Headlines last month proclaimed that “Cities Have Grown More Diverse, And More Segregated, Since the 90s.” The headlines originate in the key findings of a new, detailed study from the Othering and Belonging Institute (OBI) at UC Berkeley. The study leans heavily on a relatively new metric – the Divergence Index – which has impressed many researchers (myself included) with its versatility. But now that we have seen the Divergence Index in action, its versatility clearly comes at a cost: the Divergence Index conflates what we would intuitively call diversity with “segregation.”
As a result, more-diverse metro areas are usually ranked as more segregated by the Divergence Index. And as America became far more diverse over the past 30 years, it is logical that the Divergence Index would rise in most metro areas.
Why is it so hard to measure segregation?
Racial segregation is easy to see. You walk down the street and almost everybody in one neighborhood looks different than you and almost everybody in another neighborhood looks the same as you. The human eye and ear can also distinguish categories that are meaningful in some contexts but not others. Everybody but me in the café where I watched European soccer last week appeared to be not only Black but specifically Ethiopian. Was that café integrated or segregated? I certainly felt welcome as I bantered at the bar with an Ethiopian-American tennis instructor. But statistically, the café was far more Black and vastly more Ethiopian than the D.C. region as a whole.
In this context, “segregation” refers to places where one group is overrepresented – like the café – not to the legal regime that imposed second-class citizenship and pervaded every aspect of life for black Americans. Given the word’s loaded history, it would have been wiser for social scientists to choose another term.
The forms of segregation social scientists worry about are, of course, in areas of life more consequential than café preference. Residential and school attendance demographics are probably the most important and commonly studied areas of segregation.
But even where it matters, the statistics of segregation seem to tell us less than meets the eye.
Measurement is difficult because segregation is the characteristic of a region, not of a person or household. We cannot measure the segregation of a neighborhood in isolation; it depends on its context. A Madison, Wis., neighborhood that is equal parts white, black, Hispanic and Asian would earn a high Divergence Index – indicating high segregation – since it would sharply overrepresent all three non-white groups relative to the metro. An identical neighborhood in Miami, Florida, would score much lower, with only Asians significantly overrepresented.
This relativity exposes a gap between the conversational and statistical meanings of “segregation.” If Madison really did have a neighborhood like the one I described, nobody would call it segregated. We really should have a different word for this.
Screenshot of map by the Othering & Belonging Institute and OpenStreetMap.
The Divergence Index
The Divergence Index arrived in a sharp 2016 paper by Elizabeth Roberto, then a Princeton University post-doctoral researcher. Roberto skewered the field, which had fallen in love with using “entropy” – a concept from information theory – to measure segregation. Entropy, Roberto argued, does not even measure segregation – it measures neighborhood diversity.
Roberto proposed to fix entropy by introducing a contextual element. Her new relative entropy metric – the Divergence Index – would not mistake a lack of regional diversity for segregation. The result is conceptually simple:
- Measure the shares of each racial group in a metro
- Measure the shares of each racial group in each neighborhood
- Use a statistical formula to determine how much the neighborhoods differ from the metro
However, she may have gone too far in the opposite direction. The Divergence Index penalizes additions in regional diversity unless those additions are spread very evenly across neighborhoods. Understanding why this occurs requires two insights.
- First, the most helpful way to think of the Divergence Index is as a weighted average of concentration scores of the various groups in the model.
- Second, when one race is the overwhelming regional majority, its members will (by necessity) almost all live in neighborhoods that do not diverge much from the regional average.
Per the first insight, a newly sizable group – such as Hispanics and Asians in many cities – must be less concentrated than the weighted average of the existing population in order to decrease the Divergence Index.
As the second insight suggests, the typical biracial U.S. metro during the 20th century had a white majority with low divergence scores and a black minority with a high divergence scores. And where whites were seventy, eighty, or ninety percent of the population, the weighted average – the Divergence Index – ended up much closer to whites’ mechanically low concentration score than to blacks’ high score.
Thus, for an influx of Asians or Hispanics to decrease the Divergence Index, the new group has to hit a concentration score almost as low as whites – but without the advantage of achieving low divergence scores in any highly concentrated enclaves.
A new Asian or Hispanic minority can thus contribute to statistical segregation despite being much less segregated than the 20th-century black population.
New metric, old problems
The Divergence Index is not immune from data problems that plague most statistical measures of segregation. As Douglas Krupka has documented, bigger cities usually fare worse on segregation measures in part because of the artificial ways that lines are drawn. This seems to be the case in OBI’s study, where the nine largest U.S. metros are all among the 20 most segregated.
Implicit in Krupka’s argument is that cities with larger minorities will fare worse as well. An insular immigrant enclave that covers only a few blocks will be averaged together with the rest of its Census Tract. A much larger, but equally insular, enclave that fills out a Census Tract is caught in the statistical spotlight.
Viewing segregation holistically
This essay has been perhaps unnecessarily harsh toward the Divergence Index. The Index has problems. But so does every other measure of segregation. Still, OBI’s headlining of the Divergence Index shows that its status in the field has risen rapidly and it is ripe for critical review.
Returning to the newspaper headline that sparked this essay, is it fair to say that cities have grown more segregated since 1990? Behind the reliance on Divergence Index for headlines, OBI’s research carefully documents a half dozen segregation metrics. Drawing on the excellent interactive map, I revisited three metro areas that OBI reports as having among the greatest increases in segregation over the past 30 years: Fayetteville, Ark., Reading, Pa., and Boston.
What if we looked at these in a more holistic manner, putting Divergence Index into the context of metrics that might be less influenced by those metros’ rapidly diversifying populations? I recorded four measures of segregation for each city: Black-White Dissimilarity, Hispanic-White Dissimilarity, Black-White Exposure, and Black Isolation. As OBI notes, each “provides some insight into the phenomenon of segregation, while also concealing other facets.”
If these metros were becoming more segregated, in a holistic sense, we would expect to see most or all of the various measures pointing in the same direction. Instead, most of them point toward falling segregation, and it is likely that the rising Divergence Index indicates rising diversity in these metros.
In Fayetteville, two measures showed rising segregation, two falling. In Reading and Boston, all four measures declined. In all three cities the white population share fell and the entropy index, which measures neighborhood diversity, rose sharply.
If we take the Divergence Index as a single facet of statistical segregation in a more complete context, we should conclude that Reading and Boston exhibit clear evidence of rising diversity and falling segregation. Fayetteville is also becoming more diverse and its segregation indicators give mixed evidence.
Segregation is a loaded term, with serious moral connotations. Before warning the public that segregation is increasing, researchers and journalists ought to check that a multifaceted, careful look at the data confirms this summary of the data.
Salim Furth, Ph.D., is a DC-area housing policy researcher and lifelong urbanist. The views expressed here are not necessarily those of his employer.
