Minimum Sample Sizes in Asymptotic Confidence Intervals for Gini’s Concentration Index

Statistical inference for concentration measures has been of considerable interest in recent years. Income studies often deal with very large samples, hence precision would not seem a serious issue. Yet, in many empirical studies large standard errors are observed, and it is therefore important to provide methodologies to assess whether differences in estimates are statistically significant. This work focuses on Gini’s concentration ratio R. Hoeffding, in his seminal work (Hoeffding,1948), derived the asymptotic distribution of Gini’s index. Several years later, Giorgi and Provasi (1995) and Palmitesta et al. (1999) pointed out that the speed of convergence of the sample distribution is rather slow. Further studies (Palmitesta et al. (2000), and Giorgi et al. (2006)) revealed that the t-bootstrap method yields more accurate confidence intervals in small samples. Bootstrap methods are however computationally expensive; moreover, the difference with respect to the asymptotic approach becomes less significant as the sample size increases. In inference studies involving large samples, (i.e. income surveys), it seems therefore reasonable to retain the asymptotic approach. Latorre (1990) showed that sample sizes currently in use are large enough for constructing confidence intervals based on the maximum likelihood estimator for Gini’s concentration measure. Are they also adequate to assure a good coverage of asymptotic non parametric confidence intervals? This work’s aim is to provide an answer to this question