Methods of decomposing the difference between two rates with applications to race‐sex inequality in earnings

Four general methods of decomposing the difference between two rates into several components are provided. For data cross‐classified by several factors, all four methods can be used treating the factors either hierarchically or symmetrically, and within each treatment, the methods are expected to give very similar results. Since the results may differ significantly depending on whether the factors are hierarchical or symmetrical and since there is no objective way of arranging the factors hierarchically, symmetrical treatment of the factors is recommended. The latter approach is used to study race‐sex inequalities in mean annual earnings for year‐round full‐time workers in the United States based on the 1980 census data cross‐classified by education, age, and occupation.