The Divergence Index: A Decomposable Measure of Segregation and Inequality

TL;DR

This paper introduces the Divergence Index, an additively decomposable measure of residential segregation that leverages relative entropy (KL divergence) to compare local versus regional compositions. It clarifies the conceptual distinction between segregation and diversity, showing that entropy‑based indices like the Information Theory Index measure diversity and should complement, not substitute, segregation measures. Through analytic and empirical demonstrations—including Westchester County and the 100 largest U.S. metros from 1990 to 2010—it shows that $D$ and $H$ can move in different directions under changing population structures, with $H$ typically declining while $D$ rises, especially in suburbs. The work highlights the practical value of decomposition for understanding multi‑level segregation dynamics and the conditions under which different indexes yield complementary insights for policy and research.

Abstract

Decomposition analysis is a critical tool for understanding the social and spatial dimensions of segregation and diversity. In this paper, I highlight the conceptual, mathematical, and empirical distinctions between segregation and diversity and introduce the Divergence Index as a decomposable measure of segregation. Scholars have turned to the Information Theory Index as the best alternative to the Dissimilarity Index in decomposition studies, however it measures diversity rather than segregation. I demonstrate the importance of preserving this conceptual distinction with a decomposition analysis of segregation and diversity in U.S. metropolitan areas from 1990 to 2010, which shows that the Information Theory Index has tended to decrease, particularly within cities, while the Divergence Index has tended to increase, particularly within suburbs. Rather than being a substitute for measures of diversity, the Divergence Index complements existing measures by enabling the analysis and decomposition of segregation alongside diversity.

Figures (6)

• Figure 1: Comparing Local Values of the Divergence Index and Information Theory Index in Three Hypothetical Cities
• Figure 2: Comparing Local Values of the Indexes in City C
• Figure 3: Black-White Segregation and Diversity Between Detroit and the Suburbs
• Figure 4: Components of the Decomposition Within and Between Subareas of each Metropolitan Area
• Figure 5: Changes in Within-City and Within-Suburb Index Values for the Divergence Index and Information Theory Index in the 100 Largest Metropolitan Areas, 1990 to 2010