The Effect of Aggregate Versus Per Capita Income Per Unit Ranking on Personal Income Size Distributions - Clyman, Bernard (The Review of Economics and Statistics, 1956)
THIS paper is concerned with a problem that is of considerable importance in the analysis of personal income size distributions, namely: for any given type of unit selected for analysis (family, spending unit, or any other useful recipient unit classification), how would ranking the units by aggregate income per unit versus ranking them by per capita income per unit affect the relative income shares received by various income groups. The problem may also be interpreted as a comparison of the effect on income shares of using a unit or a person basis of classification. Of the two path-breaking studiesrecently published in this field that of the United States Department of Commerce 1 yields estimates of relative income shares received by consumer units when ranking is by aggregate income per unit, while that of Professor Kuznets 2 yields estimates of shares received by individuals when ranking is by a procedure that attempts to approximate per capita income per unit. This variation in method is used by Dr. Selma Goldsmith and her associates 3 to explain, in part, some of the difference in results obtained in the two investigations. Though this paper considers the problem primarily in the context of Delaware data, first a brief digression is undertaken to comment upon a small portion of the analysis made by the Commerce Group (Dr. Goldsmith and her associates). This digression serves three purposes. It provides some insight into the question posed. It emphasizes, by contrast, the value of having access to a sample of individual tax returns as is the case for the analysis of Delaware data. And finally, it permits the writer to correct some of the confusion of interpretation and inference that has arisen. After the digression, a comparison of aggregate and per capita variants using Delaware data is presented and an analysis is attempted showing why the income shares received by the different income groups are affected in the particular directions noted. The paper then concludes with a few observations about the per capita approximation method employed by Professor Kuznets in constructing his income size distributions.