The Oaxaca decomposition generalized to a continuous group variable

Almost universally, the Oaxaca (1973) decomposition is used to compare the outcomes between two discrete groups, e.g., black and white. In many applications, however, groups are not readily divided into discrete bins. The purpose of this paper is to extend the Oaxaca decomposition to examine differences amongst groups that are most naturally modeled as at points in a continuum. The gap can vary by values of the group variable.