A simple solution to the identification problem in detailed wage decompositions

Oaxaca and Ransom (1999) show that a detailed decomposition of the coefficients effect is destined to suffer from an identification problem since the detailed coefficients effect attributed to dummy variables is not invariant to the choice of reference groups. It turns out that the identification problem in the decomposition equation is a disguised identification problem of constant and dummy variables in a regression equation. This article proposes a simple and natural remedy for this problem by using "normalized" regressions, which enable me to identify the constant and estimates of each dummy variable.