An Application of the Durand Method for Estimating the Size Distribution of A Given Aggregate Income

Abstract

SERIES of articles have appeared in this L REVIEW on methods of adjusting a given size distribution of income to differing aggregate or per capita income levels.2 If the distribution of income remains reasonably constant and price levels keep changing, a method of adjustment for changes in per capita income will no doubt be a useful statistical tool. I do not wish to enter into the controversy between Dr. Durand and Messrs. Clark and Fishman; the simpler Durand method was used in this particular application because over thirty transformations were originally made and because the usual class intervals of income were maintained. In trying to find a satisfactory income distribution for Metropolitan Boston, a number of income curves for different years and for different social groups were adjusted to I 94I income levels. These families of curves are interesting for themselves, apart from the Boston data, and they suggest the possibility of finding such pattern curves for estimating postwar distributions of income for various social groups. The original purpose of the study was to find an income distribution for Metropolitan Boston. Since a sample study could not be made, available statistics had to be utilized for what they were worth. The Census of I940 contained distributions of income, based on wage and salary income alone, for the year I939 for Metropolitan Boston, for Massachusetts, and for New England; also, the Census provided data on individual workers for Boston alone. Income tax returns for Massachusetts for I942 were also available. Questions immediately arose concerning the usefulness of the fragmentary data relevant to Boston. Do distributions of wage and salary income alone resemble distributions of total income? Apart from their shape, would such distributions be too high or too low? If there were differences in shape or level, could these distributions still be salvaged by comparing similar Census distributions for the nation with other recognized national distributions? How do the Boston or national distributions for individual wage earners compare with desired consumer unit or family distributions of income? Clearly it was desirable to compare the fragmentary Boston data with other data on the distribution of income. Such comparisons of income distribution (retaining dollar income classes) cannot be made until allowance is made for differences in per capita income levels of different years. It was necessary, therefore, for purposes of comparison, to adjust all the relevant distributions to a base year. The year 1941 was chosen and the Durand method was then used to adjust to that base year the Consumer Purchases Study of I935-36, the various 1939 distributions from the Census of I940, the I94I and I942 income studies made by the Bureau of Labor Statistics, the I945 and I946 surveys for the Board of Governors of the Federal Reserve System, and the income tax returns for I942.3 'I am indebted to the Housing Association of Metropolitan Boston and to Mr. William Loring for assistance in carrying out the study on which this article is based. fuller description may be found in Some Economic Aspects of Urban Housing, with Special Reference to Metropolitan Boston (Ph.D. dissertation, Harvard University, I948). 2 Edward Ames, A Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, xxiv (November 1942), I84-89; David Durand, A Simple Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, xxv (November 1943), 227-30; Eugene Clark and Leo Fishman, of Methods for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXIX (February 1947), 43-46; David Durand, An Appraisal of the Errors Involved in Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXX (February 1948), 63-68; Eugene Clark and Leo Fishman, Further Remarks on Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXXII (February 1950), IO6-07. 'Differences in per capita incomes were used to transform the distributions. The statistician's judgment enters at every step; a fuller discussion of the problems and errors involved may be found in the dissertation, op. cit., ch. ii. Appendices i to v of the dissertation contain the data and transformations.