Knowledge that Transforms

PROFESSOR SAMUELSON's path-breaking article on Interaction Between Multiplier Analysis and Principle of Acceleration appeared in this REVIEW almost twenty years ago. A large literature has developed in which basic ideas of that article have been applied to both business cycle and economic growth problems. In a considerable portion of that literature, Samuelson's warning that the representation is strictly a marginal analysis to be applied to study of small oscillations has been overlooked.' Samuelson's warning can be interpreted as meaning that time series generated by any particular solution of model will determine actual income for only a short time. Given mathematical model, relevant particular solution can change due either to (i) accelerator or multiplier coefficients changing (as Samuelson suggests), or (2) imposition of new initial conditions. Goodwin2 has examined various models in which accelerator coefficient is a variable. These non-linear models are mathematically complex, and specific limit cycles that Goodwin derives obviously are due to special assumptions he makes about how path of income affects accelerator coefficient. Hicks 3 has investigated how an otherwise explosive accelerator model will be affected by floors and ceilings. In this paper such floors and ceilings will be interpreted as imposing new initial conditions, and therefore this paper can be considered a reinterpretation of Hicks's setup.4 We will work with a slightly modified version of Samuelson's model, and assume that

T-flECHNICAL progress has received unprecedented attention by economists in the last few decades, but more because statistical evidence has imposed the subject on them than as a spontaneous development of economic thought. Indeed, the whole neo-classical movement and the increasing modern application of mathematics, which have contributed so much to improving the tools of economic analysis and to conferring rigor and definiteness on economic thought, have preferred to leave technical progress aside. The trouble is that technical changes are hard variables to deal with in analytical terms. The statistical data which have appeared in the last few decades have come as quite a surprise to economists, because their theories, from the Ricardian to the neo-classical, did not lead them to expect such results. I refer in particular to some statistical evidence for the United States and for other capitalistic countries which has shown that, on the average and in the long run, shares of labor and capital in the national product have not changed very much, that wages have not remained at the subsistence level but have risen in proportion to national income, that capital per man has indeed increased but output per man has also increased in proportion, that the rate of remuneration of capital has remained almost constant. In the absence of an economic theory giving a straightforward interpretation of all these outcomes the attention of economists has been called back more and more to changes in technology; and economic statisticians, in trying to evaluate these changes, have followed the easiest way: they have normally taken ratios of production to man-hours (labor productivities) and computed their changes through time. The procedure is very useful for many purposes but, among other limitations for example, the impossibility of taking into account qualitative improvements it has the major defect of referring only to labor, while the production process involves as well other factors of production whose productivity might change in a different way. This leads to different conclusions as to the productivity of the system as a whole. There have been some attempts by economists to complete these evaluations and to introduce capital into the picture, by making use of theoretical notions like the production function, but these attempts in the writer's opinion have neglected an important characteristic of capital that it is reproducible and that its process of production is also subject to technical change. It is my purpose in this paper to go into these problems. I shall try to give a short theoretical economic interpretation of technical change and suggest a procedure for evaluating it, with respect to all factors of production. When particular studies about qualitative improvements are available they may be incorporated in the same framework.

IN the current debate on the financing of education, estimates of the money benefits which school attendance confers on ex-students are occasionally invoked. In an effort to shed some further light on this subject, this note presents some crude and limited calculations on the relation between education and income. The approach to the estimation of life-time income chosen here is the so-called crosssectional one, which involves the analysis of incomes received by people of different ages and educational histories during a single year. Relevant data are available from the I950 Census of Population,' which tabulates total money incomes received in I949 by a 3 /3 per cent sample of the population aged I4 and over. Only males, irrespective of color, are considered in this paper.la The principal difficulty raised by this source of information 2 is that mean incomes are not stated; the table only gives the frequency distribution and the median for each educationage group. The median is clearly not the appropriate type of average for the present purpose; since the distributions are all positively skew, it is uniformly less than the (estimated) mean. Moreover the ratio of mean to median is larger at higher levels of education, indicating that the distribution is more unequal there than at lower levels. Hence a calculation based on medians would not even give the right proportions between life-time incomes for varying school attendance. It was consequently necessary to estimate the mean incomes. For every income group (irrespective of age and education) a representative income was selected by inspection of the income distribution.3 The figures used were as follows:

M ETROPOLITAN areas are growing fast and so are their problems. To make this growth smoother and fiscal problems less burdensome, the consolidation of metropolitan area governments is widely advocated on the premise that it will reduce per capita expenditures of local government services. It is argued that, just as there are economies of scale in manufacturing, average municipal costs and expenditures likewise decline as the size of the local government unit increases. This paper will attempt to develop a theoretical framework for analyzing the question What are the likely expenditure effects of metropolitan growth and consolidation? The deductive answers will then be tested by an empirical analysis of I49 government units in the St. Louis metropolitan area and some Massachusetts cities.

IN his paper Approach of Operational Research to Planning in India,' Professor Mahalanobis presented a model of Indian economic planning. The importance of this model can be seen from the fact that it is the statistical basis of his Draft Plan-Frame for the Second Five-Year Plan,2 which in turn is one of the most important working papers used in the preparation of the Indian Second FiveYear Plan.3 The purpose of the present note is to raise some questions about Professor Mahalanobis' planning model. Three problems in Professor Mahalanobis' model will be discussed from a theoretical point of view in this note. First, the model seems to neglect the demand side of economic planning (see section ii, below). Second, if Professor Mahalanobis' formulation of economic planning is accepted, then the increase in national income can be more than his solution gives, so that the latter is not necessarily, as he claims, an optimum allocation of resources (see section iii, below). Third, the model pays no attention to the problem of factor prices; and when possible patterns of factor prices are examined, a doubt is raised as to the estimates of parameters used in his model (see section iv, below). Section i summarizes Professor Mahalanobis' model of Indian economic planning.

T HE three possible hypotheses with respect to what an investor pays for when he acquires a share of common stock are that he is buying (i) both the dividends and the earnings, (2) the dividends, and (3) the earnings. It may be argued that most commonly he is buying the price at some future date, but if the future price will be related to the expected dividends and/or earnings on that date, we need not go beyond the three hypotheses stated. This paper will critically evaluate the hypotheses by deriving the relation among the variables that follows from each hypothesis and then testing the theories with cross-section sample data. That is, price, dividend, and earnings data for a sample of corporations as of a point in time will be used to test the relation among the variables predicted by each hypothesis. variation in price among common stocks is of considerable interest for the discovery of profitable investment opportunities, for the guidance of corporate financial policy, and for the understanding of the psychology of investment behavior.' Although one would expect that this interest would find expression in cross-section statistical studies, a search of the literature is unrewarding. Cross-section studies of a sort are used extensively by security analysts to arrive at buy and sell recommendations. values of certain attributes such as the dividend yield, growth in sales, and management ability are obtained and compared for two or more stocks. Then, by some weighting process, a conclusion is reached from this information that a stock is or is not an attractive buy at its current price.2 Graham and Dodd go so far as to state that stock prices should bear a specified relation to earnings and dividends, but they neither present nor cite data to support the generalization.3 distinguished theoretical book on investment value by J. B. Williams contains several chapters devoted to the application of the theory, but his empirical work is in the tradition of the investment analyst's approach.4 only study along the lines suggested here that is known to the writer is a recent one on bank stocks by David Durand.5 In contrast with the dearth of published studies the writer has encountered a number of unpublished cross-section regressions of stock prices on dividends, earnings, and sometimes other variables. In these the correlations were high, but the values of the regression coefficients and their variation among samples (different industries or different years) made the economic significance of the results so questionable that the investigators were persuaded to abandon their studies. There is reason to believe that the unsatisfactory nature of the findings is due in large measure to the inadequacy of the theory employed in interpreting the model, and it is hoped that this paper will contribute to a more effective use of cross-section stock price studies by presenting what might be called the elementary theory of the variation in stock prices with dividends and earnings. Before proceeding, it may be noted that there have been some time series studies of the variation in stock prices with dividends and other variables. focus of these studies has been the relation between the stock market and the business cycle6 and the discovery of profitable * research for this paper was supported by the Sloan Research Fund of the School of Industrial Management at Massachusetts Institute of Technology. author has benefited from the advice of Professors Edwin Kuh, Eli Shapiro, and Gregory Chow. computations were done in part at the M.I.T. Computation Center. 'Assume that the hypothesis stock price, P f (xi, X2,...), is stated so that it can be tested, and it is found to do a good job of explaining the variation in price among stocks. model and its coefficients thereby shed light on what investors consider and the weight they give these variables in buying common stocks. This information is valuable to corporations insofar as the prices of their stocks influence their financial plans. It is also true that a stock selling at a price above or below that predicted by the model deserves special consideration by investors. 2 Illustrations of this method of analysis may be found in texts on investment analysis such as: Graham and Dodd, Security Analysis, 3rd ed. (New York, i95i); and Dowrie and Fuller, Investments (New York, I94I). ' Graham and Dodd, op. cit., 454 ff. 'The Theory of Investment Value (Cambridge, I938). 5Bank Stock Prices and the Bank Capital Problem, Occasional Paper 54, National Bureau of Economic Research (New York, I957). 'J. Tinbergen, The Dynamics of Share-Price Formation, this REVIEW, XXi (November I939), 153-60; and Paul G. Darling, A Surrogative Measure of Business Con-

Journal Article A Problem Encountered in the Comparison of Technical Coefficients Get access Zivia S. Wurtele Zivia S. Wurtele Cambridge, Mass. Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 26, Issue 2, February 1959, Pages 148–152, https://doi.org/10.2307/2296172 Published: 01 February 1959

Journal Article Cash Circulation in the Planned Economies of Eastern Europe Get access J. Baracs J. Baracs London Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 27, Issue 1, October 1959, Pages 50–57, https://doi.org/10.2307/2296050 Published: 01 October 1959