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This paper provides a comprehensive overview of decomposition methods that have been developed since the seminal work of Oaxaca and Blinder in the early 1970s. These methods are used to decompose the difference in a distributional statistic between two groups, or its change over time, into various explanatory factors. While the original work of Oaxaca and Blinder considered the case of the mean, the authors' main focus is on other distributional statistics besides the mean such as quantiles, the Gini coefficient or the variance. The authors discuss the assumptions required for identifying the different elements of the decomposition, as well as various estimation methods proposed in the literature.
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