Asymptotic Confidence Intervals for a New Inequality Measure

Abstract

This work aims at assessing, by simulation methods, the performance of asymptotic confidence intervals for Zenga's new inequality measure. The results are compared with those obtained on Gini's measure, perhaps the most widely used index for measuring inequality in income and wealth distributions. Our findings show that the coverage accuracy and the size of the confidence intervals for the two measures are very similar in samples from economic size distributions.

Keywords:

• Confidence intervals
• Economic size distributions
• Empirical distri-bu-tion function
• Gini index
• Inequality measures
• Influence function
• Lorenz curve
• Zenga curve
• Zenga index

Mathematics Subject Classification:

• 62G15
• 92B82

Notes

¹Several consistent estimators have been proposed in literature, provided the functional satisfies quite general smoothness conditions. See Shao and Tu (1995) for an overview about sufficient conditions.

²Notice that if in (8), then and P = P _* on the left-hand side.