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

Abstract

The Gini coefficient is a downward-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 subsamples, 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 led to misperceptions about trends in industry concentration. A small-sample adjustment results in a reduced bias, which can no longer be signed. This remaining bias rises with the dispersion and falls with increasing skewness of the distribution. 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 set of firms that is stochastically identical (in terms of relative size) to those of smaller shipp...