Our paper, Oaxaca-Blinder decomposition of changes in means and inequality: A simultaneous approach, with Emmanuel Flachaire, was just published in the Economics Bulletin,

In this paper, we show that a decomposition of changes in inequality, with the mean log deviation index, can be
obtained directly from the Oaxaca-Blinder decompositions of changes in means of incomes and log-incomes. It allows practitioners to conduct simultaneously empirical analyses to explain which factors account for changes in means and in inequality indices between two distributions with strictly positive values.

Note that the Oaxaca-Blinder decomposition actually originated in the work of Evelyn Kitagawa in the 1950’s, to quantify gender discrimination in labour economics.

Kitagawa, E. M. (1955). Components of a difference between two rates. Journal of the American Statistical Association, 50 (272), 1168–1194.