Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

Marchetti Stefano () and Tzavidis Nikos ()
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Marchetti Stefano: University of Pisa, Department of Economia e Management, Via C. Ridolfi 10, 56124 Pisa (PI), Italy.
Tzavidis Nikos: University of Southampton, Social Statistics and Demography Social Sciences, Southampton SO17 1BJ, United Kingdom.

Journal of Official Statistics, 2021, vol. 37, issue 4, 955-979

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 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.

Keywords: Small area estimation; M-quantile models; inequality indicators (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:offsta:v:37:y:2021:i:4:p:955-979:n:9

DOI: 10.2478/jos-2021-0041

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