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This paper examines methods of decomposing a difference in levels between groups for a dependent variable such as income. Applied to regression equations, this technique estimates the contribution to the difference from divergent characteristics and divergent rates of converting characteristics into the dependent variable. The consequences of an "interaction" component being present in the decomposition is examined. The paper, using data from the 1960 Census, shows how ignoring the interaction term can influence results.
Iams et al. (Sat,) studied this question.