Shapley Decomposition of Inequality

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.