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 shipping cartels.

We investigate the impact of passenger shipping cartels on trans-Atlantic migration during the early twentieth century. We assemble from primary sources a detailed database of passenger flows and cartel operations and show that cartel operation reduced migratory flows by approximately 20% to 25%. Further, we show that there was no strong intertemporal substitution in migration to North America (at least in the short run) and, therefore, that the effects of cartel operation were not “undone” by later migration. Lastly, we find that cartel operation had no appreciable effect on the variability of migration flows, providing evidence against the notion that unfettered competition was destabilizing to turn-of-the-century transportation markets.