segregsmall: A command to estimate segregation in the presence of small units

• Published in: The Stata journal Vol. 21; no. 1; pp. 152 - 179
• Main Authors: D’Haultfœuille, Xavier, Girard, Lucas, Rathelot, Roland
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.03.2021
• Subjects: segregation indices; st0631; Duncan index; Theil index; Coworker index; Atkinson index; Gini index; small-unit bias; partial identification
• ISSN: 1536-867X; 1536-8734
• DOI: 10.1177/1536867X211000018

Suppose that a population, composed of a minority and a majority group, is allocated into units, which can be neighborhoods, firms, classrooms, etc. Qualitatively, there is some segregation whenever allocation leads to the concentration of minority individuals in some units more than in others. Quantitative measures of segregation have struggled with the small-unit bias. When units contain few individuals, indices based on the minority shares in units are upward biased. For instance, they would point to a positive amount of segregation even when allocation is strictly random. The command segregsmall implements three recent methods correcting for such bias: the nonparametric, partial identification approach of D’Haultfœuille and Rathelot (2017, Quantitative Economics 8: 39–73); the parametric model of Rathelot (2012, Journal of Business & Economic Statistics 30: 546–553); and the linear correction of Carrington and Troske (1997, Journal of Business & Economic Statistics 15: 402–409). The package also allows for conditional analyses, namely, measures of segregation accounting for characteristics of the individuals or the units.