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	Theil Inequality Decomposition	Atkinson Index	Shapley Decomposition of Inequality
Fagområde	Økonomi	Sociology	Økonomi
Familie	Process / pipeline	Process / pipeline	Process / pipeline
Oprindelsesår	1967	1970	2013
Ophavsperson	Henri Theil (1967); decomposition class by Anthony Shorrocks (1980)	Anthony Barnes Atkinson	Anthony Shorrocks (working paper 1999; published 2013)
Type	Decomposable inequality measure	Welfare-based, parameterized inequality index	Axiomatic decomposition procedure
Oprindelig kilde	Theil, H. (1967). Economics and Information Theory. Amsterdam: North-Holland. ISBN: 9780444814630	Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.	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.
Aliasser	Theil Index, Theil's T and L, Generalized Entropy Decomposition, Within-Between Inequality Decomposition	Atkinson inequality measure, Atkinson's A, welfare-based inequality index	Shapley Decomposition, Shorrocks Shapley Decomposition, Factor Decomposition of Inequality, Shapley Value Distributional Decomposition
Relaterede	3	5	4
Resumé	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.	The Atkinson index is a welfare-based measure of inequality that incorporates an explicit, analyst-chosen parameter for how much society dislikes inequality. Introduced by Anthony Atkinson in 1970, it asks what fraction of total income could be discarded, under an equal distribution, while leaving social welfare unchanged — making the ethical judgement behind any inequality comparison transparent rather than hidden.	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.