Knowledge that Transforms

HE field of industrial organization has acT quired an abundance of hypotheses about what comprises market structure.1 Neoclassical analysis was premised on the firm's market share, atomistic or pure monopoly. Then came the Chamberlinian group of the 1930's, Bain's entry barriers of the 1950's, and firm size and advertising in the 1960's. This abundance yields vitality, but it has also left uncertain the relative importance and interrelations of the individual structural elements. Empirical analyses, relying mainly on partial tests relating one or two elements with a dimension of behavior, have not resolved the patterns. This paper attempts to compose these differences by fitting models of structure to recent data on large United States industrial corporations. Section I prepares testable models of the elements, both in static and in comparativestatic contexts. Data on a panel of 231 large United States industrial firms during 19601969 are described in section II. Section III presents the empirical analysis, and the results are summarized in section IV.

M OST of the measures of income inequality are derived from the Lorenz curve; indeed Morgan (1962) states that the Gini index is the best single measure of inequality. The present article reviews some of the theoretical properties of the Lorenz curve, relates them to characteristics of the frequency function underlying the income distribution and develops methods for obtaining accurate bounds on the Gini index which do not depend on curve fitting. In the process we should also like to lay to rest some myths concerning the Gini index such as: (a) its relative insensitivity (Rltet6 and Frigyes, 1968), (b) difficulty in computation (1968), and (c) problems related to the inclusion of negative incomes (Budd, 1970). The basic idea of our approach is to obtain upper and lower bounds to the Gini index from data which are grouped in intervals and the mean income in each interval is known. The usual method (Morgan, 1962) of estimating the Gini index yields a lower bound by assuming that all incomes in any interval equal the average income. We derive an upper bound to the grouping correction (Goldsmith, et al., 1954, p. 10) and hence to the Gini index by distributing the income to maximize the spread within each group. On the 1967 Internal Revenue Service tax data, the difference between our bounds is less than 0.006. As most income distributions come from a frequency function (density) which decreases in the large income range, we develop improved bounds for the Gini index based on this assumption. Fortunately, this assumption can be checked from the data so that we can use the sharper bounds only for the appropriate intervals. Using this second method the difference between our bounds is ? .002. Because Soltow (1965) detects a change in the Gini index of 0.8 of one per cent or about 0.003 or 0.004, our bound seems quite adequate. In section VI we extend our method to obtain upper and lower curves for the Lorenz curve. After reviewing the basic properties of the Lorenz curve we proceed to derive bounds on the mean difference and Gini index. In section IV we analyze an actual sample and show that the method used by the Census Bureau (1967) often leads to estimates which are outside the mathematically possible bounds we derived. Finally, in an appendix we show that the Pareto law does not give a good fit to current United States tax data.