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Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas
[journal article]
Abstract Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studi... view more
Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article, we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study.... view less
Keywords
statistics; inequality; social inequality; indicator; construction of indicators; estimation; measurement; Italy; area
Classification
Methods and Techniques of Data Collection and Data Analysis, Statistical Methods, Computer Methods
General Sociology, Basic Research, General Concepts and History of Sociology, Sociological Theories
Free Keywords
Small area estimation; M-quantile models; inequality indicators; EU-SILC
Document language
English
Publication Year
2021
Page/Pages
p. 955-979
Journal
Journal of Official Statistics, 37 (2021) 4
DOI
https://doi.org/10.2478/jos-2021-0041
ISSN
2001-7367
Status
Published Version; peer reviewed
Licence
Creative Commons - Attribution-Noncommercial-No Derivative Works 3.0