Oaxaca-Blinder Meets Kitagawa: What is the Link?

Recently, papers have started combining the naming of two popular decomposition methods: the Oaxaca-Blinder method and the Kitagawa method, a popular method in demographics and sociology. Although the two approaches have the same objective in terms of decomposing outcome differences in some variable of interest between two populations, they are framed quite differently and do not overlap except in a special set of circumstances. Consequently, the combined labeling of these two approaches can be misleading. This note establishes the conditions under which the two methodologies are identical and when they are not. It also provides the citation history of the two methods and examples of "misuses" of the naming convention when the methods are not equivalent, accompanied by a proposal for the way forward.