An analysis of the bounds for the Gini coefficient

The bounds on the Gini coefficient obtained by Gastwirth for the case of grouped data are considered. While the population bounds will always include the value of the population Gini coefficient and the estimated bounds will always include a suitably chosen estimate of the Gini coefficient, estimated bounds need not include the value of the population Gini coefficient.The distributions of the estimators of the bounds are considered and it is shown that a failure to take account of sampling variation can lead to very misleading results. In fact, increasing the number of income groups used tends to decrease the difference between the bounds, but the relative frequency with which the estimated bounds includes the population Gini coefficient decreases. The relationship between sample size, the nature of income groups and estimator precision is considered.