In this paper we derive inferential results for a new index of inequality,specifically defined for capturing significant changes observed both in theleft and in the right tail of the income distributions. The latter shifts arean apparent fact for many countries like US, Germany, UK, and France in thelast decades, and are a concern for many policy makers. We propose twoempirical estimators for the index, and show that they are asymptoticallyequivalent. Afterwards, we adopt one estimator and prove its consistency andasymptotic normality. Finally we introduce an empirical estimator for itsvariance and provide conditions to show its convergence to the finitetheoretical value. An analysis of real data on net income from the Bank ofItaly Survey of Income and Wealth is also presented, on the base of theobtained inferential results.
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