Liliane Bonnal, Rachid Boumahdi, and Pascal Favard, “The easiest way to estimate the Oaxaca-Blinder decomposition”, Applied Economic letters, vol. 20, n. 1, 2013, pp. 96–101.
This article studies the relation between the Oaxaca–Blinder decomposition and the estimated coefficient of a dummy variable for a linear regression. We calculate the unexplained part of the decomposition from the estimated coefficient of the dummy variable. More precisely, if the exogenous variables are uncorrelated to the dummy variable, the estimated coefficient and its variance give directly the value and the variance of the unexplained part of the decomposition. If the independent variables are correlated a simple relation is obtained. Moreover, we show that the significance of the unexplained part can be deduced from the significance of the estimated coefficient of the dummy variable.