Inferential results for a new measure of inequality

In recent decades, substantial changes have been observed in the left and right tails of income distributions in countries like the USA, Germany, the UK, and France. These changes are a major concern for policy makers. Here, we derive inferential results for a new inequality index that is specifically designed for capturing such significant shifts. We propose two empirical estimators for the index and show that they are asymptotically equivalent. Afterward, we adopt one estimator and prove its consistency and asymptotic normality. Finally, we introduce an empirical estimator for its variance and provide conditions for its consistency. An analysis of real data from the Bank of Italy Survey of Income andWealth is also presented on the basis of the obtained inferential results.