Segregation and Poverty Concentration: The Role of Three Segregations

Transcription

1 447793ASR / QuillianAmerican Sociological Review 2012 Segregation and Poverty Concentration: The Role of Three Segregations American Sociological Review 77(3) American Sociological Association 2012 DOI: / Lincoln Quillian a Abstract A key argument of Massey and Denton s (1993) American Apartheid is that racial residential segregation and non-white group poverty rates combine interactively to produce spatially concentrated poverty. Despite a compelling theoretical rationale, empirical tests of this proposition have been negative or mixed. This article develops a formal decomposition model that expands Massey s model of how segregation, group poverty rates, and other spatial conditions combine to form concentrated poverty. The revised decomposition model allows for income effects on cross-race neighborhood residence and interactive combinations of multiple spatial conditions in the formation of concentrated poverty. Applying the model to data reveals that racial segregation and income segregation within race contribute importantly to poverty concentration, as Massey argued. Almost equally important for poverty concentration, however, is the disproportionate poverty of blacks and Hispanics other-race neighbors. It is thus more accurate to describe concentrated poverty in minority communities as resulting from three segregations: racial segregation, poverty-status segregation within race, and segregation from high- and middle-income members of other racial groups. The missing interaction Massey expected in empirical tests can be found with proper accounting for the factors in the expanded model. Keywords neighborhoods, poverty concentration, racial inequality, segregation Because of racial segregation, a significant share of black America is condemned to experience a social environment where poverty and joblessness are the norm, where a majority of children are born out of wedlock, where most families are on welfare, where educational failure prevails, and where social and physical deterioration abound. Through prolonged exposure to such an environment, black chances for social and economic success are drastically reduced. Massey and Denton, American Apartheid, p. 2 In the United States, a notable difference in the typical lives of whites, blacks, and Hispanics is the economic class of the people in their social environments. White middle-class families overwhelmingly live in middle-class neighborhoods and send their children to a Northwestern University Corresponding Author: Lincoln Quillian, Department of Sociology, 1810 Chicago Avenue, Evanston, IL l-quillian@northwestern.edu

2 Quillian 355 middle-class schools. Many black and Hispanic middle-class parents, however, live in working-class or poor neighborhoods and send their children to high-poverty schools. About one in three poor white families live in poor neighborhoods and send their children to high-poverty schools, compared to two in three poor black and Hispanic families. 1 Much evidence indicates that the socioeconomic levels of residential neighborhoods and schools affect quality of life and life chances. Concentrated disadvantage in neighborhoods is one of the most durable predictors of high rates of violent crime, and much of the racial gap in exposure to violence is explained by differences in neighborhood disadvantage (Peterson and Krivo 2005). Sampson and Wilson (1995) argue that high-poverty environments are criminogenic, encouraging youth to pursue criminal rather than legitimate careers. Spatial separation of the affluent and the poor produces spatial mismatch between the demand for jobs and job seekers, contributing to high unemployment in poorer neighborhoods (Kain 1968; Kasarda 1995; Mouw 2000). Likewise, high-poverty schools tend to be ineffective and have disproportionately high dropout rates (Orfield and Lee 2005; Rhumburger and Palardy 2005). Racial gaps in the affluence of neighborhood and school environments contribute importantly to persistent racial inequalities. In their seminal book, American Apartheid, Douglas Massey and Nancy Denton argue that the concentration of poverty in black and Latino neighborhoods is the most pernicious consequence of contemporary racial residential segregation. 2 In their account, concentration of poverty in minority communities is due to high levels of racial segregation and racial gaps in poverty rates, combined with some segregation of the poor from the nonpoor within race. They develop this argument through a series of simulation models and confirm it through an empirical analysis of segregation, group poverty rates, and poverty concentration in U.S. cities. Their theory is primae facie compelling, but there has been controversy regarding its empirical support. At the center of this debate is Massey s (1990) core point that segregation and minority poverty rates interact, or intensify in combination, to produce concentrated poverty. Jargowsky (1997), however, found no evidence of an interactive effect in his analysis of data on U.S. cities. Massey and Fischer s (2000) response and reanalysis found some support for an interaction but also many negative results, despite efforts to account for potential methodological problems. How can we account for this discrepancy between Massey s compelling theoretical model and the failure of its key prediction to hold in data? This article develops a new model of how racial segregation combines with other spatial and demographic conditions to produce concentrated poverty among minority groups. Massey s theory emphasizes two forms of segregation racial segregation and segregation of the poor within race as key causes of poverty concentration. The decomposition model developed here reveals that to better account for concentrated poverty, we must include a third form of segregation: the segregation of high- and middle-income members of other racial groups from blacks and Hispanics. Blacks and Hispanics other-race neighbors are disproportionately impoverished, a factor that contributes to these groups high contact with neighborhood poverty. The revised model validates Massey s core arguments regarding the importance of segregation, expands his model to include other important substantive conditions that concentrate poverty, and explains the anomaly of the missing interaction as a result of these omitted conditions. Background Two perspectives on the causes of concentrated poverty in U.S. cities have dominated sociology. First are Wilson s theories about the confluence of central city deindustrialization and class-specific migration patterns among African Americans (Wilson 1987, 1996). Second are Massey and Denton s theories emphasizing the importance of racial

3 356 American Sociological Review 77(3) residential segregation (Massey and Denton 1993). While these theories are not exhaustive of factors influencing concentrated poverty, Wilson s and Massey s perspectives provide the major sociological accounts of poverty concentration and its growth in U.S. cities since the 1970s. Wilson s theory of the causes of concentrated poverty is part of his broader discussion of the creation of the urban underclass, which includes poverty concentration as a key component (Wilson 1987, 1996). Wilson argues that a series of historical changes produced poverty concentration in minority communities in urban areas in the 1970s and 1980s. The primary condition he emphasizes is the deindustrialization of urban cores and changes in the skill requirements of urban jobs, which produced spatial and skill mismatches of blue-collar inner-city workers with new urban economies based on services. The result was a surge in unemployment and poverty rates in working-class minority neighborhoods. Wilson also suggests that with declines in legalized segregation, middle-class blacks increasingly moved away from black neighborhoods and into white neighborhoods, leaving behind poorer blacks. These two historical changes provide the main pillars of Wilson s theory of the rise in concentrated poverty. His wide-ranging discussion also encompasses several other processes, including the declining prevalence of two-parent families and dysfunctional cultural responses resulting from concentrated unemployment. In Wilson s account, these processes in the 1970s and 1980s led to neighborhoods with low rates of employment, high rates of poverty, and correspondingly high levels of social problems. Massey and Denton s (1993) theory of poverty concentration responds to and builds from Wilson s theory. Although Wilson s and Massey s disagreements have attracted much attention, they agree on many points. Massey accepts Wilson s central contention that deindustrialization and growing joblessness have been key factors driving the increasing concentration of poverty in minority communities and Wilson s arguments about the deleterious consequences of concentrated poverty. Massey disagrees with Wilson on two major points, one general and one specific. The general disagreement is that Wilson overlooks the importance of continuing racial segregation, which concentrates the effect of changing economic conditions on black and Hispanic neighborhoods. Without racial segregation as a persistent and actively maintained condition, Massey argues deindustrialization would not have had such devastating effects on minority neighborhoods, and few neighborhoods would experience extremes of poverty concentration. Massey s specific disagreement with Wilson is that he suggests black middle-class outmigration did not occur, or at least not to any significant extent (see Massey, Gross, and Shibuya 1994). Correspondingly, Massey finds that racial residential segregation persists at high levels for African Americans regardless of income (Massey and Denton 1993; Massey and Fischer 1999). Massey s theory of racial segregation and poor neighborhood formation is based on population dynamics of segregation in the context of racial inequality in poverty rates. The core idea is simple: racial segregation separates high-poverty racial groups from low-poverty racial groups. The result of this separation is that poverty is concentrated in communities of high-poverty racial groups while low-poverty racial groups are shielded from poverty contact. By adding some degree of poverty-status segregation within race, poverty is further concentrated, producing high neighborhood poverty contact for the poor of high-poverty racial groups. Massey illustrates this theory through a series of simple simulations of hypothetical cities with identical demographic profiles except for the level of segregation (first published in Massey [1990] and later reproduced with small modifications in chapter 5 of American Apartheid). Neighborhoods are represented as 16 boxes within a larger square that represents a city. The city has only black and white residents. The black population of each city has a 20 percent poverty rate and the

4 Quillian 357 white population a 10 percent poverty rate. Massey shows that as segregation increases across four hypothetical cities, the level of neighborhood poverty contact for blacks increases sharply, while it decreases for whites. Adding poverty-status segregation within race to the simulation further increases average poverty contact for the black poor, resulting in highly concentrated poverty in some black neighborhoods. These simulations illustrate that segregation matters more for poverty concentration as the segregated non-white group s poverty rate increases, and changes in non-white poverty rates translate more strongly into neighborhood poverty in more segregated metropolitan areas. In statistical terms, this represents an interaction: segregation and group poverty intensify each other s effects in producing spatially concentrated poverty in minority communities. Massey argues it is the interactive combination of segregation and racial group poverty disparities that explains why most of the processes that Wilson emphasized would have much less impact on concentrating poverty were it not for racial segregation. The disproportionate impact of deindustrialization on working-class minority workers became a disproportionate impact on working-class minority neighborhoods because of segregation. This produced the double-disadvantage of personal and contextual poverty for many poor blacks and Hispanics. Massey also notes that a recession that increases minority poverty rates in a segregated city can begin a downward economic spiral in which demand for local businesses declines, which harms neighborhood residents, which then potentially harms local businesses further. The net result of these processes is that black and Hispanic chances for social and economic success are drastically reduced (Massey and Denton 1993:2). Massey and Wilson s disagreement about black middle-class out-migration is linked to their debates about the role of segregation in neighborhood poverty concentration. In his theory of black middle-class out-migration, Wilson describes how desegregation can increase poverty concentration if movement into white neighborhoods occurs primarily among middle-class blacks, leaving poorer blacks segregated by race and class. By contrast, Massey describes desegregation as occurring equally over income levels, thus reducing poverty concentration by mixing lower-poverty racial groups (whites and Asians) with higher-poverty racial groups (blacks and Hispanics). As this contrast reveals, segregation s effect on poverty concentration depends on possible patterns of class-selectivity in processes of segregation or desegregation. Wilson and Massey come to opposite conclusions about the poverty-concentrating effects of desegregation because they make different assumptions about classselectivity in desegregation processes. Empirical Studies Interaction of Racial Segregation and Group Poverty Rates To provide empirical support for Massey s model of the importance of racial segregation in concentrating poverty, Massey and colleagues focused on the idea that an interactive combination of segregation and poverty rates produces concentrated poverty in minority communities. Using data from decennial censuses with large metropolitan areas as units of analysis, Massey and Eggers (1990) found a significant interaction of race group poverty rates and racial segregation in regression models predicting levels of metropolitan neighborhood poverty concentration. They conclude that their model is supported and that segregation is the key factor accounting for variation in the concentration of poverty (p. 1183). A few years later, Massey and Denton (1993) presented many of these arguments as central conclusions of American Apartheid. This conclusion, however, would soon be challenged. Published shortly after Wilson s and Massey s initial statements, Jargowsky s (1997) Poverty and Place was an influential

5 358 American Sociological Review 77(3) empirical analysis of many of Wilson s and Massey s ideas. Jargowsky found some evidence for and against Massey s and Wilson s specific hypotheses, but overall, he provides more support for Wilson s perspective. In particular, he found that metropolitan opportunity structure the average level of income or poverty is by far the best predictor of metropolitan neighborhood poverty concentration. His results contradict Massey s key point about an interaction between racial segregation and measures of the opportunity structure (including measures of group poverty rates). That is, he finds no tendency for concentrated poverty rates to be especially elevated in metropolitan areas in which racial segregation and high group poverty rates are combined, contradicting Massey s key prediction that these conditions combine interactively to concentrate poverty. Jargowsky s (1997) analysis parallels Massey and Eggers s (1990) earlier test of their model in most respects. Like Massey and Eggers, Jargowsky models metropolitan poverty concentration as a function of various metropolitan factors, including race group poverty rates and racial segregation, allowing for their interaction. Unlike Massey and Eggers, however, he includes the main effects of segregation and group poverty rates together with their interaction in the same model; Massey and Eggers present only the interaction without the main effects, contrary to standard statistical practice. Massey and Eggers (1990:1183) justify this choice as a result of multicollinearity among the regressors that is, because the segregation measure and minority poverty rate are highly correlated with the interaction term that is the product of these two variables, which makes it impossible to precisely estimate their separate effects with the interaction term. Jargowsky argues that this is needed to avoid the possibility that the interaction is just capturing a main effect. With main effects of level of segregation included, none of the interactions are statistically significant tested separately or jointly. 3 He concludes that Massey and Eggers results are in error: the [interaction] effect either does not exist or is too subtle to be demonstrated with the available data (p. 183; see also Korenman, Sjaastad, and Jargowsky 1995). The final salvo in this debate is from Massey and Fischer (2000), who present a revised analysis of interactions between segregation and group poverty rates in response to Jargowsky. Recognizing that low variation in the extent of segregation across metropolitan areas can contribute to multicollinearity problems, they increase variation by treating whites, blacks, Latinos, and Asians of each metropolitan area as separate cases, using segregation measures computed between each group and whites. Each group-by-metropolitan case is assigned to one of four segregation categories based on its level of segregation from whites: zero, low, moderate, and high. 4 Massey and Fischer estimate models separately for the four categories, then compare coefficients across models and look for interaction as indicated by sharper slopes in highersegregation metropolitan-group combinations. This ingenious procedure substantially increases the variation in segregation, reducing the severity of multicollinearity problems. In a shift from the specification of Massey and Eggers (1990), Massey and Fischer (2000) use several measures of racial group income levels (mean income, inequality, and a class sorting index) rather than measures of group poverty rates. They hypothesize interactions among each of these measures of group income and segregation. 5 Because there are four categories of segregation and several measures of group income, many potential sets of coefficients can be examined for consistency with their expectation of interactions between the group income measures and segregation. In their text, Massey and Fischer highlight coefficients that show stronger effects of measures of group income level on rate of concentrated neighborhood poverty as segregation increases, concluding there is support for Massey s underlying model of interaction of group income and segregation in forming concentrated poverty. Yet a careful reading of their tables also shows that many of the coefficients fail to

6 Quillian 359 correspond to Massey s prediction of interaction. Their expectation of interaction between segregation and the income measures suggests the group income variables largest coefficients should be found in the model estimated over highly segregated metropolitan areas, with coefficients becoming progressively smaller as segregation decreases. Of the 15 sets of coefficients they present, only one has the largest coefficient in the high segregation category and coefficients declining to the smallest in the zero segregation category, as predicted by the idea of interactive effects among these variables. 6 Only about half of the paired contrasts (e.g., high versus medium segregation) work out in the correct direction. This is about the number we would expect by chance if there were no interaction. 7 Despite their efforts to support their key hypothesis and their use of a clever procedure to increase variation in segregation, a close reading of Massey and Fischer s tables actually provides much evidence that contradicts their claim of interaction of segregation and group income level in forming spatially concentrated poverty. Indeed, Massey and Fischer seem to recognize (but do not emphasize) the mixed nature of their results, suggesting that historical changes may explain the lack of interaction in the later years of their analysis. Middle-Class Black Out-Migration Wilson s theory of middle-class black outmigration claims that more affluent blacks have moved into white neighborhoods, leaving behind poorer blacks and contributing to an increase in concentrated poverty. In response, Massey s analyses of census and longitudinal data lead him to conclude that black middle-class out-migration never happened on any significant scale (Massey et al. 1994). Several later studies have investigated Wilson s black middle-class out-migration thesis with varied conclusions. Quillian (1999) found evidence suggesting out-migration produced increasing spatial separation between poor and nonpoor blacks without lasting racial desegregation because of white flight, while Crowder and South (2005) found no increases in rates of migration into white neighborhoods in the 1970s (see also Pattillo-McCoy 2000). Several differences in the questions addressed and methods used by these studies may explain these differences. As relevant for understanding racial segregation effects, however, studies agree that affluent blacks remain only a bit less segregated from whites than are less affluent blacks (Massey and Denton 1993; Massey and Fischer 1999; but see also Alba, Logan, and Stults 2000). This is consistent with Massey s assumption that segregation and desegregation are processes that occur equally across all income groups. Revising the Massey Model Limits of Massey s Analysis In light of Massey and Denton s convincing theoretical arguments and Massey s simulations, results contradicting the presence of an interaction of segregation and group poverty rates are puzzling. Indeed, even Jargowsky (1997:183) acknowledges that the interaction is logical conceptually and theoretically. The real question is: the theoretical rationale is compelling, so why does this interaction effect not appear in data as theory predicts? Multicollinearity was the initial suggestion, but this possibility seems unlikely in light of the various procedures Jargowsky (1997) and Massey and Fischer (2000) use to deal with this problem, with little change in their results. On initial consideration, it is difficult to imagine how Massey s model of segregation and poverty concentration could be wrong. A major appeal of Massey s conceptual model is that it spells out an invariate population process: segregation between groups with unequal poverty rates must concentrate poverty for the higher-poverty group regardless of the other characteristics of individuals or neighborhoods. Yet, a close inspection of Massey s simulation model shows it builds in some subtle substantive assumptions regarding spatial patterning of race and poverty status. His

7 360 American Sociological Review 77(3) neighborhood-box simulation allows for race segregation and income segregation within race, but not for the possibility that processes of segregation might be income-selective. For instance, Massey excludes the possibility that black residents of white neighborhoods might be especially likely to be nonpoor. Massey s model also excludes the possibility that whites income affects their potential contact with blacks. But if either of these assumptions are incorrect, income-selective patterns of segregation-desegregation could make desegregation operate more like Wilson hypothesized, that is, it increases rather than decreases poverty concentration. Massey and colleagues also assume that other spatial conditions, like group size and the level of within-race poverty-status segregation, have additive and linear effects on poverty concentration. This assumption is most evident in the regressions Massey and colleagues use to test the theory (Massey and Eggers 1990; Massey and Fischer 2000). In these regressions, spatial conditions, like percentage of the metropolitan area that is black and poverty-status segregation, are used as regression controls and represented as additive predictors. Yet relative group size should interact with segregation in affecting contact, suggesting interactive rather than additive combinations among conditions. A model that allows for multiple interactions will be more complicated but will more accurately capture the dynamic way these forces combine. A Formal Model of Segregation and Poverty Concentration Massey s arguments implied a mathematically necessary relationship between segregation, group poverty rates, and poverty concentration. But rather than demonstrate this through a formal demographic model, he illustrated how it worked in a hypothetical city represented as a simulation. A formal model has the advantage of allowing us to derive exactly how these population quantities must relate to each other, discerning relations that may be hidden or vaguely understood from a simulation like Massey employed. To develop a formal model requires measures of the main outcome and inputs in the Massey model. The main outcome is poverty concentration for the focal racial group: blacks or Hispanics in this analysis. The main inputs are the focal race group s racial segregation from others, poverty rates for the focal racial group and others, and poverty-status segregation within groups. Another input is relative sizes of racial groups in a city, although in Massey s simulations, the proportion of blacks and whites are held equal and thus not explicitly discussed. To match real data, however, we must allow relative group size to vary. As discussed earlier, Massey implicitly assumes that income levels do not affect patterns of crossrace contact. To the extent this assumption does not hold, we must build this into the model to represent the real situation of U.S. cities. The following describes the parameters of the model in more detail and how I derived the formal model. This section necessarily relies on equations. Readers who wish to skip the formal details of the model can go to the beginning of the next section, which discusses the interpretation and implications of the formal model. Measuring inputs and outputs of the Massey model. I measure poverty concentration using the P* index, computed with group-poor contact with poor persons (of any race). Group-poor are poor members of the focal race group. This index varies from 0 to 1 and can be interpreted as the proportion poor in the average census tract of a poor member of a group for the metropolitan area for which it is computed. Following Lieberson and Carter (1982), I write the group for whom contact is computed in subscripts to the left of P*, the group with whom they are in contact in subscripts to the right; and contact of a poor member of the focal group (group poor) with poor of any race is denoted P* p. This is the same index of poverty concentration used by Massey and colleagues in their empirical work (Massey and Eggers 1990; Massey and Fischer 2000). In the model, segregation is indicated by the variance ratio index of segregation. Past analyses of segregation, including Massey

8 Quillian 361 (1990), most often use the index of dissimilarity to assess segregation. Using the dissimilarity index would maintain convention, but it is not well-suited for use with the P* measure of contact, because the dissimilarity index and P* have different mathematical bases. The variance ratio index is in the same family of measures as the exposure index; its use maintains conceptual consistency in measurement and facilitates a formal analysis because it has a straightforward connection with P* contact measures. 8 The variance ratio index of segregation (V) is related to the P* contact index by the relation: P* = p ( 1 V ) (1) g ng ng ( g)( ng ) where p ng is the proportion of the population that is nongroup (i.e., not in the gth group or other-race), and V (g)(ng) is the variance ratio index of segregation between the group of interest and nongroup persons (or other-race persons). Like the index of dissimilarity, the variance ratio index varies from 0 to 1 and has good formal properties as a measure of segregation (James and Taeuber 1985). The Appendix shows formulas for P* and V. A formal model. In developing a formal model to represent Massey s simulation, we want to express the outcome of group-poor contact with poor ( P* p ) as a function of the key parts of Massey s model: racial segregation, poverty-status segregation within race, group poverty rates, and other distinct and interpretable demographic conditions that are important for poverty concentration. In bringing segregation into the model, a useful property of the P* index is that it is additively decomposable into contact with subgroups. Total poverty contact for poor members of a racial group in a metropolitan area is the sum of contact with poor members of their own group () and poor persons not of their own racial or ethnic group (n): P* = P* + p n (2) For instance, the average neighborhood poverty rate for poor Hispanic residents of Chicago (i.e., the concentration of Hispanic poverty) is.197; this is the sum of the average proportion of their neighbors Hispanic and poor (.133) and the average proportion non-hispanic and poor (.064). Contact with own-group poor and other-race poor will be differentially affected by segregation between group g and persons not in group g (ng). We can add segregation, as well as related measures that capture forms of cross-race poverty contact and poverty-status effects on own-race contact, using ratios of P* indexes related to these different forms of contact: P* = P* p g g + g ng g g g g Multiplying out these terms returns to Equation 2. Equation 3 adds measures of contact with own and other races, which get closer to isolating a segregation effect, and measures of effects of poverty status on contact with own-group ( P* g ) and other groups ( P* ng ). In addition, Equation 3 includes measures of poverty-status effects on contact with own-group poor ( P* g ) and other-group poor ( P* n ). Using the fact that g P* ng = 1 ng P* g and doing some algebra allows us to separate out group poverty rates, which are a key element of Massey s model, and also provides terms that are more interpretable: p g ng g g n ng g g n n gp * gp * g P* = ( 1 P* ) Pov Povg gp * + P* Pov g ng ng g n gp * ng Povng g n n (3)

9 362 American Sociological Review 77(3) I then substitute the segregation measure in place of the own-race and other-race contact measures (by using the substitution shown in Equation 1) and rearrange: P* = Pov p g p ng ( g)( ng ) ( 1 V ) Pov ng g g g Each part of this formula has an interpretable meaning. Renaming component parts from Equation 4 gives the final component formula: This final decomposition shows how grouppoor contact with poor is related to several conditions. Poverty concentration is determined by the group poverty rate (Pov g ), the other-race (nongroup) poverty rate (Pov ng ), segregation group/other-race (V ), relative group size (p ng ), and four additional components: GPxG: A ratio indicating own-group disproportionality among the group poor s neighbors. If this component is greater than one, poor group members have proportionately more own-group neighbors than the average for their group ( g). This captures any poverty-status effect on own-group contact. GPxGP: A ratio indicating poverty disproportionately among the group poor s own-race neighbors. If this component is greater than one, then poor group members tend to have more poor own-group neighbors than average for their group. This can be interpreted as a measure of poverty-status segregation g + g n gp * ng Povng g gp * gp * g Povg Povg gp * P* Pov GPxG GPxGP = ( )( ) + p g png ( 1 V g ng ) ( )( ) Povng ( GxNGP)( GPxNGP) Povg ( GPxG)( GPxGP) n n (4) (5) within race for a group and is present in Massey s model ( ). GxNGP: A ratio indicating poverty disproportionality among group members other-race neighbors. If this component is greater than one, then group members other-race neighbors are more likely to be poor than the other-race average (g n). GPxNGP: A ratio indicating poverty disproportionality among poor group members otherrace neighbors. If this component is greater than one, then poor group members tend to have poorer other-race neighbors than the average for all group members ( n). A value of one for these four components is like no effect or no disproportionality: the term multiplies out of the decomposition. For instance, a one on GPxG indicates that poor group members are no more likely than other group members to have own-group neighbors. Of these components, only GPxGP is represented in Massey and colleagues models or explicitly discussed in his simulations. GPxGP can be interpreted as a measure of poverty-status segregation within race, similar in concept to the index of dissimilarity between poor and nonpoor. To help understand how this model operates, consider blacks in the Chicago metropolitan area. The average neighborhood poverty rate for a poor black resident of Chicago is 34.6 percent ( P* p =.346). This is the measure of black poverty concentration for Chicago and the outcome we seek to understand. Inputs for Chicago include blacks segregation from other-race persons, V (g)(ng) =.667; the poverty rate of Chicago s black population, 24.6 percent (Pov g =.246); the poverty rate of Chicago s non-black population, 7.3 percent (Pov ng =.073); and the percentage of the population that is not black in the Chicago metropolitan area, 81.4 percent (p ng =.814). The final inputs are the four disproportionality ratios indicating that poor blacks have about 9 percent more black neighbors than does the black population on average (GPxG = 1.09); poor blacks have 49

10 Quillian 363 percent more poor black neighbors than does the black population on average (GPxGP = 1.49, a measure of class segregation); blacks non-black neighbors are, on average, 66 percent more likely to be poor than the average for non-blacks in the Chicago area (GxNGP = 1.66); and poor blacks non-black neighbors are 8 percent more likely to be poor than are nonpoor blacks non-black neighbors (GPx NGP = 1.08). Applying the formula from Equation 5 with the Chicago components, we get the following: P* p = (. 246)( 109. )( 1. 49) + (. 814) ( ) (. )(. )(. ) ( )( )( ) =. 326 This final number is exactly equal to the average neighborhood poverty rate for poor blacks in Chicago (32.6 percent). In fact, we can exactly predict the level of poverty concentration for any race or ethnic group in any city based on these components and this model. We can also use the model to address what effect a change in one set of conditions would have, holding the other components constant. In Chicago, segregation is a particularly important component. For instance, if black non-black segregation in Chicago were to drop to the black mean of.317, holding other conditions constant, black poverty concentration would drop from.326 to.250. To understand the potential role of segregation and minority poverty rates interacting to form concentrated poverty, it is helpful to rewrite Equation 5 in a form that multiplies out some terms: * = ( )( ) P Pov GPxG GPxGP p g + p Pov ( GxNGP)( GPxNGP) ng ng ng p Pov GPxG GPxGP g ng ( g)( ng ) g ( )( ) pngv( g)( ng) Povng ( GxNGP)( GPxNGP) + p V Pov ( GPxG)( GPxGP) (6) Note that segregation (V (g)(ng) ) multiplied by the group s poverty rate (Pov g ) appears in the last term. This multiplication indicates that segregation and the group s poverty rate interact, or intensify each other s effect, in the production of spatially concentrated poverty. The fact that this multiplication of terms occurs in the decomposition is consistent with the interaction that Massey expected. Interpretation of the Complete Model of Segregation and Poverty Concentration The final decomposition model (Equation 5 and, in different form, Equation 6) provides a way to understand how segregation on the basis of race and the focal racial group s poverty rate combine to produce concentrated poverty. It is an improved version of Massey s conceptual model, illustrated clearly in his simulation, that racial segregation, the group poverty rate, and poverty-status segregation within race affect the spatial concentration of group poverty. The model shows that to fully specify how segregation and group poverty rates affect concentrated poverty, we must introduce other features of the space over which these conditions are evaluated. There is no error term in the decomposition. With the final model (Equation 5 or 6), we can perfectly predict the level of concentrated poverty a group experiences in a metropolitan area as a function of the indicated components. From the model, we see that segregation, the group poverty rate, and the extent of poverty-status segregation within race affect concentrated poverty, as Massey emphasized. But the connection of these factors to poverty concentration also depends on factors that Massey implicitly held constant in his simulation model, such as the poverty rate among everyone not a member of the segregated group and relative group size. Segregation (appearing as the 1 V term in Equation 5) interacts (multiplies) with the difference in poverty between group and other-race members (these terms subtract) rather than with the raw group poverty rate. This is because segregation becomes more consequential for poverty concentration to the extent that group

11 364 American Sociological Review 77(3) and other-race members have different poverty rates. Segregation also matters more when other-race persons are a large share of the total population. In effect, the formula is translating from segregation to contact, and contact with another group is equal to the product of one minus segregation from the other group and relative size of the other group (White 1986). Neither of these conditions had been properly included in past empirical tests of Massey s model because past tests assumed additive, linear effects. Massey s simulation omitted consideration of how income-selective patterns may affect cross-race contact. The decomposition shows this as three terms representing the possibility that poor group members are especially likely to have contact with their own group (GPxG), that other-race members who group members are in contact with are more (or less) likely to be poor than the other-race average (GxNGP), and that poor members of the group are especially likely to be in contact with poor otherrace persons (GPxNGP, effectively cross-race income segregation). We can now return to Massey s hypothesized interaction between segregation and poverty concentration. The decomposition includes terms in which race segregation and the group poverty rate multiply. This is consistent with Massey s expectation of interactions between these conditions in the production of concentrated poverty. But the model also shows that several other conditions interact with segregation that is, several terms multiply with segregation in the formula strengthening or weakening its effects. These effects have intuitive explanations. Strengthening segregation effects are the percentage of the population who are otherrace, the effect of poverty on contact with one s own-group, and group poverty-status separation among group members (multiplying in the last term of Equation 6). If the proportion of the population other-race is greater, change in segregation results in greater changes in contact with other race groups. If the poor have more own-group contact, the own-group poverty rate matters more for poverty concentration. And if poor and nonpoor group members are more separated spatially, increased own-race contact (segregation) results in greater poverty concentration. Other factors weaken segregation s effect on poverty concentration. These factors multiply with segregation in Equation 6 and are in terms that are negative in sign. These include the poverty rate of other-race persons, group members tendency to be in contact with poor other-group members, and poor group members likelihood of being in contact with poor other-group members. As these conditions become stronger, a decrease in segregation increasingly implies that poor group members will swap poor own-group neighbors for poor other-group neighbors, producing little or no deconcentration of poverty. Because many factors strengthen or weaken segregation effects, Massey s point about the importance of segregation for poverty concentration in any particular context holds under some, but not all, conditions. Whether conditions in U.S. cities are right for Massey s conclusions about the importance of segregation and its interactive combination with group poverty rates is an empirical question I consider in the next section. Approach And Data To better understand the poverty concentration model and how it may help account for the missing interaction Massey s framework predicted, we need to examine the model in light of values the components actually take on across U.S. cities. My analysis involves two steps. First, I use data to compute components of the decomposition model (shown in Equations 5 and 6) and apply these to the decomposition to better understand its implications. Second, I use the model of the mathematical relationships among these conditions to investigate the lack of interaction in the basic regression models of Jargowsky (1997) and Massey and Fischer (2000). I use census tract data from the 2000 Census, which are a more recent version of the data used in past studies. 9 I computed summary statistics for metropolitan areas with at

12 Quillian 365 least 20,000 members of the focal racial group, because segregation measures have little meaning when a minority group is very small. For simplicity, I focus on cross-sectional analysis using the 2000 Census, although I also examined the situation using change regressions from 1990 to 2000 and many similar results hold to those I report here. I also performed the basic analysis in cross-section with the 1980 Census, which generated identical substantive conclusions (tables available from the author on request). As discussed earlier, I follow Massey and Eggers s (1990) and Massey and Fischer s (2000) empirical studies in using the P* index of census tract contact between poor members of the focal racial group and the poor of any group to measure group poverty concentration. Poverty is defined as membership in a family with income below the official federal poverty line, which is how it appears as counts in data on census tracts. To examine segregation effects, I use blacks and Hispanics as focal race groups, because these groups have higher poverty rates than whites and are the groups Massey focuses on in his model. Earlier versions of this article also included results for Asian Americans and pooled results combining blacks, Hispanics, and Asians into one model. These tables are available from the author on request. The Decomposition Model Versus the Massey Model How Well Do the Massey Model s Implicit Assumptions Hold? Massey s simulations assume income does not influence racial segregation: that is, he assumes the poverty rate of blacks living in white neighborhoods is equal to blacks overall rate, and that of whites living in black neighborhoods is equal to the overall white rate. A key difference of the decomposition model from Massey s model is that it drops this assumption. In the decomposition, income effects on cross-race contact are represented with three disproportionality measures. These measures are the extent to which poor members of the focal race group have more own-group neighbors than do nonpoor members (GPxG), the extent to which group members other-race neighbors are poorer than average for their group (GxNGP), and the extent to which poor group members other-race neighbors tend to be poorer than average for their group (GPxNGP). Massey s simulation implicitly assumed no disproportionality, which is like a value of 1 in the decomposition. (The fourth disproportionality measure, GPxGP, represents poverty-status segregation among group members and is included in Massey s simulations.) The disproportionality measures are the top four components in Table 1. Numbers greater than one in the GPxG row (the first row) of Table 1 indicate that poor members of non-white groups tend to have more own-group neighbors than do nonpoor group members. If this pattern is strong, it might undercut Massey s arguments about segregation and poverty status. But these ratios, on average, are between 1.1 and 1.2, not too far off from the poverty-status proportionality (1.0) in contact with own-group members that Massey s model implicitly assumed. While poor members of these groups do have more own-group neighbors, on average they have only 10 to 20 percent more own-group contact. For blacks, this is consistent with the longstanding finding that middle-class blacks have more non-black neighbors than do poor blacks, but not many more (Massey and Denton 1993; Massey and Fischer 1999). By contrast, numbers in the GxNGP row (third row) indicate that blacks and Hispanics other-race neighbors are significantly more likely to be poor than the other-race average. The values are and for blacks and Hispanics, respectively. This is inconsistent with Massey s assumption that income does not affect cross-race contact. Because contact with other-race neighbors tends to be with disproportionately impoverished persons, this weakens desegregation s potential to reduce black and Hispanic poverty contact, and thus the segregation effect.

13 366 American Sociological Review 77(3) Table 1. Metropolitan Means and Standard Deviations of Components of Neighborhood Poor Contact Decomposition by Group Variable Black Hispanic Disproportionality Measures GPxG: own-group disproportionality in neighbors of group poor ( g) GPxGP: poverty disproportionality in own-race neighbors of group poor ( ) GxNGP: poverty disproportionality in other-race neighbors of group (g n) GPxNGP: poverty disproportionality in other-race neighbors of group poor ( n) (.075) (.214) (.377) (.132) (.107) (.215) (.348) (.129) Other Components Segregation Group/Not Group (V (g)(ng) ).317 (.153) Group Poverty Rate (Pov g ).254 (.062) Nongroup Poverty Rate (Pov ng ).095 (.031) Percentage Not Group (p ng ).830 (.109).158 (.097).221 (.063).100 (.033).811 (.181) N (Metropolitan Areas) Note: Standard deviations are in parentheses. Whether this may account for the lack of interaction remains to be seen, but Massey s discussion of poverty concentration does not account for this condition. Factor GPxNGP indicates the extent to which poor members of non-white groups are especially likely to have poor other-race neighbors; this is segregation on the basis of poverty status between members of different race groups. The means for blacks and Hispanics are and 1.199, respectively, which indicate that poor group members are more likely than nonpoor members to have poor other-race neighbors, but this parameter is not far from Massey s implicit assumption of 1.0 (or no difference) in his simulations. The final component, GPxGP, is shown in row two of Table 1. This indicates povertystatus segregation within racial groups, which exists for all groups (ratios greater than one). Income segregation within race was built into Massey s simulation. The bottom of Table 1 shows all other components of the decomposition model. These include the extent of segregation from other-race members, group members poverty rate, other-race members poverty rate, and the percentage of metropolitan residents who are other-race. Segregation is measured by the variance ratio index of segregation between each group (black or Hispanic) and the nongroup (everyone else). 10 Results show that blacks and Hispanics have somewhat similar spatial patterns with regard to poverty concentration, except for the important distinction that blacks are much more segregated from other groups than are Hispanics. For blacks and Hispanics, poverty status matters for poverty concentration because it affects own-group neighbors poverty status, but it has little effect on the propensity toward other-race contact or other-race neighbors poverty rate. The Role of Contact with Other-Race Poor in Poverty Concentration How important are the conditions omitted from Massey s simulations for understanding population concentration in U.S. cities? To

14 Quillian 367 Table 2. Changes in Group Concentrated Poverty with Change in Spatial Conditions Black Hispanic Base Poverty Concentration Level ( ) p (poverty concentration level from decomposition at means of all components) Component Change in Poverty Concentration with 1 SD Decrease (percentage change from base below absolute change) Segregation Group/Not Group (V (g)(ng) ) % GPxG: own-group disproportionality in.011 neighbors of group poor ( g) 4.3% GPxGP (poverty segregation within race):.027 poverty disproportionality in own-race 9.9% neighbors of group poor ( ) GxNGP: poverty disproportionality in other-race.023 neighbors of group (g n) 8.6% GPxNGP: poverty disproportionality in otherrace neighbors of group poor ( n) % % % % % % Note: Other components of the decomposition are held at their means. address this question, I calculate changes in poverty concentrations from changes in these conditions within the range observed in U.S. cities using the decomposition model. Table 2 shows how a one standard deviation decline in the indicated factor would change poverty concentration based on the decomposition model, with other components at their metropolitan mean values (from Table 1). The spatial conditions are the disproportionality measures and racial segregation. 11 The base poverty concentration row at the top gives the level of concentrated poverty with all components at means. Changes in all of the spatial conditions have some impact on poverty concentration. But results in Table 2 indicate that three conditions are of primary importance: racial segregation, poverty status disproportionality within group (GPxGP, which can be viewed as a measure of poverty-status segregation within race), and poverty disproportionality in a group s otherrace neighbors (GxNGP). Their relative importance varies by group. Racial segregation is most important for black concentrated poverty, corresponding to the fact that blacks have by far the highest level of segregation from other groups. Poverty-status segregation contributes importantly to both black and Hispanic concentrated poverty. But most important for Hispanics is poverty disproportionality of other-race neighbors. Hispanics have many non-hispanic neighbors who are disproportionately poor. The disproportionate poverty of blacks and Hispanics other-race neighbors could be due to their being members of relatively poor race groups (e.g., Hispanics having many black neighbors) or because they are disproportionately poor members of their groups (e.g., Hispanics having disproportionately poor non-hispanic white neighbors). In fact, both conditions contribute to the disproportionate poverty of blacks and Hispanics other-race neighbors. Table 3 breaks down neighborhood poverty contact for the black and Hispanic poor by the race of the poor neighbors they are in contact with. Hispanics other-race neighbors are disproportionately black. But Hispanics also have many non- Hispanic white neighbors whose poverty rate is significantly above the overall non-hispanic white poverty rate. Massey s theory of poverty concentration emphasizes racial segregation combined with racial poverty gaps and notes a role for