Compare methods

	Shapley Decomposition of Inequality	Theil Inequality Decomposition
Field	Economics	Economics
Family	Process / pipeline	Process / pipeline
Year of origin	2013	1967
Originator	Anthony Shorrocks (working paper 1999; published 2013)	Henri Theil (1967); decomposition class by Anthony Shorrocks (1980)
Type	Axiomatic decomposition procedure	Decomposable inequality measure
Seminal source	Shorrocks, A. F. (2013). Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. Journal of Economic Inequality, 11(1), 99–126.	Theil, H. (1967). Economics and Information Theory. Amsterdam: North-Holland. ISBN: 9780444814630
Aliases	Shapley Decomposition, Shorrocks Shapley Decomposition, Factor Decomposition of Inequality, Shapley Value Distributional Decomposition	Theil Index, Theil's T and L, Generalized Entropy Decomposition, Within-Between Inequality Decomposition
Related	4	3
Summary	The Shapley decomposition, formalized for distributional analysis by Anthony Shorrocks (in a widely circulated 1999 working paper, published in 2013), is a general procedure for attributing an inequality or poverty statistic to its contributing factors — income sources, population subgroups, or determinants. It borrows the Shapley value from cooperative game theory: each factor's contribution is its average marginal effect on the indicator across all possible orders in which factors could be eliminated. The result is an exact, symmetric, residual-free decomposition that applies to any indicator, even those (like the Gini) that have no natural analytic decomposition of their own.	The Theil index, introduced by Henri Theil in 1967 by importing Shannon's information theory into economics, measures income inequality as the divergence between each unit's income share and its population share. Its defining advantage is exact additive decomposability: total inequality splits cleanly into a within-group component (inequality inside each subgroup) and a between-group component (inequality between subgroup means). Theil's T and its companion L (mean log deviation) are the two best-known members of the generalized-entropy class, which Anthony Shorrocks showed in 1980 to be the only inequality measures that are additively decomposable in this way.