Oaxaca-Blinder meets Kitagawa: What is the link?

Recently, papers have started combining the naming of two popular decomposition methods: the Oaxaca-Blinder (OB) 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. In the light of Kitigawa's early precedence, its more recent association with OB, and the seeming lack of any detailed analysis of the exact relationship between Kitigawa's methodology in the literature, in this paper we show the precise relationship between Kitagawa's approach and that of OB. The paper also provides a citation history of the papers.