Open AccessMeasuring segregation on small units: A partial identification analysis
Author(s) -
D'Haultfœuille Xavier,
Rathelot Roland
Publication year - 2017
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe501
Subject(s) - nonparametric statistics , binomial (polynomial) , statistics , estimator , mathematics , population , econometrics , identification (biology) , measure (data warehouse) , confidence interval , computer science , data mining , demography , botany , sociology , biology
We consider the issue of measuring segregation in a population of small units, considering establishments in our application. Each establishment may have a different probability of hiring an individual from the minority group. We define segregation indices as inequality indices on these unobserved, random probabilities. Because these probabilities are measured with error by proportions, standard estimators are inconsistent. We model this problem as a nonparametric binomial mixture. Under this testable assumption and conditions satisfied by standard segregation indices, such indices are partially identified and sharp bounds can be easily obtained by an optimization over a low dimensional space. We also develop bootstrap confidence intervals and a test of the binomial mixture model. Finally, we apply our method to measure the segregation of foreigners in small French firms.