Knowledge that Transforms

HIS paper attempts to supplement the T discussion initiated by Professor Simon Kuznets in his work on the impact of economic growth on size distribution of income (American Economic Review, XLV (March I955) and continued by Professor Irving Kravis (this Review, XLII (November I960). It will deal with (i) measures of income inequality, (2) determinants of differences in income dispersions in various countries, and (3) the sources and limitations of the data used, (Appendix).

FIRM turnover, that is, the change in rank among the leading firms, has had a long, if undistinguished, history as a measure of competition. To the best of our knowledge, it was first proposed by Rufus S. Tucker 1 in I936 and later used by Edwin B. George.2 In I953 A. D. H. Kaplan and Alfred E. Kahn 3 revived interest in the measure and more recently it has been applied by Jules Joskow.4 Recent work on the growth rate of firms by P. E. Hart and S. J. Prais,5 and H. A. Simons and C. P. Bonini 6 has led them to encourage its use, not merely as a supplement to concentration ratios but as a replacement. The Kaplan and Kahn results were subject to a barrage of criticism. Stigler,7 Markham 8 and Adelman I pointed out serious errors of fact and interpretation. But the usefulness of the turnover concept itself has not been questioned. The purpose of this article is to examine the turnover concept, to suggest that it is not very useful, and to propose another measure which is, in the authors' view, more defensible from the viewpoint of both economic and statistical theory.

HE purpose of this article is to improve T understanding of the meaning of survey data on income, and of inequality measures derived from such data. Where possible, the data are examined to see whether conceptual distinctions or difficulties make any important differences. Short-run fluctuations of income are less important than one might think in their effects on overall inequality measures. The presence of extra earners substantially reduces inequality. Less-than-full-year work increases inequality particularly among the very young and those over 45 years old. There remains some increase in inequality with age resulting from differentials in rates of advancement. Some difficulties in interpreting survey data in terms of the distribution of welfare require new data and new analysis, the main aspects of which are briefly sketched.

In the neo-classical theory of a firm's investment, the objective of the firm is to maximize its value. Its value is a function of its future income and its future income is a function of its investment. As Lutz and Lutz [8] admirably demonstrated in their standard work on the subject, given the behavior postulate and these two functions, the investment and value of a firm may be determined. Unfortunately, however, the numerous models they constructed assume the future is known with certainty and with minor qualifications that the firm can freely lend or borrow at a given rate of interest. These conditions are not realized in fact, the data of their models cannot be observed, and the models stand as elegant intellectual exercises of limited usefulness.1 A consequence is that the literature concerned with testable propositions on the investment and the valuation of the firm makes little or no reference to the neo-classical theory. Further, empirical theories of investment, for example, those discussed in Meyer and Kuh [ io], refer to the valuation of the firm only in passing, and theories of valuation such as Durand [1] make no reference to the investment of the firm. Only the normative literature, including in a sense Modigliani and Miller [ii] relates the investment and value of a firm, but this literature continues to provide little empirical information on the investment and financing that maximize the value of a firm. The purpose of this paper is to present a theory of the investment and valuation of a corporation analogous to the neo-classical theory without the assumptions that the future is certain and that funds are freely available at a given rate of interest. Specifically, the initial statement is that the value of a firm is a function of its expected future income. The future income is then represented by a function of the corporation's investment to obtain an expression in which a share's price is the dependent variable, the investment function provides the independent variables, and the parameters represent the corporation's cost of capital. In general structure the model parallels those of neo-classical theory, and similarly it may be solved to find the investment that maximizes the value of the firm. The difference is that the variables are observable and the parameters may be estimated from sample data. The model is developed under restrictive assumptions with respect to the financing policies of corporations and the form of the return on investment function. These assumptions are irritating from a theoretical point of view, but they are of limited material significance as will be evidenced by the empirical results to be presented. Work currently under way and to be reported later, however, will make the model considerably more general. The theory will be tested here as a valuation model and not as an investment model. That is, the ability of the model to explain the differences in price among common stocks will be tested, and it will be seen that under a variety of considerations the model performs better than previous efforts in this direction. By the statement that the theory will not be tested as an investment model, I mean that no attempt will be made to establish whether or not the investment of the corporation is determined by the objective of maximizing its value. Under the functional form of the stock price model established, a corporation's cost of capital is an increasing function of the rate of * The research reported here was supported by a grant from the Sloan Research Fund, School of Industrial Management, Massachusetts Institute of Technology, and the computations were carried out at the Computation Center, M.I.T. Discussions with Professors Chow, Kuh, and Solow and comments by Professor Modigliani on an earlier draft of this paper have been of considerable assistance to the writer. The advice of Ramesh Gangolli on problems of statistical inference was most helpful. I am especially indebted to Henry Y. Wan, Jr., for his unflagging energy and painstaking care in collecting the data and programming the computations. 'In the last half of their book the Lutzes withdraw the assumption that the future is certain, but this material is largely a well written distillation of the qualitative statements contained in textbooks on finance.