Arbeitsbereich

Migration und Mobilität

Auf einen Blick Projekte Publikationen Team

Projekt

Quantifying and Interpreting Measures of Segregation

Boris Barron; in Zusammenarbeit mit Matthew Hall, Tomas Arias (beide: Cornell University, Ithaca, Vereinigte Staaten), Peter Rich (University of Wisconsin-Madison, Vereinigte Staaten)

Ausführliche Beschreibung

Residential segregation shapes socioeconomic outcomes across cities worldwide, and demographic research depends on quantitative indices to track segregation patterns and trends. These indices reduce neighborhood-level population data to single values, enabling comparisons across cities and over time. For such comparisons to be meaningful, indices must accurately measure what researchers interpret them as measuring – a requirement that turns out to be surprisingly difficult to verify.

Consider the case of determining whether a segregation measure remains constant when only a city's overall racial composition changes, while the neighborhood sorting dynamics stay the same. This property, known as compositional invariance, is essential for distinguishing genuine changes in residential sorting from demographic shifts, and is routinely assumed to hold for a large class of segregation indices. Nevertheless, no formulation of compositional invariance has been empirically verified in either simulations or real-world tests. A key challenge is that varying only city composition is not possible in real populations, while simulations fail to capture real-world complexities.

The path forward therefore requires a triangulation of a variety of techniques: controlled simulations, real-world tests, and principled mathematical theory. For compositional invariance in particular, we demonstrate that standard indices fail compositional invariance in agent-based simulation tests and real-world cities by conditioning on composition via random sampling, while information theory yields accurate out-of-sample predictions, thus providing consistent evidence that indices are not capturing the intended segregating process. The substantive implication is that segregation comparisons have been inadvertently confounded by changes in composition, leading to incorrect interpretations of trends and misleading evaluations of policy implementations.

More ambitiously, the reliance on indices themselves represents a limitation, as reducing a complex distribution of neighborhood compositions to a single number, or even to a set of indices, is known to inevitably discard information. This project addresses this limitation by constructing function-based measures derived directly from a set of desirable properties by drawing on a subset of segregation literature concerned with identifying which mathematical properties would be desirable in segregation measures. We demonstrate that neighborhood-level population data can be transformed using widely accepted properties into probability distributions, thus allowing researchers to leverage statistical and information-theoretic techniques. The resulting segregation measures are therefore descriptive, capturing structural segregation patterns; and predictive, allowing researchers to combine disparate sources of information to predict broad segregation patterns.

In sum, this project aims to substantially strengthen and complement existing approaches by testing standard measures, correcting them when they do not align with intended interpretations, and extending indices into a richer mathematical framework when necessary.

Publikationen

Barron, B.; Hall, M.; Rich, P.; Cohen, I.; Arias, T.:

When all measures fail the same way: a fundamental correction to American segregation trends

MPIDR Working Paper WP-2026-016. (2026)