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Langel, Matti

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Langel, Matti
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https://libra.unine.ch/handle/123456789/547

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  • Publication
    Accès libre
    Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index
    (2012)
    Langel, Matti 
    ;
    Tillé, Yves 
    Zenga’s new inequality curve and index are two recent tools for measuring inequality. Proposed in 2007, they should thus not be mistaken for anterior measures suggested by the same author. This paper focuses on the new measures only, which are hereafter referred to simply as the Zenga curve and Zenga index. The Zenga curve Z(α) involves the ratio of the mean income of the 100 α %poorest to that of the 100 (1-α)% richest. The Zenga index can also be expressed by means of the Lorenz Curve and some of its properties make it an interesting alternative to the Gini index. Like most other inequality measures, inference on the Zenga index is not straightforward. Some research on its properties and on estimation has already been conducted but inference in the sampling framework is still needed. In this paper, we propose an estimator and variance estimator for the Zenga index when estimated from a complex sampling design. The proposed variance estimator is based on linearization techniques and more specifically on the direct approach presented by Demnati and Rao. The quality of the resulting estimators are evaluated in Monte Carlo simulation studies on real sets of income data. Finally, the advantages of the Zenga index relative to the Gini index are discussed.
  • Publication
    Accès libre
    Statistical inference for the quintile share ratio
    Langel, Matti 
    ;
    Tillé, Yves 
    In recent years, the Quintile Share Ratio (or QSR) has become a very popular measure of inequality. In 2001, the European Council decided that income inequality in European Union member states should be described using two indicators: the Gini Index and the QSR. The QSR is generally defined as the ratio of the total income earned by the richest 20% of the population relative to that earned by the poorest 20%. Thus, it can be expressed using quantile shares, where a quantile share is the share of total income earned by all of the units up to a given quantile. The aim of this paper is to propose an improved methodology for the estimation and variance estimation of the QSR in a complex sampling design framework. Because the QSR is a non-linear function of interest, the estimation of its sampling variance requires advanced methodology. Moreover, a non-trivial obstacle in the estimation of quantile shares in finite populations is the non-unique definition of a quantile. Thus, two different conceptions of the quantile share are presented in the paper, leading us to two different estimators of the QSR. Regarding variance estimation, Osier (2006, 2009) proposed a variance estimator based on linearization techniques. However, his method involves Gaussian kernel smoothing of cumulative distribution functions. Our approach, also based on linearization, shows that no smoothing is needed. The construction of confidence intervals is discussed and a proposition is made to account for the skewness of the sampling distribution of the QSR. Finally, simulation studies are run to assess the relevance of our theoretical results.
  • Publication
    Accès libre
    Variance estimation of the Gini index: revisiting a result several times published
    Langel, Matti 
    ;
    Tillé, Yves 
    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.