Appraisal of Methods for Estimating the Size Distribution of a Given Aggregate Income

Abstract

N rilsappearing in this REFVIEW, EdwadAmes and David Durand have each described a technique by means of which relative inequality of an income distribution for a given level of aggregate income, as measured by Lorenz curve, can be applied to a different aggregate income without altering income size classes of original distribution.' Mr. Ames states in conclusion to his article that his procedure should prove useful in exploring effect of income variations upon demand, sa'vings, tax yields, and so on.) Both Ames and Durand base their illustrations on income distribution for families and single individuals as given by National Resources Com'mittee study for I93 5-36,2 and they derive a hypothetical distribution for same number of families and single individuals with an aggregate income that is 33 per cent above aggregate income during I935-36. A minor shortcoming of Durand's method is fact that, for data on which illustration is based, one income class of original distribution is lost in process. However, Durand obtains, as he claims, the same practical results as Ames. Since two techniques are basically same, what is said about one in this note will apply with equal force to other. Both Ames and Durand fail to mention an important difference between I93 5-36 income distribution and income distribution derived by methods they develop. When either of their methods is used, average income within each income class of new distribution will be different from average income within corresponding class of I935-36 distribution. This difference is readily apparent from an examination of Chart i, which is an upward cumulative frequency distribution. The points along horizontal axis are on a