Knowledge that Transforms

A WIDESPREAD need exists for personal L7 income data by minor geographic areas, which would provide necessary data for market analysis, administration of local tax burdens, etc. In an attempt to provide data for these requirements, agencies in several states have prepared estimates for counties for various years.' In the South the first comprehensive set of county estimates was published in I952 for seven southeastern states.2 Of all the components of county income developed in these studies, it has generally been considered that farm proprietors' income 3 estimates by county had the least sound basis 4 and therefore probably contained larger errors than any of the other elements in the county totals. The objectives of this study are (i) to determine the factors influencing agricultural income formation for homogeneous groups of states, and (2) to develop a method which will serve as a basis for preparing county estimates of agricultural income with the minimum error. Objective and measurable determinants of agricultural income employed in the analysis are required which are equally available for states and counties. The assumption is that the rate of agricultural income formation from basic factors at the state level for homogeneous groups of states bears either a similar, or some determinable, relation to the rate of income formation from the same factors at the county level. The concept of agricultural income in this study begins with the National Income Division's series of farm proprietors' net farm income. Wages paid hired labor and rents allocated farm landlords are added. Government payments are deducted. The concept for Virginia for I949 is illustrated below:

Selma F. Goldsmith, George Jaszi, Hyman Kaitz, Maurice Liebenberg, The Effect of Aggregate Versus Per Capita Income Per Unit Ranking on Personal Income Size Distributions: Reply, The Review of Economics and Statistics, Vol. 38, No. 2 (May, 1956), p. 227

M OST of the statistical procedures used in the manipulation of income size distributions involve interpolation in some form.' The worker is frequently concerned with such problems as the determination of decile points, medians, or, in general, some income points which are meaningful for subsequent analysis or presentation. Such problems reduce, in the practical case, to the task of finding the upper limits of subintervals the frequencies of which are known. In addition to such problems, most adjustments made to distributions involve the modification of the income variate in some manner, as is the case when a given relative distribution is maintained by multiplying all incomes by a constant, or when the relative distribution is changed by modifying incomes differentially. After such shifts the initial classification of units by size of income has changed, and interpolation is required to determine the changed distribution of frequencies in the initial classes. In this type of problem the interpolated income point is known, and it is necessary to determine the frequency in the subinterval of which the known point is the upper limit. This paper presents a practical alternative to the usual graphic or computational methods of interpolation. Nomographic charts are given which incorporate formulas that have been used successfully to interpolate for income points, frequency, and income. In the sections that follow, the usual methods will be examined briefly, the basic formulas underlying the nomograms presented, and the steps in their use outlined for several types of interpolation problems. Need for Alternatives to Usual Methods

rfHERE has been considerable interest in 1the spatial aspects of the income distribution. Many studies have attempted to measure inter-area differences in income level and to investigate the factors which could be responsible for them.' Most of these studies have dealt with income differences among regions or states, but in recent years increasing attention has been devoted to the city as another unit of study. In most cases, this attention has been confined to the city-size variable, its position vis-a-vis regional income differentials, and the factors responsible for its relation to the income level.2 In the I950 Census of Population, income data were collected for individual cities, and it became possible to measure intercity income differences and to test some hypotheses concerning them. Much of the variation in city income levels was found to be associated with the two variables that had often been singled out for attention: region and city-size. But a considerable amount of variation remained. Indeed, the variation in income level among cities of comparable size in the same region was often as great as the variation among the 48 states.3 Our interest here centers about this variation in income level among cities of comparable size in the same region. In formulating any complete model intended to explain the spatial distribution of income, this variation should be taken into account. To be complete, the model should explain this variation as well as the differences in income among regions and community-size categories. Information concerning differences among these cities should be useful in setting the stage for the construction of such a model.4 With regard to the differences in income among regions and community-size categories, considerable auxiliary information is available to guide the model-builder in his selection of variables. But this is not the case with respect to cities of comparable size in the same region. Attention here is focused on the intercity differences in the characteristics of the population. The particular population characteristics were chosen with the understanding that they are sometimes only indirectly connected with the factor markets and that an observed relationship between these characteristics and income does not necessarily establish a line of causation. Though the results can be little more than suggestive, they should provide some of the information that is needed.