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.

翻译：我推广了将两组之间感兴趣变量分布差异分解为由协变量解释的部分和残差部分的先进方法。我所提出的方法放宽了重叠支撑假设，允许被比较的组不一定共享完全相同的协变量支撑。我通过重新审视美国黑人与白人之间的财富差距（作为劳动收入及其他变量的函数）来阐述我的方法。传统使用的分解方法会修剪（或赋予零权重）位于共同协变量支撑区域之外的观测值。另一方面，通过允许所有观测值对现有财富差距有所贡献，我发现这些原本被修剪的观测值在财富分布的不同部分对整体财富差距贡献了3%至19%。