A joint decomposition by sources and by subpopulations of the Zenga-84 inequality index

This paper provides a multi-decomposition (or joint decomposition) of the Zenga-84 inequality index, considering simultaneously dierent sources and subpopulations. The suggested procedure consists of two dierent stages: in the rst one, each inequality pointwise measure is decomposed by sources and by subpopulations; in the second one, the decomposition of the synthetic index is obtained, by averaging the previously decomposed pointwise measures. An important feature of this multi-decomposition is that it allows to assess the portion of the global inequality related to each source in each subpopulation, since most of the decomposition procedures proposed in the literature are not able to achieve such goal. The proposed joint decomposition permits also to obtain, as particular cases, two "marginal" decompositions by sources and by subpopulations of the Zenga-84 index, already introduced in the literature. To show the usefulness of the described multi-decomposition, an application about the household consumption is provided. The real considered dataset comes from the Household Consumption Expenditure Survey (HCES) provided by ISTAT.