Studying Segregation using the CCD: the work of Saporito and Sohoni

• The Common Core of Data is good for studying school segregation.
• In large city school districts, there are relatively more whites in private schools than blacks or hispanics.
  • So more government support for school choice might increase urban school segregation.
• On the other hand, public magnet schools do seem to reduce segregation, contrary to conventional wisdom.

Using the CCD to study school segregation

Today I wanted to take a look at what other researchers have done with the Common Core of Data (CCD). I finally settled on some excellent work by Salvatore Saporito and Deenesh Sohoni.

The CCD is useful for studying racial segregation. Combined with the Census, it would allow us to ask the important question:

are schools more segregated than neighborhoods?

If parents have preferences over the racial composition of their schools above and beyond preferences over the racial composition of their neighborhoods, then we would expect that in the resulting sorting equilibrium, schools will be more segregated than neighborhoods. A simulation justifying this claim is included at the end of this blog post. In that simulation, the time path of proportion white looks like the following figure. So the answer to this question needs to be yes if parents have racial preferences over the kinds of kids that their children play with in Kindergarten.

Saporito and Sohoni explore this question, except they restrict attention only to children. They find that children are more segregated in schools than in neighborhoods–this being because, by contrast to the model I present in my simulation, not all schools are neighborhood schools. Some are “schools of choice.”

It’d be nice to know whether implementing greater school choice could lead to significantly greater segregation. Again, it would seem a necessary condition for this to happen is that schools be more segregated than neighborhoods, and moreover, that this difference be larger where there are more schools of choice.

Saporito and Sohoni focus on answering this question. Their answer is a tentative yes

Private schools “absorb” white students

Let’s cut to the chase. They analyze the 22 largest school districts in the US in 2000. Among these districts, the racial composition of public and private schools, white:black:hispanic, is about 30:31:31. The composition of private schools is 59:19:17.

In every one of the 22 largest school districts, the racial composition of private schools is more white than the racial composition of all schools. (See table 1 of their 2009 paper for these statistics. These statistics are over all schools in these districts–elementary, middle, and high schools.)

Given these aggregate statistics, the analysis is practically over. If private schools were eliminated and whites did not leave the city as a consequence then racial segregation would go down.

Another way to cut this data is to note that for the average large urban school, there are about 5 percentage points more white students living in the attendance zone than there are white students in the neighborhood public school. Those “missing 5%” are in private schools.

Yet another way to think about this is to ask whether public elementary schools with a neighboring private elementary school have fewer white students, after controlling for the number of white students in the public school’s attendance zone. To give a picture, here’s a district with four attendance zones:

Figure 1.

blue schools are public, the red school is private. Darkness of the coloring represents percent minority. If we observed (within a given district) the pattern depicted in the above graph, we might be willing to conclude that private schools absorb whites from public schools without increasing the white population in the attendance zone. They are “attracting from within” without “attracting from without.”

In fact, according to the results of Saporito and Sohoni (2006), elementary schools that have a private school in their attendance zone on average have a much lower than expected proportion white. They present a regression of the form

reg proportion_white_in_neighborhood_public_school 
    proportion_white_in_attendance_zone
    proportion_white_in_attendance_zone^2
    proportion_hispanic_minorities
    proportion_black_minorities 
    dummy_for_1_specialty_school_in_attendance_zone: -0.565 (0.396)
    dummy_for_1_private_school_in_attendance_zone: -1.638 (0.346)
    dummy_for_2or3_private_schools_in_attendance_zone: -4.346 (0.416)
    dummy_for_3orMore_private_schools_in_attendance_zone: -10.220 (0.768)
    dummy_for_1_magnet_in_attendance_zone: 0.112 (0.801)
    dummy_for_1_charter_in_attendance_zone: 1.132 (1.127)

The important coefficients (with standard errors) are presented above in bold. Don’t get confused–the coefficients are in percentage points, so the coefficient on “dummy_for_1_private_school_in_attendance_zone” means that, in such case, we can expect about a 1.6pp reduction in the white proportion at that school.

So it does look like private schools are “absorbing” white students.

A side concern about fixed-effects–and whether these findings are evidence of racial preference

I am concerned that their model does not include district fixed-effects. Suppose we instead observed the following picture:

Figure 2.

In this case, I would say that the schools in district 2 are just bad, and private schools have come in and absorbed white students for that district.

In such a case, I would think that the “absorption of whites” by private schools is just a consequence of private schools positioning themselves where schools are bad, and whites being more able to afford to escape bad public schools, rather than the race-based preference sorting that might be implied by figure 1.

Of course, the problem of endogeneous position of private schools might occur within district as well–in figure 1, that lone private school might have positioned itself next to the worst public school. But school quality differences may plausibly be larger across districts than within districts (or maybe not), so it would be worth re-running this regression and testing sensitivity of this “local absorption” result to district fixed-effects.

Using the dissimilarity index

One more way to slice this result is to calculate the dissimilarity index separately for schools and school attendance zones for each of these 22 large school districts.

To understand the dissimilarity index, play with the slider demonstration below. This is an example of four schools in a district, each with 100 students. Each slider is the proportion black in that school. If you play with the sliders you’ll quickly get a feel for what the dissimilarity index is measuring: it really is the “dissimilarity” among the schools. (Note that dissimilarity is undefined when there are no minorities or non-minorities in the city.) Try moving the sliders so that they are in line with each other and see what happens to the calculated dissimilarity index.

Proportion of black students in school 1

50

%
Proportion of black students in school 2

50

%
Proportion of black students in school 3

50

%
Proportion of black students in school 4

50

%

Index of dissimilarity: 100%

Counter-intuitively, one way to obtain a lower dissimilarity index is to be a much more highly minority-concentrated inner city! In other words, this index measures “dissimilarity” relative to the baseline of the average city minority share, so a city that where all schools are 95% minority will have a dissimilarity index of zero, just like a city where all schools are 50% minority.

Many people write that the white-black school dissimilarity index is the proportion of all whites that would have to switch schools in order to make each school in the city match the racial composition of the city. Experimenting with these sliders, I find this interpretation hard to understand. Still, this index is clearly measuring something related to segregation.

Results in brief

• White-black dissimilarity is higher in elementary schools than neighborhoods (2006 paper). But the average difference is small (about 0.8%).
• White-hispanic dissimilarity is higher in elementary schools than neighborhoods (2006 paper). And the differences are large (about 5.4%).
• White-black segregation is overall larger than hispanic segregation, dissimilarity indices are around 60% and 50%, for white-black and white-hispanic, respectively.
• White-black segregation is higher among non-magnet elementary schools. White-hispanic segregation is about the same among non-magnet elementary schools. This suggests that magnet programs do help attract whites, but are mainly focused on reducing black-white segregation, not hispanic-white segregation.
• Their 2009 analysis is not split between blacks and hispanics so we cannot see the differences by minority subgroup for middle schools and high schools. On the other hand, their 2009 paper includes middle and high schools. Overall, dissimilarity indices tend to be lower for middle schools and high schools.
  • They say that this is because of larger attendance zones, though I don’t know how they can say it is that and not, instead, the fact that private school attendance tends to be higher for lower grades.
• From their 2009 paper, they find that the dissimilarity index is on average 4% larger across schools than across neighborhoods.
• Conclusion: schools are more sorted than neighborhoods.

The controversy of this paper

Evidence from this paper is contrary to the idea that school choice can reduce racial segregation. On the other hand, neighborhood-based magnet schools do seem to reduce segregation, contrary to fable of the KCMSD case.

Unfortunately there is a biting general equilibrium critique. If you follow this paper and shut down or handicap private schools, thinking that you are going to reduce segregation, then you might see even greater neighborhood-based white flight. In other words, if whites cannot segregate themselves by school, maybe they would segregate themselves by neighborhood. In this sense, Sohoni and Saporito have “looked under the lamp-post” on this one. For sure, in the inner city, there are proportionally more whites in private schools than blacks. So if we imagine holding neighborhood racial compositions constant and closing the private schools, certainly there would be integration. But we can’t hold that constant.

Appendix

Simulation for a claim

Recall my claim: if families have preference over school racial composition, then schools will be more segregated than neighborhoods.

• Sorting – a simulation.pdf outlines the simulation I ran and displays the results; and
• segregationSimulation.R is the R code to run the simulation.

References

Saporito, Salvatore and Deenesh Sohoni (2006). “Coloring Outside the Lines: Racial Segregation in Public Schools and Their Attendance Boundaries.” Sociology of Education.

Sohoni, Deenesh and Salvatore Saporito (2009). “Mapping School Segregation: Using GIS to Explore Racial Segregation between Schools and Their Corresponding Attendance Areas.” American Journal of Education.