Separate When Equal? Racial Inequality and Residential Segregation

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1 Separate When Equal? Racial Inequality and Residential Segregation Patrick Bayer Hanming Fang Robert McMillan January 13, 2005 Abstract Conventional wisdom suggests that residential segregation will fall when racial di erences in education and other sociodemographics decline. This paper argues that this prediction may not be accurate. We identify, both theoretically and empirically, a forceful mechanism that may lead to persistent and even increasing residential segregation as racial di erences in sociodemographics decline. The key feature of the mechanism relates to the emergence of middle-class black neighborhoods as the sociodemographics of blacks improve. We show that, middle-class black neighborhoods are in short supply given the current black sociodemographics in many U.S. metropolitan areas, forcing wealthy blacks either to live in white neighborhoods with high levels of neighborhood amenities or in more black neighborhoods with lower amenity levels. Increases in black sociodemographics in the metropolitan areas will lead to the emergence of new middle-class black neighborhoods, relieving the prior neighborhood supply constraint and leading to increases in residential segregation. We present cross-msa evidence from the 2000 Census indicating that this mechanism does in fact operate: as the proportion of highly educated blacks in an MSA increases, the segregation of educated blacks, and all blacks more generally, goes up. We also present evidence against leading alternative hypotheses. Keywords: Segregation, Racial Sorting, Racial Inequality, Neighborhood Formation. JEL Classi cation Numbers: H0, J7, R0, R2. We are grateful to Caroline Hoxby, Kim Rueben, and Jacob Vigdor as well as conference/seminar participants at the NBER and Yale for helpful comments and suggestions. We are responsible for all remaining errors. Contact Addresses: Bayer and Fang are at the Department of Economics, Yale University, P.O. Box , New Haven, CT ; McMillan is at the Department of Economics, University of Toronto, 150 St. George Street, Toronto, Ontario M5S 3G7, Canada.

2 1 Introduction There is a large literature on the causes and consequences of racial segregation (Massey and Denton [22], Cutler and Glaeser [9], Cutler, Glaeser and Vigdor [10]). Many researchers have attempted to evaluate the contributions of various socioeconomic variables to the racial segregation. For example, Bayer, McMillan and Reubin [2] used restricted-access 2000 Census microdata to show that a set of sociodemographic variables including education, income and language can explain 30 percent of Black segregation and 93 percent of Hispanic segregation in the Bay Area housing market. 1 The basic idea in this literature is simple. Given that demand for housing and neighborhood quality increases with income and that whites earn more than blacks in general, neighborhood with higher quality houses will be primarily occupied by white households. More generally, racial di erences in socioeconomic characteristics a ect households residential choices, some racial segregation would emerge even in the absence of any sorting on the basis of race. The implicit conclusion from this literature is that reductions in racial di erences in income and other important sociodemographics would decrease the level of residential segregation. In this paper, we argue that the conventional wisdom may not be accurate. We argue that improvements in the blacks socioeconomic characteristics (proxied by their level of education) in an MSA may lead more segregation of educated blacks and all blacks more generally. Our analysis is motivated by three empirical observations about the current state of racial segregation in the U.S. (see Section 2). First, in almost every metropolitan-area, there are few, if any, neighborhoods with both high fractions of blacks and highly-educated households. The shortage of such middle-class (i.e., with high average education) black neighborhoods forces highly-educated black households to choose between predominantly black neighborhoods with low average education and predominantly white neighborhoods with high levels of education. Second, faced with limited choice set of neighborhood alternatives, highly-educated blacks do live in a very diverse set of neighborhoods: while a fraction live in neighborhoods with very few other black households and many college-educated neighbors, many live in neighborhoods that have a high fraction of black households and very few other college-educated households. Third, most of the middle-class black neighborhoods are located in metropolitan areas with a signi cant proportion of highly-educated blacks. The above empirical observations suggest the following. First, neither race nor average education of the neighborhood is all-important in the location decisions of highly-educated blacks 1 See Miller and Qingley [24] for an earlier study using similar methodology. Sethi and Somanathan [29] proposed a di erent method for the decomposition of segregation measures into one component that can be attributed to the e ect of racial income disparaties alone, and another component that combines the e ects of neighborhood preferences and discrimination. 1

3 (we present more evidence of preferences over race and neighborhood characteristics in Section 3). This further implies that highly-educated blacks may have preferred to live in highly-educated majority-black neighborhoods alternatives most of the metropolitan areas in the U.S. do not currently. Second, middle-class majority-black neighborhoods, currently only existing in a handful of metropolitan areas, are more likely to emerge when the number of highly-educated blacks increases in the metropolitan area. The emergence of middle-class black neighborhoods will then lead to more residential segregation because these neighborhoods are highly attractive to middle-class black households. Section 3 presents a simple and stylized model of household residential choice and neighborhood formation that captures the essence of the above mechanism. 2 Our empirical analysis takes seriously the mechanism of decentralized residential sorting and neighborhood formation, by examining how changes in the structure of the population within a metropolitan area a ect the way that households sort on the basis of race and education. 3 Our central hypothesis relates to whether the relative exposure of highly educated black households to blacks is an increasing or decreasing function of the education level of blacks in the metro area. 4 Using 2000 Census data from 277 US metropolitan-areas (MSA or CMSAs) and summarized at the tract level, the empirical analysis involves a series of regressions that relate the racial-educational composition of an individual s tract to an individual s own race-education category, a set of MSA xed e ects, and interactions of individual and MSA race-education characteristics. The results reveal that relative to other households in the MSA, highly-educated blacks are increasingly exposed to other blacks as the education level of blacks in the metropolitan area increase. This change is driven primarily by a large relative increase in exposure to other highly-educated blacks and is more than completely o set by a decrease in exposure to highly-educated whites. These changes are likely to result in a slight decrease in the average level of education in the neighborhoods in which highly-educated blacks reside. At the same time, highly-educated blacks are also increasingly exposed to less-educated blacks and vice-versa. This e ect is consistent with the comparative-statics prediction of our model when highly-educated blacks in an MSA increase from moving from a low to a moderate proportion in an MSA. In a nutshell, Section 4 established a positive correlation at the MSA level between the educational attainment of blacks and the segregation of highly-educated blacks. 5 Section 5 attempts 2 A recent paper by Sethi and Somanathan [30] presents a di erent model in which they show that racial segregation and income inequality does not exhibit a monotonic relationship. Further discussions of this paper is in Section 3. 3 In our analysis, we use education as a proxy for socioeconomic characteristics more generally. 4 Note that the inclusion of MSA xed e ects in the regression absorbs any mechanical increase in same-race exposure due to the changing population composition. 5 Our empirical analysis exploits cross-msa variations in the proportion of highly-educated blacks; as such, our 2

4 to empirically distinguish our ndings from several other plausible mechanisms. We rst rule out reverse causality by appealing to the ndings from Cutler and Glaeser [9]. 6 They found that blacks aged in more segregated areas have signi cantly worse outcomes, including educational outcomes, than blacks of the same age group in less segregated areas. It is worth emphasizing that our ndings do not necessarily contradict Cutler and Glaeser [9]. First, they focused on the educational outcomes of blacks aged while we focus on the educational attainment of all blacks in the MSA; second, we use individual-speci c exposure rates as our measure of segregation while they use MSA-level dissimilarity index. 7 We can also rule out statistical discrimination in the housing market or mortgage lending as the explanation to our empirical ndings. Standard models of statistical discrimination generally predict that, as the average characteristics of blacks (average educational attainment, for example) in the MSA improve, highly-educated blacks would less likely be discriminated against in both the housing market and in mortgage applications. To the extent that statistical discrimination in the housing market and in mortgage application still exist, the mechanism we identify may in fact be operating more forcefully than our estimates would imply. A third alternative explanation is the selection bias where the primary concern is that highly-educated blacks that select into MSAs with a higher fraction of educated blacks have a stronger taste for segregation. We address this concern by decomposing the current metropolitan sociodemographic composition for each household into a lagged measure corresponding to the MSA where the household lived ve years ago and the di erence between the current and lagged measure. Including both the lagged and di erence measures in an analogous set of regressions reveals that the active selection related to movement over the past ve years actually weakens rather than strengthens our main ndings, implying that selection across MSAs is not likely to be a signi cant factor driving results are not directly related to time-series segregation measures conducted by Cutler, Glaeser and Vigdor [10] and Glaeser and Vigdor [15]. However, our nding is consistent with Glaeser and Vigdor s [15] nding that Segregation decline most sharply in places that... blacks made up a small portion of the population in Segregation remains extreme in the largest metropolitan areas." 6 Earlier related literature in this line include Ihlanfeldt and Sjoquist [17] and O Regan and Quigley [25]. 7 The dissimilarity index was proposed by Duncan and Duncan [?] measures the fraction of blacks that would have to switch areas to achieve an even racial distribution citywide (see Cutler, Glaeser and Vigdor [10] for more discussions). It is an aggregate-level measure. The exposure rate has the advantage over dissimilarity index in that it can be speci c to individuals. It construction can be illustrated simply as follows (see Bayer, McMillan and Ruben [2]). Let r i j be a set of indicator variables that take value 1 if household i is of race j and 0 otherwise. Let R i k be the fraction of households of race k in household i 0 s neighborhood (the Census tract, for example). The average exposure of households of race j to households of race k; denoted by E jk ; is P E jk = i ri jrk i P i ri j : 3

5 our results. The nal alternative explanation relates to omitted variable bias and selection bias, the concern being that historic patterns of black settlement, migration, and segregation in the U.S. might give rise to a spurious correlation between metropolitan sociodemographic composition and segregation. While this explanation can not be addressed to complete satisfaction due to data limitations, we show that our main ndings are completely robust to the inclusion of a full set of interactions with metropolitan size and region. Our results have several important implications. First, they suggest caution in the conventional wisdom that racial segregation will necessarily decrease with the decline of the racial di erences in socioeconomic characteristics. 8 The mechanism uncovered in our analysis in fact suggests that, overall increase in blacks educational attainment may lead to a decrease in residential segregation if highly-educated blacks are dispersed in many, instead of concentrated in few, metropolitan areas. This echoes Glaeser and Vigdor s [15] nding that segregation is lowest among growing cities in the West where there is not yet a high concentration of highly-educated blacks. Our nding is also related to Wilson [34]. He argues that reductions in institutional discrimination in the housing market in the middle of the 20th century led to large-scale reductions in the exposure of lesseducated to more-educated blacks, as more-educated blacks left the inner city neighborhoods to where they were formerly restricted. Our ndings suggest that this trend may not have been severe in cities in which the black population was more educated initially and may partially reverse itself as the black population becomes relatively more educated over time. The remainder of the paper is structured as follows. Section 2 empirically documents the neighborhood choice sets in U.S. metropolitan areas; Section 3 presents a simple model of neighborhood formation that highlights the key features of the mechanism underlying our empirical results; Section 4 presents our main empirical nding that the exposure of highly-educated blacks and all blacks more generally to other blacks increases as the proportion of highly-educated blacks in the metropolitan area increases; Section 5 evaluates leading alternative hypotheses; nally, Section 6 concludes. 2 Neighborhood Choice Sets in US Metropolitan Areas In this section we present some empirical facts about the neighborhood choice sets in U.S. metropolitan areas using Census Tract Summary Files from 2000 Census. In our analysis, a neighborhood corresponds to a census tract, which typically contains 3,000 to 5,000 individuals. The Census Tract Summary Files provides information on the distribution of education by race for each 8 This conventional view was embraced by many scholars in this literature (see Durlauf [12], Wilson [34] and Mayer [23]). 4

6 Census tract. We characterize the race and educational attainment of households as that of the head of household and focus speci cally on non-hispanic black and non-hispanic white households throughout our analysis. 9 Educational attainment of the head of the household is used to proxy the socioeconomic status of the household more generally. We characterize each neighborhood in a metropolitan area in two dimensions: the fraction of black households, and the fraction of highly-educated (i.e. educational attainment is college or above) households. We establish four empirical facts about neighborhood choices sets: Highly-educated black households constitute a small fraction of the population living in typical metropolitan areas; Neighborhoods that combine high fractions of both college-educated and black households are in extremely short supply in almost every metropolitan area; College-educated blacks choose to live in a very diverse set of neighborhoods in each metropolitan area; Middle-class black neighborhoods are concentrated in few metropolitan areas with sizeable highly-educated black households. [Table 1 About Here] Table 1 describes the joint distribution of education and race for black and white households. Based on our race de nitions, black and white households respectively constitute 11.1 and 69.5 percent of the U.S. population that reside in metropolitan areas. Among black households, 15.4 percent are headed by an individual with a college degree, while the comparable number for white households is 32.5 percent, and for all U.S. households, 27.7 percent. [Table 2 About Here] Table 2 documents the number of tracts in the U.S. by the percentage of households with a college degree and the percentage of households that are black and white, respectively. Panel 1 describes the number of tracts in which more than 0, 20, 40, 60, and 80 percent of head of households are college-educated, respectively. Panel 2 reports the number of tracts in each of these categories that contain a minimum fraction of black households equal to 20, 40, 60, and 80 percent, 9 The vast majority of households that checked two races can be characterized as either Hispanic or non-hispanic Asian or Paci c Islander. Other households that checked two or more races - a very small fraction overall - were dropped from this analysis. 5

7 respectively. As the corresponding numbers show, a much smaller fraction of the tracts with a high fraction of black households have a high fraction of households with a college degree. For example, while 23 percent of all tracts are at least 40 percent college educated (a number comparable to the fraction of U.S. households with a college degree), only 2.5 percent of tracts that are at least 40 percent black are at least 40 percent college educated, and only 1.1 percent of tracts that are at least 60 percent black are at least 40 percent college educated. Panel 2 of Table 2 shows analogous numbers for white households, reporting the number of tracts in the U.S. that meet the education criterion described in each column heading subject to a minimum fraction of white households equal to 20, 40, 60, and 80 percent, respectively. The corresponding numbers show a markedly di erent pattern of neighborhood choices for white households, with a greater fraction of neighborhoods with at least 40, 60, and 80 percent white households meeting each education criterion. [Table 3 About Here] While Table 2 revealed a paucity of neighborhoods with high fractions of both black and collegeeducated households in the U.S. as a whole, Table 3 further shows that such tracts, to the extent that they exist, are in fact concentrated in only a handful of metropolitan areas, most notably Washington, DC. This implies that the supply of such neighborhoods in most metropolitan areas is even more limited. Table 3 illustrates, for example, that of the 44 tracts (less than 0.1 percent of all tracts) that are at least 60 percent black and 40 percent college-educated, 13 are in the Washington DC PMSA, 8 in Detroit, 6 in Los Angeles, and 5 in Atlanta. Almost 75 percent of these tracts can thus be found in one of only four PMSAs. Of the 142 tracts that are at least 40 percent black and 40 percent college-educated, almost two-thirds are in the PMSAs listed above along with Chicago and New York. Tables 2-3 taken together show clearly that while neighborhoods that combine high fractions of both college-educated and white households are amply supplied in all metropolitan areas, neighborhoods that combine high fractions of both college-educated and black households are in extremely short supply. This suggests that college-educated black households in most metropolitan areas may face a trade-o between living with other blacks versus other college-educated neighbors. [Figure 1 About Here] To graphically demonstrates the potential trade-o faced by highly-educated black households, Figure 1 shows the scatterplots of neighborhoods in four metropolitan areas: Boston, Dallas, Philadelphia, and St. Louis. In each scatterplot, a circle represents a Census tract and its coordinates represent the fraction of highly-educated households (vertical axis) and the fraction of 6

8 black households (horizontal axis) in the tract. The diameter of the circle is proportional to the number of highly-educated black households in the tract, thus the largest circles correspond to the tracts where highly-educated blacks are most likely to live. 10 For these four metropolitan areas, the scatterplots demonstrate the short supply of neighborhoods that combine high fractions of both highly-educated and black households, neighborhoods that would have appeared in the north-east corner of the plot. Consequently, highly-educated black households may face a trade-o when making their residential choices. Figure 1 also demonstrates that, facing the constrained choice set, highly-educated black households do choose to live in a diverse set of neighborhoods: while a sizeable fraction of highly-educated blacks in each of the ve MSAs chooses neighborhoods with few black and many highly-educated neighbors neighborhoods in the north-western corner of the plots, another sizeable fraction choose neighborhoods with many black and few highly-educated neighbors neighborhoods in the southwestern corner of the plots. [Table 4 About Here] Panel A of Table 4 summarizes the characteristics of neighborhoods chosen by highly-educated blacks in metropolitan areas throughout the U.S. We rst rank highly-educated black households in each metropolitan area by the fraction of blacks in their Census tract and assign households to their corresponding quintile of this distribution. This corresponds to drawing four vertical lines in the scatterplot for each metropolitan area such that an equal number of highly-educated black households are in each of the quintiles. Panel A of Table 4 then summarizes the average fractions of black and Highly-educated households in the tract corresponding to the quintiles of this distribution, averaged over all U.S. metropolitan areas. The rst column of Panel A, for example, the 20 percent college-educated black households with the smallest fraction of other black households in their metropolitan are (the bottom quintile) live in neighborhoods that are on average 5.7 percent black and 38.0 percent highly-educated. The numbers corresponding to di erent quintiles show a clear trade-o for highly-educated black households between the fraction of their neighbors that are black and the fraction that are highly-educated: the average fraction of highly-educated neighbors falls from 38.0 percent for those college-educated blacks living with the smallest fraction of black neighbors to 13.8 percent for those living with the largest fraction. Panel B of Table 4 reports analogous numbers for college-educated white households. The comparison of Panels A and B reveal that, college-educated blacks in each metropolitan area who live in the bottom quintile of tracts in terms of the smallest fraction of other blacks have roughly the same 10 Note that tracts that do not contain any highly-educated blacks do not show up in these scatterplots. 7

9 fraction of college-educated neighbors as college-educated whites do on average; however, collegeeducated blacks living in the top quintile of tracts with the greatest fraction of other blacks have only about one-third of that fraction of highly-educated neighbors. We argue that such a high fraction of college-educated black households in U.S. metropolitan areas choose segregated neighborhoods with relatively low average education attainments suggest that race remains an important factor in the location decisions of a large number college-educated black households. In Section 3 we present more evidence for race preferences and propose a simple mechanism based on the emergence of highly-educated black neighborhoods to argue that such racial preferences may lead to more segregation of highly-educated black households as the average education of the block population in a metropolitan area increases. Speci cally, we argue that when the number of highly-educated black households in the metropolitan area increase, a greater supply of neighborhoods that combine high fractions of both black and college-educated neighbors may form. Figure 2 depicts the scatterplots of neighborhoods in Atlanta, Chicago, Detroit and Washington, D.C. As we showed in Table 3, these metropolitan areas contain a sizeable number of college-educated black households. Figure 2 shows that they supply substantially greater number of neighborhoods combining relatively high fractions of both black and highly-educated households, and thus relax the constraint of neighborhood choice set for highly-educated blacks. As the neighborhood supply constraint relaxes for highly-educated blacks, highly-educated blacks may be increasingly exposed to other black households. 3 A Model In this section, we present a simple model of residential choice and endogenous neighborhood emergence. This simple model formalizes our idea that the set of neighborhood available to highlyeducated blacks will expand as the fraction of highly-educated blacks increase in a metropolitan area, leading to more segregation. Sethi and Somanathan [30] presented an alternative model in which they show that low racial inequality is consistent with extreme and even rising levels of segregation in cities where the minority population is large. Their model does not explicitly emphasize the idea of neighborhood emergence since they x the total number of neighborhoods exogenously, where our model emphasize the emergence of new middle-class neighborhoods, a fact consistent with the empirical facts documented in Section 2. Basic Ingredients. Before describing the details we highlight three key ingredients of the model that drive our results. The rst key ingredient is that black households preferences are such 8

10 that, on net, they prefer to live near others of the same race and education level. 11 There is ample empirical evidence that individuals prefer to live in neighborhoods where they own race is in majority. 12 For example, in the Multi-City Survey of Urban Inequality (MCSUI) respondents were shown a card representing a neighborhood with fteen houses (in three parallel rows of ve houses each), and were asked to illustrate the racial composition of their ideal neighborhoods where they were presumed to live in the house located at the center of the middle row. Using MCSUI conducted between in Atlanta, Detroit, and Los Angeles metropolitan areas, Ihlanfeldt and Sca di [17] found that, percent of blacks designates the all-black neighborhood or the mostly black neighborhood (eleven blacks and four whites) as their top choice; and percent of the blacks chose all black or mostly black neighborhoods as one of their top two choices. 13 Our assumption that black households prefer neighbors with the same educational attainment needs more explanation. Indeed intuitive all households may prefer to live with highly-educated neighbors, due to the positive externality in human capital production (see Benabou [5] and Cutler and Glaeser [9] for example). Our assumption is sensible only because housing prices which we abstract from would have most likely capitalized such positive externalities. Many sorting models would generate the prediction that, ceteris paribus, less-educated households are not willing to pay as much as highly-educated households to live with more educated neighbors. Thus we consider our assumption on the preference to live with neighbors of same educational attainment as a convenient reduced-form, which allows us to place the role of housing prices in the background of the analysis. The second key ingredient of our model is the notion of critical neighborhood size. In the model below we capture the notion of critical neighborhood size by assuming that each resident in a neighborhood has to incur a cost that decreases with its total number of residents. Multiple interpretations can be given for this formulation. One interpretation is that the average cost of providing both formal and informal local public goods decreases in neighborhood size, at least over some range; alternatively, it can capture the idea that a larger population can sustain more local options in retail, television, restaurants, newspaper, and the internet, both in quantity and quality (see, e.g., Berry and Waldfogel [4] and reference cited therein). The third ingredient of our model is some degree of idiosyncratic location preferences, unrelated 11 Schelling [27][28] is the rst to note that individual racial preferences can lead to segregation. 12 Cornell and Hartmann [8], Farley et al [13], O Flaherty [21] and Lundberg and Startz [20] provide various theoretical arguments about why individuals might care about the racial composition of their neighborhoods. 13 Also see Vigdor [32] and Charles [6][7] for related evidence. It is important to emphasize that such evidence has to be at best considered as suggestive, as the MCSUI survey questions makes no mentions of neighborhood amenties, housing prices, or other factors that might in uence residential choices. Thus such evidence does not necessarily reveal fundamental racial preferences. King and Mieszkowski [19], Yinger [35] and Galster [14] found evidence of segregation preferences based on housing prices or rents. 9

11 to sorting on the basis of education or race, in the households residential choices. We capture this heterogeneity by assuming that households have employment locations distributed in space and would prefer to commute shorter distances. Such assumption is standard in the spatial mismatch literature (see Kain [18], Ross [26] and Weinberg [33]). Model. Consider a metropolitan area located on a straight line with length 2, represented by the interval [ 1; 1]. The population density in the metropolitan area is given by N > 0, thus its total population is 2N: There are two racial groups r 2 fb; wg and a proportion w 2 (0; 1) is white and the remaining proportion b = 1 w is black. Moreover, individuals within each racial group di er in their educational attainment: a fraction r 2 (0; 1) of race-r individuals are highly-educated (denoted by type-h) and the remaining fraction 1 r are of the low-education type (denoted by type-l). 14 Cross-race inequality in socioeconomic characteristics is re ected by the di erence w b : Clearly for all metropolitan areas in the U.S., the relevant case is w > b. Thus a narrowing in the racial gap in educational attainment can be represented by an increase in b while keeping w xed. For simplicity, we assume that whites residential locations are xed: at each endpoint of the line, there are two communities, one for highly-educated whites (called communities HW and HW ) and one for less-educated whites (called communities LW and LW ). We focus our analysis on the residential location choices of black households and the emergence of black neighborhoods. We model idiosyncratic locational preferences of the blacks by assuming that their job locations are uniformly distributed on the straight line. Commuters experience a cost of > 0 per unit distance between their work and place of residence. There is a cost of maintaining a community, and the average per-resident cost is given by c(n) where n is the number of residents in the community. 15 Naturally we assume that c decreases in n: We now describe black households preferences. Consider a black household with education e 2 (l; h) whose job location is at point z 2 [ 1; 1] on the straight-line. Its utility from living in a community j 2 J where J is the set of available communities to be determined in equilibrium, is given by: u(j; z; e) = [p b (j) + 1 p w (j)] + [p e (j) + 2 p e 0(j)] D(j; z) c (n(j)) ; (1) where e 0 6= e is the other education category; p r (j) is the proportion of residents in community j of race r; p e (j) is proportion of residents in j with education attainment e; D(j; z) is the commuting distance between community j and z s job location; n(j) is the number of residents in community 14 The heterogeneity could equally be in terms of income. 15 Technically this rules out tiny enclaves of individuals claiming to form a neighborhood of their own. 10

12 j; > 0; > 0; 1 2 (0; 1) ; 2 2 (0; 1) are constants. In utility function (1), the rst term [p b (j) + 1 p w (j)] captures the utility from interacting with people of di erent races in the same community, where 1 < 1 captures the same-race preference discussed earlier. The interpretation of the second term [p e (j) + 2 p e 0(j)] is more subtle. As we explained previously, it is meant to capture, in a reduced form, the idea that highly-educated workers will on net (taking into account both human capital externality and housing price) prefer to live in more expensive neighborhoods with many other highly-educated residents, while less-educated workers will prefer on net to live in cheaper neighborhoods with other less-educated residents. An equilibrium of this simple model is characterized by the set of neighborhoods J (including the existing neighborhoods HW, HW, LW, LW ) and the residential choices of all black households such that: (1) given J ; all black households residential choices is utility-maximizing; (2) there is a positive measure of residents in all neighborhoods j 2 J : Note that we do not need to directly impose a threshold neighborhood size in our model. The existence of the four white neighborhoods, together with the assumption that c (n) is decreasing in n; endogenously ensures that small enclaves of black households will not claim to form their own neighborhood. The equilibrium set of neighborhoods J depends on the parameters of the model. We are particularly interested in how J is a ected by an increase in b the fraction of highly-educated black households in the metropolitan area. Consider an equilibrium in which a single black community, community B, emerges at point 0. Clearly community B, were it to emerge, will consist of blacks whose job locations are close to point 0. Thus given J = {HW, HW, LW, LW, B}, black households optimal residential choices can be characterized by a pair fx h ; x l g such that all highly-educated (less-educated, respectively) black households will choose to live in community B if and only if their job location z satis es jzj x h (jzj x l ; respectively). The marginal types fx h ; x l g can be determined from the indi erence conditions (see Appendix A for details). Figure 3 depicts this type of equilibrium when b is small. 16 [Figure 3 About Here] Imagine that we increase the fraction of highly-educated blacks b from an initial low level. First, note that as b increases, the proportion of highly-educated blacks in community B, p h (B) ; will increase even if the thresholds fx h ; x l g were hypothetically unchanged. As p h (B) increases, 16 If such an equilibrium exists with a su ciently small b, one can show that x l > x h. The reason is simple: when b is small, community B is necessarily a predominantly lowly-educated all-black community. Because 2 < 1, the utility for a lowly-educated black from community B is always higher than that for a highly-educated black at any job location. Thus lowly-educated blacks are more willing to commute to community B. This is not important for the analysis but explains the ranking of x l and x h in Figure 3. 11

13 community B becomes more attractive vis-à-vis community HW for highly-educated blacks. As a result, the marginal type of highly-educated black who commutes to community B, x h ; will increase. Thus the probability of a highly-educated blacks living in all-black community B with less-educated blacks will initially increase in b. The results for less-educated blacks are more ambiguous. On the one hand, community B becomes more educated. On the other hand, the increase of the total population in community B drives down the average community cost c. Thus, whether or not community B becomes more desirable for less-educated blacks is indeterminate. It is possible that exposure of highly- and less-educated blacks to one another may increase. Moreover, the increase in exposure of highly-educated blacks to other highly-educated blacks comes at the expense of exposure to highly-educated whites (see Figure 4b for the graphical illustration). [Figure 4 About Here] When b is su ciently high, however, a point may be reached when it becomes pro table for highly-educated blacks in community B to form their own community at point 0, called BH, and leaving behind a less-educated black community BL (see Figure 4c). The exact point at which the highly-educated black neighborhood BH emerges is determined by the balance of two forces. First, by separating from the less-educated blacks living in community BL, highly-educated blacks have to incur a higher per capita cost c as a result of smaller population size; second, because community BH consists only of highly-educated blacks, the utility component p h (BH) = 1 > p h (B) + 2 p l (B) because 2 < 1: 17 This is the key insight of our simple model: a highly-educated black community BH emerges only when the proportion of highly-educated blacks b is su ciently high. Of course, the emergence of such communities also depends positively on the population density N, the overall proportion of blacks in the metropolitan area b. It also indirectly depends on the commuting cost and the community cost function c (n) via their e ects on x h. It is also worth pointing out that the emergence of community BH is likely to induce an accelerated emigration of highly-educated blacks from community WH and WH to community BH, resulting in greater racial segregation in residential locations. 4 Empirical Results We now present the main empirical analysis of this paper. We begin this section by characterizing the pattern of segregation broken out by race and education in U.S. metropolitan areas. 17 We abstract from the coordination problem among highly-educated blacks in their decision to form their own neighborhood. 12

14 We then explore how this pattern varies with the sociodemographic composition of the metropolitan area, focusing especially on how the segregation of highly-educated blacks (and blacks more generally) is a ected by the fraction of highly-educated blacks in the metropolitan area. 4.1 Segregation Patterns in US Metro Areas We begin by describing the general pattern of segregation in the United States as a whole. Panel A of Table 5 shows the average tract-level cross exposure for households in four race-education categories (black/white; college/non-college educated) for U.S. metropolitan areas. The rst entry in Panel A, for example, implies that the average black household without a college degree lives in a tract where 33.2 percent of the households are black and without a college degree. This compares to the national average exposure to less-educated blacks of 9.4 percent. Panel B reports the average cross exposure of households by race-education categories relative to the MSA average. The rst row of Panel B states that relative to an average household in the same metropolitan area, blacks without a college degree are exposed to 19.6 percentage points more blacks without a college degree and 2.1 percentage points more highly-educated blacks, etc. Table 5 illustrates a clear pattern of racial segregation in U.S. metropolitan areas for highly-educated blacks as well as those with lower levels of educational attainment. [Table 5 About Here] Table 6 reports segregation patterns in a manner analogous to Panel B of Table 5, but separately for metropolitan areas with above and below the median fraction of college-educated black households (1.23 percent). Table 6 provides some initial evidence on how segregation patterns vary with the sociodemographic composition of the metropolitan area. Table 6 shows that, the relative exposure of blacks in each education category to both highly- and less-educated blacks is signi cantly greater in metropolitan areas with above-median fractions of highly-educated black households. For both highly- and less-educated blacks, the average tract-level exposure to blacks relative to the fraction of blacks in the MSAs above the median more than doubles that for MSAs below the median. [Table 6 About Here] 4.2 A Regression-Based Approach To more formally control for the sociodemographic structure of the metropolitan area, Table 7 reports the results of a series of regressions of various tract-level exposure measures on individual 13

15 and MSA characteristics. 18 The dependent variable is listed in the head of each column. For example, column 1 corresponds to a regression whose dependent variable is individuals tract-level exposure rate to highly-educated blacks. Each regression includes a complete set of controls for individual race-education categories and MSA xed e ects. The inclusion of the MSA xed e ects ensures that all of the other parameters characterize tract-level exposure relative to the MSA average for each set of individuals. In addition, the regressions also include individual characteristics interacted with MSA characteristics. 19 The coe cients on the interaction terms characterize how tract-level exposure for various sets of individuals varies with MSA characteristics. [Table 7 About Here] Due to the various interaction terms in these regressions, coe cient estimates are di cult to interpret in isolation. In what follows we use these coe cient estimates to present two statistical tests. The rst test is about whether an increase in the fraction of highly-educated blacks, holding constant the fraction of black households, changes the relative tract-level exposure of less- and moreeducated blacks, respectively, to households in the given race-education category. This corresponds to examining the impact of an increase in the average education level of black population. The second test is about whether an increase in the fraction of highly-educated blacks, holding constant the fraction of highly-educated individuals in the metropolitan area, changes the relative tract-level exposure of less- and more-educated blacks, respectively, to households in the given race-education category. This corresponds to increasing the fraction of the educated population that is black. [Table 8 About Here] Table 8 summarizes these e ects for a 1 percentage point change in the fraction of collegeeducated blacks in the MSA population. Panel A shows that when the fraction of college-educated blacks in a metropolitan area increase by 1 percent at the expense of less-educated blacks, the relative exposure of highly-educated blacks to other highly-educated blacks increase by 1 percentage point and it is statistically signi cant; the relative exposure of less-educated blacks to highlyeducated blacks also increase by 1.1 percentage points. Overall, the relative exposures of both highly- and less-educated blacks to blacks increase by 4 and 6.1 percentage points respectively. This empirical nding is consistent with our model s prediction when b is in intermediate range (Figure 18 We include individual level characteristics to the extent that they are available in the Census Tract Summary Files. In practice this is equivalent to running weighted OLS where the weight is given by the number of individuals in each race/education cell. 19 If we do not include these interactions, the coe cients on the individual characteristics in these regressions would return the estimates reported in Panel B of Table 5. 14

16 4b), which we think is the plausible scenario for most of the U.S. metropolitan areas in the U.S. Panel B shows that similar results holds when the fraction of highly-educated blacks is increased by reducing the fraction of highly-educated whites (i.e., increasing the fraction of the educated population that is black, Panel B). For both highly- and less-educated blacks, the increased relative exposure to blacks is driven by increased exposure to blacks in both education categories. These relative increases are o set by a decrease in the exposure to (especially highly-educated) whites. On net, an increase in the average education of the black population has a slightly negative (although marginally statistically insigni cant) e ect on the average education level in the neighborhoods that blacks reside in relative to the metropolitan area average. 20 [Table 9 About Here] Table 9 reports results analogous to those reported in Table 8 with the exception that the underlying measure of highly-educated is changed to include those having at least attended college. With this de nition, the fraction of households in U.S. metro areas that are highly-educated is 54 percent, the fraction that are both highly-educated and black is 5 percent, and the fraction of black households that are highly educated is 45 percent. Our primary objective in examining an alternative de nition is to explore a de nition of highly-educated that includes a larger fraction of households and especially black households. A comparison of the results reported in Table 9 to those reported in Table 8 reveals a qualitatively similar pattern. With the expanded highlyeducated category, the relative increase in exposure of both highly- and less-educated blacks to other blacks is more evenly split between highly- and less-educated blacks. Both de nitions of highly-educated reveal a pattern of increased relative exposure of both highly- and less- educated blacks to blacks in each education category when the fraction of highlyeducated blacks in the metropolitan area increases. This pattern is consistent with the predictions of our model corresponding to an increase in b from small to moderate levels. With an increase in the average education level of the black population, highly-educated blacks move on net into 20 To ensure that the results of Table 7 are not driven by the form of the dependent variable that we employ, we also conducted a series of regressions analogous to those reported in Table 7 de ning the dependent variable as the fraction of households in a given category in an individual s tract divided by the fraction in the metropolitan area as a whole. In this way, an increase in tract-level exposure to households in a given category from 6 to 12 percent following an increase in the proportion of these households in the metro area from 3 to 6 percent would not result in an increase in the dependent variable in this case, while it would result in a 3 percentage point increase in the dependent variable used in the regressions reported in Table 7. The resulting parameter estimates led to a qualitatively identical set of conclusion, thereby ensuring that our initial results are not driven by the functional form of the dependent variable. Throughout the remainder of the paper, we present the results of regressions analogous to those reported in Table 7. 15

17 more segregated neighborhoods, increasing the average education level in some of the most segregated neighborhoods. In terms of the scatterplots, this pattern is consistent with the formation of segregated, black neighborhoods with mixed education levels that is, with shift of the implicit neighborhood supply constraint that is more upward than outward. 5 Robustness to Alternative Explanations Our main empirical nding can be summarized as the discovery of positive relationship at the MSA level between the educational attainment of blacks and the segregation of highly educated blacks. We suggested a forceful mechanism that can explain this positive correlation based on the idea that middle-class black neighborhoods may emerge as the sociodemographics of blacks improve. In this section, we present arguments and robustness tests to cast doubt on alternative explanations for our empirical ndings. The rst possible story is reverse causality. Cutler and Glaeser [9], however, cast doubt on this explanation. They studied the impact of segregation at the MSA level on educational outcomes for blacks aged 20-30, and nding a large negative e ect. 21 The second possible story is statistical discrimination, both in housing market and in mortgage market. However, statistical discrimination story would predict a negative correlation: as the fraction of highly educated blacks increases in a metropolitan area, blacks in general would be less likely to be discriminated against thus leading to less not more segregation. To the extent that statistical discrimination exists in reality, the actual mechanism that we identify in our paper may in fact be stronger than what our main estimates would imply. Below we consider in detail the possibility of omitted variables and selection biases. Omitted Variable Bias. The concern over omitted variables is that the fraction of the metropolitan area that is highly-educated and black might be correlated with other variables that are associated with di erent levels of segregation. This is a di cult problem to address satisfactorily, especially since we use cross-msa data. Here we address this problem by adding metropolitan size and region, two most prominent factors because of historic patterns of black settlement, migration, and segregation in the U.S., into our regression. Table 10 reports the results of a set of regressions analogous to those reported in Table 9 with the addition of interactions between each individual s race-education category and a measure of metropolitan size and four dummies for Census region 21 There are other di erences between their paper and ours: for example, they use dissimilarity index as the segregation measure, and the data set they used is the 1990 Census. 16

18 (Northeast, Midwest, South, West). 22 [Table 10 About Here] A comparison of the results presented in Table 10 to those in Table 9 reveals a qualitatively similar pattern in terms of both the magnitude and the statistical signi cance of the results. In particular, with the additional controls, the increase in the relative exposure of both highly- and less-educated blacks to other blacks declines by percent in magnitude, but remains highly signi cant. Changes in relative exposure to highly-educated neighbors also decline and remains insigni cant in each case. Taken together, these results give us con dence that the main conclusions of the paper are not driven by obvious omitted variable biases. While we added metropolitan size and interactions in the results reported in Table 10, we still assumed that the e ects of the fraction of highly-educated blacks on segregation does not depend on metropolitan size. The critical mass story implicit in our model implies that not only the fraction but the number of highly-educated blacks in the metropolitan area may be important for the formation of more-educated and segregated black neighborhoods. Given the same fraction of highly-educated black households, highly-educated black neighborhoods might more easily form in large (in population) rather than small metropolitan areas. [Table 11 About Here] Table 11 estimates separate regressions, including the additional 16 control variables added in Table 10, for small (0-200k), medium ( k), and large (600k+) metropolitan areas. For brevity, we only report results related to exposure to black households. A clear pattern emerges in the table the increased relative exposure of both highly- and less-educated blacks to other blacks following an increase in average education level of the black population is much greater in large versus small metropolitan areas. For highly-educated blacks, the magnitude of the e ect rises from in small, to in medium-sized, and 0.40 in large metro areas. The results tend to have higher statistical signi cance in larger metropolitan areas. A similar pattern emerges for less-educated black households. Interestingly, in large metropolitan areas, the increased exposure of highly-educated blacks to other blacks is dominated by an increased exposure to other highlyeducated blacks. Thus, for this subsample, an increase in the average education of the black population might be associated with the formation of predominantly highly-educated, segregated black neighborhoods i.e., the prediction of the model corresponding to an increase in the fraction of highly-educated blacks from a moderate to large number. 22 A total of 16 interaction terms are added to the regression. 17

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