# Calculating Gini coefficient with unbound income brackets?

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? ## 2 Answers 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.

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