D’Haultfoeuille Xavier and Rathelot Roland. Measuring Segregation on Small Units: A Partial Identification Analysis. Quantitative Economics, accepted.
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 to hire an individual from the minority group. We define segregation indices as inequality indices on these un- observed, 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.