The Gini Coefficient and the Case of Negative Values

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