Segregation as a Source of Contextual Advantage: A Formal Theory with Application to American Cities

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1 Sereation as a Source of Contextual Advantae: A Formal Theory with Application to American Cities Lincoln Quillian A frequently cited model of why sereation contributes to inequality is that sereation increases the level of contextual advantae of advantaed sereated roups and the level of contextual disadvantae of disadvantaed sereated roups. This paper provides a formal demoraphic model of this process. The model beins with two roups that differ alon a dimension of averae advantae and disadvantae, for instance, two racial roups that differ in their poverty rates. The model illustrates how the contextual advantaes and disadvantaes from sereation are affected by a series of demoraphic conditions: roup relative size, roup advantae- disadvantae rates, roup effects on advantae- disadvantae rates of nonroup neihbors, and advantae- disadvantae effects on roup contact. The paper outlines a series of eleven conclusions from the theoretical model and applies the theoretical model to understandin racial sereation effects on racial roup neihborhood poverty contact in American cities. Keywords: sereation, neihborhoods, racial inequality, poverty Sereation has lon been thouht to contribute to inequality, especially racial inequality. Althouh a variety of explanations are typically offered for why sereation may contribute to inequality, the most common in contemporary discussions is that sereation is associated with affluent contexts for whites and impoverished contexts for nonwhites. The explanation is the primary one offered by two of the most prominent social scientists who emphasize the importance of racial sereation in producin racial inequality, Doulas Massey and Gary Orfield. 1 Doulas Massey, for instance, arues that, as sereation increases, the averae residential environment of whites improves and the averae residential environment of blacks deteriorates (1990, 333). This occurs because sereation separates affluent and poor racial roups into different neihborhoods, producin racial inequality in neihborhood conditions. Massey then oes on to arue that these concentrations of neihborhood poverty are a key to the existence of an urban underclass and to racial inequality more enerally. Gary Orfield has made parallel aruments as applied to schools. Indeed, the main reason we should be concerned with sereation by race, he says, is because sereation by race is systematically linked to other forms of sereation, includin sereation by socioeconomic status, by residential location, and in- Lincoln Quillian is professor of socioloy at Northwestern University and chair of the Institute for Policy Research s Proram on Urban Policy and Community Development Russell Sae Foundation. Quillian, Lincoln Sereation as a Source of Contextual Advantae: A Formal Theory with Application to American Cities. RSF: The Russell Sae Foundation Journal of the Social Sciences 3(2): DOI: /RSF Direct correspondence to: Lincoln Quillian at l- Department of Socioloy, Northwestern University, 1810 Chicao Avenue, Evanston, IL This point is not entirely oriinal to Massey and Orfield. Their work extends previous scholarship, most notably Kenneth Clark (1989).

2 sereation as a source of contextual advantae 153 creasinly by lanuae (Orfield and Lee 2005, 14). He arues that sereation by race is primarily of concern exactly because it creates hih- poverty schools for many minority students and hih- poverty school environments are not conducive to learnin. The basic arument both these scholars make is that sereation produces neihborhoods and schools that are either predominately white and low poverty or predominately nonwhite and hih poverty. In eneral, their loic suests that as sereation increases, members of advantaed sereated roups increasinly experience hih rates of advantaed persons in their contexts, and that members of disadvantaed roups experience hih rates of disadvantaed persons. To the extent that experiencin contexts with advantaed members is itself a source of advantae and that experiencin contexts with disadvantaed members is itself a source of disadvantae as a lare body of research suests 2 sereation then increases the on- averae contextual advantae of the advantaed and the contextual disadvantae of the disadvantaed. Correspondinly, several studies note the lare ap in the affluence of neihborhoods and related social contexts experienced by whites, blacks, and Latinos and arue that this is an important factor contributin to persistent racial inequality (see, for example, Pattillo 1999; Loan 2011; Sharkey 2013). Does racial sereation always increase the concentration of poverty for members of disadvantaed racial roups and affluence for advantaed racial roups? Both Massey and Orfield suest that it does, as a necessity of the mathematical demoraphy of the combination of sereation and racial disparities in poverty. Neither, however, develop a formal model of this process or make the mathematical demoraphy explicit. Yet an increase in sereation need not increase the contextual advantae of advantaed roups and the contextual disadvantae of disadvantaed roups in all situations, nor need a decrease in sereation decrease it. A prominent example of how racial desereation can fail to reduce a disadvantaed roup s level of contextual disadvantae is William Julius Wilson s (1987) black middle- class outmiration thesis. Wilson claims that declines in residential sereation in the 1960s and 1970s were a process by which affluent blacks moved out of poor black neihborhoods leavin poorer blacks behind (see Wilson 1987, 55 58). As a result, middle- class blacks ained white neihbors thus makin this a miration flow that reduced racial sereation and poor blacks lost middle- class black neihbors. Overall, Wilson s suestion is that averae black neihborhood income showed little improvement in the wake of black middle- class miration into white neihborhoods. In this article, I consider conditions under which sereation acts more as Massey and Orfield suest than as Wilson suests. In effect, this analysis produces a set of scope conditions under which Massey and Orfield s theories operate. The contribution is in developin a broader understandin of the complex factors that determine how the spatial arranement of sereation contributes to roup contextual advantae or disadvantae. The analysis clarifies spatial factors that amplify or dampen the effects of sereation on contextual advantae and contextual disadvantae via spatial arranement. Finally, it assess the extent to which these conditions hold in contemporary U.S. metropolitan areas, and thus helps clarify the role of sereation in producin unequal neihborhood poverty rates amon persons of different racial and ethnic backrounds. A Formal Model of Sereation and Context Both Massey and Orfield s descriptions suest the concentration of disadvantae in the 2. If affluent neihborhoods tend to have low crime and ood neihborhood schools, and hih- poverty neihborhoods hih crime and bad neihborhood schools as much research indicates (Coleman 1966; Peterson and Krivo 2010) then crime and poor neihborhood schools are then also concentrated in nonwhite neihborhoods by sereation. Likewise, an increasinly convincin body of knowlede finds that neihborhood poverty is associated with lon- term disadvantaes for disadvantaed children that profoundly reduce their chance of upward social mobility (Wodtke, Hardin, and Elwert 2011; Chetty et al. 2014; Chetty, Hendren, and Katz 2015).

3 154 spatial foundations of inequality neihborhoods of blacks and Hispanics is a necessary result of the mathematical demoraphy of sereation combined with racial inequality. Neither, however, actually develops an explicit model of this process. The closest effort is a simulation model Massey developed, first published as an article in the American Journal of Socioloy (1990) that later became chapter 5 in Massey and Nancy Denton s seminal American Apartheid (1993). Massey beins with a hypothetical city with black and white residents (only) and studies chanes in poverty contact as the level of sereation chanes. In his hypothetical city, the black poverty rate is 20 percent and the white rate is 10 percent. He shows that as sereation between blacks and whites is increased, holdin other conditions constant, the averae neihborhood poverty of whites decreases and of blacks increases. In a second simulation, he adds income sereation within race, showin that as sereation of whites from blacks increases in the presence of income sereation, neihborhood poverty contact for black poor residents increases even more sharply. Massey s simulations illustrate how sereation combined with racial disparities in poverty rates produce racial inequalities in neihborhood environments. But his simulation imposes several conditions that receive little direct attention in his discussion. For instance, the simulation sets the size of the two racial roups in his hypothetical city to be equal, does not allow income to affect cross- race contact, and does not allow race to affect the income level of other- race neihbors. It is unclear how the loic of sereation concentratin poverty miht be chaned if these circumstances are chaned. Wilson s black middle- class outmiration thesis implies a different relationship between sereation and contextual advantae and disadvantae. In his account in The Truly Disadvantaed, the miration of middle- class blacks out of black central- city neihborhoods in the 1960s and 1970s resulted in decreased neihborhood poverty for middle- class blacks and increased neihborhood poverty for poor blacks (Wilson 1987, 53 57). Wilson is less clear about where middle- class blacks mirated to, but he suests the suburbs, includin some into white neihborhoods. In his account, racial desereation of residence did not decrease black neihborhood poverty but instead increased it for poor blacks and reduced it for middle- class blacks. 3 A key difference between Massey s account of the effect of sereation and Wilson s of black middle- class outmiration is that in Massey s account desereation occurs across all income levels, whereas in Wilson s only middle- class blacks see an increase in white neihbors. 4 This contrast suests a broader point: income radients in a process of sereation or desereation are important to how sereation affects contextual inequality. An income radient is an income- selective pattern of cross- race contact, such as hih- income African Americans havin more white neihbors than low- income African Americans do. If the income radient to sereation is stron, Massey and Orfield s basic aruments about how sereation contributes to contextual inequality may not operate. To et more precise about the conditions under which sereation concentrates or deconcentrates poverty, I develop a formal model. This model provides a precise description of how this process occurs and details related spatial conditions that can increase or weaken the effects of sereation on concentratin advantae and disadvantae. Effectively, it can be viewed as formalizin and eneralizin Massey s theory, which suested mathematical necessity, but without developin the math. The decomposition discussed here is closely related to a decomposition model developed 3. Wilson does not use the term desereation in discussin black middle- class outmiration, but middle- class black miration into white neihborhoods is a process that must contribute to racial desereation. 4. Massey s arument is buttressed by the findins of Denton and Massey (1989) that in the 1970s middle- class blacks were not much less sereated from whites than low- income blacks. More recent evidence suests middle- class blacks are sinificantly more likely to live in nonblack neihborhoods than poorer blacks (Sharkey 2014).

4 sereation as a source of contextual advantae 155 and applied to understand poverty concentration (Quillian 2012). The model examines the outcome of poverty concentration by roup, or the extent to which poor members of a racial roup tend to have poor neihbors. By contrast, in the analysis in this manuscript, averae poverty concentration is considered for all members of a racial or ethnic roup. The model then examines how sereation affects contextual advantae or disadvantae on averae for the sereated roups. Spatial Arranement and Substantive Sereation Effects In examinin the effects of sereation on concentratin poverty, Massey s simulations focus purely on the mathematical effect of spatial rearranement of population when sereation is increased. Other conditions, such as roup size and poverty rates, are held fixed as sereation is chaned. Yet as many scholars arue includin Massey sereation has important substantive effects on populations beyond its mechanical spatial effect on neihborhood poverty. A reduction in sereation would increase the disadvantaed roup s access to better labor markets and schools, which would decrease the disadvantaed roup s poverty rate (see, for instance, Massey and Denton 1993, chapter 6; Quillian 2014). Followin Massey s simulations, the model I develop examines spatial arranement effects of sereation only, omittin substantive effects. The spatial arranement effect can be estimated precisely once the dynamics of the system are understood: they are a mathematical function of patterns of cross- roup contact, as Massey and Orfield suest. By contrast, substantive effects depend on a behavioral model with attendant uncertainties; in the literature of substantive sereation effects, estimates vary substantially. Also, spatial rearranement effects on neihborhood poverty rates are immediate, whereas much of the behavioral effect occurs in a loner time scale radually after sereation chanes. For simplicity, in what follows I refer to spatial rearranement effects simply as sereation effects. This omits potentially important but distinct substantive effects, which are not a focus of this article. A Formal Population Model The formal model considers sereation of a social roup, the roup, from the rest of the population, the nonroup. In the most common application, the roup would be a racial or ethnic roup. In the model, aside from their roup membership, individuals are either advantaed or disadvantaed. Althouh the dimension of advantae and disadvantae can be based on anythin defined for individuals and distinct from the social roups, income is the typical dimension. Advantae or disadvantae are defined for individuals, but rates of advantae and disadvantae differ across roups. Advantaed roups are roups with low rates of individual disadvantae (and hih rates of advantae); disadvantaed roups have hih rates of individual disadvantae (and low rates of advantae). In this analysis, the disadvantaed members of each roup are operationalized as poor (income below the overnment poverty line) and the advantaed individuals as nonpoor (income above the poverty line). The roup we focus on are denoted in our models, and the poverty rate of roup is Pov. Everyone not in the focal roup is in the nonroup, denoted n. The poverty rate of the nonroup is Pov n. If the focal roup is disadvantaed, Pov > Pov n. If the focal roup is advantaed, Pov < Pov n. The most obvious application is to racial roups. In the United States, blacks or Hispanics would typically be disadvantaed roups and whites an advantaed roup. Consider the averae contact that members of the roup and the nonroup have with poor and nonpoor persons in a social context. This context could be a neihborhood, a school, a social network, or some other settin. For the ith context (neihborhood) denote the number of poor persons (both roup and nonroup) in the context as p i, the total number of persons in the context as t i, and the number of roup members in the context as i. Denote the total number of persons in the roup summed across all contexts (all neihborhoods) with G. The averae context of roup poor persons with poor persons in their social context can be denoted usin the P index of contact popularized by Stanley Lieberson (1988):

5 156 spatial foundations of inequality i i p = i G ti. This measure can be interpreted as the averae percentae poor (disadvantaed) in the contexts of members of the roup. Sereation will be measured with a standardized index related to indexes of contact, the variance ratio index of sereation, as discussed further. The theory that sereation increases contextual disadvantae for disadvantaed roups or advantae for advantaed roups effectively proposes that as sereation between disadvantaed roup and others who are not in roup (n) increases, P p increases. If roup is advantaed, then P p will decrease with sereation, reflectin declinin contextual advantae with sereation for an advantaed roup. To formalize this relationship, we need to incorporate how sereation affects the averae contact with contextual poverty of the poor and nonpoor. The additive decomposability of P indexes is useful in this reard. Averae contact with poor in the social context is the sum of contact with poor of the disadvantaed roup and contact with poor of who are not members of the roup; althouh members of the nonroup have a lower poverty rate than members of the disadvantaed roup, some members of the nonroup are poor: P = P + P. p p np This formula includes two measures that are closely related to sereation: contact of roup members with their own racial or ethnic roup and with persons not of their own race or ethnic roup. Sereation, however, is enerally defined based on contact with all members of each roup, not just their poor members. We want to introduce sereation overall to this equation but still et to a formulation 5. The variance ratio index is defined as V ( )( n ) = with components that are substantively interpretable. To do so, first I manipulate the formula to include terms for own- roup and other- roup contact: P = P p P p + P n P np n. We can improve the interpretation of the ratios in parentheses by normin them by the poverty rate of each roup: P = P p P Pov p Pov + P n P Pov np n n Pov n. (1) The two components in the lare brackets capture what we miht think of as roup membership effects on contact with poor persons of their own roup (left term) and poor persons of the nonroup (riht term). These ratios will be reater than 1 if members of the roup have disproportionate contact with disadvantaed members of their own roup (left term) or disproportionate contact with nonroup persons who are disadvantaed (riht term), disproportionate bein defined relative to their roup s or the nonroup s poverty rate. If they are more likely to be in contact with nonpoor member of their own roup (left term) or the nonroup (riht term), these ratios will be less than one. We can relate these terms mathematically to sereation by usin the variance ratio index of sereation, a measure of sereation that is in the same family of measures as the exposure indexes. The variance ratio index is a wellestablished measure that fits key criteria desired in a sereation index (see James and Taeuber 1985). 5 Like the index of dissimilarity, the variance ratio index varies from 0 (no sereation between roups) to 1 (perfect sereation). Also like dissimilarity, the variance ratio is a measure of evenness of distribution of one 2 i ti π ti, i Tπ( 1 π) where i denotes the population of the racial roup in the ith tract, t i is the total number of persons in the ith tract, T is the total population of the metropolitan area for which the measure is calculated, and π is the roup proportion of the population in the metropolitan area.

6 sereation as a source of contextual advantae 157 roup aainst the other (see Massey and Denton 1988). The variance ratio index of sereation is related to the P contact index between roup members and nonmembers by the relation: P = p ( 1 V ), (2) n n ( )( n ) where p n is the proportion of the population nonroup and V ()(n) is the variance ratio index of sereation between the roup and the nonroup. Applyin this relation to equation (1) we et: P P = ( 1 p ( 1 V )) Pov p n ( )( n ) + p n ( 1 V ( )( n ) p Pov np n ) Povn. (3) Povn This last formula, (3), allows us to understand roup neihborhood poverty contact in social context as a function of sereation (V) between the two roups and a series of other conditions: roup poverty rates (Pov and Pov n ), roup relative size (p n ), and the two ratios shown in the bi parentheses. The ratios in the two lare parentheses in (3) each have an interpretable meanin. They indicate relative contact of roup members with, first, poor roup members and, second, poor persons not in the roup. Denote these terms GxGP and GxNGP: GxGP = GxNGP = Pov Pov Rewritin (3) with these terms we et the followin: p np P ( 1 p ( 1 V )) GxGP Pov p n ( )( n) + pn ( V( )( n ))( GxNGP) P n n = ( ) 1 ov n. (4). This formula is the same as (3) but GxGP and GxNGP replace the correspondin terms. Each term has an interpretable meanin. The formula in (4) is a decomposition of roup contact with poor into a series of components. These components represent: 1. Sereation of the roup from the nonroup (V ()(n) ). 2. Relative roup size, indicated here by percentae nonroup (p n ). 3. The poverty rate of the roup (Pov ). 4. The poverty rate of the nonroup (Pov n ). 5. The ratio (GxGP), indicatin roup members have disproportionately hih or low contact with poor members of their own roup. A ratio reater than one suests disproportionate contact of the roup with poor own- roup members, a ratio less than one suests disproportionate contact with nonpoor roup members. This captures a poverty status effect on own- roup contact. 6. The ratio (GxNGP), indicatin roup members have disproportionate contact with poor persons not in their roup. A ratio reater than one suests disproportional contact of the roup with poor nonroup persons. This captures a roup effect on the income level of nonroup persons in contact with roup members. Note that equation (4) includes no error term: it is a decomposition, not a statistical model. We can perfectly predict the averae neihborhood poverty rate of a roup in any city or other area for which these components are known. The equation in a sense defines the mathematically necessary accountin relationships that Massey and Orfield s discussions suest underlie the process they observe. One factor is not included in these components: a measure of within- roup sereation between the poor and nonpoor. This is because within- roup poverty status sereation shifts poverty contact between the poor and nonpoor of a roup, but does not chane averae poverty contact across an entire roup, which is the outcome of this analysis. The components each represent different spatial conditions that we can manipulate to

7 158 spatial foundations of inequality predict poverty contact of a roup under hypothetical chanes in some of these conditions. Some combinations of component spatial conditions are not possible a topic I lack space to explore in detail here but these combinations can be avoided by focusin on small chanes from observed values. What does this imply about sereation? Equation (4) shows substantial interaction multiplication between different factors in predictin the outcome. Terms that multiply toether with sereation condition its effect, or increase or decrease the importance of sereation for increasin a roup s contact with poverty. To clarify, we can multiply out (4) and roup terms interactin with sereation, which produces P = ( GxGP) Pov + p [( GxNGP) Pov ( GxGP) Pov] + pnv( )( n )[( GxGP) Pov ( GxNGP) Povn ]. (5) p n n The term on the second line of (5) shows components that multiply with sereation. This term is the key to understandin effects that alter the spatial rearranement effect of sereation on roup poverty concentration. Sereation matters for poverty concentration, but its effect in producin contextual advantae or disadvantae depends on several other factors represented in this model. This formula implies that if the other components of the formula are held constant, then the effect of sereation is linear, and the slope of sereation is as follows: SlopeofV( )( n) pn[ GxGP Pov ( GxNGP) Povn ]. (6) = ( ) One possible application of this is to calculate the components and calculate the slope of sereation in a particular situation. For instance, usin values computed for African Americans in Milwaukee from the American Community Survey: Slope of V ()(n) = 0.835[(1.042)0.363 (1.899)0.095 = This ives an implied slope of sereation on poverty contact for blacks in Milwaukee of 0.165, holdin other conditions constant, which is a lare slope relative to most other sereation effects in American cities, as discussed further. Equation (6) suests several conclusions about sereation and poverty contact across racial roups: Conclusion 1: Under reular conditions, sereation will tend to increase the averae advantae of the contexts of the advantaed sereated roup and increase the averae disadvantae of contexts of the disadvantaed sereated roup. I will delay my discussion of reular conditions, but to preview, as lon as the subtraction in the middle of (6) is positive and roup is a disadvantaed roup, sereation will build contextual advantae and disadvantae as Massey suests. Conclusion 2: All else equal, the strenth of effect of sereation in increasin averae contextual advantae or disadvantae for a roup is proportional to the difference in the level of advantae or disadvantae between the roup and persons in other roups. Sereation does not matter for roup contextual advantae if the roup and nonroup have the same level of advantae or disadvantae. In equation (6), this is evident from how the roup poverty rate and the nonroup rate subtract. Past accounts et this point partially incorrect by focusin on only the poverty rate of the disadvantaed roup alone. In particular, Massey and Mitchell Eers (1990) emphasize that there should be an interaction between sereation and nonwhite roup poverty rates in predictin roup neihborhood poverty contact. But, in fact, the interaction should be between sereation and the difference in poverty rates between the roup and everyone not in that roup, not the roup poverty rate.

8 sereation as a source of contextual advantae 159 Conclusion 3: All else equal, the strenth of the sereation effect on contextual disadvantae of a roup is increased if the roup members in contact with their own roup are more often individually disadvantaed. In the model, the ratio (GxGP) indicates how much more likely disadvantaed roup members are to be in contact with their own roup () than all roup members. A ratio larer than one indicates disadvantaed persons have more own- roup neihbors than the averae for their roup. If black middle- class miration has occurred, resultin in affluent blacks livin in mostly nonblack neihborhoods and poorer blacks livin in black neihborhoods, we would expect a ratio sinificantly above one for blacks. A sharp own- roup income radient to sereation in which roup members who are advantaed have fewer own- roup neihbors than disadvantaed roup members tends to increase the effect of the level of sereation on creatin contextual disadvantae for disadvantaed roups (relative to the same level of sereation with a less- sharp income radient to sereation) because as sereation increases in the presence of a sharp income radient to sereation, the poorer members of the roup are sorted into poor own- roup neihborhoods, concentratin their contact amon roup members and reducin contact of nonroup members with roup poverty. In Wilson s account of black middle- class outmiration, black racial sereation decreased and the income radient to black sereation increased. He suests that these two chanes rouhly offset each other, producin no major chane in averae black poverty contact. As he emphasizes, however, this increased averae poverty concentration for poor blacks while decreasin it for middle- class blacks. Conclusion 4: The strenth of the sereation effect on contextual disadvantae for a roup is decreased if the nonroup members in contact with roup members are disproportionately likely to be disadvantaed. Conclusion 4 is based on the (GxNGP) term in equation (6). To the extent that nonroup members in contact with roup members are more likely to be disadvantaed, sereation effects are weakened because as sereation declines, roup members trade disadvantaed own- roup members for disadvantaed otherroup members. This condition is indicated by ratios of (GxNGP) substantially above one. Conclusion 5: The sereation effect on the focal roup s neihborhood poverty contact will be larer if a roup is small in relative size. Sereation chanes more stronly influence contextual disadvantae (or advantae) when roup size is relatively small. Group relative size is inversely related to the percentae nonroup, shown as P n in the slope formula of equation (6). If a roup is relatively small in size, then a chane in the standardized sereation index will have more effect on contact than if a roup is lare. A roup that is only 10 percent of the local population, for instance, will enerally have many more nonroup neihbors as sereation declines and they are spread out over the metropolitan neihborhoods that are mostly composed of other- roup members. By contrast, if a roup is relatively lare then a chane in sereation will have much weaker effect on who they are in contact with. A roup that is 80 percent of the population of an area will only have a moderate increase in otherroup neihbors with substantially lower sereation. Conclusion 6 (reularity conditions for conclusion 1): For a disadvantaed roup, if (GxGP)Pov > (GxNGP)Pov n sereation will increase contextual disadvantae as suested by the Massey model. For an advantaed roup, if (GxGP)Pov < (GxNGP) Pov n sereation will increase contextual advantae as suested by the Massey model. This condition comes straiht from the slope formula for sereation of equation (6).

9 160 spatial foundations of inequality Fiure 1. Metropolitan Neihborhood Poverty Contact, , Whites Fiure 2. Metropolitan Neihborhood Poverty Contact, , Blacks Percent Percent Proportion of Neihboors Poor Proportion of Neihboors Poor Source: American Community Survey (Minnesota Population Center 2011). Application We can examine the parts of this model to assess how sereation contributes to contextual advantae or disadvantae throuh spatial rearranement in a particular situation. My application of this model is to sereation between residential neihborhoods and racial roups in American cities from 2007 to The roups in the analysis are non- Hispanic whites, blacks, and Hispanics. 6 For this analysis, I define disadvantaed as poor and advantaed as nonpoor. Poverty is defined as livin in a family with income below the official U.S. overnment poverty threshold. I calculate the basic elements of the decomposition usin data from the American Community Survey from 2007 to I use the version of the data from the National Historical Georaphic Information System (Minnesota Population Center 2011). The context I use here is the neihborhood, census tracts servin as the usual proxy. Only metropolitan areas with at least twenty thousand persons in the roup are used for calculatin statistics by roup, because sereation measures are often thouht to have little meanin when roups are very small in size. Source: American Community Survey (Minnesota Population Center 2011). Fiure 3. Metropolitan Neihborhood Poverty Contact, , Hispanics Percent Proportion of Neihboors Poor Source: American Community Survey (Minnesota Population Center 2011). As discussed, the outcome variable is averae roup member contact with poor in their census tracts, P p, where the roups are the three racial- ethnic roups. This measure is equivalent to averae neihborhood poverty rate amon persons of each racial- ethnic roup. Calculated separately for each metropolitan area with at least twenty thousand 6. Non- Hispanic whites are persons who identify themselves as white (alone, selectin no other- race cateory) on the census race question and indicate they are not of Hispanic oriin. Blacks are respondents who identify as black alone on the race question, includin black Hispanics. The cateory Hispanic includes everyone who indicates Hispanic oriin. The black and Hispanic cateories overlap somewhat. Poverty counts in the American Community Survey are not provided separately for non- Hispanic blacks.

10 sereation as a source of contextual advantae 161 Table 1. Neihborhood Poverty Contact Decomposition, Metropolitan Means Variable White Black Hispanic Outcome: share poor neihbors in tract of averae roup resident ( P p ) (0.029) (0.049) (0.081) Sereation roup/not roup (V ()(n) ) (0.119) (0.144) (0.104) Group poverty rate (Pov ) (0.027) (0.060) (0.077) Nonroup poverty rate (Pov n ) (0.056) (0.035) (0.082) Percentae not roup (p n ) (0.162) (0.098) (0.251) GxGP: own-roup disproportionality in neihbors of roup poor (p ) (0.036) (0.060) (0.080) GxNGP: poverty disproportionality in other-race neihbors of roup ( np) (0.096) (0.264) (0.188) N (metropolitan areas) Source: American Community Survey , NHGIS version (Minnesota Population Center 2011). Note: Means calculated with weihts for MSA population of indicated roup. Metropolitan areas with twenty thousand or more roup members are included. Standard deviations in parentheses. members of each roup, the metropolitan P p fiures are shown as historams in fiures 1 throuh 3. As we can see, blacks and Hispanics have sinificantly hiher rates of neihborhood poverty contact than whites, a result also noted by John Loan (2011) and others. I calculate the components of the decomposition formula (5) from tract data for each metropolitan area. Means of components at the metropolitan level by race and ethnic roup are shown in table 1. For GPxG, the ratios above one for blacks and Hispanics indicate that poor blacks and Hispanics have more black or Hispanic neihbors than nonpoor blacks or Hispanics. But these ratios are not very far above 1, indicatin that the disparity is not very lare. The white ratio below 1 indicates that, on averae, poor whites have fewer white neihbors than nonpoor whites. For GxNGP, the ratios for blacks and Hispanics deviate further from one, averain for blacks and for Hispanics. What this suests is that the other- race neihbors of blacks and Hispanics tend to have sinificantly hiher poverty rates than the other- race averae. This is hihlihted in Quillian (2012): disproportionate poverty of the nonroup neihbors of blacks and Hispanics contributes importantly to hih neihborhood poverty contact for these roups. The Role of Sereation in Racial Disparities in Neihborhood Poverty Contact The decomposition model developed earlier validates the intuition of Massey (1990) that sereation concentrates poverty, but also demonstrates that this effect depends on a set of other spatial conditions. The first question I consider is whether the correct conditions hold for sereation to increase contextual advantae for whites and contextual disadvantae for blacks and Hispanics. To address this question, I calculate the slope of the sereation effect on contextual disadvantae for whites, blacks, and Hispanics for each metropolitan area from equation (6). This leads to a distribution of slopes for each roup across metropolitan areas. For a 1 unit chane in sereation, holdin other conditions present in the decomposition constant, the slope is the indicated chane in averae neihborhood poverty for the roup. Table 2 shows means of the slopes by roup, and fiures 4 throuh 6 show historams of the

11 162 spatial foundations of inequality Table 2. Metropolitan Sereation Slopes All Variables at Oriinal Values Whites Blacks Hispanics Mean (0.014) (0.051) (0.049) GxGP = 1 for all metro areas Mean (0.013) (0.042) (0.033) GxNGP = 1 for all metro areas Mean (0.022) (0.054) (0.061) N (metropolitan areas) Source: American Community Survey , NHGIS version (Minnesota Population Center 2011). Note: Means calculated with weihts for roup metropolitan population. Only MSAs with at least twenty thousand roup members are included. Standard deviations in parentheses. slopes over metropolitan areas for each roup. For whites, almost all of the slopes are neative, indicatin that contextual disadvantae oes down as sereation oes up. Their contextual advantae increases with sereation, indicated here by a decline in their averae neihborhood poverty rate as sereation increases. Of 379 metropolitan areas (with at least twenty thousand non- Hispanic white residents), all but one have neative slopes; the exception is Honolulu. For blacks and Hispanics almost all slopes of sereation on neihborhood poverty contact are positive. For blacks, the slope is neative rounded to two decimal places for only three of 175 metropolitan areas; for Hispanics, the slope is positive for all metropolitan areas. 7 A marinal chane in sereation, keepin other spatial conditions constant, increases neihborhood poverty rates for blacks and Hispanics in almost every American metropolitan area. This leads to a further conclusion. Fiure 4. Slope of Sereation on Neihborhood Poverty, , Whites Percent Sereation Slope Source: American Community Survey , NHGIS version (Minnesota Population Center 2011). Conclusion 7: In almost all American metropolitan areas, an increase in sereation, holdin other conditions in the decomposition constant, would decrease white neihborhood poverty contact and increases black and Latino poverty contact. The conditions for sereation to build contextual advantae via spatial rearranement amon advantaed racial roups and contextual disadvantae for disadvantaed roups hold for residential sereation in almost all American metropolitan areas. A fixed chane in sereation in eneral has a bier effect on increasin neihborhood poverty for black and Hispanics than decreas- 7. The metropolitan areas with neative black slopes are Sprinfield, Massachusetts; El Paso, Texas; East Stroudsbour, Pennsylvania; and New York City. These slopes are relatively very small, and the slope for New York is nearly zero ( 0.005).

12 sereation as a source of contextual advantae 163 Fiure 5. Slope of Sereation on Neihborhood Poverty, , Blacks 60 Fiure 6. Slope of Sereation on Neihborhood Poverty, , Hispanics 60 Percent Percent Sereation Slope Source: American Community Survey , NHGIS version (Minnesota Population Center 2011) Sereation Slope Source: American Community Survey , NHGIS version (Minnesota Population Center 2011). in neihborhood poverty for whites. As shown in fiures 4 throuh 6, the neative slopes for whites are enerally smaller in manitude than the positive slopes for blacks and Hispanics. On averae, the effect are two to two and a half times larer at increasin black and Hispanic neihborhood poverty rates than at decreasin white neihborhood poverty rates. This is mostly a result of differences in roup size (see conclusion 5). Because whites are a larer share of the population of their metropolitan areas, desereation increases averae neihborhood poverty contact only a little because other roups are too small to boost the white neihborhood poverty rate very much. By contrast, blacks and Hispanics are usually smaller shares of their metropolitan areas, with the result that decreases in sereation produce a larer percentae of nonroup members in their neihborhoods. This is another conclusion. Conclusion 8: An increase in sereation, holdin other conditions constant, would cause black and Hispanic neihborhood poverty rates to increase more than white rates drop, which larely reflects effects of roup size. A final area of investiation of the slopes relates to conclusions 3 and 4. Conclusion 3 is that sereation effects will tend to be stroner if poor roup members have disproportionately more own- roup neihbors. Conclusion 4 is that sereation effects will tend to be weaker if a roup has disproportionately poor nonroup neihbors. Table 2 addresses the question of how important in practice these conditions are for sereation effects. In the roup decomposition model, I force the situation of no income radient to own- race neihborhood residence: poor and nonpoor are then treated as equally likely to have own- race neihbors. As expected, this results in weaker sereation effects the means of the slopes are closer to zero. Althouh the effects do et smaller, the chanes are not especially lare. This is not too surprisin iven that on averae the GxGP term is close to one. The nonroup decomposition model forces the condition that other- race neihbors have poverty rates equal to the other- race averae. It shows that this condition makes a sinificant difference. The slopes increase in manitude by 25 percent (Hispanics) to about 45 percent (blacks) relative to the base slopes. This yields a further conclusion. Conclusion 9: Neihborhood sereation effects in U.S. metropolitan areas are partially suppressed because the other- race neihbors of disadvantaed roup members tend to be disproportionately poor.

13 164 spatial foundations of inequality Table 3. Chanes in Neihborhood Poverty Contact with Sereation Decrease Metropolitan Averaes Whites Blacks Hispanics Estimated effect 25 percent reduction in sereation (0.001) (0.006) (0.003) Effect as percentae chane from base P p 2.5% 3.4% 2.2% (1.5) (2.2) (1.2) Effect as percentae chane toward racial equality in 9.0% 9.8% 9.6% neihborhood poverty contact (6.0) (5.3) (9.6) N (metropolitan areas) Source: American Community Survey , NHGIS version (Minnesota Population Center 2011). Note: Means calculated with weihts for roup metropolitan population. Only MSAs with at least twenty thousand roup members are included. Standard deviations in parentheses. As sereation declines, blacks or Hispanics often trade own- race neihbors for poor otherrace neihbors, weakenin the reduction in contextual disadvantae with declines in sereation from other roups. Spatial Arranement Effects of Sereation on Contextual Advantae How much of contextual advantae for whites, and disadvantae for blacks and Latinos, can be attributed to the spatial arranement effect of sereation? I address this question initially by simulatin a 25 percent reduction in racial sereation while holdin other conditions constant based on the decomposition model. This is assumin sereation declines, but spatial patterns of how income influences crossrace contact, roup relative size, and roup poverty rates are unchaned by this miration. In holdin poverty rates constant, these estimates omit substantive effects. Empirical studies suest a decline in sereation would also tend to reduce the poverty rate of the disadvantaed roup, althouh this effect may tend to la a chane in sereation. In the spirit of the Massey (1990) simulation, I focus only on estimatin the effect from spatial rearranement with declinin sereation. The effect of a 25 percent reduction in residential sereation is estimated for all metropolitan areas by usin the slope formula to estimate the chane in neihborhood poverty for each roup with a 25 percent sereation reduction, holdin all other components of the decomposition constant. Metropolitan mean effects from this procedure are shown in table 3. Table 3 also shows effects scaled two other ways: as the percentae chane in averae neihborhood poverty contact relative to the metropolitan base level, and as a percentae chane in averae neihborhood poverty contact relative to the rate that would prevail if there was no racial inequality in poverty contact. Racial equality in neihborhood poverty contact is the situation in which each racial roup on averae lives in a neihborhood with the averae metropolitan poverty rate. The results show effects in the expected direction. For blacks the averae slope is 0.008, which corresponds to an averae chane in poverty contact from base of 3.4 percent. This is a reduction in racial neihborhood inequality of 9.8 percent. 8 For Hispanics the chane is 0.004, or an averae chane from base of 2.2 percent, which is a 9.6 percent reduction in racial neihborhood inequality in poverty contact. A 25 percent decrease in sereation then moves the black and Hispanic rate about 10 percent of the way toward the level that would hold if there were racial equality in poverty contact. As conclusion 9 states, a 25 percent reduction does not produce more chane, in part be- 8. The reduction in racial neihborhood inequality percentae is the chane in poverty contact divided by the difference between roup poverty contact and roup poverty contact if all roups experienced equal neihborhood poverty (in which case all roups would experience the averae metropolitan poverty rate).

14 sereation as a source of contextual advantae 165 Table 4. Estimates of Chane in Poverty Contact with 25 Percent Decrease in Sereation Metropolitan Area Chane % Chane from Base % Reduction in Group Inequality Whites 1 Pine Bluff, AR Albany, GA Monroe, LA Memphis, TN-MS-AR Montomery, AL Jackson, MS Yakima, WA Brownsville-Harlinen, TX Yuma, AZ Macon, GA Blacks 1 Niles-Benton Harbor, MI Milwaukee-Waukesha, WI Monroe, LA Peoria, IL St. Louis, MO-IL Sainaw, MI Detroit-Warren-Dearborn, MI Cleveland-Elyria, OH Chicao-Naperville-Elin, IL Cincinnati, OH-KY-IN Hispanics 1 Readin, PA Sprinfield, MA Allentown-Bethlehem-Easton, PA Hartford, CT Lancaster, PA Philadelphia-Camden, PA-NJ Worcester, MA-CT Kennewick-Richland, WA Providence-Warwick, RI-MA New Haven-Milford, CT Source: American Community Survey , NHGIS version (Minnesota Population Center 2011). Note: For metropolitan areas with at least twenty thousand persons in the indicated roup. Chanes are holdin other decomposition elements constant. Reduction in roup inequality is equal to chane/ (base-(total metropolitan poverty rate)). cause of the disproportionate poverty of the other- race neihbors of blacks and Hispanics. These are metropolitan averaes and hide considerable heteroeneity in the effects. Table 4 shows the effects of sereation on poverty concentration from this procedure for cities in which these effects tend to be larest. Some metropolitan areas have conditions that produce larer sereation effects. In these metropolitan areas, effects are sinificantly larer, chanin averae poverty contact by 3 percent to 8 percent from base, which produces reductions of racial inequality in neihtborhood poverty rates of 7 percent to 15 percent.

15 166 spatial foundations of inequality Conclusion 10: A 25 percent decrease in racial sereation, holdin other factors constant, produces reductions in racial inequality in neihborhood poverty of 9 to 10 percent from base due to chane in spatial arranement. The effects are not larer because of the effects of other spatial conditions like the sereation of blacks and Hispanics from more affluent other- race neihbors. The cities for which sereation effects are larest, shown in table 4, are also worth attention. The larest white contextual advantae effects from sereation are typically found in cities in the South and Texas border cities. These areas tend to have hih nonwhite poverty rates and lare shares of their population nonwhite. Sereation under these conditions especially shields whites from neihborhood poverty. Black neihborhood poverty rates are most elevated by sereation in former industrial cities, disproportionately in the Midwest, such as Milwaukee, Detroit, Cleveland, Chicao, and Cincinnati. Two primary reasons explain this phenomenon. First, these cities tend to have the hihest black- nonblack sereation scores ivin them lare chanes correspondin to a 25 percent decrease. Second, these cities tend to have hih black poverty rates and low to moderate nonblack poverty rates. Hispanic neihborhood poverty rates tend to be most sensitive to chane in sereation in several northeastern cities. These tend to be areas with relatively small Hispanic populations and hih poverty rates for their Hispanic residents. Conclusion 11: The neihborhood poverty reduction to whites from sereation, holdin other conditions constant, tend to be larest in midwestern, southern, and Texas border cities. The neihborhood poverty increase for blacks from an increase in sereation tends to be larest in midwestern cities. The neihborhood poverty increase for Hispanics from an increase in sereation tends to be larest in northeastern cities. Effects from Eliminatin Racial Sereation Finally, I consider a last counterfactual to assess sereation effects: estimated levels of poverty contact if racial sereation was in fact zero (no racial sereation at all). In this circumstance, every tract has the same percentae of each roup. This is an extremely stron counterfactual. With zero racial sereation, many of the other parameters in the model are also necessarily zero (or one in cases where that indicates no effect). For instance, the averae poverty rate of other- race neihbors for any racial roup must be the same as the nonroup averae in this circumstance, implicitly forcin GxGP to be one. I calculate the effect on roup poverty rates from a chane to zero sereation by takin the metropolitan poverty rate overall (across all roups), and then the difference between each roup s actual metropolitan neihborhood poverty rate and this rate. In complete racial interation, each roups poverty contact is equal to the overall metropolitan poverty rate. The correspondin averaes are shown in table 5. These effects are much larer than those in table 3. We miht expect them to be four times as lare as the estimates in table 3 because table 3 was based on a 25 percent reduction but because this zeros out related conditions (there can be no tendency of blacks to have poorer nonblack neihbors than whites on averae when interation is perfect) these effects are sinificantly larer. White contact with neihborhood poverty increases by 28 percent in this scenario, black poverty contact decreases by 34 percent, and Hispanic contact decreases by 21 percent. Conclusion 12: Without racial sereation there would be no metropolitan differences in neihborhood poverty exposure across racial roups, which correspond to increases (whites) or decreases (blacks, Latinos) of 20 to 34 percent in averae neihborhood poverty contact, holdin roup poverty rates constant.