I want to use the Shapley value decomposition approach to estimate the contribution of a set of factors to income inequality.
I know that the Fields (2003) method decomposes the log-variance of income where we do not need to agree on which particular inequality measure to decompose. In contrast, the Shapley value decomposition approach estimates the marginal impact of each factor on the level of inequality which differs depending on the choice of the inequality index.
I want to decompose the following three measures of inequality-
Theil index
Mean logarithmic deviation (MLD) and
the variance of logarithms of income
Now, my question is which user-written routine I should use that will give me the Shapley values for the above three measures of inequality.
I know that the Fields (2003) method decomposes the log-variance of income where we do not need to agree on which particular inequality measure to decompose. In contrast, the Shapley value decomposition approach estimates the marginal impact of each factor on the level of inequality which differs depending on the choice of the inequality index.
I want to decompose the following three measures of inequality-
Theil index
Mean logarithmic deviation (MLD) and
the variance of logarithms of income
Now, my question is which user-written routine I should use that will give me the Shapley values for the above three measures of inequality.
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