“The Integration Anomaly” Author Responds to Critics

My report, The Integration Anomaly, relies on dozens of empirical studies and logic from simulation models calibrated to real-world data to make a claim that universal school choice programs can be designed to promote greater race and class integration. 

In recent decades, Americans have been making free choices in myriad areas that are leading to more racial integration in society. The anomaly is public education—where segregation by race has increased since the early 1980s. As one public school consultant noted (see page 23 of my report),

“We have diversity everywhere, except in schools.”

In this piece, I respond to the concerns the National Education Policy Center (NEPC) has with my report.

Note: The authors of the NEPC review are Genevieve Siegel-Hawley, assistant professor of educational leadership at Virginia Commonwealth University, and Erica Frankenberg, associate professor of educational leadership at Pennsylvania State University. A condensed version of my rebuttal can be found on the NEPC’s website here. The reviewing authors are likely to post an additional response on that page as well.


Claim:  The anomaly to which the title of my report alludes isn’t backed up by the raw data or supported by other researchers.

First, Siegel-Hawley and Frankenberg appear reluctant to admit that the data show neighborhood racial integration has improved significantly since 1970.

My report cites evidence reported in a study by Edward Glaeser (Harvard University) and Jacob Vidgor (then at Duke University) that uses data from the decennial United States Census to show that American neighborhoods have become significantly more integrated by race since 1970.

Siegel-Hawley and Frankenberg offer two references (Hertz, 2015 and Alba and Romalewski, 2012), which they think refute that evidence. However, the fact that neighborhoods have become more integrated by race is not in dispute. The pieces Siegel-Hawley and Frankenberg cite as supposedly opposing this fact say things like, “Without question, residential integration of African Americans is increasing, continuing a trend of desegregation that has been evident for several decades.” (Alba and Romalewski) The other piece that Siegel-Hawley and Frankenberg suggest opposes this fact states, “Glaeser does excellent empirical work, and then draws odd conclusions from the very useful numbers he finds…” (Hertz)

Like me, Alba, and Romalewski and Hertz do not question the data, they just do not believe that neighborhoods are perfectly integrated now. It is not inconsistent to acknowledge that neighborhood racial integration has improved significantly over the past three decades, but that we have room to improve further. In fact, I stated as much on page 23 of my report where I said, “I am not suggesting that America is perfectly racially integrated ….”

The Integration Anomaly cites work by Siegel-Hawley and others that shows racial segregation across public schools has not improved in the same manner as neighborhood segregation since the early 1980s—the period prior to 2000 had a diverging trend with neighborhoods becoming more racially integrated and public schools becoming more segregated. After 2000, public school integration continued to lag neighborhood integration. And in their review of my report, the authors support my point, mentioning “our already increasingly segregated traditional public schools.”

Thus, Hertz, Alba, Romalewski, Glaeser, and Vigdor all read the available demographic data as indicating that American neighborhoods have become more racially integrated since 1970. Siegel-Hawley and coauthors, two other studies cited on page 8 in my report, and Siegel-Hawley and Frankenberg in their review read the data as suggesting that public school segregation increased between the early 1980s and 2000. Both my study and Stroub and Richards (2013) find that public school integration trends lagged neighborhood integration trends after 2000.

I am hardly alone in accepting the data that show a “puzzling divergence” in the trends of neighborhood and school segregation after the early 1980s—trends that should move closely together given the current structure of the U.S. public education system, which ties students’ assigned public schools to their ZIP Codes.

To conclude, it is inaccurate, based on the data, to blame adverse segregation trends in public schools on adverse segregation trends in neighborhoods—because neighborhood integration has improved for decades. Neighborhood integration is surely a worthy goal, but given the divergence in trends, we should not ignore the realm in which we see negative segregation trends: the public education system.


Claim: The Dissimilarity Index is not an appropriate way to define segregation and contributes to biased results.

Siegel-Hawley and Frankenberg suggest that I should not have used the dissimilarity index (DI) to measure school segregation. On page 1 of their review, they suggest that the use of the DI is a “flawed methodological decision concerning how to define segregation” that contributed to “biased results.”

I used the DI because it is easy to interpret; it is commonly used; and it facilitated comparison with the Glaeser and Vigdor data on housing segregation, as mentioned above. Fortunately, the DI is “highly correlated” with the metric that Siegel-Hawley and Frankenberg prefer—as noted by a paper recommended to me by Siegel-Hawley and Frankenberg (Fiel, 2015) and by at least two other papers, as listed below.

On page 161 of his report, Fiel (2015) states, “The most common unevenness school segregation measures are the dissimilarity index (D) and theil’s information theory index (H). Both measure schools’ deviations from the local racial composition and aggregate them into a weighted average, and they are highly correlated in empirical studies (James and Taeuber 1985; White 1986).”

Finally, Siegel-Hawley used the DI to compare neighborhood and school segregation trends in four metro areas in her own report in 2013. In another 2013 paper, the other reviewer—Frankenberg (2013)—wrote on page 5 of her study, “I primarily use the Index of Dissimilarity to measure school and housing segregation.”

Perhaps Siegel-Hawley and Frankenberg have changed their views on the appropriate use of the DI since 2013. Either way, there is no bias in using the DI to measure segregation trends over time.


Claim: African American families freely choosing schools that have a disproportionate number of African American students should be considered a negative outcome.

Given the ugly history of whites, public school districts, and other government entities restricting the choices of African Americans, I recommend Siegel-Hawley and Frankenberg express more caution when criticizing the school choices made by African American parents when they are offered a modicum of educational freedom.

On page 6 of their review, the authors indicate that it is a bad thing when “black students transfer to more segregated charter schools.”

On pages 15 and 16 in my report, I cite evidence from North Carolina that some African American parents have chosen to move their children from traditional public schools to charter schools, where the charter schools have a higher proportion of African American students. I also cite evidence from North Carolina that traditional public schools there provide more novice teachers, on average, to African American students relative to white students—even when they attend the same school. The researchers also note that there is substantial segregation within individual traditional public schools in North Carolina. Thus, African American parents may have very good reasons to move their children to charter schools with more African American students.


Claim: My report ignores research literature on the effect of charter schools on segregation.

Siegel-Hawley and Frankenberg insist I should have included certain studies that examine charter schools’ effect on segregation in schools.

The reason I did not give weight to many is not because I ignored them, but because after analyzing them, I found their findings to be unreliable. In my report (pages 14, 15), I actually explain why much of this research is flawed.

For instance, the reviewing authors think I should have cited a paper by Renzulli and Evans (2005).

Renzulli and Evans’ paper uses two measures of interracial exposure in public schools to explain the likelihood that white students attend charter schools. They term those measures as “integration” and “contact.” Using their model 1 results in Table 2 of their paper, Renzulli and Evans report that when “integration” increases by 1 that charter school white enrollment increases by 0.73 percent. Thus, Renzulli and Evans conclude that when traditional public schools are more integrated, more whites enroll in charter schools. But, this thinking ignores their next estimate—when interracial “contact” increases by 1 in public schools, white enrollment in charter schools falls by 0.86 percent. Thus, the two variables—integration and contact that measure different but intimately related concepts and are surely highly correlated with each other—have roughly equal and offsetting effects, which implies that interracial integration/contact in public schools has no discernable effect on white charter school enrollment in their study.

To be very clear, their measures of integration and contact move in tandem—when one increases, the other increases—and vice-versa. In fact, Renzulli and Evans show on page 405 of their article that their measure of integration is a mathematical function of their measure contact. It is not valid to change one of these variables without changing the other accordingly.  The offsetting signs and magnitudes in their results indicate that the effect of charter schools on segregation is approximately zero. This empirical result of theirs comports with what they report on page 404 of their study where they say, “…we find that charter schools enroll the same percent of white students, on average, as the districts in which they are located (48.12 percent for charter schools and 48.46 percent for districts).”

Indeed, there are other studies that provide evidence that charter schools do and do not contribute to school segregation. I did not cite them in the interest of space. (My report has 81 endnotes. However, I did cite the largest study on the effect of school segregation published by the RAND Corporation in 2009, and I cited the study with the most “negative” finding about charter schools, the one with data from North Carolina.

I believe my review of the literature on this topic is sufficient because it covered both of the contrary sets of findings.


Claim: I misleadingly omitted relevant research by “strangely” curating the literature included in my report.

On pages 13-14 in my report, I wrote at the very beginning of the discussion of prior research findings:

“There is a large body of research from different areas of study that can be used to shed light on this issue. However, it is not feasible to discuss in detail each of the literally hundreds of studies that can inform us. Nevertheless, in this subsection I endeavor to discuss studies that are representative of the varied findings and thinking in these large literatures that cover different areas of study.”

A full review of every single article in every single area of study I covered would likely be well over 100 pages by itself. That said, I discussed research literature that represented the diversity of findings, commented on the strengths and weaknesses of findings, and put findings into appropriate policy contexts.

On the other hand, Siegel-Hawley and Frankenberg omitted some relevant research without explanation on several occasions in their review.

1. The reviewing authors do not provide a citation or even name the RAND 2009 study in their review—but they allude to the study on page 6 in their review by stating, “[The Integration Anomaly] then misleadingly suggests findings from those studies differ when both find that black students transfer to more segregated charter schools…”

In fact, I provide a long quote from the RAND study on page 15 of my report. I do not believe that the authors of the RAND study are misleading in their own characterization of their results. In their study of charter schools in eight states, the RAND authors wrote,

“Overall, across the two analyses, it does not appear that charter schools are systematically skimming high-achieving students or dramatically affecting the racial mix of schools for transferring students. Students transferring to charter schools had prior achievement levels that were generally similar to or lower than those of their TPS peers. And transfers had surprisingly little effect on racial distributions across the sites: Typically, students transferring to charter schools moved to schools with racial distributions similar to those of the TPSs from which they came. There is some evidence, however, that African American students transferring to charters are more likely to end up in schools with higher percentages of students of their own race, a finding that is consistent with prior results in North Carolina (Bifulco and Ladd, 2007).”

2. Further, Siegel-Hawley and Frankenberg give—to use their own words—a strangely curated taxonomy of the literature review in my report.

On page 6 of their review, they characterize my report as “focusing on charter schools, within-school segregation, international school choice and simulations.” On page 14 in The Integration Anomaly I gave a clear taxonomy of the literature I reviewed:

“Next, I discuss (a) the credible research from several areas of study and (b) what that evidence means for the relationship between school choice and integration. I categorize the findings from several areas of study in the following manner and discuss each category in turn:

  • The effect of charter schools on segregation
  • Segregation within schools
  • International evidence on the impact of school choice programs on segregation
  • U.S. evidence on the impact of school choice programs on segregation
  • Simulation studies”

Readers will notice that, for undisclosed reasons, Siegel-Hawley and Frankenberg left one item off their list, “U.S. evidence on the impact of school choice programs on segregation.”

Eight of nine empirical studies of U.S. voucher programs find that U.S. voucher programs have increased school integration. One study found no effect. Like all of the other research I cited, I offer appropriate and reasonable caveats and context for the findings with respect to U.S. voucher programs.

There is another line of literature mentioned later in my report (page 23). That additional literature shows that Americans, when allowed to make free choices, are not only choosing to integrate their neighborhoods by race, but also are choosing to integrate their families via interracial marriage and adoption, and choosing integration via their political support. The reviewing authors did not mention my discussion of these findings in their description of what I cover in my report either.

It is interesting that through their free choices Americans are choosing to integrate their families, neighborhoods, and political support by race. But, when Americans are largely denied choice—or choice is available only to those with means, as is the case with the current K–12 education system in the United States—that segregation is getting worse or lagging behind.

3. A final omission found in Siegel-Hawley and Frankenberg’s review is on page 5 and in footnote 11 where the authors indicate that some school desegregation efforts have “led to declines in both school and housing segregation.” That said, one of the studies cited in footnote 11, Siegel-Hawley (2013) found neighborhood segregation in metro Louisville, Kentucky decreased while school segregation increased. I reported this same finding in The Integration Anomaly, although Siegel-Hawley analyzed a longer time frame than I did.

What’s important to notice here is that the reviewing authors also do not cite the literature that some school desegregation efforts contributed to segregation.

The two best studies on mandating equality by affirmative desegregation efforts in public schools (Reber, 2005 and Baum-Snow and Lutz, 2011) find that these desegregation efforts decreased white enrollments in central city districts by 6 to 12 percent (page 22 in my report). Although these two studies do the best job of analyzing causality, longer-term suburbanization trends may have occurred regardless.

My report clearly states on page 26, “While I support proposals to integrate schools within individual school districts, those efforts will not promote much integration by race and class because the vast majority of segregation is across districts. While not currently required by law, any efforts to promote integration across public school district lines are doomed because districts have become very large geographically over time through school district consolidations.”


Claim: The Integration Anomaly ignored research on income segregation in American neighborhoods.

Regarding the literature, Siegel-Hawley and Frankenberg mention a study, (Reardon and Bischoff, 2012), that finds that income segregation across American neighborhoods has increased significantly and consistently since 1970. My report cites or discusses that study on pages 11, 20, 26, 36, 38, and 39—thus it was not ignored.

My report also shows how the simulation evidence indicates that school choice can improve income integration across neighborhoods provided:

  1. the school choice programs are universal;
  2. the school choice programs do not incentivize parents of means who can afford public and private school options to flee a system of mandated equality (lotteries, controlled choice, etc.);
  3. and the school choice programs feature other design elements discussed on pages 23–26 of The Integration Anomaly. Certain school choice program DO’s and the avoidance of certain DON’Ts will promote race and class integration in American neighborhoods and schools based on logic and evidence reviewed in my report.


Claim: The conclusion of The Integration Anomaly makes recommendations “without supporting material” and exclude some options “backed by research.”

On page 9 of their review, Siegel-Hawley and Frankenberg write:

“A considerable amount of new information is introduced in the conclusion of the report. Without supporting material, the reader is left to wonder about key recommendation points, including whether or not it possible to “mandate equality,” or why the cost of transporting students for integration would be prohibitive, but not the cost of providing universal school choice vouchers. The author also takes off the table a number of options for connecting choice to integration (e.g., controlled choice, lottery-based admissions) backed by research.”

I disagree with the characterization that I make recommendations “without supporting material” or that I exclude some options “backed by research.” My literature review described several unintended consequences of “mandating equality.”

For example, homogenizing schools in New Zealand along with publicly ranking them by socio-economic status (with the purpose of providing more resources to schools with disadvantaged students) was associated with more sorting by ethnicity and class across schools.  As I noted, such nationwide results for New Zealand may not indicate a causal relationship between their school choice program and segregation, as segregation also increased during these time periods in American public schools, which did not have significant school choice programs. On the other hand, my report recommends giving larger scholarships to disadvantaged students under school choice policies. On page 17 in my report, I note that such a program design feature improved integration under Chile’s universal school choice program.

Also, as stated previously, the two best studies on mandating equality through affirmative desegregation efforts in public schools (Reber, 2005 and Baum-Snow and Lutz, 2011) find that these desegregation efforts decreased white enrollments in central city districts by 6 to 12 percent (page 22 in my report). While these two studies do the best job of analyzing the causal effects of affirmative desegregation efforts on segregation, longer-term suburbanization trends may have occurred anyway.

My report references a study that showed controlled choice programs have led to more segregation—please see page 25 and footnote 81 in my study and the discussions of Louisville, Kentucky above and just below. For that reason, I cannot recommend controlled choice in good conscience, especially not when policies with better track records exist.

While not mentioned in my report, a recent news account describes how a controlled choice program in Louisville, Kentucky may have unintended consequences for segregation:

“Well-off parents moving to Louisville say their friends often advise them to buy a house in nearby Oldham County, Kentucky, or in the Indiana suburbs to the north of the city to avoid busing. When one woman posted to Yelp that she was moving to Louisville from Charlotte, North Carolina, and wanted to know which area had the best schools, the responses were blunt.

‘The schools in Jefferson Co are in fact good its the whole school assignment plan that stinks. You can move next door to the school you want your child to enroll in but there is NO guarantee that your child will get in,’ one woman wrote in response. ‘Look outside the county to avoid this mess unless you want to go private.’”

The next eleven paragraphs in the news account also mention other instances of parents being denied their preferred schools by district administrators and the resulting consequences.


Claim: My report will “prompt the reader to incorrectly assume that housing integration policies will have little bearing on school segregation.”

My report makes no such claim or insinuation. To the contrary, my exposition on pages 8–11 indicates that there should be a tight link between trends in neighborhood and housing segregation. In my report, when neighborhood and school segregation trends diverge, I characterize that divergence as “puzzling.”

On page 1 of their review and elsewhere, Siegel-Hawley and Frankenberg agree with me on that point; then later in their review, they criticize my empirical work for suggesting it. That is, on page 8 of their review, the authors assert that the differences in trends between neighborhood and school segregation must be very different—“10-point” differences in trends—before they are “meaningful.” Thus, public school segregation could increase by 4.5 DI points, while neighborhood segregation could decline by 5 DI points, and Siegel-Hawley and Frankenberg suggest such a difference of 9.5 points “may in fact represent minimal or no meaningful change in segregation” (page 8 of their review).  To be clear, this is my example and their words.

In short, I agree with Siegel-Hawley and Frankenberg’s view on page 1 of their review—and I disagree with their contradictory view on page 8 of their review.


Claim: The Integration Anomaly ignores how and why parents choose schools.

I agree with some of what Siegel-Hawley and Frankenberg on page 6 of their review regarding “how and why parents choose schools.” I would also note that I did not ignore the topic.

In my report on page 26, I state,

“If the main differences between schools are the demographics of the students, then parents will sort based on student demographics—and this claim is supported by the New Zealand evidence. This claim is also consistent with the evidence about segregation across public schools and neighborhoods in studies by Uriquola and Reardon and Bischoff.”

I also reference a study on how parents choose schools in footnote 35 in the report.

Based on the empirical evidence and the simulation models reviewed in my report, the homogenization of curriculum and other offerings across public schools lead to unnecessary segregation by race and class. A choice system with true autonomy for individual public and private schools will give parents another reason to sort other than by race, class, and/or student achievement—where Siegel-Hawley and Frankenberg note, like me, that such sorting has been occurring across American public schools for decades.

If done in an economically progressive manner, a true universal school choice system, where all funds follow children to the school of their family’s choice, will provide an incentive for schools to enroll more disadvantaged students. For instance, offering larger scholarships to disadvantaged students has promoted integration in Chile’s universal school choice program (Elacqua, 2008). That report is cited on page 17 in my report.


Claim: The Integration Anomaly ignores the role of transportation in promoting school integration under school choice programs.

On page 9, Siegel-Hawley and Frankenberg state that I ignore “transportation” as a way to promote integration under school choice programs. That is not accurate.

Page 27 of my report states, “I also agree that disadvantaged students should be given larger scholarships or vouchers in order to allow them to be more attractive to schools of choice, to allow them to pay for any transportation needs, and to make more schools affordable to them.”

Perhaps one reason why disadvantaged students are underrepresented in some charter schools is because those charter schools do not receive equitable funding relative to nearby traditional public schools—thus, the charter schools may not be able to offer adequate transportation options. Allowing more charter and private schools to exist would also make such schools more accessible to disadvantaged populations.

I suppose some could suggest that we increase spending on transportation and open public school choice among traditional public schools instead of allowing parents to choose among traditional public, private, and charter schools. I suppose they may support spending more money on transportation, so that students can access the options they want within the traditional public school system.

An argument against limiting choice to only traditional public schools is:

  • Increasing transportation for public schools requires more spending and new tax revenue to afford it. These additional funds for transportation have an opportunity cost—that is, these funds then cannot be spent on other worthy purposes like health care, housing, social workers, or food assistance. Properly designed school choice programs do not require new funds to operate, but repurpose the dollars that are already used on behalf of students—to allow them to access the schools of their choice.
  • We could bus students to traditional public schools outside of their neighborhoods, free of charge to them, but as long as the majority of public schools’ curriculum, teaching methods, etc. are homogenous, families will still choose schools on the basis of peer quality—as has been occurring in the traditional public education system. My report notes that policy centralization that has homogenized public school offerings has been occurring for decades. My report cited work by Urquiola (2005), and Siegel-Hawley and Frankenberg in their review cited additional studies that found demographic sorting within the traditional public education system.
  • A better solution to promote integration and other outcomes would be to give every parent the agency and means to choose the schools that best meet their children’s needs. Parents would be able to choose among public and private schools. Schools would be allowed to differentiate their offerings—giving parents a reason other than peer quality for which to sort among schools.


Claim: My report did not consider a recent study on the effect of charter and private schools on segregation.

Siegel-Hawley and Frankenberg’s review took issue with my omitting a July 2015 study from my literature review. This study was released after I finished my work, and my report was in editing and production. As suggested by Siegel-Hawley and Frankenberg, I review Jeremy Fiel’s 2015 paper “Closing Ranks: Closure, Status Competition, and School Segregation” here.

Fiel (2015) should be commended for compiling an impressive database. That said, there are problems with his methods and Siegel-Hawley’s and Frankenberg’s interpretation of his results.

First, he regresses school segregation on neighborhood segregation. This is statistically problematic, because, as stated in endnote 13 of my report, “Clotfelter also notes that whites trying to avoid having many African American students in their children’s classrooms and schools may sort in whiter neighborhoods in order to enroll their children in whiter public schools. Thus, a desire for school segregation may cause residential segregation.”  Regressing school segregation on neighborhood segregation presents the well-known statistical problem of reverse causality—which leads to biased estimates on all regressors. In other words, we have a “chicken and egg” problem—what came first, school segregation or neighborhood segregation.  Researchers, including me, believe that both can “come first” and cause the other. Thus, to estimate the impact of one on the other requires, at least, an appropriate two equation model.  Fiel only has one equation and thus cannot estimate to what extent one form of segregation causes the other—and, what is important here, all of the other coefficient estimates are biased.

Fortunately, my reviewing authors agree with me on this point that school segregation may have a causal effect on housing segregation. As Frankenberg said on page 3 in her 2013 study that also sites Siegel-Hawley’s research on the topic, “Other research has suggested that there might be a reciprocal relationship that exists between schooling and residential segregation, namely that schools influence residential segregation patterns as well. (Siegel-Hawley, 2011; see also Frankenberg, 2005).”

A second concern is that it appears Fiel included all schools and all grade levels together when calculating school segregation. If true, private and charter schools serve more students in the earlier grades relative to traditional public schools. As noted on pages 35 and 36 of Greene (2005), elementary schools are more segregated than middle and high schools because there are more of them—so they serve smaller geographic areas. Thus, the comparison between charter schools, private schools, and traditional public schools are not apples-to-apples. The data should be restricted to like grades for a fair and accurate comparison. Given the different grade configurations between sectors, an approach like Fiel’s—even if it remedied all other issues—would show private and charter schools contributed to segregation, even if they truly did not, simply because private and charter schools disproportionately serve elementary school students.

A third problem with Fiel (2015) involves interpretation of results. The direct effects of Fiel’s estimates, listed in Table 2 of his paper, indicate small effects of private and charter schools on increasing school segregation. As discussed just above, this small effect could merely be an artifact of charter and private schools serving more students in early grades. Further, Fiel also interacted the charter and private school variables with other variables (his model includes charter and private school market shares multiplied by other variables in his model—these multiplied terms are called “interaction” terms). Fiel does not report the coefficient estimates from those interactions, but does report the signs in his Table 7. His table 7 shows that many of the interaction terms have signs on their estimated coefficients that suggest private and charter schools lead to more integration. Thus, Fiel should have reported marginal effects so that readers can see what exactly are his estimates of the total effects of charter schools and private schools on segregation. His article does not provide information that allows readers to calculate the total effects of any of his variables on segregation.

I have other concerns with Fiel’s empirical work that are too lengthy to mention here, but I want to applaud his Herculean data collection effort that should yield fruitful research in the future.


Claim: Those interested in promoting integration should first focus on improving integration across neighborhoods through housing reforms.

Siegel-Hawley and Frankenberg appear to imply that those interested in promoting integration should first focus on improving integration across neighborhoods. Fortunately, that trend has been going in the right direction for decades. Neighborhood integration could be accelerated by some housing reforms, but I believe that the more than $600 billion that taxpayers spend on subsidizing K–12 education annually should be used in a manner that also promotes integration. And I believe, based on logic and evidence, that a well-designed educational choice system as described on pages 23–26 of my report will lead to more integration than the current public education system.


Concluding Remarks

I encourage people interested in this issue to read my original report, Siegel-Hawley’s and Frankenberg’s review, and any further comments on The Integration Anomaly.

I thank Genevieve Siegel-Hawley and Erica Frankenberg for their interest in my research. That said, I stand by my report. Nothing in their review was compelling enough to convince me otherwise. I encourage readers to consider the logic and evidence and form their own judgment about the likely effects of school choice on student outcomes, including integration.


*Opinions expressed by our guest bloggers are their own and do not necessarily reflect those of EdChoice.