Although it is clear that racial segregation is linked to academic achievement gaps, the mechanisms underlying this link have been debated since James Coleman published his eponymous 1966 report. In this paper, I examine sixteen distinct measures of segregation to determine which is most strongly associated with academic achievement gaps. I find clear evidence that one aspect of segregation in particular—the disparity in average school poverty rates between white and black students’ schools—is consistently the single most powerful correlate of achievement gaps, a pattern that holds in both bivariate and multivariate analyses. This implies that high-poverty schools are, on average, much less effective than lower-poverty schools and suggests that strategies that reduce the differential exposure of black, Hispanic, and white students to poor schoolmates may lead to meaningful reductions in academic achievement gaps.

Keywords

achievement gap, school segregation, residential segregation, school poverty

Does segregation exacerbate racial educational inequality? And if so, through what mechanism? Is it racial segregation per se that matters, or the association of racial segregation with unequal schooling or neighborhood conditions? When the Supreme Court ruled in Brown v. Board of Education that “separate educational facilities are inherently unequal,” its argument was that legally sanctioned segregation based on race necessarily inflicted on African American children a psychological wound that could not be salved by the provision of materially equivalent schooling facilities and resources. In the Court’s view, it was the very act of legal exclusion that created inequality and violated the Fourteenth Amendment. Even if separate schools, in practice, had equivalent material conditions (that is, if the Plessy v. Ferguson standard of “separate but equal” were met in strictly material terms), the Court argued, black children would nonetheless be harmed by virtue of their state-sanctioned exclusion from schools enrolling white students.

This argument suggests that there is something explicitly racialized about the effects of segregation, particularly in the context of de jure segregation. The Court’s argument does not, however, imply that the race-specific nature of school segregation laws is the only way that segregation may harm children; it merely [End Page 34] suggests that there would be harm even if the material conditions of racially segregated schools were equalized.

Twelve years after the Brown decision, when Coleman wrote his Equality of Educational Opportunity report, he was concerned less with the psychological harms of de jure segregation and more with the material inequalities that existed (or were presumed to exist) in both de jure and de facto segregated school systems of the 1960s. By 1966, Brown had yet to substantially reduce segregation in the South, and one aim of the Coleman Report was to investigate the extent to which black and white students attended schools of different quality and the relationship between measures of material school quality and academic achievement.

Coleman reported several facts about school segregation in the United States. First, unsurprisingly, racial segregation was very high. Two-thirds of black students attended schools that were 90 to 100 percent black; 80 percent of white students attended schools that were 90 to 100 percent white. More importantly, he found that the academic achievement of both white and black students was higher in predominantly white schools than in predominantly minority schools. In addition, black students who had spent more time in desegregated schools had modestly higher average scores than others, a pattern that held when controlling for individual student socioeconomic background (Coleman et al. 1966, 331–32). Little of the association of test scores with school racial composition could be explained, however, with the set of school quality measures available to him. Instead, Coleman wrote, “the higher achievement of all racial and ethnic groups in schools with greater proportions of white students is largely, perhaps wholly, related to effects associated with the student body’s educational background and aspirations” (307). In other words, the negative association of segregation with academic achievement disparities appears to have been largely driven by the differences in the socioeconomic composition of the schools where black and white students were enrolled.

Geoffrey Borman and Maritza Dowling (2010), in their reanalysis of Coleman’s data, likewise find that both the racial and socioeconomic composition of schools are strongly related to student outcomes (as have numerous other studies). These findings, although correlational rather than causal in nature, suggest that any effects of racial segregation on achievement patterns are at least partly driven by factors associated with school socioeconomic composition rather than by racial composition per se. These factors might include material resources, instructional focus and quality, parental social and economic capital, social norms, and peer effects. The Coleman data (and other subsequent studies) have not, however, convincingly identified if and how such mechanisms link school segregation to unequal outcomes.

In this paper, I use new data based on over 100 million test score records from all grade 3 through 8 students in public schools from 2009 to 2012 in over 300 metropolitan areas to further investigate the association between racial segregation and racial academic achievement gaps. In particular, I assess whether it is differences in the racial or socioeconomic composition of schools that drives the persistent association between segregation and achievement inequality. A better understanding of the mechanisms driving the effects of segregation may be useful in counteracting those effects.

This paper proceeds in four parts. I first describe four related but conceptually distinct dimensions of segregation, each of which might affect academic achievement gaps. These four dimensions yield sixteen different measures of segregation, each of which I use in this analysis. I next describe the data and measures used in the paper. These are measures of academic achievement gaps and segregation patterns in roughly 320 metropolitan areas in the United States. The third section of the paper describes the analyses and results. Here I demonstrate that all sixteen measures of segregation are correlated with racial achievement gaps, but that one in particular—the disparity in average school poverty rates between white and black students’ schools—is consistently the strongest correlate of achievement gaps, a pattern that holds in both bivariate and multivariate analyses. In the final section of the paper, I discuss the implications of these findings. [End Page 35]

Table 1. Dimensions of Metropolitan Area Segregation
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Table 1.

Dimensions of Metropolitan Area Segregation

DIMENSIONS OF SEGREGATION

One of the challenges in understanding the potential effect of segregation on academic achievement patterns is that there are many different aspects of segregation, each of which might affect achievement through a different set of mechanisms. In this paper, I consider four dimensions of segregation. First is the distinction between residential and school segregation (which I call here the context dimension). Second, is the distinction between between-district and between-school or between-neighborhood segregation (the scale dimension). Third is the distinction between absolute and relative segregation (the exposure/unevenness dimension). And fourth is the distinction between racial and socioeconomic composition as the key population characteristics through which segregation affects students (the composition dimension). In this section, I discuss these different dimensions in some detail.

Table 1 illustrates that the intersection of these four dimensions give rise to sixteen possible features of segregation that may affect students. The columns of table 1 distinguish the context (school or residential) and scale (between-school or between-district) dimensions; the rows distinguish the exposure/evenness (exposure or differences in exposure) and composition (racial or socioeconomic composition) dimensions. It is worth noting that Coleman and his colleagues (1966) focused on the segregation dimensions represented in the far upper left of the table—measures of student exposure to black and poor schoolmates. The Coleman Report did not attend to residential segregation, to the distinction between between-school and between-district segregation, or to measures of unevenness.

The Context Dimension: Residential and School Segregation

Both residential and school segregation might independently affect students. If, in segregated school systems, schools’ racial composition and quality are correlated, then school segregation will lead to racial achievement gaps. Certainly there is considerable evidence indicating that white, black, and Hispanic students’ schools often differ in important ways (Hanushek and Rivkin 2007; Johnson 2011; Kozol 1991; Lankford, Loeb, and Wycoff 2002). Owing to residential segregation—by which I mean the patterns of where children live, as opposed to which school they attend—white and black or Hispanic children live in different neighborhoods. Because neighborhood conditions appear to affect children’s cognitive development and long-term educational outcomes (Burdick-Will et al. 2011; Chetty, Hendren, and Katz 2016; Sampson, Sharkey, and Raudenbush 2008; Sharkey 2010; Wodtke, Harding, and Elwert 2011), residential segregation may lead to achievement gaps and other forms of educational disparities if it causes children of different races to live in systematically higher-and lower-quality neighborhoods.

Because school and residential segregation are linked (many children attend schools near their homes) and because school and neighborhood [End Page 36] quality are linked (schools in communities with abundant resources can draw on those resources in ways that schools in poor communities cannot), it is not clear whether school or residential segregation patterns are most important in shaping achievement gaps. If school quality is the key factor shaping schooling outcomes, then residential segregation may matter only to the extent that it leads to school segregation. On the other hand, if neighborhood conditions in early childhood lead to hard-to-change patterns of inequality in school readiness, then school segregation may matter little, net of residential segregation. Or it may be that both neighborhood and school segregation contribute independently to academic achievement gaps.

The Scale Dimension: Distinguishing Between-School and Between-Neighborhood Segregation from Between-District Segregation

The overall residential or school segregation of a population (a metropolitan area, for example) can be thought of as the sum of two distinct organizational and geographic components: between-and within-district segregation. Most metropolitan areas contain multiple school districts (sometimes only a few, but often dozens or more). In the average metropolitan area, roughly two-thirds of between-school racial segregation is due to differences in the racial composition of school districts (Reardon, Yun, and Eitle 2000; Stroub and Richards 2013); the same is true of residential segregation (Bischoff 2008). There is considerable variation, however, in the proportions of both school segregation and residential segregation that lie between districts.

It is not clear how the scale of segregation is related to patterns of educational outcomes. Consider two metropolitan areas with the same level of total between-school segregation; suppose that in one all of the segregation is due to between-district segregation (within each district, all schools have equal racial composition), while in the other all of the segregation is due to within-district segregation (all districts have an equal racial composition but are internally segregated). Depending on the processes that link segregation to students’ opportunities to learn, we might expect one or the other to have larger achievement gaps.

Between-district segregation may be particularly consequential for achievement gaps because there are often substantial differences in school and community resources among school districts. If racial between-district segregation is linked to disparities in either the quality of school districts or the availability of other municipal or community resources that benefit children, then between-district segregation may lead to large achievement gaps. And if school resources and learning opportunities are relatively evenly distributed within school districts (for example, if a district provides equal funding for all schools and randomly assigns teachers to schools, and if municipalities randomly assign spaces in high-quality publicly funded preschools regardless of where in the city a child lives), then within-district segregation patterns might matter less.

On the other hand, if the effects of segregation are largely driven by processes at the school level—for example, if schools’ ability to attract and retain the most skilled teachers is largely driven by their racial and socioeconomic composition, regardless of their district characteristics—then total segregation may be more important in driving achievement patterns than between-district segregation. More generally, if resources are allocated unevenly among schools and neighborhoods in ways that are correlated with racial composition, and if these allocation processes operate within districts as strongly as they do between districts, then the organizational scale of segregation will be less important than total segregation.

Exposure and Unevenness

Segregation is generally measured in one of two ways. First are exposure measures (sometimes called isolation measures), which describe the average racial or socioeconomic composition of the schools or neighborhoods of children of a given race. For example, the average proportion of students in a black student’s school (or neighborhood) who are black is a measure of the racial isolation of black children. The average proportion of poor children in the black students’ schools or neighborhoods [End Page 37] is likewise an exposure measure. Second are evenness (or unevenness) measures, which describe the difference in the average racial or socioeconomic composition of schools or neighborhoods between children of different races. That is, exposure measures describe the average contexts of children of a given race, and unevenness measures describe the difference in average contexts between two racial groups: unevenness measures can be thought of as simply differences in exposure measures. For example, if the average black student enrolls in a school where 60 percent of the students are poor, black exposure to poverty will be 0.60—a very high exposure to poverty. But if the average white student in the same school district is also enrolled in a school where 60 percent of students are poor, the unevenness in exposure to poverty will be zero.

If the racial or socioeconomic composition of schools or neighborhoods affects students of all races equally, then unevenness measures of segregation should be more strongly associated with achievement gaps than black or Hispanic exposure measures. But if attending a high-poverty school or living in a high-poverty neighborhood is harmful for black and Hispanic students but not for white students (perhaps because white students have access to other resources that buffer them against any negative effects of high-poverty contexts), then the exposure of black students to poor school-mates and neighbors may be more strongly associated with achievement gaps than the black-white difference in such exposure. In other words, if school composition (and the factors associated with it) affects white and black students equally, then the composition of black students’ schools (exposure) will be associated with achievement gaps only to the extent that black and white students’ schools differ, on average, in composition.

The Composition Dimension: Racial and Socioeconomic Contexts

As noted earlier, both the Coleman Report and other studies find that both the racial and socioeconomic composition of schools are strongly related to student outcomes. The distinction between segregation processes that operate through racial composition per se and those that operate through other processes that are correlated with racial composition is important, though difficult to disentangle. Given the correlation between race and socioeconomic status, children in predominantly black or Hispanic schools and neighborhoods are typically exposed to much higher poverty levels than those in predominantly white schools. Indeed, the black-white and Hispanic-white difference in exposure to poverty is generally much greater than would be predicted based on racial differences in family income alone: even middle-class black and Hispanic children live in neighborhoods and attend schools with higher poverty rates than most poor white children (Reardon, Fox, and Townsend 2015; Saporito and Sohoni 2007). As a result, schools with high proportions of black students tend also to be schools with high proportions of poor students. Nonetheless, the correlation is not perfect, and it would be useful to know whether it is exposure to minority students or exposure to poverty that is more strongly predictive of achievement gaps.

ANALYTIC STRATEGY

This discussion suggests that many or all of the sixteen types of segregation defined in table 1 may be related to achievement patterns. The goal of this paper is to investigate which of these dimensions are most strongly predictive of racial achievement gaps. My strategy will be to measure achievement gaps and each of the sixteen types of segregation in metropolitan areas of the United States and then to assess the correlation of each measure with achievement gaps, both with and without a set of control variables. This analysis cannot determine the effect of any specific dimension of segregation (nor their aggregate effect). It does, nonetheless, provide detailed descriptive information about the relative strength of association between segregation measures and achievement gaps and so is useful for guiding future analyses and providing a set of stylized facts that a model of segregation’s effects should be able to explain.

The one study I am aware of that is similar to this is David Card and Jesse Rothstein’s (2007) study of the relationship between achievement gaps on the SAT and patterns of residential and [End Page 38] school segregation. That study finds that residential segregation is at least as strong a predictor of racial achievement gaps as school segregation, or even stronger. Moreover, the analyses suggest that the association between residential segregation and achievement gaps is driven largely by black-white differences in neighborhood income levels: in metropolitan areas where black children live in much poorer neighborhoods than white children, achievement gaps tend to be larger. The Card and Rothstein (2007) study is quite valuable but has several shortcomings relative to my purpose here. First, it relies on SAT tests, which are not taken by all students. Although Card and Rothstein use a selection model to adjust for differences in SAT-taking rates, this relies on a set of assumptions that cannot be verified and so may be subject to bias. Second, the Card and Rothstein analysis does not examine all the dimensions of segregation that I do here. In particular, they do not consider between-district segregation or exposure measures of segregation. And third, I examine both black-white and Hispanic-white segregation and achievement gap patterns; their analysis is restricted to black-white achievement gaps.

DATA

Achievement Gap Data

I use students’ state accountability test scores in grades 3 through 8 in the years 2009 to 2012 in every public school district in the United States. These data were provided by the National Center for Education Statistics under a restricted data use license. The data include, for each public school district in the United States, counts of students scoring at each of several academic proficiency levels (often labeled something like “Below Basic,” “Basic,” “Proficient,” and “Advanced”). These counts are disaggregated by race (here I use counts of non-Hispanic white, non-Hispanic black, and Hispanic students), grade (grades 3 to 8), test subject (math and English language arts), and year (school years 2008–2009 through 2011– 2012). I combine the proficiency counts in charter schools with those of the public school district in which they are formally chartered or, if not chartered by a district, in the district in which they are physically located. Thus, a “school district” includes students in all local charter schools as well as in traditional public schools.

There are 384 metropolitan areas and roughly 12,200 school districts serving grades 3 to 8 in the United States. To construct metropolitan area achievement gaps, I aggregate data from all public school districts (including their charter schools) within a given metropolitan area, so long as the metropolitan area falls entirely within a single state. Because districts in different states use different achievement tests, proficiency categories in different states are not comparable, so I cannot construct aggregated data for the 45 (of 384) metropolitan areas that cross state boundaries. The 339 metropolitan areas that do not cross state boundaries include 81 percent of black and 92 percent of Hispanic public school students in grades 3 to 8 in metropolitan areas (and 69 percent and 79 percent of black and Hispanic students in the United States).

The data span six grades, two subjects, and four years, making a total of 16,272 possible metropolitan area–grade–subject–year combinations (in the 339 metropolitan areas). Several states do not have sufficient data to compute achievement gaps in some years. (Nebraska and Wyoming are both missing one or more years of data.) In addition, some metropolitan areas have too few minority students to reliably estimate achievement gaps: I exclude cells with fewer than 20 white or 20 black/Hispanic students. After excluding cells with too few students, I am able to estimate white-black and white-Hispanic achievement gaps in at least one grade-year-subject for all but a few metropolitan areas. In total, the sample includes roughly 14,200 white-black and white-Hispanic metropolitan area achievement gaps, an average of roughly 42 gaps per area.

I estimate achievement gaps in each metropolitan area using the methods described by Andrew Ho and myself (Ho and Reardon 2012; Reardon and Ho 2015). The achievement gaps are measured using the V-statistic, which measures the difference between two distributions in pooled standard deviation units. The advantage of V is that it relies only on the ordered nature of test scores, which allows comparability [End Page 39] of gap estimates across tests that measure achievement in on different scales. Given that the data include achievement measured on roughly 600 different standardized tests (typically one for each state-grade-subject combination, sometimes with variation across years), this comparability is a key feature of the V-statistic for measuring gaps.

Measures of Segregation

I compute thirty-two measures of segregation for each metropolitan area (sixteen for white-black segregation and sixteen for white-Hispanic segregation), corresponding to the sixteen cells of table 1. School segregation measures are computed from 2008–2009, 2009–2010, and 2010–2011 enrollment data from the Common Core of Data (CCD), which includes racial composition and counts of students by free-or reduced-price-lunch eligibility status for every public school and district in the United States. Residential segregation measures are computed from 2006–2010 American Community Survey (ACS) data, which include racial composition and poverty rates for each census tract in the United States.

The exposure measures are computed by averaging school, district, or census tract racial composition or poverty rates within each metropolitan area, weighting by the number of black or Hispanic students in the school, district, or tract, as appropriate. The unevenness measures are simply the difference in black (or Hispanic) and white students’ exposure-relevant measures. Because the ACS and CCD data are based on full population counts (in CCD) or on large samples pooled every five years (in ACS), the segregation measures are very precise.

Not surprisingly, the sixteen segregation measures are correlated, often quite highly, with one another (see appendix tables A1 and A2). Nonetheless, in some cases the correlations are quite modest, suggesting that we may be able to distinguish their associations with achievement gaps.

Additional Covariates

I include a set of additional variables as controls in some of the models shown here. The controls are constructed from CCD data and School District Demographic System (SDDS) data. The SDDS is a special tabulation of the 2006–2010 ACS data that includes tabulations of the demographic characteristics of the families living in each school district who have children enrolled in the public schools. I aggregate these to the metropolitan-area level and construct measures of family socioeconomic characteristics (income inequality, median family income, parental educational attainment, occupational status, poverty rates, unemployment rates, single-parent household rates, home value and median rent, racial disparities in family socioeconomic characteristics, and racial composition); in each case these measures apply to families in the metropolitan area with children enrolled in public schools. From the CCD, I construct a measure of metropolitan-area school district fragmentation. This is the Herfindahl index applied to school district enrollment; it measures the degree to which students are concentrated in a small number of large districts or dispersed among many small districts, and it has been shown to be related to between-district segregation patterns (Bischoff 2008; Reardon and Yun 2001). From the CCD, I also include a measure of metropolitan-area average per-pupil public school spending. These variables are used in controls in some of the models shown here. Because some of the SDDS-based measures are not available for all metropolitan areas, I limit all analyses here to those with complete data on all measures: 311 metropolitan areas for white-black gap analyses and 318 for the white-Hispanic gap analyses.

BIVARIATE AND PARTIAL CORRELATIONS BETWEEN SEGREGATION AND ACHIEVEMENT GAPS

To begin, I examine the bivariate correlations among various segregation measures and racial achievement gaps. Table 2 reports the correlation of each of the sixteen segregation measures with the white-black achievement gap. Note that almost all of the segregation measures are positively correlated with the achievement gap. However, the correlations range from 0.013 to 0.628. Table 2 makes clear several patterns. First, each measure of school segregation [End Page 40] is more highly correlated with achievement gaps than the corresponding measure of residential segregation. Second, in every case, segregation among schools or census tracts is more correlated with achievement gaps than is segregation between school districts. Third, racial differences in exposure to black or poor schoolmates or neighbors are more strongly related to achievement gaps than is simple exposure, though this pattern holds more consistently for exposure to poverty than for racial exposure. Fourth, although achievement gaps are more highly correlated with black students’ exposure to other black students or neighbors than with exposure to poor schoolmates or neighbors, this pattern is reversed when we consider the association between achievement gaps and racial differences in exposure to black or poor peers. The bottom panel of table 2 shows that differences in exposure to poverty are more strongly correlated with achievement gaps than are differences in exposure to same-race peers.

Table 2. Bivariate Correlations Between the White-Black Achievement Gap and Various Dimensions of Segregation, 311 Metropolitan Areas, 2009–2012
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Table 2.

Bivariate Correlations Between the White-Black Achievement Gap and Various Dimensions of Segregation, 311 Metropolitan Areas, 2009–2012

Table 3. Bivariate Correlations Between the White-Hispanic Achievement Gap and Various Dimensions of Segregation, 318 Metropolitan Areas, 2009–2012
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Table 3.

Bivariate Correlations Between the White-Hispanic Achievement Gap and Various Dimensions of Segregation, 318 Metropolitan Areas, 2009–2012

Table 3 shows the corresponding correlations [End Page 41] between white-Hispanic achievement gaps and the measure of Hispanic students’ segregation. The magnitude of the correlations is roughly similar to those in table 2, except for the correlations with differences in exposure to Hispanic neighbors and schoolmates, where the correlations with white-Hispanic gaps are larger than those in table 2. Likewise, the general pattern of correlations is similar.

Table 4. Partial Correlations Between the White-Black Achievement Gap and Various Dimensions of Segregation, 311 Metropolitan Areas, 2009–2012
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Table 4.

Partial Correlations Between the White-Black Achievement Gap and Various Dimensions of Segregation, 311 Metropolitan Areas, 2009–2012

With only a few exceptions then, the bivariate correlations follow a clear pattern: achievement gaps are more highly correlated with school segregation than residential segregation; more highly correlated with segregation among schools and tracts than among districts; and more highly correlated with differences in exposure to poor or same-race school-mates or neighbors than with simple exposure measures. The measure of segregation most highly correlated with the metropolitan-area achievement gap is the racial difference in students’ exposure to poor schoolmates (white-black r = 0.628; white-Hispanic r = 0.678).

I next examine the partial correlations between achievement gaps and measures of segregation, conditional on a set of metropolitan-area characteristics. For the exposure measures, I control for racial differences in family socioeconomic characteristics in the metropolitan area and the fragmentation of the metropolitan area. I do not include measures of the racial or socioeconomic composition of the metropolitan area because these are mechanically related to the exposure measures (all else being equal, black students will have more black schoolmates in a predominantly black metropolitan area); their inclusion in the model would change the interpretation of the coefficient on the exposure measure to be similar to that of the differential exposure measures. The coefficients would indicate the extent to which achievement gaps are larger, on average, in metropolitan areas where black students attend schools with more black schoolmates than would be expected given the racial composition of the metropolitan-area public school population. This is essentially what the evenness segregation measures capture. To preserve the interpretation of the exposure measure coefficients, then, I do not include covariates indicating the racial or socioeconomic composition of the metropolitan area in computing the partial correlations in the top panels of tables 4 and 5. [End Page 42]

Table 5. Partial Correlations Between the White-Hispanic Achievement Gap and Various Dimensions of Segregation, 318 Metropolitan Areas, 2009–2012
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Table 5.

Partial Correlations Between the White-Hispanic Achievement Gap and Various Dimensions of Segregation, 318 Metropolitan Areas, 2009–2012

I do include such measures, however, in the models for the bottom panels. Here the segregation measures are not mechanically related to composition (that is the virtue of the evenness measures), so the composition measures can be used as controls without altering the interpretation of the coefficients on the segregation measures. Therefore, the estimates in the bottom panels control for metropolitan-area racial composition, family socioeconomic characteristics, racial differences in these characteristics, metropolitan fragmentation, and metropolitan-area average per-pupil public school spending.

Table 4 reports these partial correlations for the white-black achievement gaps. In general, the partial correlations are weaker than the bivariate correlations. This is particularly true in the second row of table 4: after controlling for racial differences in family socioeconomic characteristics, measures of black students’ exposure to poor schoolmates or neighbors are at best only very weakly correlated with achievement gaps. The correlations with the unevenness measures of segregation are generally about 10 to 30 percent smaller than the uncontrolled correlations in table 2. They are modest in size but not trivial, ranging from roughly 0.18 to 0.51. Just as in table 2, the largest correlation is the correlation with racial differences in exposure to poor schoolmates (r = 0.509).

Table 5 reports the analogous correlations of the segregation measures and the white-Hispanic achievement gap. Here the partial correlations with exposure to Hispanic school-mates or neighbors are not statistically different from zero. Interestingly, white-Hispanic achievement gaps are negatively correlated with Hispanic students’ exposure to poor peers and neighbors. This correlation reverses, however, in the bottom panel of the table once the models include metropolitan-area racial and socioeconomic composition measures. Thus, the negative correlations with exposure to poverty may simply reflect a correlation between achievement gaps and overall poverty rates.

In the bottom panel of table 5, white-Hispanic achievement gaps remain correlated with differences in exposure to poverty after controlling for metropolitan socioeconomic characteristics and composition in addition to racial socioeconomic disparities. Nonetheless, the correlations are only modest in size and [End Page 43] are considerably smaller than their counterparts in table 4.

Tables 4 and 5 together reveal a clear pattern: net of a set of key covariates, achievement gaps are more highly correlated with school segregation than residential segregation; they are more highly correlated with segregation among schools and tracts than among districts; and they are generally more highly correlated with differences in exposure to poor or same-race schoolmates and neighbors than with simple exposure measures (though the last point is not true of exposure to black students or neighbors in table 4). Net of the set of covariates in the models, the racial difference in students’ exposure to poor schoolmates remains the measure of segregation most highly correlated with metropolitan-area achievement gaps (white-black r = 0.509; white-Hispanic r = 0.357).

DISENTANGLING MULTIPLE ASPECTS OF SEGREGATION

The bivariate and partial correlations in tables 2 through 5 are useful for assessing whether segregation measures are associated with achievement gaps, net of a vector of metropolitan-area socioeconomic conditions and disparities. But because the segregation measures are correlated with one another (see appendix tables A1 and A2), the individual correlations do not indicate which of the segregation dimensions are most important.

To investigate the relative importance of the different dimensions of segregation, I regress achievement gaps on various measures of segregation, controlling for the full set of metropolitan-area covariates included in the bottom panels of tables 4 and 5. In these models, I include various combinations of the differential exposure segregation measures; I exclude the simple exposure measures because, as noted earlier, they are mechanically related to the other measures once racial and socioeconomic composition are included in the models.

Tables 6 and 7 display selected coefficients from a series of models designed to isolate the primary dimensions of segregation driving the general association between segregation and achievement gaps. Each model includes the metropolitan-area covariates described earlier. The first column (model 0) simply reports the R-squared statistic from the model that includes the covariates but none of the segregation measures (R2 = 0.66 in the white-black model; R2 = 0.72 in the white-Hispanic model). Model 1 includes the four between-district segregation measures; model 2 includes the four total segregation measures (between-school enrollment segregation and between-tract residential segregation); model 3 includes all eight measures.

Below the coefficients are the p-values from a set of hypothesis tests. The first tests the null hypothesis that the coefficients on the residential segregation terms in the model are all equal to zero (that is, the coefficients in the rows labeled b, d, f, and h in the table are all zero). The second tests the hypothesis that the school segregation terms are all nonsignificant. The third and fourth test the hypotheses that the four between-district terms are all nonsignificant and that the four total segregation terms are all nonsignificant, respectively. The fifth tests that the coefficients on the four racial exposure terms are zero; the sixth tests that those on the four poverty exposure terms are all zero. The seventh tests the hypothesis that all of the terms other than the two describing the differential exposure to poor school-or districtmates are zero. The final tests the null hypothesis that all the coefficients except that on the differential exposure to poor school-mates are zero. This effectively tests whether that one measure of segregation contains all the predictive power of the full set of eight measures.

The coefficients and hypothesis tests in tables 6 and 7 tell a very consistent story. In each model, we cannot reject the null hypothesis that the residential segregation terms are not predictive of achievement gaps, conditional on the school segregation terms. We can, however, reject the opposite hypothesis (that school segregation is uninformative, conditional on residential segregation). In other words, the segregation of schools is predictive of achievement gaps; net of that, variation in neighborhood segregation patterns is not correlated with achievement gaps.

In the Hispanic-white models (table 7), we [End Page 44]

Table 6. Coefficient Estimates and Hypothesis Tests from Multivariate Regression Models of the Association Between the White-Black Achievement Gap and Segregation, 311 Metropolitan Areas, 2009–2012
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Table 6.

Coefficient Estimates and Hypothesis Tests from Multivariate Regression Models of the Association Between the White-Black Achievement Gap and Segregation, 311 Metropolitan Areas, 2009–2012

[End Page 45]

Table 7. Coefficient Estimates and Hypothesis Tests from Multivariate Regression Models of the Association Between the White-Hispanic Achievement Gap and Segregation, 318 Metropolitan Areas, 2009–2012
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Table 7.

Coefficient Estimates and Hypothesis Tests from Multivariate Regression Models of the Association Between the White-Hispanic Achievement Gap and Segregation, 318 Metropolitan Areas, 2009–2012

[End Page 46]

cannot reject the null hypothesis that between-district segregation (whether residential or school segregation) is nonpredictive once we include measures of total between-school and between-tract segregation in the model. In the black-white models (table 6), however, the hypothesis test suggests some association between between-district segregation and gaps, net of total segregation (p = 0.045). In both tables, however, we reject the opposite hypothesis: total district segregation measures are predictive of achievement gaps, net of between-district segregation (p < 0.001). Although there is some evidence that between-district segregation is independently associated with white-black achievement gaps, the magnitude of this association is small relative to the association with total segregation.

The p-values from the fifth and sixth hypothesis tests show that differential exposure to same-race schoolmates and neighbors is not predictive of white-Hispanic achievement gaps (p = 0.499) and is modestly associated with white-black gaps (p = 0.032), conditional on differential exposure to poverty. Differential exposure to poor schoolmates and neighbors is predictive, however, conditional on racial exposure patterns (p < 0.001).

Together the first six hypothesis tests strongly suggest that differential exposure to poor schoolmates is the key dimension of segregation associated with racial achievement gaps. The seventh hypothesis test indicates whether excluding the four residential segregation measures and the two measures of exposure to same-race schoolmates reduces the fit of the model. In the white-Hispanic models (table 7), we fail to reject the hypothesis that all six of those terms can be excluded from model 3 (p = 0.572). In the white-black models (table 6), however, these six terms do carry a very small amount of predictive power (p = 0.045); a comparison of the adjusted R-squareds from models 3 and 4 in table 6, however, shows that adding these six terms to the model increases the R-squared by only 0.01.

In both the white-black and white-Hispanic models, we also fail to reject the hypothesis (hypothesis 8) that seven of the eight terms can be excluded (all but the measure of differential exposure to school poverty) from the model. Models 4 and 5 include only the differential exposure to poor school-and districtmates measures. The district-level measure is not significant in model 4, leaving model 5 as the preferred model.

DISCUSSION

The results of these descriptive analyses are unequivocal. Racial segregation is strongly associated with racial achievement gaps, and the racial difference in the proportion of students’ schoolmates who are poor is the key dimension of segregation driving this association. Conditional on that measure, the other measures in tables 6 and 7 collectively explain no additional variance in achievement gaps. The adjusted R-squareds are nearly identical in model 5 and model 3 (which includes seven additional measures of segregation).

The coefficients on the difference in exposure to poor schoolmates in model 5 in tables 6 and 7 are relatively large. To get a sense of their magnitude, consider figure 1, which shows that in some metropolitan areas there is no difference in exposure to poor school-mates between black or Hispanic and white students, while in others the difference is as high as 40 percent. The coefficients in tables 6 and 7 imply that a 40 percent difference in exposure to poverty corresponds to a roughly 0.30-or 0.23-standard-deviation increase in the white-black and white-Hispanic achievement gap, respectively, relative to a metropolitan area where there is no racial difference in exposure to poverty. In the average metropolitan area, the racial difference in exposure to poverty is roughly twenty percentage points, corresponding to an achievement gap of 0.12 to 0.15. This implies that racial segregation—specifically racial differences in exposure to poverty—accounts for roughly one-fifth of the average racial achievement gap.

What should we make of these findings? First, it is important to reiterate that the coefficients in tables 4 to 7 should not be interpreted causally. They do not imply that reducing segregation will reduce achievement gaps. The models here simply provide evidence that segregation—specifically segregation that produces racial differences in exposure to poor schoolmates—is strongly correlated with [End Page 47]

Figure 1. Exposure to Poor and Minority Schoolmates, by Race, U.S. Metropolitan Areas, 2009–2012 Source: Author’s calculations.
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Figure 1.

Exposure to Poor and Minority Schoolmates, by Race, U.S. Metropolitan Areas, 2009–2012

Source: Author’s calculations.

achievement gaps net of a wide range of covariates that are strongly related to achievement gaps, including racial disparities in family income, poverty rates, unemployment rates, and parental education. In metropolitan areas where racial segregation is higher than predicted from racial disparities in socioeconomic conditions, achievement gaps are, on average, significantly larger. While that is certainly suggestive of a causal link between segregation and achievement gaps, the correlation might arise from mechanisms other than segregation. One might imagine, for example, that metropolitan areas that are more segregated than expected are those in which racial prejudice and discrimination are particularly high in general; if such discrimination affects students’ opportunity through some mechanism other than segregation, this might explain the observed association between segregation and achievement gaps. Additionally, there may be racial-ethnic differences in family background —such as differences in wealth, immigration history and experiences, or English fluency— that are not captured by our measures of socioeconomic status but that lead to both segregation and to differences in academic achievement patterns. Again, this might account [End Page 48] for the observed correlation of segregation with achievement gaps. The association between segregation and achievement gaps is large, however, even after controlling for a number of measures of socioeconomic disparities, so such alternative pathways would need to lead to sizable effects on achievement gaps. Thus, the results presented here are suggestive of powerful effects of segregation, but are not definitive.

Second, the pattern of results here strongly suggests that the mechanisms through which segregation is related to achievement gaps are related to differences in students’ exposure to poor schoolmates. The greater the difference in poverty rates in white and black students’ schools, the larger the achievement gap, on average. There are a number of potential explanations for this pattern. One is that a school’s poverty rate is a proxy for general school quality—quality of instruction and opportunities to learn. High-poverty schools may have fewer resources, a harder time attracting and retaining skilled teachers, more violence and disruption, and poorer facilities. Additionally, the parents of students in such schools generally have fewer resources—economic, social, and political—that can be used to benefit their children’s schools.

Another possibility is that exposure to poor schoolmates affects students’ learning and academic performance through some direct or indirect form of peer influence. For example, high-poverty schools, because they typically have more low-performing students than do schools with fewer poor students, may typically offer less advanced curricula than low-poverty schools. In a classroom where most students’ skills are well below grade level, students—even those whose skills are at grade level—are therefore unlikely to encounter challenging curricula and instruction. In this way, having low-performing schoolmates may limit one’s own learning because it alters instructional and social processes in the classroom. The data here do not speak to which, if any, of these processes drive the association between school poverty and academic achievement, of course; there are clearly many such potential mechanisms. Nonetheless, the estimates imply a strong association between school poverty and school quality (where school quality is understood to encompass the full set of instructional, parental, and peer resources in a school).

Indeed, another way of assessing the magnitude of the coefficients in tables 6 and 7 is to think of them simply as estimates of the association between school poverty rates and average achievement levels, controlling for students’ family socioeconomic background and race. To see this, note that my estimates here are akin to those that would be obtained from a metropolitan-area fixed-effects model that estimates the average within-race and within-metropolitan-area association between academic achievement and average exposure to poverty, controlling for other measures of family socioeconomic status and school composition.1 The results here therefore are consistent with a model in which high-poverty schools are, on average, less effective at promoting achievement than lower-poverty schools. The coefficient of 0.75 on the racial difference in exposure to poverty measure in model 5 of table 6, then, implies that a ten-percentage-point difference in school poverty rates is associated with an average difference of 0.075 standard deviations of student achievement. In metropolitan areas where black or Hispanic students disproportionately attend high-poverty schools, then, achievement gaps tend to be larger.

Third, the results here suggest that residential segregation is not associated with racial achievement gaps, once we take into account family socioeconomic characteristics [End Page 49] and school segregation patterns. This appears somewhat at odds with Card and Rothstein’s (2007) finding that black-white differences in poor neighbors were the key mechanism driving the association between segregation and racial achievement gaps. However, Card and Rothstein did not include differential exposure to both poor schoolmates and poor neighbors in their models simultaneously. When I include both in the model (see model 2 in tables 6 and 7), I find that school differences in exposure to poverty are strong predictors of achievement gaps, while residential differences in exposure to poverty are not statistically significant predictors. (In models not shown, I replicate the Card and Rothstein models; I find that neighborhood differential exposure to poverty is a strong predictor of achievement gaps if school differential exposure to poverty is not in the model, consistent with their results.) This suggests that Card and Rothstein’s conclusion might have been different had they included both terms in their models. Nonetheless, both their findings and mine here suggest that racial segregation may matter most when coupled with large differences in white and minority students’ exposure to poverty.

Does this mean that residential segregation is inconsequential for academic achievement? No. Residential segregation may contribute to achievement gaps primarily through its effect on school segregation patterns. As tables A1 and A2 show, racial differences in exposure to poor schoolmates are strongly correlated (0.78 and 0.72, respectively, in the black-white and Hispanic-white cases) with racial differences in poor neighbors. This is not surprising, given that most students attend schools relatively close to home; residential segregation is a key factor shaping school segregation patterns. Thus, residential segregation—particularly racial differences in exposure to neighborhood poverty—may affect achievement patterns (for evidence that neighborhood poverty affects long-term educational outcomes, see, for example, Chetty, Hendren, and Katz 2016), but it may do so primarily by leading to differences in school quality.

Finally, does the importance of racial differences in exposure to poverty imply that we should not worry about racial segregation per se? One might read tables 6 and 7 and conclude that racial differences in exposure to white and minority schoolmates and neighbors do not appear to affect achievement gaps. Does this mean that we should abandon Brown and efforts toward racial integration and focus instead on the socioeconomic integration of schools, as some have suggested (see Kahlenberg 2006)?

It does not. The data clearly show an association between racial school segregation and achievement gaps, net of many socioeconomic differences between white and minority families (see row 3 of tables 4 and 5). Tables 6 and 7 do not undermine this; rather, they show that the association between racial segregation and achievement gaps is driven by the strong association between racial segregation per se and racial differences in school poverty. Indeed, the correlation between racial differences in exposure to minority schoolmates and racial differences in exposure to poor schoolmates is roughly 0.80 (see appendix tables A1 and A2, row 14, column 10); in metropolitan areas where black and Hispanic students disproportionately attend schools with same-race school-mates, they also disproportionately attend schools with poor schoolmates. This is a result of (a) the fact that poverty rates are much higher among black and Hispanic students; (b) patterns of residential segregation that concentrate black and Hispanic students in much poorer neighborhoods than even equally poor white students (Logan 2011; Pattillo 2013; Reardon, Fox, and Townsend 2015; Sharkey 2014); and (c) school assignment and school choice policies that further isolate poor and minority students (Saporito and Sohoni 2006, 2007). Given the large differences in poverty rates between white and black families and patterns of residential segregation, there is no feasible way of eliminating racial disparities in school poverty without substantially reducing racial segregation per se. Moreover, race-specific integration policies may be the most effective way of eliminating racial disparities in school poverty. Income integration policies are rare in the United States and have produced little racial integration even in the few instances where they have been implemented (Reardon, Yun, and Kurlaender 2006; Reardon and Rhodes 2011 [End Page 50] ). In sum, racial integration policies remain essential for reducing racial disparities in school poverty rates.

Moreover, racial segregation per se may affect outcomes other than academic achievement gaps. In Brown, the Court was concerned about the psychological harms of racial segregation, not about its effects on academic achievement. Nothing in the results presented here should be construed as demonstrating that there are no direct harms from racial isolation. It is certainly possible that de facto racial segregation, even in the absence of de jure segregation and differences in exposure to poverty, may damage minority students’ self-concept in the ways documented by Kenneth and Mamie Clark and others cited in the Brown decision (Clark and Clark 1939a, 1939b, 1950; Deutscher, Chein, and Sadigur 1948). It may also lead to lower between-group understanding and empathy and increased prejudice (Pettigrew and Tropp 2006). It may degrade students’ ability to collaborate in diverse settings and hamper the collective functioning of a democratic society (Page 2008). It may lead to segregated social networks that persist long beyond high school and create unequal opportunities in the labor market and unequal access to social and political capital. My finding here that racial segregation per se is not independently associated with academic achievement gaps, net of racial differences in exposure to poverty, does not rule out these many other potential consequences of racial isolation.

This study is not new in identifying a strong association between racial segregation and academic achievement gaps. It does, however, provide a much sharper description of the features of segregation patterns that are most strongly predictive of academic achievement gaps. The evidence here very clearly shows that racial differences in exposure to poor schoolmates is linked to achievement gaps. Black and Hispanic students’ test scores, relative to whites’, are much lower when black and Hispanic students attend schools with more poor schoolmates. Reducing school segregation—in particular, reducing racial disparities in exposure to poor schoolmates—may therefore be an effective means of improving the equality of students’ access to high-quality educational opportunities. [End Page 51]

Sean F. Reardon

Sean F. Reardon is endowed professor of poverty and inequality in education at Stanford University.

Direct correspondence to: Sean F. Reardon at sean.reardon@stanford.edu, 520 CERAS Building, no. 526, Stanford University, Stanford, CA 94305.

Appendix

Table A1. Correlation Matrix of Metropolitan-Area Black-White Segregation Measures, 311 Metropolitan Areas, 2009–2012
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Table A1.

Correlation Matrix of Metropolitan-Area Black-White Segregation Measures, 311 Metropolitan Areas, 2009–2012

[End Page 53]

Table A2. Correlation Matrix of Metropolitan-Area Hispanic-White Segregation Measures, 318 Metropolitan Areas, 2009–2012
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Table A2.

Correlation Matrix of Metropolitan-Area Hispanic-White Segregation Measures, 318 Metropolitan Areas, 2009–2012

[End Page 55]

REFERENCES

Bischoff, Kendra. 2008. “School District Fragmentation and Racial Residential Segregation: How Do Boundaries Matter?” Urban Affairs Review 44(2): 182–217.
Borman, Geoffrey D., and Maritza Dowling. 2010. “Schools and Inequality: A Multilevel Analysis of Coleman’s Equality of Educational Opportunity Data.” Teachers College Record 112(5): 1201–46.
Burdick-Will, Julia, Jens Ludwig, Stephen W. Raudenbush, Robert J. Sampson, Lisa Sanbonmatsu, and Patrick Sharkey. 2011. “Converging Evidence for Neighborhood Effects on Children’s Test Scores: An Experimental, Quasi-Experimental, and Observational Comparison.” In Whither Opportunity? Rising Inequality and the Uncertain Life Chances of Low-Income Children, edited by Greg J. Duncan and Richard J. Murnane. New York: Russell Sage Foundation.
Card, David, and Jesse Rothstein. 2007. “Racial Segregation and the Black-White Test Score Gap.” Journal of Public Economics 91(11): 2158–84.
Chetty, Raj, Nathaniel Hendren, and Lawrence F. Katz. 2016. “The Effects of Exposure to Better Neighborhoods on Children: New Evidence from the Moving to Opportunity Experiment.” American Economic Review 106(4): 855–902.
Clark, Kenneth B., and Mamie K. Clark. 1939a. “Segregation as a Factor in the Racial Identification of Negro Preschool Children: A Preliminary Report.” Journal of Experimental Education 8(2): 161–63.
———. 1939b. “The Development of Consciousness of Self and the Emergence of Racial Identification in Negro Preschool Children.” Journal of Social Psychology 10(4): 591–99.
———. 1950. “Emotional Factors in Racial Identification and Preference in Negro Children.” Journal of Negro Education 19(3): 341–50.
Coleman, James S., Ernest Q. Campbell, Carol J. Hobson, James McPartland, Alexander M. Mood, Frederick D. Weinfeld, and Robert L. York. 1966. Equality of Educational Opportunity. Washington: U.S. Department of Health, Education, and Welfare, Office of Education.
Deutscher, Max, Isidor Chein, and Natalie Sadigur. 1948. “The Psychological Effects of Enforced Segregation: A Survey of Social Science Opinion.” Journal of Psychology 26(2): 259–87.
Hanushek, Eric A., and Steven G. Rivkin. 2007. “School Quality and the Black-White Achievement Gap.” Working Paper 12651. Cambridge, Mass.: National Bureau of Economic Research.
Ho, Andrew D., and Sean F. Reardon. 2012. “Estimating Achievement Gaps from Test Scores Reported in Ordinal ‘Proficiency’ Categories.” Journal of Educational and Behavioral Statistics 37(4): 489–517.
Johnson, Rucker C. 2011. “Long-Run Impacts of School Desegregation and School Quality on Adult Attainments.” Working Paper 16664. Cambridge, Mass.: National Bureau of Economic Research.
Kahlenberg, Richard D. 2006. “A New Way on School Integration.” New York: The Century Foundation.
Kozol, Jonathan. 1991. Savage Inequalities: Children in America’s Schools. New York: Crown.
Lankford, Hamilton, Susanna Loeb, and James Wycoff. 2002. “Teacher Sorting and the Plight of Urban Schools: A Descriptive Analysis.” Educational Evaluation and Policy Analysis 24(1): 37–62.
Logan, John R. 2011. “Separate and Unequal: The Neighborhood Gap for Blacks, Hispanics, and Asians in Metropolitan America.” US 2010 Project: Brown University and Russell Sage Foundation. Providence, R.I.: Brown University.
Page, Scott E. 2008. The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies. Princeton, N.J.: Princeton University Press.
Pattillo, Mary. 2013. Black Picket Fences: Privilege and Peril Among the Black Middle Class. Chicago: University of Chicago Press.
Pettigrew, Thomas F., and Linda R. Tropp. 2006. “A Meta-analytic Test of Intergroup Contact Theory.” Journal of Personality and Social Psychology 90(5): 751.
Reardon, Sean F., Lindsay Fox, and Joseph Townsend. 2015. “Neighborhood Income Composition by Race and Income, 1990–2009.” Annals of the American Academy of Political and Social Science 660(1): 78–97.
Reardon, Sean F., and Andrew D. Ho. 2015. “Practical Issues in Estimating Achievement Gaps from Coarsened Data.” Journal of Educational and Behavioral Statistics 40(2): 158–89.
Reardon, Sean F., and Lori Rhodes. 2011. “The Effects of Socioeconomic School Integration Policies on Racial School Segregation.” in Integrating Schools in a Changing Society, edited by Erica [End Page 56] Frankenberg and Elizabeth DeBray. Chapel Hill: University of North Carolina Press.
Reardon, Sean F., and John T. Yun. 2001. “Suburban Racial Change and Suburban School Segregation, 1987–1995.” Sociology of Education 74(2): 79–101.
Reardon, Sean F., John T. Yun, and Tamela McNulty Eitle. 2000. “The Changing Structure of School Segregation: Measurement and Evidence of Multi-racial Metropolitan Area School Segregation, 1989–1995.” Demography 37(3): 351–64.
Reardon, Sean F., John T. Yun, and Michal Kurlaender. 2006. “Implications of Income-Based School Assignment Policies for Racial School Segregation.” Educational Evaluation and Policy Analysis 28(1): 49–75.
Sampson, Robert J., Patrick Sharkey, and Stephen W. Raudenbush. 2008. “Durable Effects of Concentrated Disadvantage on Verbal Ability Among African-American Children.” Proceedings of the National Academy of Sciences 105(3): 845–52.
Saporito, Salvatore, and Deneesh Sohoni. 2006. “Coloring Outside the Lines: Racial Segregation in Public Schools and Their Attendance Boundaries.” Sociology of Education 79(2): 81–105.
———. 2007. “Mapping Educational Inequality: Concentrations of Poverty Among Poor and Minority Students in Public Schools.” Social Forces 85(3): 1227–53.
Sharkey, Patrick. 2010. “The Acute Effect of Local Homicides on Children’s Cognitive Performance.” Proceedings of the National Academy of Sciences 107(26): 11733–38.
———. 2014. “Spatial Segmentation and the Black Middle Class.” American Journal of Sociology 119(4): 903–54.
Stroub, Kori J., and Meredith P. Richards. 2013. “From Resegregation to Reintegration: Trends in the Racial/Ethnic Segregation of Metropolitan Public Schools, 1993–2009.” American Educational Research Journal 50(3): 497–531.
Wodtke, Geoffrey T., David J. Harding, and Felix Elwert. 2011. “Neighborhood Effects in Temporal Perspective: The Impact of Long-Term Exposure to Concentrated Disadvantage on High School Graduation.” American Sociological Review 76(5): 713–36. [End Page 57]

The research described here was supported by grants from the Institute of Education Sciences (R305D110018) and the Spencer Foundation (201500058). The paper would not have been possible without the assistance of Ross Santy, who facilitated access to the data. This paper benefited substantially from ongoing collaboration with Andrew Ho, Demetra Kalogrides, and Kenneth Shores. Some of the data used in this paper were provided by the National Center for Education Statistics (NCES). The opinions expressed here are my own and do not represent the views of NCES, the Institute of Education Sciences, the Spencer Foundation, or the U.S. Department of Education.

Footnotes

1. To see this, note that a metropolitan-area fixed-effects model of the form Ymi = α(WHITEi) + β(SCHPOVi) + XiΓ + Δm + emi (where m indexes metropolitan areas, i indexes individuals, SCHPOVi is the poverty rate in student i’s school, and Xi is a vector of socioeconomic covariates) is the same as the model inline graphic (where the subscripts mw and mb indicate white and black populations in metropolitan area m). My models are similar to the latter form (though they differ in that they include additional metropolitan-area covariates). In either model, β is interpreted as the association between exposure to poverty and academic achievement.

Additional Information

ISSN
2377-8261
Print ISSN
2377-8253
Pages
34-57
Launched on MUSE
2016-10-21
Open Access
Yes
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