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I need to compute the Gini coefficient on some population data arranged in income brackets: for example

$0->$1000 : 10000 people
$1000->$10000: 50000 people

My problem is that the last bracket is unbounded i.e it's in the form:

$1000000 < : 500 people

Is there any way to calculate the Gini coefficient given this data?

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You can put a lower bound on the Gini coefficient by assuming all 500 of the highest earners earned $1000000. The upper bound is 1. Any attempt to try to narrow it down is probably impossible without further information. How would you know that a billionaire didn't move into the area? Placing a distribution would be very dangerous - fitted distributions are rather speculative in their upper tails. Maybe if you have defensible absolute upper bound, you could get an upper and lower Gini coefficient bound.

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The book by Handcock & Morris: "Relative Distribution Methods in the Social Sciences" (Springer), solve that problem the following way, quoting:

" We have imputed values for these topcoded earnings in each year (about 0.5% of the cases) using a Pareto distribution. The mean of these imputed values is about 1.45 times the topcode; the value traditionally assigned to topcoded earnings. "

(They give no reference for that "traditional" use).

A relevant paper you could have a look at: http://www.ce.utexas.edu/prof/bhat/ABSTRACTS/Imputing_a_continuous_income.pdf

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