Résumés
Abstract
In this paper, we compare three methods presently used to split up the Gini index in order to evaluate the contribution of one particular factor (for example, age) to the value of this index: the B-M-P decomposition*, Paglin's measures and Love & Wolfson indexes. The problem with the decomposition of the Gini index is that it is impossible to cut it in two parts, one, representing the value of inequality attributable to the factor analysed and the second, inequality due to other factors. We also have to include the value of overlaps. This is clearly shown by Bhattacharya and Mahalanobis.
By using a very simple example for which we can forecast the results, we can compare the reaction registered by each method when we introduce a change in the distribution of income and consequently evaluate the lightness of these methods. We confirmed our convictions by decomposing two other measures which can be separated in the two parts mentioned above: Theil's entropy and the square of the coefficient of variation.
We conclude that the indexes used in the B-M-P decomposition are exact. Paglin's age-Gini index is accurate, but not his residue, the Paglin-Gini's index. And, Love and Wolfson's index did not behaved as expected to our modifications.
We also showed, by using the B-M-P decomposition, that overlaps is an important component. Finally, we noted that our indexes changed in value when we changed the number of groups analysed (example: if, to analyse the effect of age we divide our population into 5 or 10 age groups). So, it is important in a longitudinal study always to use the same group definitions to obtain comparable results.
* Bhattacharya, Mahalanobis and Pyratt.