Variance estimation of the Gini index: revisiting a result several times published

• Published in: Journal of the Royal Statistical Society. Series A, Statistics in society Vol. 176; no. 2; pp. 521 - 540
• Main Authors: Langel, Matti, Tillé, Yves
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.02.2013; Blackwell Publishing; Oxford University Press
• Subjects: Approximation; Error; Estimating techniques; Estimation; Estimation methods; Estimators; Gini; Gini index; Income inequality; Inequality; Inference; Influence function; Linear models; Linearization; Population estimates; Regression analysis; Sampling; Standard error; Statistical analysis; Statistical variance; Survey sampling; Variance; Variance estimation
• ISSN: 0964-1998; 1467-985X; 1467-985X
• DOI: 10.1111/j.1467-985X.2012.01048.x

Since Corrado Gini suggested the index that bears his name as a way of measuring inequality, the computation of variance of the Gini index has been subject to numerous publications. We survey a large part of the literature related to the topic and show that the same results, as well as the same errors, have been republished several times, often with a clear lack of reference to previous work. Whereas existing literature on the subject is very fragmented, we regroup references from various fields and attempt to bring a wider view of the problem. Moreover, we try to explain how this situation occurred and the main issues that are involved when trying to perform inference on the Gini index, especially under complex sampling designs. The interest of several linearization methods is discussed and the contribution of recent references is evaluated. Also, a general result to linearize a quadratic form is given, allowing the approximation of variance to be computed in only a few lines of calculation. Finally, the relevance of the regression-based approach is evaluated and an empirical comparison is proposed.