  I generalize state-of-the-art approaches that decompose differences in the
distribution of a variable of interest between two groups into a portion
explained by covariates and a residual portion. The method that I propose
relaxes the overlapping supports assumption, allowing the groups being compared
to not necessarily share exactly the same covariate support. I illustrate my
method revisiting the black-white wealth gap in the U.S. as a function of labor
income and other variables. Traditionally used decomposition methods would trim
(or assign zero weight to) observations that lie outside the common covariate
support region. On the other hand, by allowing all observations to contribute
to the existing wealth gap, I find that otherwise trimmed observations
contribute from 3% to 19% to the overall wealth gap, at different portions of
the wealth distribution.
