Optimal Grouping of Income Distribution Data

We consider the problem of grouping income distribution data into a given number of groups such that the concealed income differences due to grouping are minimized. When income differences are measured by Gini's pairwise differences, this means minimizing the area between the grouped and ungrouped Lorenz curves. In this case, the necessary condition for optimal grouping is that each group limit be equal to the average income in its two adjacent groups. An iterative procedure for computation and applications including fractile groupings are discussed. Alternative optimal groupings based on other measures of income differences are also considered.