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Technical Presentation on Baum-Snow and Lutz’s “School Desegregation, School Choice, and Changes in Residential Location Patterns by Race”

by Christopher Bradford TP_BradfordChristopher

Baum-Snow and Lutz consider the responses to school choice and residential location following the desegregation of the American public school system. Data include 92 metropolitan statistical areas (MSAs) that underwent large-scale court-mandated desegregation between 1960 and 1990. The study uses these data to determine the extent to which desegregation was a causative agent for changes in public/private school enrollment and for residency in central districts/suburban areas for both whites and blacks.

The authors note that, while the 1954 case Brown v. Board of Ed of Topeka ruled school segregation unconstitutional, most large school districts did not initiate robust school desegregation until specific court orders forced them to do so. As such, the authors devise a model that accounts for this variation in school desegregation over time, Equation 1:


(1)     ln yrjt = αrj + βrt + cDrjt + εrjt


Here r represents a region (e.g. South), j represents a specific MSA, t represents time, βrt accounts for year-specific effects, Drjt represents the central district’s degree of desegregation at time t, and yrjt represents the variable of interest. The three main variables of interest yrjt for which the authors solve are (1) public school enrollment by race, (2) private school enrollment by race, and (3) population in central districts by race.

As a methodological note, the authors comment that identification of the constant c, the parameter of interest that modifies the degree of desegregation at a given time Drjt, necessitates that timing of desegregation is uncorrelated with any time-dependent, causative omitted variables. The authors feel that desegregation implementation occurred with “pseudo-random timing” due to two observations (8). First, the NAACP tended to file cases in the order in which they were most likely to succeed, not according to where the perceived need for desegregation was greatest. Second, the time between court uptake of a case and issuance of the court’s verdict and implementation was highly variable by district. In an attempt to correct for omitted variables in the overall model, the authors allow the term βrt to differ for South and non-South Census regions, as unmeasured (or immeasurable) variables such as differential degrees of discrimination could vary by region.

In order to gauge racial integration following court-mandated desegregation, the authors utilize a “dissimilarity index,” which ranged from 0 (perfect integration) to 1 (perfect segregation). This dissimilarity index is given by:

(St) St = ½ *TP_Bradbit/Bt – wit/Wt]


Here bit and wit represent the number of black and white students at a given school i at time t, and Bt and Wt represent the total number of black and white students in that district at time t. Using data from the 1970, 1980, and 1990 Censuses, the authors find that the dissimilarity index decreased by a national average of 0.15 due to desegregation, representing a reduction of nearly one standard deviation.

In addition to the dissimilarity index, the authors construct an “exposure index,” which gives the percent of black students in the average white student’s school. This exposure index is given by:

(Et) Et = 1/WtTP_Bradwit * bit/tit


Here tit represents the total enrollment of both races in a given school i. Substituting the exposure index into Equation 1 yields the result that desegregation increased interracial exposure in schools by 0.09, or roughly half of one standard deviation.

To account for spatial variation in desegregation, the authors amend Equation 1. Each North and South region r is divided into four location segments s. The modified Equation 2 takes the form:


(2)     ln E (yirjts) = arjs + brts +  ϒrs Drjt


Here i represents a Census tract within a given MSA j. While the parameter of interest in Equation 1 is c, it is ϒrs in Equation 2. This term accounts for spatial variation by region and segment.

Taking data from 77 MSAs that contained a suburban region, the authors find that over 90% of these MSAs were less racially integrated than the MSA central district in 1970. The average Southern suburb had an exposure index value 0.15 less than in the central district of the MSA. In the North this discrepancy was even larger, at 0.26. The implication of these large differences in integration is that departing central district residences for the suburbs allowed whites to escape exposure to black students.

Indeed, the study finds that white enrollment in public schools in central districts declined by a national average of 12% from 1960 to 1990 due to desegregation. The figure in the South is slightly higher than the national average and slightly lower in non-Southern regions. The models predict that in non-Southern regions, desegregation led to a 16% increase in white private school enrollment in the 30-year period. The authors fail to find statistically significant evidence on the effect of desegregation on white private school enrollment in the South. Data supported that white enrollment declines in central districts public schools were offset by increased enrollment in suburban public schools, however. The evidence for non-Southern regions suggests a causal relationship between desegregation and private school enrollment for whites.

Moreover, the models predict that desegregation caused an average of 6% nationally of the central district’s white population to relocate outside the central district. Again, these results are more pronounced in the South, where 12% on average of whites residing in the central district relocated due to desegregation. Significantly, these predictions attribute a proportion of residential white flight from integrated urban school districts to suburban districts directly to desegregation.

For blacks, the models predict that desegregation resulted in a 14% increase in public school enrollment in the central district on average. These results were captured in a period of at least 5 years after court-mandated desegregation policies were implemented. Desegregation caused the percentage of blacks enrolled in private schools in central districts to decrease by 20-28% nationwide within five years of implemented integration. This figure was much larger in the South than in other regions. The data suggest that large numbers of black students left private schools to enroll in newly desegregated public schools, particularly in urban central districts.

The population of blacks living in central districts nationwide increased by about 8% due to desegregation. This result was only obtained in the non-South; the effects of desegregation on central district population in the South were indeterminate. The authors note that the effects of desegregation on black schooling and residency patterns display much more cross-regional variation than for whites. Accordingly, unobserved interregional variables may have played a larger role for influencing black schooling and residency patterns post-desegregation.

Using their models, the authors confirm two predictions of Tiebout sorting. The first predicts that public enrollment and relocation will occur more in the periphery of the central city, where wealthy individuals tend to live in. A Tiebout assumption is that the marginal utility of local public goods (such as public schooling) increases with income. Accordingly, high-income residents are predicted to be the most susceptible to decreases in marginal utility due to school quality deterioration, which is an oft-perceived consequence of school desegregation. Indeed, the study finds that both white public school enrollment and total white population decreased the most in the outer fourth of central districts.

The second prediction is that private school enrollment changes will be more dramatic near city centers. Tiebout sorting predicts that residents who use private schooling will tend to live closer to the city center than those who use public schools, as savings on commuting costs can partially defray the cost of private school tuition. This prediction is also confirmed, as the authors observe the increase in private school enrollment for blacks and the corresponding decrease for whites in regions closer to city centers than they observe the enrollment responses for public schools.

In their conclusion, the authors note that the magnitudes of population shifts due to desegregation are insufficiently large to account for the majority of total central district population loss in the past half century. The authors calculate that, had court-mandated desegregation not occurred, the decrease in white central district population would have declined by 10% from 1960 to 1990, whereas the actual decline was 13%. For blacks in the hypothetical no-desegregation scenario, the authors predict a 44% increase in central district population as compared to the 54% actual figure. Accordingly, the authors conclude that other factors must have been responsible for the brunt of city center population changes.

What the study does show is that desegregation contributed to decreased white enrollment in central district public schools and an increase in enrollment in these schools for blacks. It also shows that desegregation was a causative agent for changing both the racial makeup of urban central districts and private school enrollment for whites and blacks.

School integration remains to this day a large policy issue in America. It is also a significant local concern, with the recent struggles of the Wake County district a prominent example. For my term paper, I may explore topics that branch out from this paper, such as how racial integration in public schools correlates with educational achievement. Or I may take a different angle, and investigate residency patterns by race, perhaps by considering whether residential segregation today correlates with the time at which court-mandated school integration began.



Baum-Snow, Nathaniel and Byron F. Lutz. “School Desegregation, School Choice and Changes in Residential Location Patterns by Race.” American Economic Review, 101(7): 3019-46. 2011.

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