The Dissimilarity Index Was Never Compositionally Invariant

The prevailing view is that White/Black segregation has experienced modest declines in recent decades, while White/Hispanic and White/Asian segregation have remained stable. This consensus is based on the assumption that segregation measures, such as the ubiquitous dissimilarity index, are free of systematic bias on city compositions, a property known as compositional invariance. This property is necessary because, while the Black population has remained stable in the U.S., the Hispanic and Asian populations have experienced significant growth. In this paper, we demonstrate that the assumption of compositional invariance for the dissimilarity index is fundamentally flawed and propose an easily-implementable adjustment factor to facilitate meaningful segregation comparisons of cities over space and time. The implications of this adjustment are stark: we find that White/Hispanic and White/Asian segregation have substantially decreased, with Hispanic segregation declining more rapidly than Black segregation. Our findings also highlight the exceptional nature of Black segregation, with the gap in their measured dissimilarity - after adjusting for compositional changes - persisting when compared to White segregation with other racial/ethnic groups.