in racially homogeneous areas. This preference to reside in diverse neighborhoods is potentially amplified by the presence of children. A number of black-white couples in Dalmage’s (2000:103) study feared leaving diverse neighborhoods because their children could be harmed either psychologically or physically. Other mixed-race couples with children, however, search out diverse neighborhoods for more optimistic reasons. This can be witnessed in Moran’s qualitative analysis of black-white couples: a number of these couples reported being drawn to diverse neighborhoods so their children could gain an enhanced understanding of their unique racial heritage (2001:156).

A third explanation is that mixed-race couples with children face barriers to entering predominately white and more affluent neighborhoods. Many studies have demonstrated that some racial and ethnic groups are more likely to convert their economic resources into more affluent neighborhoods than others and that no racial and ethnic minority group matches the ability of whites to attain affluent neighborhoods (Logan 2011). Both Latinos and blacks tend to be observed in poorer neighborhoods no matter their level of economic resources (Sharkey 2014). Even the most economically advantaged racial minority group—Asians—encounter difficulties in converting their resources into more advantaged spaces, often residing in poorer neighborhoods than whites (Logan 2011). Known as the place stratification theory, numerous scholars have asserted that these differential outcomes across racial and ethnic groups are caused by discrimination in the United States housing market that disadvantages racial and ethnic minority groups’ capacities to enter and remain in more affluent areas (Charles 2003; Logan and Molotch 1987; South et al. 2005). In particular, scholars have observed multiple forms of discrimination toward racial and ethnic minority groups that can impede their attainment of more affluent neighborhoods, such as racially discriminatory lending practices (Rugh et al. 2015) and racial steering by real estate agents (Turner et al. 2013). Given this research, mixed-race couples with children, especially those with black partners, might encounter discriminatory obstructions to migrating to more affluent neighborhoods.

Underpinning each of these theoretical models is a fairly cursory and increasingly problematic conceptualization of race and ethnicity in which households are often described as white, black, Asian, or Latino. For simplicity, limitations related to the available data, or due to mixed-race couples being a relatively small cross-section of the United States population in the past, a common practice when studying the locational attainment of racial and ethnic groups is to use the race of the household head to represent the race of the entire household. In reality, many contemporary households include a mix of races and ethnicities and thus do not fit easily into one of the aforementioned racial/ethnic categories. This is increasingly the case: 10 % of all marriages in 2015 in the United States were between individuals of different races and ethnicities—more than a threefold increase from 1980 (Livingston and Brown 2017)—making the inclusion of mixed-race couples in studies of locational attainment an issue of growing importance. This growing importance is coupled with the fact that mixed-race couples present a challenge to traditional theories of locational attainment created when racial and ethnic household mixing was rare, requiring a deeper investigation into the nuances of these theories as they relate to contemporary processes of locational attainment. Doing so provides the opportunity to discover potentially new ways of applying these theories that will become increasingly important as the racial and ethnic diversity of the United States continues its upward trajectory.

## Hypotheses

Here we outline hypotheses drawn from prior theoretical and empirical scholarship. First, given the legacy of racially stratified patterns of locational attainment, we hypothesize that

• 1. Mixed-race couples with children are more likely to migrate into neighborhoods with higher levels of diversity than white couples with children.

Second, the place stratification theory suggests that despite individual economic resources, racial and ethnic minorities are less likely to enter higher-income neighborhoods. Thus, we further hypothesize that

• 2. Mixed-race couples with children are more likely to migrate into neighborhoods with lower levels of affluence than white couples with children.

Findings consistent with Hypotheses 1 and 2 would largely corroborate previous findings. Our next hypotheses go further, testing theoretical arguments that have yet to be empirically explored given the constraints of traditional locational attainment models. In particular, we aim to adjudicate between the simultaneous sorting of couples by neighborhood diversity and neighborhood affluence. Prior research has indicated that place stratification sorts couples of equal economic status into more or less affluent neighborhoods along a racial hierarchy, but what remains unclear is whether this economic sorting explains why mixed-race couples with children are especially likely to locate in diverse neighborhoods. We anticipate that economic sorting does not explain the locational attainment of mixed-race couples with children based on evidence of their unique preferences for diverse areas. Therefore, we hypothesize that

• 3. Mixed-race couples with children are more likely to migrate into neighborhoods with higher levels of diversity than white couples with children, even after racial sorting by neighborhood income is accounted for.

Finally, given the findings from the relatively nascent line of research concerning mixed-race couples’ preferences for diverse neighborhoods in general, there is a distinct possibility that the ability of mixed-race couples with children to actualize their preferences for heightened levels of neighborhood diversity will vary by their level of economic resources. Hence, we hypothesize that

• 4. Higher-income mixed-race couples with children—those who are best positioned to actualize their preferences—have a higher propensity to migrate to diverse neighborhoods than lower-income mixed-race couples with children.

## Data and Methods

We investigate the locational attainment of mixed-race couples with children by using data from the PSID linked to neighborhood-level data drawn from the U.S. Census. The PSID started in 1968 with 4,802 families, interviewing families annually until 1997 and biennially thereafter. As children from original panel families left their households to form their own households, they continued to be interviewed by the PSID. The PSID is advantageous for our analysis because its longitudinal design allows us to identify the residential location of individuals at each interview and to track their residential mobility between neighborhoods across time.

Starting in 1985, the PSID data included information on the race and ethnicity of the household head and her/his spouse or long-term cohabiter.2 Hence, we focus our analysis on the observation years between 1985 and 2013. Because we are interested in comparing mixed-race couples with children to racially homogenous couples with children, we focus on those households with a partner present at both the beginning and end of an observation period3 (the time between sequential interviews) and with a child under the age 18 living in the home. In the few instances when a PSID member ends their relationship and forms a new couple with children present in the home, the observations for each period are included in our sample. Given theoretical debates about the effects of broader metropolitan context on residential outcomes, we focus on households living in a census-defined metropolitan area at the beginning and end of an observation period. Thus, our sample is nationally representative of U.S. metropolitan areas and is spread across 359 unique metropolitan areas.

We use the PSID’s Geospatial Match Files to identify the residential location of PSID respondents at each interview and attach information about the racial and ethnic composition of their neighborhoods. We follow prior work in this area by using census tracts to represent neighborhoods (Crowder et al. 2012) because they include demographic data for the analysis of locational attainment and approximate the typical conception of a neighborhood (White 1987). We use tract-level data from 1980, 1990, 2000, and 2010 censuses, employing linear interpolation to estimate values for tract attributes in noncensus years. Tract boundaries are standardized in all years to the year 2010.

We construct each couple’s data record into a series of couple-period observations, with each observation referring to the one- or two-year period between PSID interviews. Our sample consists of 4,355 couple-periods, representing 2,713 unique couples. We compare couples of various combinations of racial and ethnic groups: non-Hispanic black (black), non-Hispanic white (white), Latino (of any race), and Asian. We include four categories of mixed-race couples with children in our analysis: black-white (N = 94), black-Latino (N = 87), white-Latino (N = 206), and white-Asian (N = 26).4 We also include two sets of monoracial couples: those in which both partners are black (black-black, N = 1,584), and those in which both partners are white (white-white, N = 2,358). We focus on couples with one black or one white partner because members of other groups are underrepresented in the PSID.

## Discrete-Choice Analysis: An Alternative Approach

Our hypotheses require an alternative approach from traditional locational attainment models, such as ordinary least squares (OLS) regression. The first concern with traditional locational attainment models is the bundling problem (Quillian 2015). Traditional regression methods used in prior studies cannot account for the fact that neighborhoods are a bundle of attributes that couples with children reflect on when choosing a neighborhood. These attributes may include diversity and affluence, opportunities for renting or owning, and many other considerations. Couples with children are not likely to migrate to a neighborhood that they perceive as perfect; neighborhood choice represents a series of trade-offs that couples negotiate to choose the neighborhood with which they are content. However, prior quantitative analyses on the residential location of mixed-race couples have used traditional methods with one outcome used as the dependent variable (Gabriel 2016; Wright et al. 2013). Yet, when one neighborhood outcome is considered, it may be confounded with other correlated neighborhood attributes (Bruch and Mare 2012), and past research has shown that neighborhood racial and ethnic composition and neighborhood affluence are correlated (Massey and Tannen 2016). Moreover, in reality, couples with children are rarely trying to maximize a single outcome. More likely, they are trying to balance a variety of neighborhood attributes simultaneously. Some scholars (e.g., Massey et al. 1994) have attempted to address this weakness in OLS regression by using multinomial logit models that consider various neighborhood attributes concurrently. This strategy, however, can represent only a minimal number of neighborhood attributes before the number of attributes grows unwieldy (Quillian 2015). Thus, using traditional locational attainment models makes it difficult to assess the trade-offs that mixed-race couples with children encounter between neighborhood diversity and neighborhood affluence, along with other neighborhood attributes.

The second concern is the availability problem. Traditional regression models cannot recognize that the potential destinations of couples are constrained by the destinations that are available in their broader area. Mixed-race couples with children may be more likely than other couples to migrate to diverse neighborhoods because they tend to reside in metropolitan areas where diverse neighborhoods are more available. Additionally, neighborhoods that are both diverse and affluent may be rare in some metropolitan areas, intensifying the trade-offs between neighborhood diversity and neighborhood affluence for some couples with children. Furthermore, more affluent couples may be better positioned to seek out neighborhoods that meet most of their preferences, whereas less affluent couples may have to make more compromises. Although some studies have attempted to account for broader metropolitan attributes in locational attainment (Gabriel 2016; Wright et al. 2013), the use of one metropolitan attribute fails to capture how the distribution of available neighborhoods is related to the eventual locational attainment of mixed-race couples with children.

To account for the facts that neighborhoods are combinations of attributes and that the choice of particular neighborhoods is based on their availability, we use discrete-choice models (Bruch and Mare 2012). These models compare the neighborhood chosen by the couple against other neighborhoods in their metropolitan area across several dimensions, giving a clearer sense of the couple’s choices given the available alternatives. This modeling orientation allows us to build on the research of prior scholars by investigating whether mixed-race couples with children are more likely to choose neighborhood diversity over neighborhood affluence, or can achieve both, based on the distribution of neighborhoods in their metropolitan areas. Although these models cannot fully adjudicate residential preferences from unseen events such as housing discrimination, these models can observe how mixed-race couples with children match up with neighborhoods of varying diversity and affluence.

To estimate the discrete-choice models in our analysis, we first construct the choice set of potential destinations for each couple-period observation. The choice set represents a sample of tracts to which the couple might have migrated, including the tract chosen. Theoretically, the choice set would include every tract in the same metropolitan area given that they are all possible choices for local movers. Such a large choice set would be prohibitive in terms of data and estimation, so we follow common practice by taking a 5 % random sample of tracts in the metropolitan area (Bruch and Mare 2012; Quillian 2015).5 We adjust for the probability of inclusion in the choice set with sampling weights equal to 1.0 for tracts that were chosen (because they have 100 % chance of being in the choice set) and 0.5 for the 5 % sample of other tracts. In total, our sample consists of 158,819 observations, each representing one potential tract in the choice set for every couple-period (which we refer to as couple-period-tract alternatives).

We estimate a conditional logistic regression equation predicting the tract chosen, given the set of available alternatives. We include a number of tract-level measures that may influence whether a tract is chosen: entropy score (scaled between 0 and 100),6 average family income (in constant 2010 dollars and logged), percentage change in the entropy score over the previous five years, number of housing units (logged), percentage owner-occupied housing units, distance in miles from the couple’s origin tract (logged), and population density per square mile (logged). Average family income is missing for a small number of tracts; we estimate the missing values with multiple imputation.7

We estimate models that interact the race/ethnicity of the couple and the neighborhood entropy score and/or interact the race/ethnicity of the couple and neighborhood average family income. Couple’s race/ethnicity is not included outside the interactions because attributes not measured at the neighborhood level (e.g., individual- and metropolitan-level attributes) are constant within the choice set for each period (unlike neighborhood attributes, which vary). Thus, individual attributes enter the model only when they are interacted with neighborhood attributes. To investigate whether mobility processes differ between nonaffluent and affluent couples with children, we estimate models separately for couples whose total family taxable income (in constant 2010 dollars) is below four times the poverty rate for a family of four and for couples whose total family taxable income is at or above four times the poverty rate for a family of four (cf. Dwyer 2007; Massey and Eggers 1993; St. John 2002).

## Results

We begin our analysis with Table 1, which highlights descriptive statistics of couples with children and their corresponding family incomes in constant 2010 dollars. Overall, when looking at family incomes, couples with white partners evince the highest incomes. White-Asian couples are the most economically advantaged group, having family incomes of $111,360. These couples are followed by white-white couples who report a family income of$83,550, with white-Latino couples typically earning $74,190 annually. Of all couples with a white partner, black-white couples report the lowest family incomes, at$64,840. Of couples without white partners, black-black couples have higher family incomes than black-Latino couples, at $56,180 and$53,930, respectively.

Table 1 also displays the percentage of couples with children who are affluent, which we define as couples who have family incomes at or above four times the poverty rate for a family of four (equivalent to \$88,200). A similar pattern in disparities between different types of couples emerges: 46.15 % of white-Asian couples have family incomes at or above four times the poverty rate for a family of four, compared with 32.10 % for white-white couples and 24.87 % for white-Latino couples. Conversely, couples with black partners are much less likely to be affluent than couples without black partners. Black-Latino couples are slightly more likely to be affluent than black-white couples, with 16.27 % of black-Latino couples being considered affluent compared with 16.12 % of black-white couples. Because of their traditionally lower levels of income, it is not surprising that black-black couples are least likely to be affluent, with 14.45 % crossing the threshold into the affluent category. In sum, given the importance of economic resources in locational attainment, these stark couple category differences in family income and the percentage of those who are affluent are likely to influence the quality of neighborhoods accessible to each of these couples.

Table 2 shows mean attributes for origin, chosen, and nonchosen tracts among residentially mobile mixed-race and monoracial couples with children, providing initial insight on the relationship these couples have with neighborhood diversity and neighborhood affluence. The average level of diversity (entropy) in the destination neighborhoods of mobile black-white couples was less than their origins but more diverse than other neighborhoods in their metropolitan areas. Conversely, black-Latino couples saw increased levels of neighborhood diversity in their destinations compared with their origin neighborhoods. These same couples were likely to migrate to neighborhoods that were much more diverse than the neighborhoods they did not choose in their metropolitan areas. Black-black couples also migrated to neighborhoods with marginally greater levels of diversity than their origin neighborhoods––close to the average level of diversity in nonchosen neighborhoods. White-Latino couples migrated to slightly less-diverse neighborhoods than their origins, and the neighborhoods they migrated to possessed a similar level of diversity as the neighborhoods they did not choose. Of all mixed-race couples, white-Asian couples were most likely to migrate to the lowest diversity neighborhoods. Additionally, they chose neighborhoods that were substantively lower in diversity compared with their nonchosen neighborhoods. Similar to white-Asian couples, white-white couples migrated to lower-diversity neighborhoods than the neighborhoods they originated in; moreover, white-white couples migrated to neighborhoods that were lower in diversity than the neighborhoods they did not choose.

When assessing the couple category differences in neighborhood affluence (average family income) for couples with children that migrate, a number of salient patterns become apparent. An overarching pattern across all couples is the improvement in neighborhood affluence from their origin to destination neighborhoods, but these improvements differed across couples. Of all couples, white-Asian couples saw the largest gain in neighborhood affluence, followed by white-white, black-black, white-Latino, black-Latino, and last, black-white. Traditional patterns of racial stratification in neighborhood affluence are especially stark when comparing the average family income in neighborhoods that were chosen compared with those that were not. Black-black couples had the largest disparity in neighborhood affluence from the neighborhoods they chose compared with those they did not. Black-Latino couples also witnessed a relatively large difference in neighborhood affluence between their chosen and nonchosen neighborhoods, followed by black-white couples. For those couples without black partners, white-Latino couples had the largest disparity, with white-white couples falling relatively close behind. White-Asian couples were the only ones to have their chosen destination neighborhoods be higher in affluence than their nonchosen neighborhoods.

## Destination Choice

The descriptive statistics we present herein on mixed-race and monoracial couples with children provide initial insight on the association between neighborhood diversity and neighborhood affluence. However, to gain a fuller understanding of the relationship between these neighborhood attributes, we present results from conditional logit models predicting the destination neighborhood choice of mixed-race and monoracial couples with children. The models presented in Table 3 use a series of interactions among couple categories, neighborhood diversity (entropy), and neighborhood affluence (average family income) to assess the relative roles of these two neighborhood attributes in determining locational attainment. First, Model 1 of Table 3 highlights that all couples are significantly more likely to choose neighborhoods with lower incomes. The statistically nonsignificant effect of neighborhood entropy indicates that all couples are not impacted by neighborhood diversity. Furthermore, all couples are less likely to choose neighborhoods that are significantly farther from their origin neighborhoods given the distance-dependence of interneighborhood migration (Long 1988) and are less likely to choose neighborhoods with higher population densities. All couples are also more likely to choose neighborhoods with larger numbers of housing units in owner-occupied areas. This finding is congruous with the notion that couples will choose homes where there is sufficient supply.

In Model 2, we include an interaction between couples with children and neighborhood entropy to assess whether compared with white-white couples, mixed-race couples are more likely to choose diverse neighborhoods upon neighborhood migration. All else being equal, the results indicate that all mixed-race couples are more likely to migrate to diverse neighborhoods than white-white couples (consistent with our first hypothesis) except for white-Asian couples, who fail to be statistically significantly different from white-white couples. In particular, for mixed-race couples with black partners, black-Latino couples have the highest odds of choosing a diverse neighborhood. Additionally, black-white and black-black couples appear uniquely drawn to diverse neighborhoods compared with white-white couples. Of all mixed-race couples that are significantly different than white-white couples in their neighborhood diversity, white-Latino couples are least likely to choose diverse neighborhoods upon migration, but they still choose areas that are more diverse than white-white couples.

In Model 3 of Table 3, we estimate a separate interaction between couples with children and neighborhood average family incomes net of a collection of other neighborhood attributes. Aligning with the descriptive findings, black-white, black-Latino, and black-black couples are significantly more likely to migrate to neighborhoods that possess lower average incomes compared with white-white couples. White-Latino couples also tend to migrate to neighborhoods that are slightly lower in socioeconomic status. Taken together, these findings suggest that black-white, black-Latino, and white-Latino couples migrate to neighborhoods that are less affluent than white-white couples, congruent with our second hypothesis, but differences between white-Asian couples and white-white couples are not apparent.

Model 4 includes two sets of interactions, one between couples with children and neighborhood entropy and a separate interaction between couples with children and neighborhood average family incomes. This model allows neighborhood diversity and neighborhood affluence to simultaneously determine the residential location of couples.8 Net of controls for other neighborhood attributes and the interaction between couples with children and neighborhood average incomes, all mixed-race couples except white-Asian couples emerge with significantly lower odds of migrating to highly diverse neighborhoods compared with Model 2. The odds of migrating to diverse neighborhoods decline substantially for black-Latino couples and modestly for black-white, white-Latino, and black-black couples. Therefore, it appears that when we simultaneously adjust for the sorting of mixed-race couples into less affluent neighborhoods, the odds of mixed-race couples choosing diverse neighborhoods decline. This finding indicates that some of the apparent draw toward diverse neighborhoods reflects sorting into less affluent neighborhoods, which, on average, are more diverse––a finding that traditional locational attainment models would miss. But even with income sorting considered, mixed-race couples with children (with the exception of white-Asian couples) are much more likely to locate in diverse neighborhoods than white-white couples with children, which is in line with our third hypothesis.

## Family Income and Destination Choice

Previously mentioned theoretical arguments point to the fact that the ability for mixed-race couples with children to choose either diverse or affluent neighborhoods, or possibly both, is partially determined by economic resources. In response, we estimate two sets of models stratified by the family income of couples with children to explicate the role of economic resources on families sorting into neighborhoods defined by their respective levels of neighborhood diversity and neighborhood affluence. Table 4 includes the first set of results of this experiment in which destination neighborhood choice is modeled for couples with children with family incomes below four times the poverty rate for a family of four. We then estimate the same models for families that have family incomes at or above four times the poverty rate for a family of four; these results are presented in Table 5.9

Model 1 of Table 4 reveals that neighborhood entropy is statistically nonsignificant for all couples, indicating that nonaffluent couples with children are, in general, not affected by neighborhood diversity. However, as expected, nonaffluent couples with children are significantly likely to sort into lower-income areas that are closer to their origin neighborhoods and have lower population densities while also possessing more housing and larger shares of owner-occupied housing units. Model 2 includes an interaction between couples with children and neighborhood entropy to explore variations within nonaffluent families. Nonaffluent black-Latino couples evince the highest odds of entering into a diverse neighborhood, and black-white couples have the second highest odds, followed by black-black and white-Latino couples. Also, nonaffluent white-white couples tend to avoid diverse neighborhoods upon migrating. Nonaffluent white-Asian couples appear to follow suit, given that they are not significantly different from white-white couples.

In Model 3 of Table 4, we assess an interaction between couples with children and neighborhood average family incomes net of a series of neighborhood attributes. Because all the couples in these models are considered nonaffluent (with family income below four times the poverty rate for a family of four), the finding that white-white couples have significantly lower odds of entering affluent neighborhoods is not surprising. Similarly, both nonaffluent black-Latino and black-black couples have relatively low odds of entering into higher-income neighborhoods upon a move. This result for black-black couples aligns with past research that lower-income black households have lower odds than white households of entering higher-income areas (Crowder and South 2005).

Model 4 of Table 4 allows both neighborhood entropy and neighborhood average family income to concomitantly determine the destinations for nonaffluent couples with children while controlling for various neighborhood attributes. The results of this model indicate that when neighborhood average family income is allowed to interact with couples, the odds for the interaction between mixed-race couples and neighborhood entropy are strongly reduced. Compared with white-white couples, black-Latino couples still emerge with relatively high odds of choosing a diverse neighborhood, followed by black-black, black-white, and white-Latino couples. The interaction coefficient for white-Asian couples and neighborhood entropy is not significantly different than that of white-white couples. Moreover, the coefficients for the interactions between most mixed-race couples and neighborhood average family income increase slightly, but these couples still remain likely to migrate to lower-income neighborhoods compared with white-white couples. The combination of the relatively stable lower odds of mixed-race couples entering more affluent neighborhoods from Model 3 to Model 4 and the decreasing odds of mixed-race couples entering diverse neighborhoods from Model 2 to Model 4 highlights that nonaffluent mixed-race couples appear to migrate to diverse neighborhoods that are relatively lower in income.

In contrast to the models highlighted in Table 4, those models in Table 5 allow neighborhood diversity and neighborhood affluence to simultaneously determine the destination choice of mobile mixed-race and monoracial couples with children that have a family income at or above four times the poverty rate for a family of four, net of neighborhood controls. Model 1 illustrates that affluent couples are not significantly likely to migrate to diverse neighborhoods. Yet, because of the affluence of their households, these couples tend to choose to migrate to higher-income neighborhoods. Also reflecting their higher economic status, the neighborhoods that affluent couples choose are less crowded than those chosen by nonaffluent couples. Affluent couples are also more likely to choose neighborhoods with higher levels of owner-occupied housing and are less likely to migrate long distances from their origin neighborhoods.

Model 2 of Table 5 displays an interaction between affluent couples with children and neighborhood entropy while controlling for various neighborhood attributes. Aligning with theoretical expectation, affluent white-white couples are not likely to choose higher-diversity neighborhoods upon migration. Most apparent among the interactions between couples and neighborhood entropy are the large odds of affluent black-Latino couples significantly migrating to highly diverse neighborhoods compared with white-white couples. Additionally, emerging as significant for the first time are affluent white-Asian couples who choose more diverse neighborhoods than white-white couples. We also witness black-white, white-Latino, and black-black couples having significantly higher odds of migrating to diverse areas than white-white couples. Moving to Model 3, we estimate an interaction between couples with children and neighborhood average family income net of neighborhood attributes. This model illustrates that white-white couples are likely to choose higher-income neighborhood settings. Both affluent white-Latino and black-black couples have lower odds of migrating to higher-income areas than white-white couples. The estimates for the remaining types of couples fail to reach statistical significance.

In Model 4, we estimate two sets of interactions for affluent couples with children net of neighborhood controls: couples by neighborhood entropy and couples by neighborhood average family incomes. These models allow us to contemporaneously determine the effect of neighborhood diversity and neighborhood affluence on the destinations that affluent couples with children choose. This model indicates slight reductions in the size of the coefficients for the interactions between black-Latino, black-white, and black-black couples and neighborhood entropy from Model 2 to Model 4. However, most surprising is that high-earning white-Asian couples emerge with more than a threefold increase in the odds of migrating to a diverse neighborhood after neighborhood average family income is allowed to determine their residential location. The emergence of affluent white-Asian couples having relatively high and increasing odds of migrating to diverse neighborhoods while simultaneously possessing higher odds of migrating to higher-income neighborhoods indicates that these couples choose neighborhoods with substantial diversity and higher incomes. In conjunction with this finding, we observe that the effects for neighborhood average family income for black-Latino and black-white couples are not different than the significantly positive effect for white-white couples, providing some support for the notion that these couples are also choosing diverse neighborhoods with higher incomes. Additionally, affluent white-Latino couples are significantly less likely to migrate to higher-income neighborhoods after contemporaneous variations in neighborhood diversity between couples are accounted for. This finding potentially reflects affluent white-Latino couples encountering some form of discrimination in the housing market.

In total, these findings demonstrate that certain types of mixed-race couples with children appear to migrate to a unique set of neighborhoods that white-white couples with children seemingly avoid. Comparing the results for affluent and nonaffluent couples with children reveals that across levels of affluence, mixed-race couples with children are more likely than white couples with children to enter diverse neighborhoods. However, consistent with our fourth hypothesis, the attraction to diversity is especially pronounced among affluent mixed-race couples with children.

## Conclusion

Using almost three decades of data from the PSID linked with information from the U.S. Census, we aspired to understand how the neighborhood destination choices of mixed-race couples with children are simultaneously influenced by neighborhood diversity and neighborhood affluence. Although prior research has suggested that mixed-race couples with children are likely to prefer residing in diverse neighborhoods (Dalmage 2000), past scholars have yet to determine the relative importance of neighborhood diversity versus neighborhood affluence in the residential choices of these families (Gabriel 2016; Wright et al. 2011, 2013). We attempted to address this unresolved question through the use of discrete-choice models.

Our findings suggest that given the set of available alternatives, most residentially mobile mixed-race couples with children choose more diverse neighborhoods than white-white couples with children. This is particularly true for couples with black partners. This overall pattern remains prevalent even when other neighborhood attributes—such as income, housing market conditions, distance from their origin neighborhood, population density, and trends in neighborhood diversity—are equivalent. The same is true after accounting for couple category variations in the draw of neighborhood income but to a slightly lesser degree. The observation that most mixed-race couples with children choose more diverse neighborhoods is explained partially by the fact that they are sorted into lower-income neighborhoods. These results suggest that mixed-race couples with children have a stronger preference for diverse neighborhoods than white-white couples with children. Black-Latino couples, in particular, stand out as possibly holding the strongest preferences for neighborhood diversity, followed by black-white and white-Latino couples. We assert these claims cautiously given that we did not directly ask respondents about their preferences; however, these findings do align with previous qualitative studies on the topic (Dalmage 2000; Romano 2003). An alternative explanation is that discriminatory tactics in the housing market bar some mixed-race couples with children from entering neighborhoods that are less diverse but equivalent in terms of income compared with the neighborhoods they actually migrate to.

Our results also imply that the process of neighborhood sorting is stratified by the economic resources of couples with children. For instance, neighborhood diversity seems to be a stronger driver of neighborhood choice for affluent mixed-race couples with children than for nonaffluent mixed-race couples with children. This finding may highlight the trade-offs between neighborhood diversity and neighborhood affluence that mixed-race families encounter when choosing a destination. Nonaffluent mixed-race couples with children, who may not have the economic resources to actualize their preferences for both diversity and affluence, may opt for somewhat less diverse neighborhoods that have greater economic advantages, such as better schools, increased safety, and heightened stability. In contrast, affluent mixed-race couples with children are in a better economic position to realize their preferences for both neighborhood diversity and neighborhood affluence. We see this pattern manifest most strongly among affluent white-Asian couples, followed by affluent black-Latino and black-white couples.

These findings add complexity to future studies of locational attainment. Typically, higher-income neighborhoods have been synonymous with higher percentages of whites (Charles 2003). However, we demonstrate that some affluent mixed-race couples with children, such as white-Asian couples, convert their higher economic status into living in neighborhoods that are relatively diverse and affluent. This pattern is likely influenced by increasing racial and ethnic diversity in the United States and by the resultant changes in the racial and ethnic composition of neighborhoods (Logan and Zhang 2011), likely leading to more neighborhoods having higher socioeconomic status while concurrently being racially and ethnically diverse. Hence, going forward, we might exercise caution when assuming that all mixed-race families follow traditional patterns of spatial assimilation. Instead, some affluent mixed-race couples with children appear to value neighborhood diversity and neighborhood affluence. At the same time, nonaffluent mixed-race couples with children are possibly trading their preferences for neighborhood diversity to migrate to neighborhoods with higher incomes—something that a portion of affluent mixed-race families do not seem to have to compromise. This pattern necessitates policy efforts to improve the accessibility of high-quality, diverse neighborhoods for lower-income mixed-race couples with children who would prefer to reside in diverse neighborhoods without sacrificing neighborhood quality. In part, this might be partially accomplished through executing the Affirmatively Furthering Fair Housing rule of the Fair Housing Act; this legislation was designed to prompt cities to lower levels of racial and ethnic segregation, which in turn would likely lead to greater numbers of high-quality diverse neighborhoods for lower-income mixed-race couples with children to migrate to.

Last, researchers might explore a number of future directions when investigating the locational attainment of mixed-race families using the discrete-choice framework. For instance, researchers might assess the role of neighborhood change on the likelihood that mixed-race families will choose neighborhoods of varying diversity and affluence. Researchers might also investigate the role of contextual conditions, such as region of the United States and the metropolitan-level attributes of income and racial and ethnic composition. Because of the considerable heterogeneity in skin shade and other phenotypical features among Latinos, future researchers might use data that can assess how within-Latino heterogeneity in physical appearance is potentially associated with differing locational attainment outcomes across mixed-race couples with Latino partners. Overall, investigating these various directions will become increasingly important in coming decades as households in the United States become more diverse.

## Notes

1

A newborn is defined as a child under the age of 1.

2

The PSID defines a long-term cohabiter as someone who is in a relationship with a PSID individual with whom the individual has lived for at least 12 months.

3

Because of the small numbers of same-sex couples in the PSID, we analyze only different-sex couples.

4

We are unable to compare mixed-race couples with children against those without because of the small sample size among some couples without children.

5

We tested the sensitivity of our results with a 10 % and 20 % random sample of nondestination tracts and found largely similar results to those estimated with the 5 % sample.

6

As a measure of diversity, the entropy score indicates the extent to which whites, blacks, Latinos, and others represent equal shares in a tract. A value of 0 signals that one group is present, and a value of 100 designates an even distribution among the four groups.

7

Average family income is missing for 70 origin tracts, 75 destination tracts, and 814 nonchosen tracts in our sample. PSID respondents’ family income is missing for seven couple-periods. Following White et al. (2011), all covariates and outcomes from our analysis are included in the imputation model.

8

The online appendix shows figures of the odds of destination tract choice for couples by entropy score and family income from the coefficients in Model 4 in Tables 3, 4, and 5, respectively.

9

We conducted a supplemental analysis in which we estimated the destination choice of couples who had family incomes below the national average and separately for those who had family incomes at or above the national average. The results from this supplemental investigation were substantively similar to the results reported in the present analysis.

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