Some inequality and multidimensional poverty measures can be decomposed. As of December 2016, the decomposition methods in
convey are limited to group decomposition.
For instance, the generalized entropy index can be decomposed into between and within group components. This sheds light on a very simple question: of the overall inequality, how much can be explained by inequalities between groups and within groups? Since this measure is additive decomposable, one can get estimates of the coefficients, SEs and covariance between components. For a more practical approach, see (Lima 2013Lima, Luis Cristovao Ferreira. 2013. “The Persistent Inequality in the Great Brazilian Cities: The Case of Brasília.” MPRA Papers 50938. University of Brasília. https://mpra.ub.uni-muenchen.de/50938/.).
The Alkire-Foster class of multidimensional poverty indices can be decomposed by dimension and groups. This shows how much each group (or dimension) contribute to the overall poverty.
This technique can help understand where and who is more affected by inequality and poverty, contributing to more specific policy and economic analysis.