The Small Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research

Abstract

The Gini coefficient is a downwardly biased measure of inequality in small populations when income is generated by one of three common distributions. The paper discusses the sources of bias and argues that this property is far more general. This has implications for (i) the comparison of inequality among sub-samples, some of which may be small, and (ii) the use of the Gini in measuring firm size inequality in markets with a small number of firms. The small sample bias has often lead to mis-perceptions about trends in industry concentration. A small sample adjustment results in a reduced bias which can no longer be signed as positive or negative. Finally, an empirical example illustrates the importance of using the adjusted Gini. In this example it is shown that, controlling for market characteristics, larger shipping cartels include a stochastically identical (in terms of relative size) set of firms as smaller shipping cartels.