The bias of Gini coefficient

The Gini coefficient is a crucial statistical measure used widely across various fields. The interest in the study of the properties of the Gini coefficient is highlighted by the fact that every year the World Bank ranks the level of income inequality between countries using it. In order to calculate the coefficient, it is common practice to assume a Gamma distribution when modeling the distribution of individual incomes in a given population. The asymptotic behavior of the sample Gini coefficient for populations with Gamma distributions has been well-documented in the literature. However, research on the finite sample bias has been absent due to the challenge posed by the denominator. This study aims to fill this gap by demonstrating that the sample Gini coefficient is an unbiased estimator of the population Gini coefficient for a population with Gamma distribution. Furthermore, our findings provide an expectation of the downward bias due to grouping when group sizes are equal.