Urban sprawl and racial inequality in intergenerational mobility

Abstract

Persistent racial inequality in socioeconomic status within urban areas has been a significant concern in both the US and European countries. Differences across racial groups in intergenerational mobility (IM) have been identified as a key source of this persistence. However, efforts to understand racial inequality in IM have rarely considered the role of urban sprawl. This article argues that urban sprawl affects differences in IM between racial groups directly and indirectly through racial segregation, racial bias, and social capital. We analyze data from 874 metropolitan counties in the US using structural equation models to test these direct and indirect effects of sprawl on racial inequality in IM. We found that urban sprawl was negatively associated with racial inequality in IM. The direct effect, which we partially attribute to higher racial disparities in social capital in more compact counties, was statistically significant. For the indirect effects, racial segregation had the largest mediating effects between urban sprawl and racial inequality in IM, followed by economic connectedness (EC) and racial bias. The net indirect effect of sprawl on racial inequality in IM was negative because negative indirect effects through racial segregation and EC outweigh positive indirect effects through racial bias. Our findings demonstrate the significant role of urban form in racial inequality in IM.

Full text

Urban sprawl and racial inequality in
intergenerational mobility
Ning Xiong
1
, Yehua Dennis Wei
1,
, Sergio J. Rey
2
1
Department of Geography, University of Utah, Salt Lake City, UT 84112, United States
2
Department of Geography, Center for Open Geographical Science, San Diego State University, San Diego, CA 92182,
United States
Corresponding author. Department of Geography, University of Utah, 260 S Central Campus Dr, Rm 4625 Salt Lake City,
UT 84112, USA. E-mail: wei@geog.utah.edu
Abstract
Persistent racial inequality in socioeconomic status within urban areas has been a significant con-
cern in both the US and European countries. Differences across racial groups in intergenerational
mobility (IM) have been identified as a key source of this persistence. However, efforts to understand
racial inequality in IM have rarely considered the role of urban sprawl. This article argues that urban
sprawl affects differences in IM between racial groups directly and indirectly through racial segrega-
tion, racial bias, and social capital. We analyze data from 874 metropolitan counties in the US using
structural equation models to test these direct and indirect effects of sprawl on racial inequality in
IM. We found that urban sprawl was negatively associated with racial inequality in IM. The direct
effect, which we partially attribute to higher racial disparities in social capital in more compact
counties, was statistically significant. For the indirect effects, racial segregation had the largest
mediating effects between urban sprawl and racial inequality in IM, followed by economic connect-
edness (EC) and racial bias. The net indirect effect of sprawl on racial inequality in IM was negative
because negative indirect effects through racial segregation and EC outweigh positive indirect effects
through racial bias. Our findings demonstrate the significant role of urban form in racial inequality
in IM.
Keywords: racial inequality; intergenerational mobility; urban sprawl; compact development; county
JEL classifications: J62, D63, O20, R10, R58
1. Introduction
Racial inequalities have persisted in almost every aspect of socioeconomic status (SES) and have been
a major concern, as evidenced by studies from the US (Margo 2016) and European countries (Heath
and Brinbaum 2007;Khan and Shaheen 2017). The determinants of racial inequalities have been ex-
tensively examined and discussed, ranging from systematic discrimination (Charles and Guryan 2008;
Ikram et al., 2015;Pearman 2022), segregation (Lancee 2010;Ananat 2011), to social capital gaps (Lin
2000;Lancee 2010). Because most of these studies have examined the causes of racial inequality using
data from one generation, they are unable to address racial disparity across generations.
The intergenerational mobility (IM) gap plays a central role in persisting racial disparities. This is
because only policies that narrow the IM gap could diminish racial disparities over generations in the
long run, while other projects that do not influence IM only have temporary impacts in one generation
(Mazumder 2014;Chetty et al., 2020). The efforts to understand the racial IM gap are mainly in two
directions. Both US and European research document family background accounts for some of the
Received: 24 January 2023. Editorial decision: 27 December 2023. Accepted: 29 December 2023
#The Author(s) (2024). Published by Oxford University Press. All rights reserved. For permissions, please email: journals.
permissions@oup.com
Journal of Economic Geography, 2024, 24(2), 309–332
https://doi.org/10.1093/jeg/lbad039
Advance Access Publication Date: 17 January 2024
Original article
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racial IM gap (Platt 2005;Mazumder 2014;Fox 2016;Li and Heath 2016). Another direction found that
neighborhoods, where people grew up, had causal effects on racial inequality in IM, and the social
structure of neighborhoods is correlated with the racial IM gap (Chetty et al. 2020). Still, there is no evi-
dence on how physical structure (e.g. urban form) affects racial inequality in IM, although some stud-
ies found that physical barriers, such as highways and railroad tracks, could affect racial segregation
(Roberto and Korver-Glenn 2021). In other words, though a body of research has shown that urban
form affects income inequality (Wei and Ewing 2018), insufficient attention has been given to the so-
cial dimension of inequality, especially racial inequality in IM.
Economic geographers have studied race and racial inequality, focusing on racially unequal out-
comes produced in place and the central role of space in constructing race and racial inequality
(Bonds 2013). Specifically, racial segregation and spatial mismatch are two main topics for economic
geographers to understand the role of spatial organization in producing racial inequality (Rose 1972;
Holloway 1996;Kaplan 2004;Feng, Flowerdew, and Feng 2015). Another direction is racial capitalism,
which takes effects in urban space by facilitating the spatial organization of dispossession and dis-
placement of people of color (White spatial exclusivity or spatial exploitation of people of color)
(Dantzler 2021;Dorries, Hugill, and Tomiak 2022). Additionally, geographers have acknowledged spa-
tial relations as an operationalization of racial inequality (Jackson 1987;Pulido 2002). In other words,
racism is formed in a place that, in turn, constructs racialized identities, and racialization processes
are inherently spatialized (Inwood and Yarbrough 2010). Despite these geographers arguing that place
and space affect racial inequalities (Sundstrom 2003), a fundamental question remains: whether/how
does urban form affect racial inequality in IM?
We used racial inequality in IM between Black and White people in the USA as a relevant case/con-
text to study how urban sprawl, a typical feature of American urban form, affects racial inequality in
IM. Significant intergenerational gaps between Blacks and Whites persist over generations in the USA
(Hertz 2005;Mazumder 2014;Chetty et al. 2020). Whites have larger upward mobility and lower down-
ward mobility than Blacks (Bhattacharya and Mazumder 2011;Mazumder 2014;Chetty et al. 2020). It
should be noted that, unlike North America, most European countries do not have long-established or
indigenous/native minorities. Instead, the offspring of postwar migrants are the primary established
ethnic minorities in most European countries today. Although this situation might differ from the cu-
mulative disadvantages faced by Blacks in the USA, some racial minorities in some European countries
have also experienced cumulative penalties. Additionally, racial/ethnic inequality in IM does exist and
has persisted in Europe and other countries (e.g. Pott 2001;Khan and Shaheen 2017).
Therefore, this article studies the place–space–race theme in geography by examining whether ur-
ban sprawl contributes to racial inequality in IM and investigating the underlying mechanisms linking
sprawl and racial inequality in IM. We separated their direct and indirect effects and hypothesized
three mediating variables between urban sprawl and racial inequality in IM: racial segregation, racial
bias, and social capital. We then used structural equation modeling (SEM) to test these hypotheses and
estimate the magnitude of various pathways between urban sprawl and racial inequality in IM.
This study makes two main contributions. First, we explicitly identify urban form as a key factor in
producing racial inequality in IM and demonstrate that urban sprawl as an urban form is an important
factor affecting racial inequality in IM. This is an improvement over explanations that generally em-
phasize place and space. Second, we separate and test sprawl’s direct and indirect effects on racial in-
equality in IM using SEM. This improves our understanding of underlying mechanisms connecting
urban sprawl to racial inequality in IM.
2. Literature review
Efforts have been made to understand the causes of IM, with a primary focus on individual and family
levels, such as family income, education, and background (Bj€
orklund and J€
antti 2009;Gallagher,
Kaestner, and Persky 2019). Institutional and social factors, including schools, income inequality, and
neighborhood sorting, have also been studied (Hertel and Groh-Samberg 2019;Cholli and Durlauf
2022). Recently, academics have increasingly focused on the impact of urban space and neighbor-
hoods, including their SES (Chetty et al. 2014,2018) and physical environment (Ewing et al. 2016).
What is less understood is the role of race in IM, although race is one of the strongest predictors of IM
(Connor and Storper 2020). Wei, Xiong, and Carlston (2023) found that the relationship between race and
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IM was mediated by racial segregation, social capital, unemployment, education, and family structure.
Still, it is unclear whether this association is caused by lower IM for certain racial groups or lower IM for
all races in areas with a high percentage of certain racial groups. To address this, a few studies have re-
cently paid more attention to racial inequality in IM and found substantial racial disparities in IM in
Western countries (Platt 2005;Mazumder 2014;Fox 2016;Li and Heath 2016), especially between Whites
and Blacks in the USA. For example, Hertz (2005) comprehensively analyzed the racial IM gap and found
that Whites had larger upward mobility and lower downward mobility than Blacks, while Blacks were
more likely to remain at the bottom of the income distribution over generations. A few studies build on
Hertz’s (2005) work and confirm the findings (Bhattacharya and Mazumder 2011;Mazumder 2014;Chetty
et al. 2020). Chetty et al. (2020) further found that large IM inequality persists in the same census tract.
Moreover, these findings suggest IM disparities worsened, given that most Black children are born into
low-income households. Family-level factors have been investigated to understand the determinants of
IM gaps. Parental class and family structure of children are positively associated with racial IM gaps (Platt
2005;Mazumder 2014;Fox 2016;Li and Heath 2016). However, IM gaps remain substantial even after con-
trolling for differences in parental wealth (Chetty et al. 2020). Parental marital status and education only
slightly affect racial inequality in IM (Chetty et al. 2020).
Social scientists are increasingly paying attention to the role of geography, especially neighborhood
effects, in racial inequality in IM (Chetty et al. 2020;Ryabov 2020). Ryabov (2020) found that neighbor-
hoods played an important role in racial inequality in the intergenerational transmission of SES.
Chetty et al. (2020) found that neighborhoods, where people grew up, had causal effects on racial in-
equality in IM. However, the current knowledge of racial inequality in IM is limited. Studies only focus
on the effects of social characteristics of neighborhoods on IM, and insufficient attention has been
given to how urban form affects racial inequality in IM.
The literature on the effects of urban form on spatial/income inequality provides inspiration and di-
rection for the question of whether urban form influences racial disparity in IM. For example, urban
sprawl as an urban form does affect income/class inequality (Frenkel and Israel 2018;Wei and Ewing
2018) through residential income segregation (Pendall and Carruthers 2003;Frenkel and Israel 2018).
The essential features of sprawl include low density and automobile dependency, single-use develop-
ment, noncontiguous scattered or “leapfrog”development, fragmented land ownership, and strip com-
mercial development (Galster et al. 2001;Ewing and Hamidi 2015). While studies have shown that
urban sprawl increases income inequality (Wheeler 2008;Lee, Ambrey, and Pojani 2018;Wei and
Ewing 2018), insufficient attention has been given to the social dimension of inequality, especially ra-
cial inequality in IM. These inequality studies undervalue the significance of race in their analyses.
Race is fundamental in defining the “community”and understanding society in Western countries.
The positive association between sprawl and income inequality does not necessarily mean that sprawl
increases racial inequality. This is because systematic racism exists and has been persistent in
Western countries, and race itself has its unique culture and identity influence. On the one hand, pre-
vious research has found the effects of racism to be more powerful than class (Duncan 1968). Racial
capitalism also argues that racism is formed irrespective of class relations (Pulido 1996) and whiteness
itself is a property used to be traded (Beeman, Silfen Glasberg, and Casey 2011;Dantzler 2021;Dorries,
Hugill, and Tomiak 2022;Fluri et al. 2022). On the other hand, race also differs from class in terms of
culture. Racial culture affects behaviors and life chances, which in turn affects IM. For example, homo-
phily may lead to individuals socializing more with members of their own race, which may make it
less likely they interact with White individuals, thereby precluding the establishment of social ties
that may improve their IM (Lin 2000).
Major augments/debates related to the relationship between urban form and racial inequality in IM
are the connections between place, space, and race in geography. These arguments claim the central
role of place and space in producing and reproducing racial inequalities (Pulido 2002;Bonds 2013).
They argue that spatial relations serve as an operationalization of racial inequalities (Jackson 1987;
Pulido 2002). Geographers also focus on studying racial segregation and spatial mismatch to under-
stand the impacts of spatial organization in producing racial inequalities (Rose 1972;Holloway 1996;
Kaplan 2004;Feng, Flowerdew, and Feng 2015). However, whether and how urban form affects racial
inequality in IM is still unclear.
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3. Sprawl and racial inequality in IM: research hypotheses
Motivated by the literature, we aim to investigate whether and how urban sprawl affects racial in-
equality in IM, focusing on their direct and indirect links. We argue that urban sprawl may affect social
structures that influence racial inequality in IM, meaning that sprawl may affect racial inequality in
IM through indirect pathways. These pathways might exhibit countervailing effects. We explicitly the-
orize three potential pathways below, that is, racial segregation, racial bias, and social capital.
3.1 Sprawl, racial segregation, and racial inequality in IM
One possible pathway through which urban sprawl affects racial inequality is racial segregation.
Racial segregation shapes racial inequality (Lancee 2010;Ananat 2011;Van Ham et al., 2016). Racial
segregation is related to exacerbated exposure of racial minority people to disadvantaged neighbor-
hoods across locations (Massey and Denton 1993;Hess 2021). In the presence of segregation, racial mi-
nority people are more likely to live in disadvantaged neighborhoods (Adelman 2004). As a result,
racial minority people are sorted into disadvantaged neighborhoods while Whites are placed into
advantaged neighborhoods in racially segregated regions. As neighborhoods affect people’s various
outcomes (Sampson, Morenoff, and Gannon-Rowley 2002;Minh et al. 2017), these racial disparities in
neighborhood conditions lead to racial inequality in SES opportunities and outcomes over generations
(Sharkey 2013;Feng, Flowerdew, and Feng 2015). This racial disparity is even worsened given that the
adverse effects of the disadvantaged neighborhood on Blacks are larger than on Whites (Sampson
2009). Additionally, these disadvantaged neighborhoods are segregated from resources and opportuni-
ties in segregated regions, contributing to racial inequality in IM. For example, racial segregation geo-
graphically restricts Black people’s access to job opportunities, resulting in lower Black employment
rates and greater racial inequality (Stoll and Raphael 2000). Thus, segregation impedes Black IM and
could perpetuate racial inequality (Lundberg and Startz 1998).
Urban sprawl may, however, lower residential segregation. Jaret et al. (2006) found that high racial
residential segregation persists in areas with high density, high mixed-land use, and a more urban
street pattern, while the lowest segregated metropolitan areas have a high value on sprawl even after
adjusting for other factors. Galster and Cutsinger (2007) further found that housing price was the pri-
mary mechanism through which urban sprawl reduces racial residential segregation. In particular,
they argue that sprawl lowers the average price, lessens the interracial affordability housing gap, and
thus decreases racial segregation. In other words, sprawl increases housing affordability; as a result,
racial minority people, such as Blacks, are more likely to have homeownership and possess larger
homes in sprawling areas (Kahn 2001).
Moreover, the suburbanization of Blacks is associated with the availability of affordable suburban
housing and housing supply (Howell and Timberlake 2014). Blacks and Whites are less segregated in
the suburbs than in central cities (Massey and Tannen 2018). These findings further support that ur-
ban sprawl reduces racial segregation by lowering housing prices. Notably, Ragusett (2014) found that
urban sprawl decreased the racial consumption gap only after reaching a minimum level of sprawl.
Furthermore, population density as an essential aspect of sprawl is positively associated with racial
segregation (Bond Huie 2000).
On the other hand, urban sprawl might increase racial segregation through other pathways. For ex-
ample, the spatial mismatch hypothesis argues that employment suburbanization in sprawling
regions isolated Blacks from employment opportunities, promoting racial segregation based on in-
creasing racial income inequality (Galster and Cutsinger 2007; Boustan and Margo 2009). Measures
that curb urban expansion/sprawl could also lower racial segregation. For example, urban contain-
ment reduces residential segregation (Nelson, Dawkins, and Sanchez 2004;Nelson, Sanchez, and
Dawkins 2004).
Although there are some countervailing mechanisms between urban sprawl and racial segregation,
we argue that, on balance, urban sprawl reduces racial segregation overall because the role of the spa-
tial mismatch hypothesis is declining as Blacks become more suburbanized in sprawling regions
(Boustan and Margo 2009;Bartik and Mast 2021). In summary, we argue that urban sprawl could re-
duce racial inequality in IM by lowering racial segregation.
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3.2 Sprawl, racial bias, and racial inequality in IM
Racial bias shapes neighborhood racial inequality in IM (Chetty et al. 2020). In particular, racial bias
affects racial inequality in almost all aspects of SES status, such as the racial wage gap (Charles and
Guryan 2008), the racial health gap (Ikram et al. 2015), and the racial test score gap (Pearman 2022).
Urban sprawl reduces social interaction opportunities (Farber and Li 2013). In particular, increased
automobility use in sprawling areas diminishes social interaction and participation in social activities
(Freeman 2001). Additionally, new urbanism claims that dense, pedestrian-street design, and mixed-
land use strengthen face-to-face interaction (Talen 1999;Lund 2003). For example, local residential
walkability is positively associated with knowing neighbors, participating in neighbors’social activi-
ties, and local social connectedness (Leyden 2003). Sprawl also affects inter-group contacts through ra-
cial/ethnic segregation (Semyonov and Glikman 2009).
On the other hand, inter-group contact theories suggest social interaction and contact between ra-
cial groups could reduce bias and prejudice (Pettigrew and Tropp 2006;Wagner et al. 2006). In particu-
lar, intergroup contact has been defined as “face-to-face interaction between members of clearly
defined groups”by Pettigrew and Tropp (2006: 754). Allport (1954) officially proposed the hypothesis
that intergroup contact could reduce prejudice. The initial four conditions in which intergroup contact
ameliorates intergroup intentions and attitudes while reducing prejudice are: equal group status, com-
mon goals, intergroup cooperation, and support from authorities, law, or custom (Allport 1954).
Pettigrew (1998) added friendship potential as a fifth condition because it could induce positive emo-
tions and attitudes toward outgroup members and elicit other conditions for positive intergroup con-
tact influences. However, these conditions merely enhance the effect of intergroup contact on
prejudice reduction; they are not required for this effect to occur (Pettigrew et al. 2011). Even superfi-
cial interactions between different groups decrease prejudice (Dixon and Rosenbaum 2004;Pettigrew
and Tropp 2006).
Although some scholars argue that intergroup contact only leads to intergroup conflicts, Pettigrew
and Tropp (2006) obtained a consistent result of intergroup contact reducing prejudice through a
meta-analysis of 515 studies from 38 countries. Longitudinal studies further support this result (Levin,
Van Laar, and Sidanius 2003). Therefore, it appears that intergroup contact does reduce prejudice and
bias. In contrast, the absence of contact and interaction could reinforce discrimination and increase
racial hostility based on previous stereotypes (Stolle, Soroka, and Johnston 2008).
To summarize, as neighborhood racial bias is negatively associated with neighborhood racial in-
equality in IM (Chetty et al., 2020), we argue that urban sprawl could increase racial inequality in IM
through racial bias.
3.3 Sprawl, social capital, and racial inequality in IM
Another possible channel through which IM may be affected is social capital. Inequality in social capi-
tal exists across racial groups because of their structural positions in social networks in Western soci-
ety (Lin 2000;Lancee 2010;Munn 2019). For example, Marsden (1988) found that Blacks had less social
capital than Whites and Hispanics in terms of both network diversity and size. Moreover, Blacks are
less likely to receive financial help from their social network (Parish, Hao, and Hogan 1991) and even
any assistance from parents (Eggebeen and Hogan 1990). Furthermore, African Americans receive
lower social capital returns than Whites (Dunham and Wilson 2007). The racial disparity in social capi-
tal contributes to racial inequality in economic status and mobility (Lin 2000). This is not surprising
given that social capital involves transferring information, offering opportunities (e.g. job referrals),
and shaping behaviors, leading to persistent differences in outcomes across groups (Lancee 2010;
Jackson 2021;Ily
es et al. 2022).
Urban sprawl influences social capital. Putnam (2000) suggested that urban sprawl decreases social
interaction and lowers social capital. Empirically, urban sprawl negatively affects social contact oppor-
tunities (Farber and Li 2013) and shows a negative relationship between automobile usage and social
ties Freeman (2001). However, some studies found the opposite relationship and showed that the story
is more complex than Putnam suggests (Brueckner and Largey 2008;Nguyen 2010). This variation in
results likely stems from how the various aspects of the built environment affect sprawl differently
(Mazumdar et al., 2018). In particular, high walkability and a mixed-used environment could promote
social capital by encouraging social interaction and political involvement (Leyden 2003). However,
there was a negative relationship between density and social capital (Brueckner and Largey 2008;
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Nguyen 2010;French et al. 2014). Studies even found that density was unrelated to social capital
(Freeman 2001;Glaeser and Gottlieb 2006). This mixed evidence may also be explained by the fact that
urban sprawl might increase some types of social capital while lowering others (Nguyen 2010).
Although the empirical evidence on the effects of urban sprawl on social capital is mixed, social capital
definitely acts as a channel between sprawl and racial inequality.
Urban sprawl could affect racial inequality through social capital in two ways. First, urban sprawl
influences the extent to which racial minority people interact with Whites (intergroup contact), which
could affect the extent to which racial minority people can access the social resources of Whites
(Stanton-Salazar 1997;Lin 2000), viewed as a form of “bridging”capital, and thus affect racial inequal-
ity in social capital, which in turn influences racial inequality in IM.
Second, urban sprawl contributes to racial disparity in IM by affecting racial minority people and
Whites’social capital separately, which determines each group’s IM. In particular, people prefer to so-
cialize with those of the same race; thus, their social capital is more likely to be obtained from same-
race neighbors. For example, Black boys receive much fewer benefits than Whites from the presence
of higher-income neighbors unless these neighbors are Blacks (Ellen and Turner 1997;Turley 2003).
Moreover, this homophily means that individuals feel more connected to people of their own race, en-
abling them to access greater social resources and influence from their own race (Noguera 2003). As a
result, social groups tend to form networks involving the same race. This is somewhat supported by
the finding that aggregate social capital is positively associated with some types of racial inequality
and inversely correlated with Black outcomes (Hero 2003). Thus, urban sprawl affects the extent to
which Blacks interact with Blacks, and Whites interact with Whites separately, leading to their racial
inequality in social capital. Additionally, social capital influences IM (Mitra 2008;Chetty et al., 2014,
2022a,2022b). Thus, the social capital of Blacks and Whites affects their respective IM, leading to racial
inequality in IM.
In summary, urban sprawl could affect racial inequality in IM through racial segregation, racial
bias, and social capital. In particular, based on previous propositions, we propose the following
three hypotheses.
Hypothesis (1): Urban sprawl reduces racial inequality in IM by lowering racial segregation.
Hypothesis (2): Urban sprawl increases racial inequality in IM through increasing racial bias.
Hypothesis (3): Urban sprawl affects racial inequality in IM through social capital.
Notably, our argument does not require any assumption that urban sprawl is the only or predominant
cause of racial inequality in IM. It requires only the more limited assumption that urban sprawl is val-
ued for racial inequality in IM. Our empirical findings support all these hypotheses.
4. Data and methodology
4.1 Study area
Metropolitan counties in the contiguous USA, excluding Alaska, Hawaii, and Territories of the USA, are
the study areas, accounting for 81.16 per cent of the total population in the USA in 2000. We had 876
metropolitan counties as defined by the 2003 US Census Bureau, excluding 131 metropolitan counties
without IM data for Blacks or Whites due to population of Blacks or Whites below 20, excluding 81 met-
ropolitan countries primarily due to the absence of sprawl data. We further deleted two outlier coun-
ties (New York and San Francisco) whose compactness is much larger than other counties, although
the main results of our study remain when including these two counties. As a result, there are 874
metropolitan counties (80.33 per cent of total metropolitan counties and 91.33 per cent of metropolitan
counties having IM data for both Blacks and Whites) (Supplementary Appendix Fig. A1) in this study. It
accounts for 76.21 per cent of the total population in the contiguous USA, 92.03 per cent of the total
population in metropolitan counties, and 92.91 per cent of the total population in metropolitan coun-
ties having IM data for both Blacks and Whites in 2000. More detailed information about the process of
deleting data is shown in Supplementary Appendix Table A1. We compared data statistics for racial in-
equality in IM (see Supplementary Appendix Fig. A2), suggesting that these counties should not differ
systematically from metropolitan counties excluded from the analysis.
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4.2 Data and variables
This section elaborates on the variables and their data sources used in the baseline empirical model to
examine how urban sprawl affects racial inequality in IM through hypothesized mediating variables.
The variables include the outcome variable, the main analysis variable, and their mediating variables.
To conserve space, we do not describe each variable in great detail, and more technical information
can be found in the cited papers.
4.2.1 Outcome Variable: Racial Inequality in IM
The racial IM gap was calculated as the difference in mean individual income rank in the national indi-
vidual income distribution (relative to other children in the same year) for White and Black people in
the same county where they grew up whose parents were at the 25th percentile of the parents’na-
tional income distribution. This difference was calculated using the race-specific IM data from the
Opportunity Atlas Database of Chetty et al. (2018). IM index used children in the 1978–1983 birth
cohorts born in the USA or authorized immigrants who came to the USA in childhood. The children’s
individual income rank was calculated using their mean annual incomes as reported to the IRS in 2014
and 2015 when the children were between 31 and 37 years. These counties are where these individuals
lived before the age of 23, called childhood counties. The absolute IM index has been widely used be-
cause of its more stable and robust properties (Chetty et al. 2014). Notably, IM of the current cohort is
highly correlated with future cohorts, and the rate of their correlation decay is very slow over time
(Chetty et al. 2018), implying the stability of IM over time. More information can be found in Chetty
et al. (2018).
4.2.2 Main analysis variable: urban sprawl and compactness
The sprawl/compactness variable is the exogenous variable that interests us the most. Early studies
have tried to measure urban sprawl by concentrating on just one dimension, primarily density, which
could produce conflicting results (Ewing et al. 2014). Galster et al. (2001) extended urban sprawl mea-
surement by developing multi-dimensional metrics: density, continuity, concentration, clustering,
centrality, nuclearity, mixed uses, and proximity. Similarly, Ewing, Pendall, and Chen (2002) estab-
lished a multi-dimensional index for quantifying the extent of urban sprawl by using 2000 data and po-
sitioned compact development as the opposite end of urban sprawl. This sprawl index has been
refined and updated to 2010 by Ewing and Hamidi (2014), including more indices, more counties, and
more construct validity. This index includes four dimensions: density, mixed-use, centering, and street
accessibility. Jobs and housing density are both examples of density, and “sprawl”is usually considered
a lack of density. However, certain areas may be dense, but it is hard to get around on a walk and have
an unbalanced job-housing balance. Since mixed-use development requires a balance between em-
ployment and housing and the ability to walk to commercial districts, it is also a significant signal of
sprawl. The connectivity of the streets, especially for pedestrians, is indicated by their accessibility.
The concentration of activities that provide agglomeration economies, a sense of location, and support
for alternative transportation are measured by “centering.”
This index has been widely used to study the costs and benefits of sprawl/compactness (Ewing et al.
2016). We adopted this index, which was downloaded from the National Cancer Institute. The full set
of variables to calculate the index can be found in Ewing and Hamidi (2014) and Supplementary
Appendix Table A2. The overall compactness score is an index with a mean of 100 and a standard devi-
ation of 25. Counties with more sprawling have index values below 100, while those with more com-
pact have values above 100. More information can be found in Ewing and Hamidi (2014). In this study,
we divided the compactness score by 100. Notably, it would be preferable to use an index for the year
before individuals were 23 years old (before 2006), which IM reveals itself. However, Hamidi and Ewing
(2014) reported that urban form had not changed significantly from 2000 to 2010.
4.2.3 Mediating variables: racial segregation, racial bias, and economic connectedness
We hypothesize three mediating variables indirectly linking urban sprawl and racial inequality in IM:
racial segregation, racial bias, and social capital. Based on the data sources of these mediating varia-
bles used in the empirical model, we describe them below.
We obtained ‘racial segregation’from the Opportunity Insights website of Chetty and Hendren
(2018). This index used a multi-group Theil index calculated at the census-tract level over four groups:
Urban sprawl and racial inequality | 315
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White alone, Black alone, Hispanic, and Others using 2000 Census SF1 100 per cent data. It assesses
the degree to which the racial distribution in every census tract differs from the general racial distribu-
tion in the county. Its value ranges from 0 to 1, where a value of 0 indicates the same racial composi-
tion within each census tract in the county, while a value of 1 indicates only one racial group within
each census tract. Compared to other segregation indexes, the Theil index (information theory index)
is the superior measure conceptually and mathematically because it obeys the principle of transfer
and can be decomposed into its parts (Reardon and Firebaugh 2002). Moreover, Chetty et al. (2014)
obtained similar results when employing two group measures of Black–White segregation, such as iso-
lation or dissimilarity indices.
‘Racial bias’was derived from the Race Implicit Association Test (IAT) Database available on the
Journal of Open Psychology Data website (Xu et al. 2014). We used both explicit racial bias and implicit ra-
cial bias since they have different effects on racial inequality regarding the magnitude and significance
of SES outcomes (Hehman, Flake, and Calanchini 2018;Riddle and Sinclair 2019;Pearman 2022).
Following prior research, explicit racial bias was measured as the difference in respondents’reported
warmth toward White versus Black people (where 1 equals very cold and 10 equals very warm) (Riddle
and Sinclair 2019;Pearman 2022). The race IAT score is an implicit racial bias indicator calculated by
comparing a participant’s ability to match positive and negative words to Black versus White faces,
with higher IAT scores indicating a stronger implicit bias toward black faces. It is the most robust and
well-validated measure of implicit racial bias (Greenwald et al., 2009).
We excluded respondents who were too slow or had significant errors in classification following
Nosek, Banaji, and Greenwald (2002). We only included the respondents who are White (not Hispanic
or Latino origin) in the USA and have their geographic information associated with a US county.
Following previous studies (Hehman, Flake, and Calanchini 2018;Chetty et al., 2020), we calculated
mean explicit racial bias and implicit racial bias scores for White participants at the county scale, pool-
ing data from 2002 to 2020 to obtain more counties’racial bias and more accurate racial bias esti-
mates, assuming that racial bias has not been changed significantly over the years between 2002 and
2020 at the county scale.
‘Economic connectedness’(EC) is one of the types of social capital and among the strongest predic-
tors of IM found to date (Chetty et al., 2022a,2022b). EC is defined as two times the share of high-SES
friends among low-SES individuals averaged over all low-SES individuals in the county. A value of 0 for
EC suggests no connections between low-SES and high-SES people in a network, whereas a value of 1
indicates that low-SES individuals have an equal number of low-SES and high-SES friends. EC meas-
ures the degree to which individuals with low and high SES are friends, which could be used to study
how social relationships with affluent individuals impact people’s SES opportunities and outcomes.
EC is determined by two factors: (1) ‘high-SES exposure’(exposure hereafter), mean exposure to
high-SES individuals by county for low-SES individuals in groups and (2) ‘friending bias’,“the rate at
which people befriend high-SES individuals conditional on the share of high-SES members in the
group”(Chetty et al. 2022a,2022b: 122). In particular, exposure was calculated as two times the aver-
age share of high-SES individuals in individuals’groups, averaged over low-SES users, such that a
value of 1 for a group means that 50 per cent of people have high-SES. Friending bias is calculated as
one minus the ratio of the share of above-median-SES friends to the percentage of above-median-SES
peers in the individual’s group. In the adopted dataset, it was calculated as one minus the ratio of EC
to mean exposure to high-SES individuals. Its value, which is larger than 0, indicates a lesser likelihood
of having high-SES friends than if friendships were made at random within a particular group. These
two factors are important to understanding the mediating effects of EC between sprawl and racial in-
equality in IM.
These three indices (EC and its two determinants) and their explanations/definitions mentioned
above and below in this study were from the Social Capital Atlas Database of Chetty et al. (2022a,
2022b). We adopted EC restricting attention to friendships that can be allocated to the group in which
they were formed to be consistent with exposure and friending bias measures. The results remained
because its correlation with EC with all friendships considered is very high (0.972). These indices of EC,
exposure, and friending bias were calculated using 70.3 million Facebook users aged 25–44 years resid-
ing in the USA as of 28 May 2022 (82 per cent of the US population aged 25–44 years), which is signifi-
cantly larger than other datasets and provides more adequate precision and information for
measuring EC. Facebook friendship links can offer data about individuals’real-life friends because
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these Facebook friendships must be confirmed by both parties and most of these friendships are be-
tween people who have social interactions in person (Jones et al. 2013). Moreover, a similar EC was
obtained when only using people’s ten closest friends (correlation ¼0.99 between counties). SES was
computed by combining twenty-two measures of SES, such as median household incomes in the indi-
vidual’s census block group and education level, using a gradient-boosted regression tree. The terms
high-SES and low-SES refer to below-median and above-median SES in the national SES distribution in
the same birth cohort, respectively. The Facebook samples are proved to be well representative of the
US population and the SES measure is consistent with external data.
Notably, it would be preferable to calculate these indices using 1978–1983 birth cohorts, the same
birth cohorts used to calculate racial inequality in IM. However, Chetty et al. (2022a,2022b) adopted
the same year EC and IM data to study their potential causal relationship and performed robustness
checks (reverse causality, causal effects of place versus selection, and connectedness versus other fac-
tors) to confirm that this index will not affect understanding causal linkages between EC and IM.
Moreover, Chetty et al. (2022a,2022b) found stability of county-level EC across birth cohorts over time,
as well as stability of the correlation of IM and cohort-specific EC over time, minimizing the effects of
misalignment.
Definitions of variables are shown in Table 1, and their descriptive statistics are shown in
Supplementary Appendix Table A3.
Table 1. Variable definitions and sources in the empirical models.
Variables Definitions Sources Abbrev.
Racial inequality in IM Difference in mean individual income
rank for White and Black people at
the county level whose parents were
at the 25th percentile of the national
income distribution
Opportunity Atlas
Database of Chetty
et al. (2018)
RIneq
Endogenous variables: Mediating variables
Racial segregation Multi-group Theil Index calculated at
the census-tract level over four
groups: White alone, Black alone,
Hispanic, and Other, 2000
Opportunity
Insights Website
RSeg
Explicit racial bias Mean IAT racial bias scores for White
study participants at the county level,
pooling data from 2002 to 2020
Race Implicit
Association Test
(IAT) Database
ERBias
Implicit racial bias Mean difference in respondents’
reported warmth toward White
versus Black people, pooling data
from 2002 to 2020
Race Implicit
Association Test
(IAT) Database
IRBias
Economic connectedness Two times the share of high-SES friends
among low-SES individuals averaged
over all low-SES individuals in the
county, restricting attention to
friendships that can be allocated to
the group in which they were
formed, 2022
Social Capital Atlas
Database of Chetty
et al. (2022a)
EC
Exposure Mean exposure to high-SES individuals
by county for low-SES individuals:
two times the average share of
high-SES individuals in individuals’
groups, averaged over low-SES
users, 2022
Social Capital Atlas
Database of Chetty
et al. (2022b)
Expo
Friending Bias 1-(economic connectedness/exposure
to high-SES individuals), 2022
Social Capital Atlas
Database of Chetty
et al. (2022b)
FBias
Exogenous variables
Compactness index Composite index/100: density factor,
mix use factor, centering factor,
street factor, 2010
National
Cancer Institute
Comp
Notes: Abbrev. is the abbreviation.
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4.3 Analytical method
Path analysis was used to test our hypotheses and investigate sprawl’s direct and indirect influences
on racial inequality in IM. Path analysis is an SEM technique to investigate competing causal effects
and test mediation effects through a set of simultaneous equations. The framework can have several
endogenous variables, which can be specified as functions of the exogenous variables and other en-
dogenous variables. Each endogenous variable has an equation in the system.
There are several reasons for choosing SEM compared to Baron and Kenny’s (1986) causal steps ap-
proach (a set of regression models used to infer indirect effects by testing their constituent paths).
Recent mediation literature encourages using SEM and discourages using the causal step approach be-
cause of its severe drawbacks, such as potentially rejecting statistically significant mediating relation-
ships (Hayes 2009;Rungtusanatham, Miller, and Boyer 2014). SEM seeks to evaluate how well
theoretically justified conceptual models are against data based on variances and covariances of varia-
bles, which enables isolating the direct and indirect effects. Most importantly, compared to causal step
approaches, it allows for directly testing indirect effects with the highest statistical power and deter-
mining the magnitude of indirect effects. It is substantially more plausible and produces more reliable
results than the causal steps approach. These capabilities and advantages allow for effectively testing
our theoretical model with direct and indirect effects. Notably, SEM evaluates effects based on correla-
tions between variables and its results cannot be interpreted as causality.
Four criteria are used to assess SEM: (1) theoretical model justification; (2) absolute fit index: chi-
square; (3) relative fit index: comparative fit index (CFI); (4) noncentrality-based indices: root mean
square error of approximation (RMSEA) or standardized root mean square residual (SRMR). To formally
test the statistical significance and estimate the effects of the mediator paths, we used R SEM packages
(lavaan) to calculate the direct, indirect, and total effects of these effects for paths, with standard errors
included.
Figure 1. Baseline empirical SEM model for direct and indirect effects of sprawl/compactness on racial inequality
in IM without exposure and friending bias (A) and with exposure and friending bias (B). Rectangles contain
variables; dark gray rectangle contains economic connectedness; light gray rectangles contain exposure and
friending bias; single directional arrow represents the direct effects of one variable on another variable; red arrows
indicate the paths through economic connectedness; RBias represents racial bias, including explicit racial bias and
implicit racial bias.
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4.4 Empirical model
A baseline empirical model for the pathways between urban sprawl and racial inequality suggested by
the literature is outlined in Fig. 1, which shows direct and indirect correlations. As there was no avail-
able data on the social capital gap between Whites and Blacks, the overall absolute social capital—eco-
nomic connectedness—was used to check the mediation effects of the racial social capital gap.
Because, as one of the types of social capital, EC is among the strongest predictors of IM found to date
and other types of social capital are not strongly correlated with IM (Chetty et al. 2022a,2022b).
Moreover, EC remains strongly correlated with race-specific IM (Chetty et al. 2022a,2022b). Notably,
EC could only reflect one aspect of social capital and not fully represent racial inequality in social capi-
tal theorizing in Section 3. Thus, the direct pathway between urban sprawl and racial inequality in IM
partially reflects racial inequality in social capital. The directional arrows show the hypothesized
structure of relationships between the key variables. Endogenous variables include racial segregation,
racial bias, and EC, the three hypothesized mediating variables connecting sprawl indirectly with ra-
cial inequality in IM. Exogenous variables include the compactness index. The baseline empirical
model consists of a group of four equations. One is for racial inequality in IM, a function of all four var-
iables. The other three equations are for three mediating variables that include sprawl/compactness
in their equations.
As explicit racial bias and implicit racial bias are correlated (Fig. 2) and they have different effects
on racial inequality in the magnitude and significance of SES outcomes (Hehman, Flake, and
Calanchini 2018;Riddle and Sinclair 2019;Pearman 2022), we added them separately into empirical
SEM model as indicated in Fig. 1 under Model 1 and Model 2 to understand their different effects bet-
ter. To further understand the mediation effects of EC, we added exposure and friending bias, which
are determinants of EC (Chetty et al., 2022a,2022b), to the empirical SEM model shown in Fig. 1 under
Model 1S and Model 2S.
There are also alternative explanations for the correlation between sprawl and racial inequality in
IM that do not rely on a causal effect of sprawl on racial inequality in IM directly and indirectly
through racial segregation, racial bias, and EC. In other words, it is possible that highly compact coun-
ties have other characteristics that produce racial inequality in IM. To control these possible explana-
tions, we included control variables (confounders) that could affect both urban sprawl and racial
inequality in IM or affect both urban sprawl and respective mediating variables in the baseline empiri-
cal models. There are five dimensions of control variables: land use regulation, political fragmentation,
Figure 2. Scatter plot for explicit racial bias and implicit racial bias. Note:fitted value (red line); county (blue
hollow circle)
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public subsidies, political affiliation, and geographic fixed effects. The justifications of each control
variable in these five dimensions are shown in Supplementary Appendix A. The definitions and
sources of these control variables are shown in Supplementary Appendix Table B and Supplementary
Appendix Table A3, and their descriptive statistics are shown in Supplementary Appendix Tables
A4–A5. The empirical models with these control variables are shown in Supplementary Appendix Fig.
A3. We used control variables for the year before individuals were 23 years old (before 2006), which IM
reveals itself.
5. Results
We begin with the results of the bivariate analysis of key variables. We then turn to the results of the
SEM, looking at how urban sprawl affects racial inequality in IM.
5.1 Descriptive statistics
Figure 3 shows a scatter graph of the compactness and racial inequality in IM that illustrates a positive
relationship between compactness and racial inequality in IM, indicating a more compact county
might be more likely to have higher racial inequality in IM. This relationship needs more rigorous sta-
tistical methods to be tested and explained. Figures 4 and 5provide a glimpse of the different channels
between compactness and racial inequality in IM through scatter graphs. Compactness was negatively
associated with explicit and implicit racial bias while positively related to racial segregation. On the
other hand, racial segregation was positively related to racial inequality in IM, while there seems to be
no obvious relationship between racial bias and racial inequality in IM. The lack of obvious relation-
ships might suggest that we need a more rigorous statistical approach to control other variables. There
are weak positive correlations of EC with compactness and racial inequality in IM. Figure 5 further
shows the steeper slope between EC and IM for Whites than IM for Blacks, suggesting that EC could af-
fect racial inequality in IM.
5.2. Main results of SEM: hypotheses testing
The results of path analysis are shown in Tables 2–4, where Table 2 shows the direct effects between
key variables in the empirical models, Table 3 shows the results for mediation effects of compactness
on racial inequality in IM through racial segregation, racial bias, and EC, and Table 4 shows the total
effects of each key variable on racial inequality in IM. These tables present standardized coefficients
Figure 3. Scatter plot for compactness and racial inequality in IM. Note:fitted value (red line); county (blue
hollow circle)
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by normalizing variables to obtain the relative importance of the parameters. These tables provide the
results of baseline empirical models and empirical models with main control variables. For simplicity,
we do not provide the effects of the main control variables on racial inequality in the tables. Goodness-
of-fit measures at the bottom of Table 2 indicate a good fit. In particular, a low ratio of chi-square and
degree of freedom (<5) indicates a good absolute model fit. RMSEA and SRMR are less than 0.08, indi-
cating a good fit to the data. CFI values suggest that the model explains almost all the data variation.
We noted that the most statistically significant relationships are as hypothesized and similar to the
results of scatter plots in the empirical SEM models. Compared to baseline empirical models, the direct
and total effects of compactness on racial inequality in IM is greater while its indirect effects are
smaller in the empirical models with main control variables. We present results on hypotheses (1)–(3)
below based on empirical models with main control variables because they can theoretically generate
more accurate estimated coefficients.
The specific indirect effect of compactness on racial inequality in IM through racial segregation was
statistically significant and positive (Model 1 and Model 2 of Table 3), suggesting that racial segregation
mediates the impact of compactness on racial inequality in IM. Speaking of its constituent paths, com-
pactness index was significantly and positively associated with racial segregation, while racial
Figure 4. Scatter plots for compactness and endogenous variables: explicit racial bias (A), implicit racial bias (B),
racial segregation (C); racial inequality in IM and endogenous variables: explicit racial bias (D), implicit racial bias
(E), racial segregation (F). Note:fitted value (red line); county (blue hollow circle)
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segregation had a significantly positive relationship to racial inequality in IM (Model 1 and Model 2 of
Table 2). These results remain across Model 1S and Model 2S of Table 3 for indirect effect and Model 1S
and Model 2S of Table 2 for the constituent paths when exposure and friending bias were included in
the models. These results support hypothesis (1), stating urban sprawl reduces racial inequality in IM
via lowering racial segregation.
Next, the specific indirect effects of compactness on racial inequality in IM through explicit racial
bias and implicit racial bias were statistically significant and negative (Model 1 and Model 2 of Table 3,
respectively), indicating compactness reduces racial inequality in IM through explicit racial bias and
implicit racial bias. Speaking of its constituent paths, the compactness index was negatively associated
with both explicit and implicit racial bias, while explicit and implicit racial bias had significantly posi-
tive relationships to racial inequality in IM (Model 1 and Model 2 of Table 2, respectively). These results
hold across Model 1S and Model 2S of Table 3 for the indirect effects and Model 1S and Model 2S of
Table 2 for the constituent paths, respectively, when exposure and friending bias were included in
these models. These results support hypothesis (2), stating urban sprawl increases racial inequality in
IM through increasing racial bias. Notably, explicit racial bias had more statistically significant and
stronger indirect adverse effects between compactness and racial inequality in IM than implicit racial
bias. This may be because explicit racial bias is more likely to be associated with overt discrimination,
whereas implicit racial bias is a less deliberate or controlled process. Another possibility is that explicit
bias has historically had stronger impacts on psychological factors, affecting racial inequality in IM.
Last, the specific indirect effect of compactness on racial inequality in IM through EC is statistically
significant and positive (Model 1 and Model 2 of Table 3), indicating that compactness increases racial
inequality in IM through EC. Regarding its constituent paths, compactness had a significantly positive
association with EC, while EC was significantly positively associated with racial inequality in IM (Model
1 and Model 2 of Table 2). These results support hypothesis (3), stating urban sprawl affects racial in-
equality in IM through social capital. Further support is from the result that the direct effect of com-
pactness on racial inequality was also statistically significant and positive. This direct effect partially
reflects the mediation of social capital because EC can only reflect one aspect of social capital and not
fully represent the social capital gap between Blacks and Whites.
Figure 5. Scatter plots for economic connectedness and variables: compactness (A), racial inequality in IM (B), IM
for Whites (C), and IM for Blacks (D). Note:fitted value (red line); county (blue hollow circle)
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Table 2. Direct effects of variables in the empirical SEM models.
Baseline All controls
Coeff. Std. Err. P-value Coeff. Std. Err. P-value
Model 1: Explicit racial bias
RIneq RSeg 0.16872 0.04307 .00009 0.15529 0.04569 .00068
RIneq ERBias 0.10765 0.03301 .00111 0.11497 0.03459 .00089
RIneq EC 0.17726 0.03587 .00000 0.13724 0.04276 .00133
RIneq Comp 0.20328 0.04110 .00000 0.17844 0.04806 .00021
RSeg Comp 0.55153 0.02822 .00000 0.50321 0.03469 .00000
ERBias RSeg 0.07991 0.03911 .04105 0.04594 0.03867 .23481
ERBias Comp −0.29945 0.03911 .00000 −0.14681 0.04537 .00121
EC RSeg −0.55160 0.03599 .00000 −0.42477 0.03198 .00000
EC Comp 0.32337 0.03599 .00000 0.22428 0.03871 .00000
Model fit statistics: Chi-square/df ¼0.004; CFI ¼1; RMSEA ¼0.000; SRMR ¼0.000
Model fit statistics (Controls): Chi-square/df ¼4.887; CFI ¼0.972; RMSEA ¼0.067; SRMR ¼0.013
Model 2: Implicit racial bias
RIneq RSeg 0.16393 0.04352 .00017 0.15046 0.04607 .00109
RIneq IRBias 0.09157 0.03331 .00597 0.08839 0.03469 .01084
RIneq EC 0.18409 0.03593 .00000 0.14236 0.04286 .00090
RIneq Comp 0.20046 0.04158 .00000 0.17843 0.04823 .00022
RSeg Comp 0.55153 0.02822 .00000 0.50321 0.03469 .00000
IRBias RSeg 0.18737 0.03883 .00000 0.14713 0.03877 .00015
IRBias Comp −0.34535 0.03883 .00000 −0.17975 0.04549 .00008
EC RSeg −0.55160 0.03599 .00000 −0.42477 0.03198 .00000
EC Comp 0.32337 0.03599 .00000 0.22428 0.03871 .00000
Model fit statistics: Chi-square/df ¼3.875; CFI ¼0.996; RMSEA ¼0.057; SRMR ¼0.015
Model fit statistics (Controls): Chi-square/df ¼3.692; CFI ¼0.980; RMSEA ¼0.056; SRMR ¼0.011
Model 1S: Explicit racial bias including exposure and friending bias
RIneq RSeg 0.16872 0.04308 .00009 0.15529 0.04572 .00068
RIneq ERBias 0.10765 0.03301 .00111 0.11497 0.03459 .00089
RIneq EC 0.17726 0.03588 .00000 0.13724 0.04270 .00131
RIneq Comp 0.20328 0.04108 .00000 0.17844 0.04806 .00020
RSeg Comp 0.55153 0.02822 .00000 0.50321 0.03469 .00000
ERBias RSeg 0.07991 0.03911 .04105 0.04594 0.03867 .23481
ERBias Comp −0.29945 0.03911 .00000 −0.14681 0.04537 .00121
EC Expo 0.91866 0.00170 .00000 0.91866 0.00170 .00000
EC FBias −0.21855 0.00170 .00000 −0.21855 0.00170 .00000
Expo RSeg −0.54505 0.03589 .00000 −0.40748 0.03160 .00000
Expo Comp 0.40145 0.03589 .00000 0.28407 0.03826 .00000
FBias RSeg 0.08977 0.04043 .02640 0.13241 0.04106 .00126
FBias Comp 0.32229 0.03845 .00000 0.24615 0.04698 .00000
FBias Expo −0.26732 0.03390 .00000 −0.26873 0.04028 .00000
Model fit statistics: Chi-square/df ¼4.371; CFI ¼0.996; RMSEA ¼0.062; SRMR ¼0.022
Model fit statistics (Controls): Chi-square/df ¼2.980; CFI ¼0.992; RMSEA ¼0.048; SRMR ¼0.014
Model 2S: Implicit racial bias including exposure and friending bias
RIneq RSeg 0.16393 0.04353 .00017 0.15046 0.04610 .00110
RIneq IRBias 0.09157 0.03331 .00597 0.08839 0.03469 .01084
RIneq EC 0.18409 0.03594 .00000 0.14236 0.04280 .00088
RIneq Comp 0.20046 0.04157 .00000 0.17843 0.04822 .00022
RSeg Comp 0.55153 0.02822 .00000 0.50321 0.03469 .00000
IRBias RSeg 0.18737 0.03883 .00000 0.14713 0.03877 .00015
IRBias Comp −0.34535 0.03883 .00000 −0.17975 0.04549 .00008
EC Expo 0.91866 0.00170 .00000 0.91866 0.00170 .00000
EC FBias −0.21855 0.00170 .00000 −0.21855 0.00170 .00000
Expo RSeg −0.54505 0.03589 .00000 −0.40748 0.03160 .00000
Expo Comp 0.40145 0.03589 .00000 0.28407 0.03826 .00000
FBias RSeg 0.08977 0.04043 .02640 0.13241 0.04106 .00126
FBias Comp 0.32229 0.03845 .00000 0.24615 0.04698 .00000
FBias Expo −0.26732 0.03390 .00000 −0.26873 0.04028 .00000
Model fit statistics: Chi-square/df ¼4.278; CFI ¼0.996; RMSEA ¼0.061; SRMR ¼0.027
Model fit statistics (Controls): Chi-square/df ¼2.448; CFI ¼0.994; RMSEA ¼0.041; SRMR ¼0.013
Notes: This table presents standardized coefficients of direct effects of one variable on another variable without being
mediated by a third variable in the four empirical SEM models, respectively. The models with “All controls”additionally
include the main control variables in the SEM models, whose direct effects are not included in the table. df is the degree of
freedom. Coeff. is the abbreviation of Coefficient. Std. Err. is the abbreviation of Standard Error. Number of metropolitan
counties used in the models is 874.
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Table 3. Indirect effects of compactness on racial inequality in IM in the empirical SEM models.
Med. Relationships Baseline All controls
Coeff. Std. Err. P-value Coeff. Std. Err. P-value
Model 1: Explicit racial bias
RSeg Comp!RSeg!RIneq 0.04387 0.02159 .04211 0.05147 0.02153 .01681
ERBias Comp!ERBias!RIneq −0.03223 0.01074 .00270 −0.01688 0.00728 .02042
EC Comp!EC!RIneq 0.05732 0.01324 .00001 0.03078 0.01096 .00499
Model 2: Implicit racial bias
RSeg Comp!RSeg!RIneq 0.04387 0.02161 .04233 0.05183 0.02154 .01614
IRBias Comp!IRBias!RIneq −0.03162 0.01204 .00862 −0.01589 0.00742 .03224
EC Comp!EC!RIneq 0.05953 0.01338 .00001 0.03193 0.01108 .00396
Model 1S: Explicit racial bias including exposure and friending bias
RSeg Comp!RSeg!RIneq 0.04381 0.02158 .04237 0.05130 0.02152 .01716
ERBias Comp!ERBias!RIneq −0.03223 0.01074 .00270 −0.01688 0.00728 .02042
Expo Comp!Expo !RIneq 0.06953 0.01539 .00001 0.03811 0.01292 .00319
FBias Comp!FBias !RIneq −0.01249 0.00293 .00002 −0.00738 0.00270 .00616
Model 2S: Implicit racial bias including exposure and friending bias
RSeg Comp!RSeg!RIneq 0.04381 0.02161 .04260 0.05165 0.02154 .01649
IRBias Comp!IRBias!RIneq −0.03162 0.01204 .00862 −0.01589 0.00742 .03224
Expo Comp!Expo !RIneq 0.07221 0.01551 .00000 0.03953 0.01303 .00241
FBias Comp!FBias !RIneq −0.01297 0.00297 .00001 −0.00766 0.00273 .00499
Notes: This table presents standardized coefficients of indirect effects of compactness on racial inequality in IM via three
mediating variables (racial segregation, racial bias, and economic connectedness (exposure and friending bias)) in four
empirical SEM models, respectively. This table only shows total mediating effects via each mediating variable between
compactness and racial inequality in IM. In other words, this table does not include standardized coefficients of specific
pathways through each mediating variable between compactness and racial inequality in IM. These specific pathways
through each mediating variable can be seen in Supplementary Online Appendix Fig. A4. The models with “All controls”
additionally include the main control variables in the SEM models. Med. is abbreviation of Mediator (mediating variables).
Coeff. is the abbreviation of Coefficient. Std. Err. is the abbreviation of Standard Error. Number of metropolitan counties
used in the models is 874.
Table 4. Total effects of key variables on racial inequality in IM in the empirical SEM models.
Variables Baseline All controls
Coeff. Std. Err. P-value Coeff. Std. Err. P-value
Model 1: Explicit racial bias
RSeg 0.07954 0.03892 .04100 0.10227 0.04219 .01535
ERBias 0.10765 0.03301 .00111 0.11497 0.03459 .00089
EC 0.17726 0.03587 .00000 0.13724 0.04276 .00133
Comp 0.27224 0.03255 .00000 0.24381 0.04295 .00000
Model 2: Implicit racial bias
RSeg 0.07954 0.03897 .04122 0.10299 0.04222 .01470
IRBias 0.09157 0.03331 .00597 0.08839 0.03469 .01084
EC 0.18409 0.03593 .00000 0.14236 0.04286 .00090
Comp 0.27224 0.03258 .00000 0.24630 0.04295 .00000
Model 1S: Explicit racial bias including exposure and friending bias
RSeg 0.07944 0.03892 .04126 0.10194 0.04219 .01569
ERBias 0.10765 0.03301 .00111 0.11497 0.03459 .00089
EC 0.17726 0.03588 .00000 0.13724 0.04270 .00131
Expo 0.17320 0.03508 .00000 0.13414 0.04175 .00131
FBias −0.03874 0.00785 .00000 −0.02999 0.00933 .00131
Comp 0.27190 0.03255 .00000 0.24358 0.04295 .00000
Model 2S: Implicit racial bias including exposure and friending bias
RSeg 0.07944 0.03896 .04148 0.10264 0.04222 .01504
IRBias 0.09157 0.03331 .00597 0.08839 0.03469 .01084
EC 0.18409 0.03594 .00000 0.14236 0.04280 .00088
Expo 0.17987 0.03514 .00000 0.13915 0.04185 .00089
FBias −0.04023 0.00786 .00000 −0.03111 0.00936 .00088
Comp 0.27189 0.03258 .00000 0.24606 0.04294 .00000
Notes: This table presents standardized coefficients of the total effects of key variables on racial inequality in IM in four
empirical SEM models, respectively. The models with “All controls”additionally include the main control variables in the
SEM models, whose total effects are not included in the table. The total effects are the sum of the direct and indirect effects
between two variables. Coeff. is the abbreviation of Coefficient. Std. Err. is the abbreviation of Standard Error. Number of
metropolitan counties used in the models is 874.
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A possible explanation of the positive association between compactness and EC is that people are
more likely to be exposed to high-SES individuals and interact with each other in more compact coun-
ties, increasing EC. Notably, given the EC gap between Blacks and Whites (Lin 2000;Munn 2019), the
possibility of different degrees of the association (slope) between compactness and EC for Blacks and
Whites could lead to even smaller or larger racial inequality in EC. There are two possible explanations
for the positive relationship between EC and racial inequality in IM. First, a higher EC county might
have higher racial inequality in EC, leading to racial inequality in IM. Second, Blacks might receive
lower EC returns than Whites (Ellen and Turner 1997;Turley 2003). As a result, the racial gap in EC
could be larger in higher EC counties, resulting in larger racial inequality in IM. This is partially sup-
ported by the steeper slope between EC and IM for Whites than IM for Blacks, shown in Fig. 5. In other
words, two principles could be combined to explain why increased EC with increasing compactness
could lead to increased racial inequality in EC: existing racial inequality in EC (Lin 2000;Munn 2019)
and the preference for socializing with persons of the same race (Ellen and Turner 1997;Noguera 2003;
Turley 2003). When compactness increases EC via increasing exposure to high-SES individuals, Blacks
and Whites tend to increase it separately within networks of their own race due to the tendency for
individuals to interact with people of the same race. The degree of association between compactness
and EC for Whites is higher than for Blacks because of the existing racial inequality in EC.
We further look at the results from the models with exposure and friending bias to better under-
stand the mediation effects of EC. The specific indirect effect of compactness on racial inequality in IM
through exposure was statistically significant and positive, while the specific indirect effect of com-
pactness on racial inequality in IM through friending bias was statistically significant and negative
(Model 1S and Model 2S of Table 3). The magnitude of the mediation effect through exposure was sub-
stantially larger than the magnitude of the mediation effect through friending bias (Model 1S and
Model 2S of Table 3), suggesting exposure is much more important than friending bias in the pathway
between compactness and racial inequality in IM through EC. These results imply that, whereas com-
pactness could increase overall EC mainly via increasing exposure to high-SES individuals, it might
also exacerbate racial inequality in EC, amplifying racial inequality in IM. Further, though racial in-
equality in EC remains constant when the overall EC increases in more compact counties, racial in-
equality in EC returns could be higher in counties with larger EC, worsening racial inequality in IM.
The overall trend of scatter graphs of these variables is shown in Supplementary Appendix Fig. A5.
Although compactness was negatively related to racial inequality in IM through explicit racial bias,
the net indirect effect of compactness on racial inequality was positive because of the increase in ra-
cial segregation and EC accompanying compactness (Model 1 and Model 2 of Table 3). Regarding the
magnitude of indirect effects of compactness on racial inequality in IM, racial segregation had the larg-
est mediating effects through compactness and racial inequality in IM, followed by EC and racial bias
(Model 1 and Model 2 of Table 3). The direct effect of compactness on racial inequality was also posi-
tive (Model 1 and Model 2 of Table 2). When compared to the magnitude of the total effects of other
key variables on racial inequality in IM (Model 1, Model 2, Model 1S, and Model 2S of Table 4), compact-
ness is definitely an important factor in determining racial inequality in IM. Future research that theo-
rizes additional mediation effects reflective of this direct effect is encouraged.
5.3 Robustness check of main results
We have conducted various robustness checks of our main results. To further deal with the concern of
misalignment of EC and racial inequality in IM, which could affect causal relationships between EC
and racial inequality in IM, we used childhood EC, childhood exposure, and childhood friending bias
on the basis of childhood friendships and parental SES into the model instead for robustness check.
Because childhood friendships are made before people start working, they cannot be directly affected
by racial inequality in IM. The results of the empirical models using these variables instead are shown
in Supplementary Appendix Tables A6–A8. The results align with our main results despite the magni-
tude of coefficients not being exactly the same as the main results.
To address the potential bias of results from choosing incorrect measurements of control variables,
we further used a variety of alternative highway measures and political affiliations instead (see
Supplementary Appendix Table A3 for their definitions and sources) for robustness checks of the main
results. The results are also consistent with our main results. Moreover, it is better to add the change
of interstate highways into empirical models to further control the effects of public subsidies on the
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correlation between sprawl and racial inequality in IM, since federal-aid highway and highway reve-
nue acts were released in 1944 and 1956, the interstate highway was not designed to facilitate local
commuting, and the interstate highway was mainly built between 1950 and 1990. We, therefore, added
the change in Metropolitan Statistical Area interstate highway density between 1950 and 1990 into the
empirical models with main control variables excluding 285 counties with no such highway data. The
results (Supplementary Appendix Tables A9–A11) are in line with our main results.
5.4 Supplementary analyses: heterogeneous effects by gender
There is a very small or no racialized gap in IM for White and Black women and large racial inequality
in IM for White and Black men (See Supplementary Appendix Table A3 for definitions and
Supplementary Appendix Figs. A6–A7 for distributions), which might indicate heterogeneous effects of
sprawl on racial inequality in IM by gender. Thus, we used racial inequality in IM for White and Black
men and racial inequality in IM for White and Black women separately instead of racial inequality in
IM for White and Black people in the empirical models. The results by gender are shown in
Supplementary Appendix Tables A12–A14 for racial inequality in IM for White and Black men and
Supplementary Appendix Tables A15–A17 for racial inequality in IM for White and Black women.
We found heterogeneous effects of sprawl on racial inequality in IM by gender. In particular, we
found that the results for men were consistent with the main results, supporting all the hypotheses.
Compactness positively affected racial inequality in IM for men both directly and indirectly (Model 1
and Model 2 of Supplementary Appendix Table A12). Compactness affects racial inequality in IM for
men positively through racial segregation and EC and negatively through racial bias Model 1 and
Model 2 of Supplementary Appendix Table A13. In contrast, the indirect effects of compactness on ra-
cial inequality in IM for women through racial segregation and implicit racial bias were not statistically
significant, although the direct effect of compactness on racial inequality in IM for women was statisti-
cally significant, as were the positive and indirect effects through EC and explicit racial bias (Model 1
and Model 2 of Supplementary Appendix Tables A15–A16). These results are in line with previous stud-
ies showing that racial segregation had a major impact on the racial inequality between White and
Black men but not on the racial inequality between White and Black women (Thomas and Moye 2015).
We further found that direct, indirect, and total effects of compactness were greater for racial inequal-
ity in IM for men than for women (Model 1 and Model 2 of Supplementary Appendix Tables A12–A17).
These results suggest that the processes that produce the effects of compactness on racial inequality
in IM vary by gender.
6. Discussion and conclusion
To our knowledge, this study is the first to investigate the relationship between urban sprawl and ra-
cial inequality in IM. In particular, we set out to argue that urban sprawl could affect racial inequality
in IM and hypothesize three potential pathways between sprawl and racial inequality in IM: racial seg-
regation, racial bias, and social capital. We tested for the direct and indirect effects of sprawl and racial
inequality in IM using SEM.
This study produced the following main findings, which confirm our argument and hypotheses. We
found that urban sprawl both directly and indirectly affected racial inequality in IM. On the one hand,
compactness had a direct positive effect on racial inequality in IM that partially reflected the social
capital pathway. On the other hand, compactness had an overall positive indirect effect on racial in-
equality in IM, with a positive effect through increasing racial segregation and EC, while a negative ef-
fect through reducing explicit racial bias and implicit racial bias. Racial segregation played a major
role in mediating the effects of compactness on racial inequality in IM, followed by EC and racial bias.
Additionally, exposure to high-SES individuals had much larger effects than friending bias in the path-
way between compactness and racial inequality in IM through EC. We further found that direct, indi-
rect, and total effects of compactness were greater for racial inequality in IM for men than for women.
We believe these findings deliver new and important insights.
Our theorizing and findings have various implications. First, the highest mediating effects of racial
segregation imply that neighborhoods where low-income individuals live play a major role in deter-
mining IM and, therefore, racial inequality in IM. It appears that providing affordable housing for
Blacks, especially in good White neighborhoods in compact counties, is becoming increasingly
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important in lowering racial segregation and, hence, racial inequality in IM. This finding is consistent
with Nelson, Sanchez, and Dawkins (2004) and Nelson, Dawkins, and Sanchez (2004), who found that
urban containment that curbs outward urban expansion and is especially effective in increasing the
supply of affordable housing reduces racial segregation. American planners should be careful to avoid
exacerbating racial segregation when aiming to increase the compactness of counties. Additionally, re-
ducing the racial income gap in compact counties is also key to reducing class-based residential segre-
gation, thus racial segregation and racial inequality in IM. Second, racial bias is the only pathway in
which compactness lessens racial inequality in IM, suggesting that reducing racial bias in sprawling
areas is important to reduce racial inequality in IM. The smaller effect of racial bias on racial inequal-
ity in IM might reflect the declining significance of racial bias (Roland and Fryer 2011), or there might
be other kinds of racial bias we did not include in the model. Third, the existing mediating effects of EC
imply that racial identity and historically constructed racial inequality in social capital play essential
roles in the pathway of sprawl and racial inequality in IM through EC. In other words, race significantly
impacts people’s lives. Our findings also suggest that interracial integration to increasing exposure to
high-SES individuals, especially in compact counties, could be powerful tools for reducing racial in-
equality in EC and hence racial inequality in IM, especially given that EC is among the strongest predic-
tors of IM found to date (Chetty et al. 2022a,2022b).
Our findings demonstrate the significant role of urban form in racial inequality in IM and add an-
other possible way to address racial inequality in IM, which future studies could vet and investigate
further. Although compactness has a net positive indirect effect on racial inequality through tested
mediating variables, there are both positive and negative mediating effects. This study recommends
that the American planning community help minimize the adverse impacts of sprawl on racial in-
equality while keeping the positive ones.
Our study invites studies on international comparisons, which are evidently necessary to better under-
stand racial inequality in IM and the impacts of urban form. Racial/ethnic inequality in IM does exist and
has persisted in European countries and other countries (e.g. Pott 2001;Khan and Shaheen 2017), and cities
in European nations are typically more compact than those in the US. Thus, research is needed to examine
the effects of urban form on racial inequality in IM in these countries. If our finding holds in other coun-
tries, planners and geographers should focus more on studying racial inequality in IM, particularly the im-
pact of the built environment and sprawling development patterns, and explore solutions to the issues of
racial inequality in IM.
Our study also invites more research to theorize mechanisms between compactness and racial in-
equality more deeply, employing different modeling approaches and data. We found a significant di-
rect effect between compactness and racial inequality in IM, which we partially attribute to social
capital. Possibly, the existence of this significant direct effect implies that there may be additional
mechanisms at play that we have not theorized or examined in this study. Furthermore, given the het-
erogeneous effects by gender, further research could theorize/examine mechanisms connecting com-
pactness and racial inequality by gender to develop gender-specific interventions for minimizing racial
inequality. Notably, though we provide theoretical reasoning for our model, account for control varia-
bles, and do robustness checks to the best of our ability, we cannot confirm the causal effects in our
study without an experimental design.
Acknowledgments
We would like to thank the Editor of the Journal of Economic Geography, Simona Iammarino, and the
anonymous reviewers for their constructive and challenging comments and suggestions.
Supplementary data
Supplementary data is available at Journal of Economic Geography online.
Conflict of interest statement
None declared.
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