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From |
Jen Zhen <jenzhen99@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Computing the Gini or another inequality coefficient from a limited number of data points |

Date |
Fri, 10 Feb 2012 09:52:02 +0100 |

Dear list members, I would like to compute a measure of income inequality similar to the Gini index. I do not know everyone's income, so need to make an approximation. (1) For the 5 most recent years, I know for 6 income brackets how many individuals there are and their joint income, hence also the average income in the bracket. For the full-fledged Gini index I would need to know the area under the curve which shows the cumulative income against the cumulative number of tax payers (to visualize what I mean, look e.g. at the 2nd figure here: http://en.wikipedia.org/wiki/Gini_index). Now I believe that with the information I have I don't know the entire curve but I know only 7 points on it (the six points mentioned plus the origin). So I think I can approximate the said area if I simply assume that between the 7 points the line is straight, but that will systematically underestimate the true degree of inequality. So I'm wondering if there is a sensible way to smooth the curve and hence get a better approximation? (2) For the 5 earliest years unfortunately I know only the number of individuals in each bracket but not their joint income. So my idea was that I would regress the mean income in each bracket on a 3rd-order function in the year to see how it develops in the 5 latest years and use this to predict/estimate the mean income for each bracket in the 5 earlier years, then use the procedure described in (1). A simpler alternative would be to just use the midpoint of each bracket, but I guess this would be less good. Does this procedure sound sensible? Or is there a better way to compute inequality from these data? Thank you so much and best regards, JZ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Computing the Gini or another inequality coefficient from a limited number of data points***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: Computing the Gini or another inequality coefficient from a limited number of data points***From:*Daniel Feenberg <feenberg@nber.org>

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