A hybrid method for creating Lorenz Curves with an application to measuring world income inequality

We first suggest a bi-parametric Lorenz curve, which is a simple rational function, and then analyze the curvature structure of the function. We then build a series of single-parameter Lorenz curves with varied curvatures, which are special cases of the rational function. A hybrid method is then introduced for creating efficient functional models for the Lorenz curve from the single-parameter functional forms. A set of models is created and first tested using income distribution data from the United States. The test show that the models perform well. As an application, one of the models is then used to study world income inequality between 1950 and 2006. We find that the aggregate Gini coefficient is higher than 0.55 for more than half of the period. The index stabilized at an average level larger than 0.59 after 1983. Decomposition calculations show that the within contribution to the Gini is less than 0.10 for most of the years. Therefore, the large aggregate Gini is attributable to income difference across countries. Our estimates suggest that it may not be possible to rank world income distribution in terms of aggregate Lorenz curves.