The extended Amato index and its application to income data

The research proposes an alternative inequality index, an extension of the Amato index, which we term the extended Amato index. The original Amato index, which represents the length of the Lorenz curve and forms part of the inequality zone’s perimeter, serves as the foundation for this extension. The authors derive this index by computing the ratio of the inequality zone’s perimeter to the inequality triangle’s perimeter, both of which emerge from the egalitarian line and the Lorenz curve. The study apply the extended Amato index to empirical and Lorenz function formulations, using data on income employment per household from The Ghana Living Standards Survey IV. The results suggest that the extended Amato index fulfils all properties of the inequality measure, except egalitarian zero. However, the authors rectify this by performing minimum-maximum scaling adjustments on the extended Amato index, yielding the adjusted extended Amato index, which satisfies all properties of the inequality measure, including egalitarian zero. The empirical findings reveal high levels of income inequality in Ghana in 1998, as indicated by the value of the extended Amato index. Furthermore, when the value of the extended Amato index is calculated using the Lorenz function formulation, the accurate specification of the Lorenz function is validated due to its strong alignment with the empirical Lorenz curve. Ultimately, these findings can guide policies aimed at reducing inequality through wealth redistribution.