There are many approaches to the decomposition of inequality by income sources. This paper focuses on the “classical” methods, i.e., those that have emerged in the literature during the previous century and are still prevalently used in empirical studies. The methods are classified into “natural decompositions”, “marginal decompositions”, Shapley decompositions and quasi-marginal approaches. The paper focuses on the former three types of methods and the Gini-based and variance-based inequality indices. First, the relationships between contributions obtained by Shapley versus natural and marginal decompositions were scrutinised to reveal new equivalences between different methods. Second, an empirical investigation was performed using data for 15 EU countries, wherein the contributions of income sources were calculated using all the methods under consideration and then compared. The main conclusion was that some of the Shapley decompositions of the Gini index obtain odd results for taxes and social benefits; natural decompositions should be used instead. Third, selected methods are analysed in light of different inequality views to conclude that natural decompositions belong to the absolute inequality view while marginal decompositions belong to the relative inequality view.
