Segregation and Poverty Concentration: The Role of Three Segregations

Abstract

A key argument of Massey and Denton’s American Apartheid (1993) is that racial residential segregation and non-white group poverty rates combine interactively to produce spatially concentrated poverty. Despite a compelling theoretical rationale, the empirical tests of this proposition have been negative or mixed. This paper develops a formal decomposition model that expands the Massey 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, but that almost equally important for poverty concentration is the disproportionate poverty of the non-group neighbors of blacks and Hispanics. The missing interaction Massey expected in empirical tests can be found with proper accounting for the factors in the expanded model.

“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.

”--Douglas Massey and Nancy Denton, American Apartheid, p. 2

A notable difference in the typical lives of whites, blacks, Hispanics, and Asians in the United States is the economic class of persons in their social environments. White middle-class families overwhelmingly live in middle-class neighborhoods and send their children to middle-class schools, but many black and Hispanic middle-class parents 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 differences in neighborhood disadvantage explains much of the racial gap in exposure to violence (Peterson and Krivo 2005). Sampson and Wilson (1995) argue that high poverty environments are “criminogenic,” encouraging youth to pursue criminal rather than legitimate careers. The spatial separation of the affluent and poor produces spatial mismatch between the demand for job and job seekers, contributing to high unemployment in poorer neighborhoods (Kain 1968, Kasarda 1995, Mouw 2000). Likewise, high-poverty schools tend to be ineffective educationally and have disproportionately high dropout rates (Orfield and Lee 2005; Rhumburger and Pallardy 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, the concentration of poverty in minority communities is the result of the combination of high levels of racial segregation with racial gaps in poverty rates, combined with segregation on the basis of poverty status within race. They develop their argument through a series of simulation models and confirm it through an empirical analysis of segregation, group poverty rates, and poverty concentration in American cities.

While their theory is primae facie compelling, 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 American cities. A later response and re-analysis by Massey and Fischer (2000) 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 paper 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 emphasized two forms of segregation, racial segregation and poverty status segregation 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 medium income members of other groups from blacks and Hispanics. The non-group neighbors of blacks and Hispanics 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 additional conditions.

BACKGROUND

In sociology, there have been two dominant perspectives on the causes of concentrated poverty in American cities. The first are the theories of W. J. Wilson about a confluence of deindustrialization of central cities and class-specific migration patterns among African-Americans (Wilson 1987, 1996). The second are theories of Douglas Massey and Nancy Denton emphasizing the importance of racial residential segregation (Massey and Denton 1993). While their theories are not exhaustive of factors influencing concentrated poverty, Wilson’s and Massey’s perspectives provide the major sociological accounts of the concentration of poverty and its growth in American 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 the concentration of poverty as a key component (Wilson 1987, 1996). Wilson argues that a series of historical changes had the effect of producing poverty concentration in minority communities in urban areas in the 1970s and 1980s. The primary condition Wilson emphasizes is the deindustrialization of urban cores and changes in the skill requirements of urban jobs, producing 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 secondarily several other processes, including declining prevalence of two-parent families and dysfunctional cultural responses resulting from concentrated unemployment. In Wilson’s account, the combined result of these processes was the development in the 1970s and 1980s of 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 both responds to and builds from Wilson’s theory. Although the disagreements between Wilson’s and Massey’s perspectives 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. There are two major points on which Massey disagrees with Wilson, one general and one specific. The general disagreement is that Wilson overlooks the importance of continuing racial segregation, which functions as a key conditioning factor that 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 the devastating effects on minority neighborhoods that it did and few neighborhoods would experience extremes of poverty concentration. The specific disagreement is that Massey suggests that black middle-class out-migration was a process that 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 chapter 4; Massey and Fischer 1999).

Massey’s theory of racial segregation and poor neighborhood formation is based on the 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 the 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 the city has a 20% poverty rate and the white population a 10% poverty rate. Massey shows that as segregation increases across four hypothetical cities, the level of neighborhood poverty contact for blacks increases sharply, while for whites it decreases. Adding poverty status segregation within race to the simulation further increases the average poverty contact for the black poor, resulting in highly concentrated poverty in some black neighborhoods.

A key point that the simulations illustrate is 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.

The interactive combination of segregation and racial group poverty disparities is the basis of Massey’s argument that most of the processes Wilson emphasizes 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, producing the double-disadvantage of personal and contextual poverty for many black and Hispanic families. 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 in turn further 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, p. 2).

Massey and Wilson’s disagreement about black middle-class out-migration is distinct but linked to their debates about the role of segregation in neighborhood poverty concentration. In his theory of black middle-class out-migration, Wilson offers a description of how desegregation can increase poverty concentration if movement into white neighborhoods occurs primarily among middle-class blacks, leaving poorer blacks segregated by both race and class. By contrast, Massey describes desegregation (and conversely, segregation) as occurring equally over income levels, thus reducing poverty concentration by mixing lower-poverty racial groups (whites, Asians) with higher-poverty racial groups (blacks, Hispanics). As this contrast reveals, the effect of segregation 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 class-selectivity in desegregation processes.

EMPIRICAL STUDIES

The Interaction of Racial Segregation and Group Poverty Rates

To provide empirical support for Massey’s model of the importance of segregation in concentrating poverty, Massey and colleagues focused on the idea that there is an interactive combination of segregation and poverty rates that produce 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. Their conclusion is 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 many of these arguments were presented as central conclusions of Massey and Denton’s American Apartheid (1993).

This conclusion, however, would not go unchallenged for long. Published shortly after Wilson and Massey’s initial statements, Jargowsky’s (1997) Poverty and Place was an influential empirical analysis of many of Wilson and Massey’s ideas. While Jargowsky finds some evidence for and against specific hypotheses of Massey and Wilson, he overall provides more support for Wilson’s perspective. In particular, he finds that the metropolitan opportunity structure—the average level of income or poverty—is by far the best predictor of metropolitan neighborhood poverty concentration. On Massey’s arguments about segregation, his results contradict Massey’s key point regarding an interaction between racial segregation and measures of the opportunity structure (including measures of group poverty rates). That is, he finds no tendency for rates of concentrated poverty 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 paralleled Massey and Eggers’ (1990) earlier test of their model in most respects. Like Massey and Eggers’ analysis, 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 both 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 justify this choice as a result of “multicollinearity among the regressors” (1990, p. 1183)—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, making it impossible to precisely estimate their separate effects with the interaction term. Jargowsky argues that the main effects are 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 His conclusion is 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).

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 the 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 looking for interaction as indicated by sharper slopes in higher-segregation 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, there are many potential sets of coefficients that can be examined for consistency with their expectation of interactions between the group income measures and segregation. In their text, they 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 correspond to Massey’s prediction of interaction. Their expectation of interaction between segregation and the income measures suggest the largest coefficients of the group income variables 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 paired contrasts (high segregation vs. medium segregation, etc.) work out in the correct direction. This is about the number we would expect by chance if there is 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 the tables of Massey and Fischer actually provide much evidence that contradicts the 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 out-migration 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 in any significant scale (Massey, Gross, and Shibuya 1994). Several later studies have subsequently 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 non-poor blacks without lasting racial desegregation because of white flight, while Crowder and South (2005) find no increases in rates of migration into white neighborhoods in the 1970s (see also Pattillo-McCoy 2000). Several differences in the exact questions addressed and methods of 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 less affluent blacks (Massey and Denton 1993; Massey and Fischer 1999; but see also Alba, Logan, and Stults 2000). This is consistent with the Massey model’s assumption that segregation and desegregation in cross-section are not income-selective.

REVISING THE MASSEY MODEL

Limits of Massey’s Analysis

In light of Massey and Denton’s convincing theoretical arguments and Massey’s simulations, the results contradicting the presence of an interaction of segregation and group poverty rates are puzzling. Indeed, even Jargowsky acknowledges that “the interaction is logical conceptually and theoretically” (1997, p. 183). The real question then is: because the theoretical rationale is compelling, 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 other characteristics of individuals or places.

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 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, in his simulation, Massey excludes the possibility that the black residents of white neighborhoods might be especially likely to be non-poor. Massey’s model also excludes the possibility that the income of whites 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 in his black middle-class out-migration thesis to increase the concentration of poverty rather than decrease it.

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 in most evident in the regressions Massey and co-authors use to test the theory (Massey and Eggers 1990; Massey and Fischer 2000): in these regressions spatial conditions like percentage of the metropolitan area black and poverty status segregation are used as regression controls and represented as additive predictors. Yet relative group size should interact with segregation in effecting 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 that it allows us to derive exactly how these population quantities must relate to each other, discerning relations that may seem 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 racial segregation of the focal race group from others, poverty rates for the focal racial group and others, and poverty-status segregation within group. Another input is the relative sizes of the racial groups in the 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 previously, Massey implicitly also assumes that income levels do not affect patterns of cross-race contact. To the extent this assumption does not hold, we must built this into the model to represent the real situation of American cities.

In what follows I describe the parameters of the model in more detail and derive the formal model. This section necessarily relies on equations. Readers who wish to skip the formal details of the model can skip to the beginning of the next section, which discusses the interpretation and implications of the formal model.

Measuring the “inputs” and “outputs” of the Massey Model

Poverty concentration is measured using the P* index, computed with group poor contact with poor persons (of any race). This is an index that 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), the group for whom contact is computed is written in subscripts to the left of P*, the group with whom they are in contact is written in subscripts to the right; contact of a poor member of the focal group (group poor) with poor of any race would be denoted _gpP*_p. This is the same index of poverty concentration used by Massey and coauthors 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 (1990), use the index of dissimilarity to assess segregation. The dissimilarity index is a choice that maintained convention, but it was 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:

$${}_{g}P{\ast }_{ng}=p_{ng}(1-V_{(g)(ng)})$$ [1]

where p_ng is the proportion of the population non-group (not in the gth group), and V_(g)(ng) is the variance ratio index of segregation between the group of interest and non-group members. 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). Formulas for P* and V are shown in the appendix.

A Formal Model

In developing a formal model representing Massey’s simulation, we want to find how to express the outcome of group poor contact with poor (_gpP*_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 the poor members of a racial group in a metropolitan area is the sum of contact with poor members of their own group (gp) and poor persons not of their own racial or ethnic group (ngp):

$${}_{gp}P{\ast }_p={}_{gp}P{\ast }_{gp}+{}_{gp}P{\ast }_{\mathit{ngp}}$$ [2]

For instance, the average neighborhood poverty rate for poor Hispanic residents of Chicago (the concentration of Hispanic poverty) is .197, which is the sum of the proportion of their neighborhoods Hispanic and poor (.133) and the proportion non-Hispanic and poor (.064). Contact with own-group poor and non-group 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:

$${}_{gp}P{\ast }_p={}_{g}P{\ast }_g\left(\frac{{}_{gp}P{\ast }_g}{{}_{g}P{\ast }_g}\right)\left(\frac{{}_{gp}P{\ast }_{gp}}{{}_{gp}P{\ast }_g}\right)+{}_{g}P{\ast }_{ng}\left(\frac{{}_{g}P{\ast }_{\mathit{ngp}}}{{}_{g}P{\ast }_{ng}}\right)\left(\frac{{}_{gp}P{\ast }_{\mathit{ngp}}}{{}_{g}P{\ast }_{\mathit{ngp}}}\right)$$ [3]

Multiplying out the terms above returns to [2]. Formula [3] adds the measures of contact with own and other races, which get closer to isolating a segregation effect, and also adds measures of effects of poverty status on contact with own-group (_gpP*_g) and other groups (_gpP*_ng). In addition, formula [3] includes measures of poverty status effects on contact with own-group poor (_gpP*_g) and other-group poor (_gpP*_ngp).

Using the fact that _gP*_ng=1− _ngP*_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:

$${}_{gp}P{\ast }_p=(1-{}_{g}P{\ast }_{ng}){\mathit{Pov}}_g\left(\frac{\frac{{}_{g}P{\ast }_{gp}}{{}_{g}P{\ast }_g}}{{\mathit{Pov}}_g}\right)\left(\frac{{}_{gp}P{\ast }_{gp}}{{}_{g}P{\ast }_{gp}}\right)+{}_{g}P{\ast }_{ng}{\mathit{Pov}}_{ng}\left(\frac{\frac{{}_{g}P{\ast }_{\mathit{ngp}}}{{}_{g}P{\ast }_{ng}}}{{\mathit{Pov}}_{ng}}\right)\left(\frac{{}_{gp}P{\ast }_{\mathit{ngp}}}{{}_{g}P{\ast }_{\mathit{ngp}}}\right)$$

Then substituting the segregation measure in place of the own-race and other-race contact measures (by using the substitution shown in equation [1]), and rearranging:

$${}_{gp}P{\ast }_p={\mathit{Pov}}_g\left(\frac{{}_{gp}P{\ast }_g}{{}_{g}P{\ast }_g}\right)\left(\frac{{}_{gp}P{\ast }_{gp}}{{}_{g}P{\ast }_{gp}}\right)+p_{ng}(1-V_{(g)(ng)})\left[{\mathit{Pov}}_{ng}\left(\frac{\frac{{}_{g}P{\ast }_{\mathit{ngp}}}{{}_{g}P{\ast }_{ng}}}{{\mathit{Pov}}_{ng}}\right)\left(\frac{{}_{gp}P{\ast }_{\mathit{ngp}}}{{}_{g}P{\ast }_{\mathit{ngp}}}\right)-{\mathit{Pov}}_g\left(\frac{\frac{{}_{g}P{\ast }_{gp}}{{}_{g}P{\ast }_g}}{{\mathit{Pov}}_g}\right)\left(\frac{{}_{gp}P{\ast }_{gp}}{{}_{g}P{\ast }_{gp}}\right)\right]$$ [4]

Each part of this formula has an interpretable meaning. Renaming component parts from [4] gives the final component formula below:

$${}_{gp}P{\ast }_p={\mathit{Pov}}_g(\mathit{GPxG})(\mathit{GPxGP})+p_{ng}(1-V_{(g)(ng)})\left[{\mathit{Pov}}_{ng}(Gx\mathit{NGP})(\mathit{GPxNGP})-{\mathit{Pov}}_g(\mathit{GPxG})(\mathit{GPxGP})\right]$$ [5]

This final decomposition shows how group poor contact with poor is related to several conditions. Poverty concentration is determined by the group poverty rate (Pov_g), the nongroup poverty rate (Pov_ng), segregation group/nongroup (V), relative group size (p_ng), and four additional components. The four components are:

• GPxG: A ratio indicating own-group disproportionality in neighbors of group poor. If this component is greater than one, poor group members have proportionately more own-group neighbors than the average for their group (gp → g). This captures any poverty status effect on own-group contact.

• GPxGP: A ratio indicating poverty disproportionately in own-race neighbors of group poor. 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 measure can be interpreted as a measure of poverty-status segregation within race for group and is present in Massey’s model. (gp → gp).

• GxNGP: A ratio indicating poverty disproportionality in other-race neighbors of group members. If this component is greater than one, then group members tend to have non-group neighbors who are more often poor than the non-group average (g → ngp).

• GPxNGP: A ratio indicating poverty disproportionality in the other-race neighbors of poor group members. If this component is greater than one, then poor group members tend to have poorer non-group neighbors than the average for all group members (gp → ngp).

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 to have own-group neighbors than group members. Of these components, only GPxGP is represented in Massey and coauthor’s 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 the example of the Chicago metropolitan area for African-Americans. The average neighborhood poverty rate for a poor African-American resident of the Chicago metropolitan area is 34.6% (_gpP*_p=.346). This is the measure of African-American poverty concentration for Chicago and the outcome we seek to understand. The inputs for Chicago include the segregation of the group from others, V_(g)(ng)= .667; the poverty rate for the Chicago African-American population of 24.6% (Pov_g=.246); the poverty rate among the Chicago population not African American of 7.3% (Pov_ng=.073); and the percentage of the population not African-American in the Chicago metropolitan area of 81.4% (p_ng=.814). The final inputs are the four disproportionality ratios indicating that poor blacks have about 9% more black neighbors than the black population on average (GPxG=1.09), that poor blacks have 49% more poor black neighbors than the black population on average (GPxGP = 1.49, a measure of class segregation), that the non-black neighbors of blacks are on average 66% more likely to be poor than average for non-blacks in the Chicago area (GxNGP=1.66), and poor blacks have non-black neighbors that are 8% more likely to be poor then nonpoor blacks (GPxNGP=1.08).

Applying the formula from [5] with the Chicago components, we get:

$${}_{gp}P{\ast }_p=(.246)(1.09)(1.49)+(.814)(1-.667)[(.073)(1.66)(1.08)-(.246)(1.09)(1.49)]=.326$$

This final number is exactly equal to the average neighborhood poverty rate for poor African-Americans in Chicago of 32.6%. 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 the case of Chicago, segregation is a particularly important component. For instance, if segregation black-nonblack in Chicago was 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 in interacting to form concentrated poverty, it is helpful to rewrite [5] in a form that multiplies out some terms:

$$\begin{array}{l}{}_{gp}P{\ast }_p={\mathit{Pov}}_g(\mathit{GPxG})(\mathit{GPxGP})+p_{ng}{\mathit{Pov}}_{ng}(Gx\mathit{NGP})(\mathit{GPxNGP})\\ -p_{ng}{\mathit{Pov}}_g(\mathit{GPxG})(\mathit{GPxGP})-p_{ng}{V}_{(g)(ng)}{\mathit{Pov}}_{ng}(Gx\mathit{NGP})(\mathit{GPxNGP})\\ +p_{ng}{V}_{(g)(ng)}{\mathit{Pov}}_g(\mathit{GPxG})(\mathit{GPxGP})\end{array}$$ [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 Massey’s expectation of an interaction.

Interpretation of the Complete Model of Segregation and Poverty Concentration

The final decomposition model (in equation [5] and in different form in [6]) provides a way to understand how segregation on the basis of race and the poverty rate of the focal racial group combine to produce concentrated poverty. It is an improved version of Massey’s conceptual model, illustrated most 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 also introduce other features of the space over which these conditions are evaluated. There is no error term in the decomposition: with the final model (in [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. These include 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 members and non-group 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 and non-group members have different poverty rates. Segregation also matters more when the non-group is a large share of the total population. This is because, 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 have been properly included in past empirical tests of Massey’s model because past tests have assumed additive, linear effects.

Omitted from Massey’s simulation are ways in which there may be income-selective patterns of cross-race contact. These are shown in the decomposition as three terms representing the possibility that poor group members are especially likely to have contact with their own group (GPxG), that the non-group members that group members are in contact with are more (or less) likely to be poor than the non-group average (GxNGP), and that poor members of the group are especially likely to be in contact with non-group members who are poor (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 interaction between these conditions in the production of concentrated poverty. But the model also shows that several other conditions also interact with segregation—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 not group members, the effect of poverty on contact with own-group, and group poverty status separation among group members (multiplying in the last term of [6]). Change in segregation results in greater changes in contact with the other group when the proportion of the population not own-group is greater. If the poor have more own-group contact, the own-group poverty rate matters more for poverty concentration. As contact among group members more often puts poor in contact with poor, then segregation matters more for poverty concentration.

Other factors weaken the effect of segregation on poverty concentration. These multiply with segregation in [6] and are in terms that are negative in sign. These include the poverty rate of non-group members, the tendency of group members to be in contact with poor other-group members, and the tendency of poor group members to be more often in contact with poor other-group members. As these other 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 (if strong enough) 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 conditions, but not under all conditions. Whether the conditions are “right” for Massey’s conclusions about the importance of segregation and its interactive combination with group poverty rates to hold in American cities is an empirical question considered in the next section.

APPROACH AND DATA

To better understand the poverty concentration model, and how it may help to 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 American cities. My analysis involves two steps. First, I use data to compute components of the decomposition model (shown in [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 is a more recent version of the data used in past studies.⁹ Summary statistics are computed for metropolitan areas with at least 20,000 members of the racial group for which segregation is computed, 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 have 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 previously, I follow past empirical studies of Massey and Eggers (1990) and Massey and Fischer (2000) 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, since these groups have higher poverty rates than whites and are the groups Massey focuses on in his model. Earlier versions of this paper also included results for Asian-Americans and pooled results combining black, Hispanic, and Asians into one model. These tables are available from the author on request.

THE DECOMPOSITION MODEL CONTRASTED TO 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 rates of blacks living in white neighborhoods is equal to the overall black rate, and 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 disproportionately measures. These measures are the extent to which poor members of the focal race group have more own-group neighbors than nonpoor members (GPxG), the extent to which other-race neighbors of group members are poorer than average for their group (GxNGP), and the extent to which other-race neighbors of poor group members tend to be poorer than average for their group (GPxNGP). Massey’s simulation implicitly assumed no disproportionality, whichi s 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 4 components in table 1.

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 (gp -> g)	1.127 (0.075)	1.160 (0.107)
GPxGP: Poverty disproportionality in own- race neighbors of group poor (gp -> gp)	1.388 (0.214)	1.419 (0.215)
GxNGP: Poverty disproportionality in other- race neighbors of group (g -> ngp)	1.549 (0.377)	1.366 (0.348)
GPxNGP: Poverty disproportionality in other-race neighbors of group poor (gp -> ngp)	1.136 (0.132)	1.199 (0.129)
Other Components
Segregation Group/Not Group (V(g)(ng))	0.317 (0.153)	0.158 (0.097)
Group Poverty Rate (Povg)	0.254 (0.062)	0.221 (0.063)
Non-Group Poverty Rate (Povng)	0.095 (0.031)	0.100 (0.033)
Percentage Not Group (png)	0.830 (0.109)	0.811 (0.181)
N (Metropolitan Areas)	166	144

Notes: Standard Deviations in Parentheses.

The numbers greater than one in the GPxG row (the first row) of table 1 indicate that poor members of all non-white groups tend to have more own-group neighbors than non-poor 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 assumed. While poor members of these groups do have more own-group neighbors, on average they have only 10% to 20% more own-group contact. For blacks, this is consistent with the longstanding finding that middle-class blacks have more non-black neighbors than poor blacks, but not many more (e.g. Massey and Denton 1993 chapter 4; Massey and Fischer 1999).

By contrast, the numbers in the GxNGP row (third row) indicate that the non-group neighbors of blacks and Hispanics are significantly more likely to be poor than the non-group average. The values are 1.549 and 1.366 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 members of other groups, this weakens the potential of desegregation to reduce black and Hispanic poverty contact, and thus the segregation effect. Whether this may account for the lack of interaction remains to be seen, but this is a condition not accounted for in Massey’s discussion of poverty concentration.

Factor GPxNGP indicates the extent to which the 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 1.136 and 1.199, which indicate that poor group members are more likely to have poor other-race neighbors than non-poor group members, but this parameter is not far from Massey’s assumption (of 1.0).

The final component, GPxGP, is shown in row two. This effectively indicates poverty status segregation within racial group, which exists for all groups (ratios greater than 1). Income segregation within race was built into Massey’s simulation.

Table 1 also shows all other components of the decomposition model toward the bottom of the table. These include the extent of segregation from non-group members, the poverty rate of group members, the poverty rate of non-group members, and the percentage of metropolitan residents not group. Segregation is measured by computing the variance ratio index of segregation between each group (black, Hispanic) and the nongroup (everyone else).¹⁰

The 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 Hispanics. For blacks and Hispanics, poverty status matters for poverty concentration because it affects the poverty status of own-group neighbors, but has little effect on the propensity toward other-race contact or the poverty rate of other-race neighbors.

The Role of Non-Group Poor Contact in Poverty Concentration

How important are the conditions omitted from Massey’s simulations for understanding population concentration in American cities? To address this question, I calculate changes in poverty concentrations from changes in these conditions within the range observed in American 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.

Table 2.

Changes in Group Concentrated Poverty With Change in Spatial Conditions

	Black	Hispanic
Base Poverty Concentration Level (gpP*p) (Poverty concentration level from decomposition at means of all components)	0.267	0.227

Component	Change in Poverty Concentration with 1 SD Decrease (Percentage change from base below absolute change)
	Black	Hispanic
Segregation Group/Not Group (V(g)(ng))	−0.029	−0.016
	−11.0%	−6.9%
GPxG: Own-group disproportionality in neighbors of group poor (gp -> g)	−0.029	−0.016
	−4.3%	−7.0%
GPxGP [Poverty Segregation within Race]: Poverty disproportionality in own-race neighbors of group poor (gp -> gp)	−0.029	−0.034
	−9.9%	−15.0%
GxNGP: Poverty disproportionality in other-race neighbors of group (g -> ngp)	−0.029	−0.030
	−8.6%	−13.2%
GPxNGP: Poverty disproportionality in other-race neighbors of group poor (gp -> ngp)	−0.029	−0.019
	−4.1%	−8.2%

Notes: Other components of the decomposition are held at their means.

Changes in all of the spatial conditions have some impact on poverty concentration. But the 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 other-race neighbors of group (GxNGP). Their relative importance varies by group. Racial segregation is most important for black concentrated poverty, corresponding to the fact that African-Americans have by far the highest level of segregation from other groups. Poverty status segregation is of primary importance for Hispanic concentrated poverty. But nearly as important for Hispanics is poverty disproportionality of other-race neighbors. Hispanics have many non-Hispanic neighbors and also disproportionately poor non-group neighbors.

The disproportionate poverty of the non-group neighbors of blacks and Hispanics could result because their non-group neighbors are members of relatively poor 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 the non-group neighbors of blacks and Hispanics. Table 3 breaks down neighborhood poverty contact by the contacting group and the groups they are in contact with. Hispanics have somewhat disproportionately black non-group neighbors. But they also have many non-Hispanic white neighbors and the poverty rate of the non-Hispanic whites they are in contact with is significantly above the non-Hispanic white rate overall.

Table 3.

Metropolitan Average Contact (P*) with Neighborhood Poverty by Contacting and Contactee Group

Group In Contact With	Contacting: Poor Members of Indicated Group
	Black	Hispanic
Non-Hispanic White Poor	0.045 (0.022)	0.052 (0.027)
Non-Hispanic Black Poor	0.167 (0.074)	0.036 (0.028)
Hispanic Poor	0.030 (0.036)	0.109 (0.074)
Asian Poor	0.005 (0.009)	0.007 (0.009)
Other (not above) Poor	0.006 (0.004)	0.006 (0.005)
Total Neighborhood Poverty Contact (gpP*p)	0.262 (0.055)	0.218 (0.062)
N	166	144

Notes: Standard Deviations in Parentheses.

Massey’s theory of poverty concentration emphasized racial segregation combined with racial poverty gaps, and also noted a role for poverty status segregation within race. The decomposition model with data confirms these two conditions are important in general, but we should give nearly equal emphasis to a third condition in evaluating disproportionate neighborhood poverty of blacks and Hispanics: the disproportionate poverty of their non-group neighbors. Thus a third form of segregation, the segregation of blacks and Hispanics from middle and high-income members of other groups, plays an important role in poverty concentration.

Implications of the Decomposition Model for Interaction of Segregation and Poverty Rates

What does the decomposition model in [5] imply about the interaction of segregation and group poverty rates? In the model, these terms multiply, suggesting interaction. The magnitude and exact nature of the interactive effect, however, depends on the values of other components in the model.

To examine the interaction of segregation and poverty concentration in the decomposition model with values typical for American cities, I predict levels of concentrated poverty from the decomposition model ([5]) while holding the other components constant at metropolitan means (by group). Five metropolitan segregation levels are employed, ranging from segregation two standard deviations below the mean to two standard deviations above the mean. Figures 1, 2, and 3 show the level of concentrated poverty as group poverty rates change from this model. The range of variation in the poverty rate (the range of x for which the lines are shown) is plus or minus two standard deviations from the group poverty rate mean. This holds all other components of the decomposition at their means (shown in table 1), with their relations specified in the analytically derived relationship from formula [5].

Figure 1. Black Neighborhood Poverty Concentration and the Black Poverty Rate by Metropolitan Segregation Level.

Note: Predictions are from decomposition models with other components at black means.

Figure 2. Hispanic Neighbrohood Poverty Concentration and the Hispanic Poverty Rate by Metropolitan Segregation Level.

Note: Predictions are from decomposition models with other components at Hispanic means.

An interaction of segregation and the poverty rate is evident in all figures: the lines tracing poverty change have sharper slopes for high segregation than for low-segregation metropolitan areas. This is especially notable for blacks and Hispanics. For blacks in Figure 1, in a highly segregated city (+2 SD), each one percent increase in the black poverty rate is associated with almost a 1% increase in black poor contact with poor in their neighborhood environments; in a low-segregation city (−2 SD), each one percent increase in the black poverty rate is associated with about a 0.3% increase. For Hispanics, shown in Figure 2, in a high-segregation city, a 1% increase in the Hispanic poverty rate is associated with a 0.8% increase in the Hispanic concentrated poverty rate; in a low-segregation city, a 1% increase in the Hispanic poverty rate is associated with a 0.3% increase. The stronger interaction for blacks than Hispanics outside of the lowest segregation category primarily reflects the fact that segregation is significantly higher for blacks than Hispanics.

As we can see from the figures, a surge in a high-poverty group’s poverty rate will increase group poverty concentration substantially more when the extent of group-nongroup segregation is high, holding other conditions constant. Broadly, this demonstrates that Massey’s theoretical argument is correct: segregation and poverty concentration interact for the reasons Massey’s simulation model made clear.

THE LACK OF SEGREGATION-POVERTY STATUS INTERACTION IN BASIC REGRESSIONS

Results from the decomposition model demonstrate that the interaction of segregation and group poverty rates does occur when a series of other spatial and demographic conditions are held constant. But why, then, is there no interaction of segregation and group poverty rates in the basic regressions such as those used by Jargowsky (1997) and Massey and Fischer (2000)? The answer to this question must have to do with the components that are not held constant in the decomposition model.

Confirming Past Results

Before considering in more detail why past studies using regression have not found an interaction of segregation and group poverty rates, I first confirm that the interaction fails to hold using 2000 census data and using the exact measures in the decomposition model.

Table 4 shows basic regressions of group poverty concentration on segregation, group poverty rates,¹² and their interaction. Following a specification used by Jargowsky (1997) and Massey and Fischer (2000), the models represent segregation with dummy variables for categories of medium and high segregation (with low as the reference category).¹³ Other controls include the metropolitan share that is a member of the minority group and segregation of poor from nonpoor. The left numeric column shows results using the index of dissimilarity to measure segregation. The right numeric column uses the variance ratio index.

Table 4.

Coefficients of OLS Regressions of Metropolitan Group Poor Contact with Poor (_gpP^*_g) on Segregation, the Group Poverty Rate, and Interaction

	(1)		(2)
	Dissimilarity Index		Variance Ratio Index
BLACK (N=166 metropolitan areas)
Variables	Coef.	Std. Err.	Coef.	Std. Err.
Race Segregation Medium (vs. Low)	0.002	0.019	0.040	0.016 *
Race Segregation High (vs. Low)	−0.010	0.020	0.027	0.017
Black Poverty Rate	0.581	0.048 ***	0.516	0.041 ***
Black Poverty Rate x Seg. Medium	0.046	0.075	−0.081	0.064
Black Poverty Rate x Seg. High	0.112	0.074	0.032	0.064
Seg Poor/Not Poor	0.343	0.034 ***	0.665	0.050 ***
Percentage Black	0.057	0.018 **	−0.019	0.016
Constant	−0.023	0.017	0.054	0.010 ***
HISPANIC (N=144 metropolitan areas)
Variables	Coef.	Std. Err.	Coef.	Std. Err.
Race Segregation Medium (vs. Low)	−0.034	0.017 *	−0.028	0.021
Race Segregation High (vs. Low)	−0.014	0.017	−0.013	0.023
Hispanic Poverty Rate	0.633	0.063 ***	0.593	0.075 ***
Hispanic Poverty Rate x Seg. Medium	0.138	0.080	0.209	0.095 *
Hispanic Poverty Rate x Seg. High	0.046	0.078	0.139	0.097
Seg Poor/Not Poor	0.430	0.036 ***	0.447	0.079 ***
Percentage Hispanic	0.153	0.012 ***	0.087	0.015 ***
Constant	−0.096	0.018 ***	0.034	0.016 *

Note:

^*p < .05;

^**p < .01;

^***p < .001

Results using both measures are highly consistent. In neither case is there support for an interaction between segregation and the group poverty rate in predicting the group’s poverty contact. Only two interactions of segregation levels and group poverty rates are statistically significant: the medium segregation category based on the dissimilarity index in the pooled model and the medium segregation category based on the variance ratio index in the Hispanic model. The former interaction is in the opposite direction of Massey and coauthors’ expectations. The latter interaction is consistent with their expectations. This means that of 12 coefficients, only one is statistically significant and in the direction predicted by Massey’s theory.

In short, the results of this analysis are similar to those found with earlier years of data and similar models by others. While correlation between main effects and interactions may cause some inflation of the standard errors of the model, the use of dummy variable categories and pooling across race groups to increase variation in segregation still produces no significant effects. As the group poverty rate increases, the contact of minority poor with poor increases, but in simple regression it does so at a rate that is no faster in cities with relatively low levels of segregation than it does in cities with high or medium levels of segregation.

The Missing Segregation and Poverty Concentration Interaction

The reason basic regressions do not show an interaction is because other conditions specified in the decomposition are not held constant. These other spatial conditions are correlated with group poverty rates and segregation in a way that counteracts the interactive intensification that Massey expects.

In regression, the standard approach to holding additional factors constant is to add these factors to the model as control variables. The problem with this approach in this case is that it requires that the relationship between the controls and the outcome be linear, or to be represented through linear transformations. But as [5] makes clear, the relationship between the independent factors and concentrated poverty is complexly non-linear. Simply controlling for these terms in a linear model would not correctly specify their effect in producing concentrated poverty. Moreover, the combination of additive and multiplicative terms in [5] cannot be easily linearized in the components. Taking logs, for instance, does not produce a more linear form.

Instead, I use a two-step procedure to determine which components are suppressing the interaction. First, I use the decomposition model ([5]) to create six sets of metropolitan by race group predictions of the level of concentrated poverty. The predictions are made holding the six components at their means one at a time, with all other components left at their original values. In the second step, I estimate six regressions with the decomposition predictions of concentrated poverty as the dependent variables and the independent variables of table 4. From the interaction slopes in these six regressions, we can investigate which of the components of the decomposition suppress the presence of the interaction in a basic regression model.

The coefficients of the interactions of segregation and poverty concentration from these regressions are shown in table 5. Main effects of segregation and the group poverty rate and controls for class segregation and percentage group are included in the regressions, but these coefficients are not shown in table 5 (model specification is identical to column 2 of table 4). Results are estimated separately for black and Hispanic segregation.

Table 5.

Coefficients of Interactions from OLS Regressions of Decomposition-Predicted Group Poverty Concentration on Group Poverty Rate and Segregation, Holding Indicated Component at the Mean of Decomposition Prediction

Variable	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Component Held At Mean in Decomposition
	None (same as Table 1)	% Not Group (png)	GPxG	GPxGP	Nongroup Pov. Rate (Povng)	GxNGP	GPxNGP
BLACK (N=166)
Black Pov. Rate x Seg. Medium	−0.081 (0.064)	−0.084 (0.067)	−0.041 (0.061)	0.058 (0.056)	0.003 (0.096)	−0.037 (0.095)	−0.113 (0.066)
Black Pov. Rate x Seg. High	0.032 (0.064)	−0.011 (0.067)	0.091 (0.061)	0.294*** (0.056)	0.210* (0.095)	0.014 (0.095)	−0.016 (0.066)
HISPANIC (N=144)
Hisp. Pov. Rate x Seg. Medium	0.209* (0.095)	0.296** (0.101)	0.209* (0.089)	0.239** (0.089)	0.046 (0.131)	0.294* (0.118)	0.126 (0.081)
Hispanic Pov. Rate x Seg. High	0.139 (0.097)	0.170 (0.103)	0.153 (0.092)	0.208* (0.091)	0.153 (0.134)	0.268* (0.120)	0.095 (0.082)

Note: Standard Errors in Parentheses.

^*p < .05;

^**p < .01;

^***p < .001.

Bolded coefficients appreciably larger than coefficient in model 1. Variables included in regression but not shown: Dummy variables (main effects) for race segregation medium, race segregation high, main effect for group poverty rate, segregation poor/nonpoor measure, percentage group.

The top panel of table 5 shows results for black segregation (vs. nonblack). Holding own-group poverty disproportionality (GPxGP) or the nonblack poverty rate constant results in a statistically significant interaction term in the direction Massey suggests. The second panel shows results for Hispanic segregation. Two components produce statistically significant interaction terms: own-group poverty disproportionality (GPxGP) and disproportionality in the poverty status of non-group neighbors (GxNGP).

Because the decomposition model shows many interactive effects among components, the combination of several changes together may be substantially different than the single-component changes shown in table 5. To examine how the segregation by poverty-rate interaction is affected by multiple changes, I computed predictions from the decomposition model involving changing two components and three components to the mean simultaneously, for all possible combinations of two and three components.¹⁴ Then I estimated regressions in which the predicted poverty concentration scores are regressed on the basic regression model.

Table 6 shows the models with two components simultaneously at means and three components simultaneously at means for each group that had the largest impact on the interactions between segregation and the group poverty rate.¹⁵ Coefficients of the main effect terms and control variables are also displayed. The components that were the strongest individually produce the largest changes in combination. When two or three key components are set to means, the interaction emerges strongly as the Massey model predicts. This is shown for black and Hispanic segregation in model (1) to (4). The factors that suppress the interaction are moderately consistent across groups.

Table 6.

Coefficients of Regressions of Predicted Contact of Group Poor with Poor from Decomposition, Holding Multiple Components at Means

Variable	(1)	(2)	(3)	(4)
	BLACK		HISPANIC
	Outcome is Predicted Group Poverty Concentration with Indicated Components Held at Mean In Decomposition
	GPxGP and Povng	GPxGP and Povng and GxNGP	Povng and GxNGP	GPxGP and Povng and GxNGP
Race Seg. Med. (vs. Low)	0.008 (0.022)	−0.037 (0.013) **	−0.025 (0.017)	−0.035 (0.017) *
Race Seg. High (vs. Low)	−0.051 (0.024) *	−0.091 (0.014) ***	−0.057 (0.019)**	−0.077 (0.018) ***
Group Poverty Rate	0.345 (0.056) ***	0.286 (0.032) ***	0.211 (0.061) **	0.305 (0.060) ***
Group Pov. x Seg. Med.	0.141 (0.088)	0.232 (0.050)***	0.123 (0.078)	0.154 (0.077) *
Group Pov. x Seg. High	0.472 (0.088) ***	0.528 (0.050) ***	0.286 (0.080) ***	0.355 (0.079) ***
Seg Poor/Not Poor	0.338 (0.069) ***	0.227 (0.040) ***	0.354 (0.065) ***	0.321 (0.064) ***
% Group	0.027 (0.021)	0.123 (0.012) ***	0.125 (0.012) ***	0.208 (0.012) ***
N (metros)	166	166	144	144

Note: Shown are predicted poverty concentration with two and three components at mean which had the largest effects on the interactions. Standard errors in parentheses.

^*p<.05;

^**p<.01,

^***p<.001. Constant term included but not shown.

The most consistently important factor is the level of disproportionality in poverty-status contact among own-group members (GPxGP). For blacks, there is a strong negative relationship between this component (GPxGP) and the group poverty rate: the correlation of GPxGP and metropolitan poverty rates is −0.7. The same pattern holds for Hispanics, but more weakly: the correlation of GPxGP and the group poverty rate is −0.5.¹⁶ This implies that when the share poor of a group is a low percentage in a metropolitan area, group poor are more likely to be residentially isolated from more middle-class members of their own group. Massey’s model predicts that as the group’s poverty rate increases, this will increase the poverty rates of the neighborhoods of the poor more in more segregated environments. Empirically however, higher poverty rates for blacks and Hispanics are associated with less spatial separation of group poor from the group nonpoor, which reduces the concentration of group poverty, and partially offsets Massey’s expected interaction.

The fact that poor and nonpoor group members are less segregated from each other when group poverty rates are high is an unexpected but consistent fact in the data. When group poverty rates are low, it appears that nonpoor blacks can better separate themselves from poor blacks; the same pattern holds but is less pronounced for Hispanics. The Washington D.C. and Atlanta metropolitan areas, for instance, have relatively low black poverty rates overall and also high spatial differentiation, marked by distinct middle-class and poor black neighborhoods. By contrast, cities with high-poverty black populations, like many smaller metropolitan areas in the south, poor and nonpoor blacks are more spatially mixed. The reasons for this pattern are beyond the scope of this analysis and are a good topic for future research (for a related analysis see Bayer, Fang, and MacMillan 2011).

As a result, as black poverty rates increase, it is nonpoor blacks who on average have especially large increases in their poverty contact, because their degree of spatial separation from poor blacks tends to decrease. The combination of high segregation and high black poverty rates produces an interactive intensification in poverty contact for nonpoor blacks rather than poor blacks.¹⁷

A second factor that suppresses the interaction of segregation and poverty rates for blacks and Hispanics is the nongroup poverty rate (Pov_ng), or the poverty rate among persons not in the focal race group. The nongroup poverty rate is correlated with the group poverty rate because both group and nongroup poverty rates tend to fluctuate together with business cycles and local labor market conditions. This correlation makes segregation less important, because a reduction in the level of segregation then results in poor group members having fewer poor own-group neighbors but more poor other-group neighbors, with little change in the level of neighborhood poverty contact.

A third factor that suppresses the interaction is poverty-disproportionality in other-race contact (GxNGP). This is a measure of the extent to which the other-race neighbors of group members are poorer than the other-race average. Suppression of the interaction from this factor occurs for much the same reason as the nongroup poverty rate. In metropolitan areas with high group poverty rates, the non-group members that group members tend to be neighbors of are more often poor than in metropolitan areas with low group poverty rates. This weakens segregation effects on concentrated poverty, because changes in segregation result in less contact with poor group members but more contact with nonpoor group members. This process is especially important for Hispanics, who on average have many non-Hispanic neighbors.

The processes that suppress Massey’s expected interaction vary by group. For blacks, it is predominately that poor and nonpoor blacks are more spatially mixed in cities with high black poverty rates. For Hispanics, it is predominately that as segregation declines, Hispanics often swap poor Hispanic neighbors for poor non-Hispanic neighbors, thus weakening the intensification of segregation plus high poverty rates Massey expected. The result of these other conditions is that Massey’s expected “intensification” from high poverty rates with high segregation fails to appear because it is offset by these other conditions. The intensification is evident if these other conditions are held constant by the decomposition model. Massey’s basic logic of how segregation and high minority poverty rates should interact is correct, but other conditions in metropolitan areas associated with high segregation or group poverty have the effect of offsetting some of the increase in poverty concentration.

DISCUSSION

The failure of past studies to establish an interaction of segregation and poverty concentration has been puzzling. The theoretical account developed by Massey and Denton (1993) and elaborated through simple simulations by Massey (1990) was compelling. Yet this account was called into question by the failure of past studies including Jargowsky (1997) and Massey and Fischer (2000) to find the proposed interaction of group poverty rates and segregation in data. It seemed that either the very idea that segregation and high minority group poverty rates play an important role in concentrating poverty was wrong, or the process was not empirically important, or there was some fundamental but unexplained problem in empirical tests employed in past work. If the results indicated a conceptual problem in Massey’s model, this would undermine a major rationale offered by Massey and Denton and other scholars as to why racial segregation is a significant problem of social concern and undercut a key argument of American Apartheid.

This analysis demonstrates that the reason this interaction was not found in past work is because Massey’s substantive model of how segregation concentrated poverty, while correct in its broad logic of how segregation and group poverty disparities should combine interactively, was incomplete and at points too simple. The decomposition model developed here is an expansion of Massey’s model to include additional conditions and to allow for a more accurate description of the complicated way demographic and spatial conditions of race and poverty status combine.

Massey’s theory of concentrated poverty in minority communities hypothesizes that it results from two segregations: the segregation of the non-white poor from members of other lower-poverty racial groups (racial segregation with racial inequality) and from the non-poor of their own racial group (poverty status segregation within race). This is a compelling picture, and it does represent an important pair of conditions that contribute to the formation of concentrated poverty in non-white neighborhoods.

Yet the results here indicate that we must also add a third spatial pattern that is empirically important to understanding poverty concentration for blacks and Hispanics: poverty disproportionality in cross-race contact. The non-group neighbors of blacks and Hispanics are about 50% more likely to be poor than the non-group average, with little additional effect of the poverty status of the black or Hispanic person. In effect, blacks and Hispanics are segregated from higher-income members of other racial groups. It is then 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. Disproportionate contact with poor members of other groups is especially important for Hispanics owing to their relatively low racial segregation. For Hispanics, disproportionate poverty of non-group neighbors has more impact on high Hispanic levels of neighborhood poverty concentration than segregation. Massey’s model is incomplete in omitting this process.

Massey’s model was too simple because he assumed that only the group poverty rate interacted, or intensified the effect, of segregation. He took other important conditions such as within-group poverty status segregation as having separable, linear effects on poverty concentration (others testing his framework implicitly adopted this view as well). The decomposition model shows that several other conditions also combine interactively with segregation in producing concentrated poverty. Racial segregation “effects” on poverty concentration are thus the product of a complex set of other spatial and demographic conditions that may strengthen or weaken them, including poverty status segregation within-group, the tendency of blacks or Hispanics to be in contact with especially poor non-group members, and relative group size.

Massey expected metropolitan areas with high group poverty rates and high group segregation to have multiplicatively higher rates of concentrated poverty for the segregated minority group. Without controls, they do not have multiplicatively higher rates because other conditions change with segregation and group poverty rates and somewhat offset (suppress) intensified poverty concentration from the combination of segregation and high group poverty rates. When these other conditions are held constant statistically, we can locate Massey’s expected interaction in data.

In the case of black segregation, the interaction of segregation and the metropolitan black poverty rate is suppressed primarily because segregation based on poverty status (income segregation) among blacks is lower in cities with high black poverty rates. For this reason, the main increase in neighborhood poverty contact in segregated cities with high black poverty rates are for working-class and middle-class blacks, who absorb the increase in poverty contact rather than the black poor. This is consistent with literature emphasizing the high contact of middle-class blacks with the black poor in contributing to their “fragile” economic position (Pattillo 1999).

In the case of Hispanic segregation, Massey’s analysis was undone by failing to account for the important role of poor neighbors from other racial and ethnic groups in their neighborhood poverty contact. In less segregated environments, the Hispanic poor tend to have fewer Hispanic poor neighbors but more non-Hispanic poor neighbors. Because of this, reduced segregation for Hispanics has a weaker effect in reducing poverty contact than we would expect from the Massey model.

In their debates about the relative role of race and class factors in concentrating poverty, Massey’s and Wilson’s perspectives hypothesize opposite relations between racial segregation and poverty concentration. Massey’s theory posited that segregation increased poverty concentration and desegregation would decrease it. Wilson’s theory hypothesized that racial desegregation had increased poverty concentration because it was accomplished primarily by more affluent members of disadvantaged groups moving into white neighborhoods.

The results here provide more support for the Massey view of the effects of segregation on poverty concentration: overall, racial segregation in American cities is a key lynchpin of highly concentrated poverty. When we assign group-nongroup segregation levels for blacks or Hispanics that are similar to Asians (the least segregated major racial-ethnic grouping in the Census), the concentration of poverty for these groups declines notably. Yet the results also provide some support for the idea that there are income effects in cross-race contact that matter, although not primarily the black income effect on cross-race contact that Wilson suggested. Instead, the relatively high poverty rates of the non-group neighbors of blacks and Hispanics have an important influence on poverty concentration.

One puzzle that the high poverty rate of non-group members helps to explain is the high neighborhood poverty concentration of Hispanics. Hispanics experience neighborhood poverty concentration that is only a bit below the levels of African-Americans. This is impossible to explain via the Massey model with its focus on racial segregation, because Hispanics have a poverty rate similar to blacks, but a much lower level of segregation from other groups. Yet because the non-group neighbors of Hispanics are often impoverished, their lower segregation only weakly translates into lower neighborhood poverty contact.

While decreasing racial segregation through efforts like aggressive enforcement of anti-discrimination policies in housing would significantly reduce the concentration of poverty, we need to attend to the possibilities of income-selective effects in desegregation. Income selectivity can undercut the potential of desegregation to reduce the concentration of poverty. Policies that aim to provide broader housing choices may not deconcentrate poverty if blacks and Hispanics can only find places in the most disadvantaged desegregated neighborhoods.

Appendix: Measures used in formal model

The concentration of poverty for a group is assessed as the share poor in the tract of a poor member of the group in question. This can be calculated for a metropolitan level from tract-level data with the formula (see Lieberson and Carter 1982):

$${}_{gp}P{\ast }_p=\sum _i\left(\frac{{gp}_i}{GP}\right)\left(\frac{p_i}{t_i}\right)$$

Where gp_i denotes the number of poor persons in race group g in the ith tract, p_i is the number of poor persons of any race in the ith census tract, GP is the total number of poor in the group in the metropolitan area for which the index is calculated, and t_i is the total population of the ith neighborhood tract. This measure can be interpreted as the average percentage of the population poor in the neighborhood of the average poor member of racial group g. While this measure is referred to as a measure of “contact” in the literature, this is shorthand for co-residence in the same census tract; there is no direct measure of contact in personal interactions.

The variance ratio index of segregation between group g and persons not in group g (ng) can be calculated from the tract data for a metropolitan area as (see James and Taeuber 1985):

$$V_{(g)(ng)}=\sum _i\frac{t_i{\left(\frac{g_i}{t_i}-\pi \right)}^2}{T\pi (1-\pi )}$$

Where g_i denotes the population of the racial group 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 group proportion of the population in the metropolitan area.