期刊名称：Electronic Journal of Applied Statistical Analysis
电子版ISSN：2070-5948
出版年度：2019
卷号：12
期号：1
页码：85-107
DOI：10.1285/i20705948v12n1p85
出版社：University of Salento
摘要：When calculating the Gini coefficient for distributions which include negative
values, the Gini coefficient can be greater than one, which does not make
evident its interpretation. In order to avoid this awkward result, common
practice is either replacing the negative values with zeros, or simply dropping
out units with negative values. We show how these practices can neglect significant
variability shares and make comparisons unreliable. The literature
also presents some corrections or normalizations which restrict the modified
Gini coefficient into the range [0-1]: unluckily these solutions are not free
of deficiencies. When negative values are included, the Gini coefficient is no
longer a concentration index, and it has to be interpreted just as relative
measure of variability, taking account of its maximum inside each particular
situation. Our findings and suggestions are illustrated by an empirical
analysis, based on the Survey of Household Income and Wealth, released by
Banca d’Italia.
其他摘要：When calculating the Gini coefficient for distributions which include negative values, the Gini coefficient can be greater than one, which does not make evident its interpretation. In order to avoid this awkward result, common practice is either replacing the negative values with zeros, or simply dropping out units with negative values. We show how these practices can neglect significant variability shares and make comparisons unreliable. The literature also presents some corrections or normalizations which restrict the modified Gini coefficient into the range [0-1]: unluckily these solutions are not free of deficiencies. When negative values are included, the Gini coefficient is no longer a concentration index, and it has to be interpreted just as relative measure of variability, taking account of its maximum inside each particular situation. Our findings and suggestions are illustrated by an empirical analysis, based on the Bank of Italy SHIW.
