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Simple question: If the GINI coefficient (market incomes) goes up, is it a necessary feature that the mean income rises relative to the median?

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No, since you can change the Gini coefficient by altering the distribution of incomes in the top half (keeping the total the same) without changing the mean or median income; you can also change the Gini coefficient by altering the distribution of incomes in the bottom half without changing the mean or median income.

Compare the Gini coefficients of {2,2,2,2,2,6,10,10,10,10,10} and of {1,1,1,1,6,6,6,6,6,6,26}: the former will have a Gini index of about 0.33 while the latter will have a Gini index of about 0.46 though the mean and median do not change (6 each)

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  • $\begingroup$ Your numerical example does not coincide with the two general examples in your first paragraph. Although the counterexample is enough to prove the "No" of your answer, you have not provided a proof of the first statement. $\endgroup$ – luchonacho Jul 4 '17 at 6:36
  • $\begingroup$ @luchonacho: I regarded my first paragraph as an obviously true statement (you can change the distribution and Gini coefficient without affecting the mean and median), and the answer to the question. My numerical example changes the distribution both ways: in the top half from 10,10,10,10,10 to 6,6,6,6,6,26 (both adding up to 50) and in the bottom half from 2,2,2,2,2 to 1,1,1,1,6 (both adding up to 10), so the mean is unchanged and the median of 6 is unaffected. Not surprisingly, each of these changes increases the Gini coefficient as a measure of inequality $\endgroup$ – Henry Jul 4 '17 at 7:36
  • $\begingroup$ My point is that the answer looks misleading, as it seems you are giving an example to support the statement in the previous paragraph. I think a clarification would improve it. $\endgroup$ – luchonacho Jul 4 '17 at 10:15
  • $\begingroup$ @luchonacho Thank you so much for your answers. I am facing this problem since i am testing the median voter theorem, which states that as the gap between mean and median income increases demand for redistribution increases. If using gini in market incomes to test this as a lot of journals do, they implicitly assume that an increase in this gap is reflected in the gini ? I know that the same gini may cover different distributions but if mean rises realtive to median gini should increase as well no? $\endgroup$ – Madslassen Jul 4 '17 at 12:32
  • $\begingroup$ As Milanovich states:" When individuals are ordered according to their factor or market incomes, the median voter, the individual with the median level of income, will be, in more unequal societies, relatively poorer. His or her income will be lower in relation to mean income" $\endgroup$ – Madslassen Jul 4 '17 at 12:41

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