The New Measures of Lorenz Curve Asymmetry: Formulation and Hypothesis Testing

Abstract

The existence of an asymmetric empirical Lorenz curve requires a measure of asymmetry that directly involves the geometry of the Lorenz curve as a component of its formulation. Therefore, establishing hypothesis testing for Lorenz curve asymmetry is necessary to conclude whether the Lorenz curve exhibits symmetry in actual data. Consequently, this study aims to construct a measure of Lorenz curve asymmetry that utilizes the area and perimeter elements of the inequality subzones as its components and establish a procedure for hypothesis testing the symmetry of the Lorenz curve. This study proposes two types of asymmetry measures, ℛA and ℛP, constructed based on the ratio of area and perimeter obtained from the inequality subzone. These measures effectively capture the asymmetric phenomenon of the Lorenz curve and provide an economic interpretation of the values of ℛA and ℛP. The Lorenz curve symmetry hypothesis testing, based on ℛA and ℛP through a nonparametric bootstrap, yields reliable results when applied to actual data.