Knowledge that Transforms

T HE basic idea of consistent forecasting is very simple: make forecasts of the output of each industry, the wage rate, and perhaps other variables in such a way that, if business acts on the basis of the forecasts, they will come true and full employment will be obtained. The idea is not new, but the possibilities of putting it to work in the American economy have not been developed. I believe that these possibilities are considerable and hope that this paper can be a first step in making from them an effective tool for assisting a free economy to maintain steady growth and full employment. The forecasts yielded by a model like the present one would be intended to guide capital investment planning by business. Short-term movements will be given scant attention here. Section I explains the theory of the model. Since the version presented here is only a first step toward consistent forecasting of practical use for business planning, it seemed advisable to keep it as simple as possible and then, by numerical work, compare its functioning with the actual performance of the American economy. In this way, its greatest needs for extension and refinement can be brought to light and used as guides for future work. The model becomes the Leontief open dynamic system if it is known that full employment can be maintained with a of a constant wage rate. A method of getting the economically relevant solution to this special case is developed and then extended to the variable wage rate case. The last paragraph of the section discusses how consistent forecasting could fit into a free economy. In Section II, a ten-sector model of the American economy is used to forecast from I953 to I960, with only the course of the total labor force and the exogenous final demandsexports, government, and capital replacement known in advance. A comparison of the results with the actual course of events indicates that increasing productivity of new capital and a limited amount of variation of input coefficients must be included before practical forecasting can be done. At the same time, however, the comparison suggests that even the simple model is getting at something very relevant to the economy and that, after taking account of the suggested improvements, a useful tool can be obtained. The comparison also offers, as a sort of by-product, a surprisingly clear-cut explanation of the I954 and I958 recessions. But the result of the comparison which I would like for the reader to bear in mind, particularly when considering business acceptance of the forecasts, is that they are quite sensible looking and businesslike.

F OLLOWING a pioneering article by Solow [71 the problem of measuring technical change has been investigated by many authors, viz., Hogan [4], Massell [i], Pasinetti [6], Solow [7]. What almost all the papers above attempt to do is to construct a series which indexes or measures technical change. The term is slightly inaccurate in that the series really purport to describe the time profile of that part of output which is not explained by the specified inputs, viz., capital and labor. It may be preferable to employ the term in accounting for such variations in observed output, a terminology which will be adhered to below. We shall provide a simple method of estimating a productivity parameter in a firm or sectoral or global production function. We shall then apply this method in estimating the appropriate parameter for the Manufacturing and Service Sector of the United States post-war economy. Finally, we shall indicate a method for testing a statistical hypothesis on the equality of two parameters so estimated. It will be found that the data does not warrant the conclusion that the rate of change of productivity differs significantly as between the two sectors.

IN recent years, economists have shown a lively and growing interest in the factors determining how rapidly a new technique is substituted for older methods. This rate of substitution, or rate of diffusion, merits such attention because it determines how rapidly productivity rises in response to the new technique. The full social benefits from the innovation will not be realized if the diffusion process goes on too slowly.' This paper for the first time studies the intrafirm rate of diffusion the rate at which a particular firm, once it has begun to use a new technique, proceeds to substitute it for older methods.2 Once they become familiar with an innovation, some firms abandon the older technology and replace it very quickly with the new. Others are much slower to make the transition. Given that a firm has begun to use a new type of equipment, what determines how rapidly it goes on to substitute it for an older type? To help answer this question, we single out one of the most significant innovations that occurred in the interwar period the diesel locomotive. We construct and test an econometric model to help explain differences among railroads in the rate at which, once they had begun to dieselize, they substituted diesel motive power for steam. Although this model is rough and over-simplified, it seems to stand up quite well; and with appropriate modification, it is likely to prove useful for other innovations as well.3 * The work on which this report is based is part of a larger project on industrial research and technical change supported by a grant from the National Science Foundation, by research funds of the Graduate School of Industrial Administration at Carnegie Institute of Technology, by a contract with the Office of Special Studies of the National Science Foundation, by a Ford Foundation Faculty Research Fellowship, and by the Cowles Foundation for Research in Economics at Yale University. It will be reprinted as a Cowles Foundation Paper. I am particularly indebted to K. Healy, whose comments on an earlier draft eliminated several errors. In addition, the paper has benefited from discussions with various colleagues, particularly A. Meltzer, J. Muth, R. Nelson, and N. Seeber. My thanks also go to G. Haines and D. Remington for their assistance and to the many people in the railroad and related industries who provided information. 1 It seems obvious that productivity in an industry can be regarded as a weighted average of the productivity with the old technique and the productivity with the new, the weights reflecting the extent to which the new technique has replaced the old. (Whether one has in mind labor, capital, or total productivity is irrelevant, although it affects the sort of weights one would use.) Thus, if the productivity with the new technique exceeds that with the old, productivity in the industry will rise as the new technique is substituted for the old. The rate at which it rises depends clearly on the rate of diffusion. And if the diffusion process goes on more slowly than it should, productivity will not rise sufficiently rapidly and output will fall below its potential. (Of course, if the diffusion process goes on too rapidly, inefficiencies result as well.) For further discussion, see Salter [16]. 2Note that the intrafirm rate of diffusion measures how quickly a firm substitutes the new technique for the old once it has begun to use the technique. It does not tell us anything about the speed at which it began to use it. (See Section II.) Note too that some innovations can be introduced only on such a large scale that the intrafirm rate of diffusion is of little relevance. The firm either adopts the innovation or it does not. In addition, we presume here that there is an old technique that the innovation replaces. Assuming that the new technique will completely displace the old, a reasonable, but arbitrary, measure of the intrafirm rate of diffusion is the time interval separating the date when the innovation accounts for 10 per cent of the firm's output from the date when it accounts for 90 per cent of the firm's output. This sort of measure (which is inversely related to the intrafirm rate of diffusion) is used in Section II. If the new technique will eventually displace the old in B per cent of the cases, .1B and .9B can be used instead of 10 and 90. Studies of the diffusion process are relatively rare for industries other than agriculture. For some studies bearing on the spread of innovations among industrial firms, see Enos [6], Healy [9], Mansfield [12, 13, 15], and Sutherland [18]. For some investigations of agricultural innovations, see Beal and Bohlin [1] and Griliches [8]. For the diffusion of an antibiotic, see Coleman, Katz, and Menzel [4]. Some attention was devoted to the diesel locomotive by Healy [9]. Moreover, Yance [20] did some unpublished work on this innovation. But most of their work pertained to the spread of the diesel locomotive among firms, not to the intrafirm rates of diffusion. Thus, the amount of overlap with the present study is relatively small. 3 Given that one knows the per cent of the firms in the industry that have begun to use the innovation at each point in time and the average per cent of output produced with the innovation (or some similar measure of the intrafirm rate of diffusion) by these firms at each point in time, one can simply multiply them to get the corresponding measure of the rate of diffusion in the industry (if the firms are roughly of the same size). The rate at which firms begin to use an innovation is studied in [12], and the factors determining whether one firm will be quicker than another to begin using it is studied in [13]. Thus, the combined results of these previous papers and the present one

1. The theoretical foundations of the aggregate production function give one grounds for doubting whether the concept is at all useful. Nevertheless, the temptation to discuss movements in indices of input and output in terms of such a function is difficult to resist. And there is no doubt that it is useful to rationalize the data along these lines. In his analysis of the aggregate production function in the United States, Solow derived many useful results.1 These findings, however, depended on the assumption of constant returns to scale in the aggregate production function. This assumption simplified the analysis considerably. Solow found the capital coefficient a, in the Cobb-Douglas, from the proportion of income going to capital; then, by subtracting from output per unit of capital (X/K) the product of (1 a) and capital per

OUR empirical knowledge of the demand and structural interrelationships of the economy at the regional level is indeed limited. Some understanding of these interrelationships can be gained through (1) the economic baseforeign trade multiplier approach, (2) the regional interindustry (input-output) approach, and (3) various other approaches, involving linear programming and the like, which are not of concern here.' Although the interindustry approach seems superior to the base-multiplier approach for most, though not all, purposes, the real difficulty lies in translating either approach into an operational one so that meaningful estimates of these interrelationships can be generated at a reasonable cost. This is a rather unfortunate state of affairs because it means that decision makers have no firm guidelines to use in attempting to assess the impact of autonomous demand forces upon regional economies or specific sectors within them. In an attempt to at least partially remedy this situation, we have developed an alternative type of framework which, for the lack of a better name, can be called an intersectoral flows model. This model incorporates certain features of the base-multiplier approach in addition to certain features of a regional interindustry approach hopefully some of the best features of each in terms of our objectives. In designing the model, one of the main concerns was that it be operational, in the sense that the necessary data could be obtained at a reasonable cost. Thus, to the extent that this objective is achieved, the restrictions on making such studies and repeating them may no longer be so formidable. The particular region chosen for study is California and the three major subregions within the State. Since the interest here is in the model and its implementation, as contrasted with the implications for the California economy, major attention will be focused on these topics.

7ROM among various recent contributions to the problem of risky investment decisions and portfolio diversification, the work of Harry Markowitz and that of James Tobin deserve particular attention.2 Both these authors interpret the as an individual who is attracted by certain characteristics of assets, and is repelled by other characteristics. A high mean of the expected frequency distribution of yields is viewed as an attractive feature; high dispersion (say, high variance) about the mean is considered a repelling feature for the investor; 3 and the question of how much of the attractive feature the individual is willing to trade for how much avoidance of the repelling feature is then said to depend on his preference system. At any rate, the with these tastes should abstain from acquiring portfolios (security-mixes) which have smaller yield and greater expected variance than other portfolios. Analytical frameworks of this kind suggest the use of indifference-functions. In particular the individual's gains from deciding how much of various assets to hold express themselves readily in a rise to a higher preference level, since he is essentially comparing objective marginal rates of transformation, which are provided by market opportunities, with subjective marginal rates of substitution between expected yield and avoidance of variance. For large numbers of securities the analysis becomes involved, but the basic principles remain the same and I will not go into further detail here. However, I would like to take my departure from the comments which Markowitz and Tobin have made on the probabilistic background of their analysis. Both authors feel that a set of axioms expressing the principles of operational utility and numerical subjective probability underlies their approach. My own position in this regard may be summarized in the following three points. (i) If we postulate strictly probabilistic behavior that is, if we interpret the decisionmaker as being guided by subjective degrees of belief that are consistent with one another by the specific standards of probability theory and as maximizing his utility-expectations then it is clearly desirable to develop the analysis in terms of alternative surpluses expressed in cardinal utility. In the present article I shall make such an attempt. A high degree of generality may be claimed for the validity of the results of such analysis, as long as one accepts strictly probabilistic basic assumptions. (2) I must, however, say that I do not regard it as generally fruitful to interpret the decisionmaking process in strictly probabilistic terms, say, in terms of L. J. Savage's axioms alone. One reason for this was expressed in articles by Daniel Ellsberg and by myself on an earlier occasion.4 In these two articles the reader will 'I am grateful to my colleague, John W. Hooper, for having read the manuscript of this article and for having made valuable suggestions. 2 Harry M. Markowitz, Journal of Finance, vii (March I952), and Portfolio Selection, Efficient Diversification of Investments, Cowles Foundation Monograph No. i6, New York: John Wiley & Sons, I959; James Tobin, Liquidity Preference as Behavior towards Risk, Review of Economic Studies, xxv (2) (February I958). 'The typical investor in this sense is a person with decreasing marginal utility of wealth. Such an will find a given mathematical expectation of money gains more attractive if it is associated with little dispersion than if the dispersion is great. However, acceptance of the variance as the uniquely relevant measure of dispersion implies specific (additional) constraints. It implies a quadratic aggregate utility function and/or a frequency distribution of expected returns which can be fully described by the mean and the second moment about it. See particularly Tobin, op. cit., and Marcel K. Richter, Cardinal Utility, Portfolio Selection and Taxation, Review of Economic Studies, XXVII (3) (June I960). See also p. I82 ff. These specific constraints on the utility functions and/or on the frequency distributions play a role in theories relating to the desirable degree of whenever the among which the diversifies have different probabilistic properties, but not so if these bets have the identical properties. In the latter case diversification will always diminish dispersion in the relevant sense, and in this latter case diversification will always be desirable to an with monotonically decreasing marginal utility. See section on limits of diversification, i8i if. 4See the symposium on Decisions under Uncertainty in