Knowledge that Transforms

1) Like a too-powerful headlamp, Professor Samuelson's brilliant article on induced innovation illuminates much but casts other matters into greater obscurity.' In this short note, I am hoping to make the illumination a bit more evenly-diffused. On the whole I shall argue that where there is a differentiation of the Samuelson from the WeizsackerKennedy product, Samuelson himself has tended to exaggerate the quality difference involved. Before coming to this, however, I should like first to allude to one aspect of the matter about which Samuelson has scarcely commented. 2) I think there is a rather fundamental difference in what might be called the methodological intention of our two approaches. Following Kaldor,2 and recognizing the very great difficulty in principle and impossibility in practice of distinguishing factor substitution from bias in innovation. I had hoped that the innovation-possibility frontier might be able, so to speak, to swallow up the traditional production function and replace it altogether. Samuelson, on the other hand, by adopting the factor-augmenting form for the production function has allowed the production function to do the swallowing up. Each of these two approaches has its weakness and its strength. The strength of the one is the weakness of the other, and vice versa. The weakness of the Samuelson approach is the great reliance still placed on the tenuous concept of the production function, a reliance that the KaldorKennedy approach successfully avoids. The weakness of the Kaldor-Kennedy approach is that it fails to provide an explanation of the determination of prices in the short run, while the Samuelson approach is admirably suited to doing just that. While I still have hopes of the Kaldor-Kennedy approach, I do not think it can be taken much farther until some reasonably convincing alternative explanation of the determination of prices in the short run can be built into it.3 Without beconming a confirmed factor augmenter, for the purpose of the rest of this note I am prepared to go along with the factoraugmenting form of the production function.4 Let me at the same time accept everything that Samuelson wrote concerning stability conditions together with the implied criticism that my own piece was weak on stability questions. 3) Having conceded this much, I am going to put up much more resistance on most other points. The core of Samuelson's own analysis is in his section II. Stability questions aside, the reason and the only reason why he obtains a different result from mine in my own discussion of the one-pr-oduct model is that he has replaced one of my assumptions by one of his own.5 In the place of my assumption that the rate of interest is constant, Samuelson has assumed that capital, in natural units, is accumulati g relative to in natural units. The reason why I have not utilized the Hicksian insight that capital tends to grow relative to labor is that I have no need of it. Since a determinate rate of capital-deepening comes out as one of the results of my analysis of the one-product model, it would obviously be worse than superfluous to incorporate it also as an assumption. 4) I do not see any particular reason why a model which assumes an exogenous rate of growth of capital relative to should be regarded as superior or inferior to one which assumes a constant rate of interest. The most one might say is that the former is more appropriate for relatively short-run analysis and the latter for relatively long-run analysis. Both models fail to explain the fact that the interest or profit rates show no clear trend upward or downward. For this reason, I would agree that my own theory is not a complete theory of the constancy of distributive shares. but rather a theorv contingent ' A Theory of Innovation Along KennedyWeizsacker Lines, this REVIEW, XLVII (Nov. 1965). See also my own Induced Bias in Innovation and the Theory of Distribution, Economic Journal (Sept. 1964). Since Samuelson is kind enough to mention the seminar held at M.I.T. on May 28, 1964, may I take this opportunity of acknowledging the very great courtesy shown by himself and his colleagues at M.I.T. in giving me a hearing on a date and at a time that for them could hardly have been more inconvenient. May I also take this opportunity of mentioning again my indebtedness to Professor Ahmad, of the University of Khartoum. Regrettably, his name was misspelled in the acknowledgement in the Economic Journal. I have not had the advantage of seeing Weizsacker's unpublished paper. 2Essays on Economic Stability and Growth (Duckworth, 1960), 264 et seq. 3 I suspect Kaldor might claim that he had provided an alternative explanation -but I am not sure that it is convincing as yet. 4 With the reservation that augmenting can be negative as well as positive. See below, section 5. 5 See Samuelson, op. cit., 348, footnote 3. With reference to that footnote, please observe that, in Kennedy's case, the Harrod-neutral result is not supposed to come about, it does come about!

T HIS paper reports on a study of the relation between peoples' incomes and the way they allocate their time to income and leisure. Time can be spent either on the earning of income (work) or on a host of alternative noneconomic activities (leisure). It is a question of real significance whether, as incomes rise, people systematically change their distribution of time between these activities. However, it is a question to which economics provides no agreed upon answer. No a priori or theoretical answer is possible because we know that, as sellers of their own time, people are pulled in opposite directions by conflicting income and substitution effects. On the other hand, no empirical evidence has thus far been widely accepted despite surprisingly consistent empirical results. But since economic growth and rising incomes are part of a pervasive economic climate, this aspect of peoples' behavior the way they respond to increased economic well-being is of very real importance, in part because it will feed back as an influence on the rate and pattern of growth itself, both in advanced and in underdeveloDed countries.' This subject, of course, is discussed in the theory of public finance as the incentive effect of tax and expenditure, in macro and labor theory as the shape of the long-run aggregate labor supply curve, and in the literature of economic development as the response to changing sectoral terms of trade. This study is empirical. It uses aggregate international cross-sectional data to reveal the typical relation between incomes and hours of work-i.e., between incomes and the allocation of effort (as synonymous with time) to the acquisition of income. Previous empirical studies either have shown that relationship to be negative -work effort decreases with increasing incomes or at the least, have failed to show a positive correlation. The data used in those earlier studies were intercity and interindustry cross-sections [2, 7, 8], industry data over time [71, and cross-sections of occupational sub-groups within a society [2]. The major purpose of this study is to test the conclusions of those earlier investigations to see if these very different international aggregate data confirm that the relation is negative. A secondary objective is to use these data to evaluate possible influences, additional to income, on a society's allocation of effort.

Paul A. Samuelson, Samuelson on Induced Innovation: Rejoinder: Agreements, Disagreements, Doubts, and the Case of Induced Harrod-Neutral Technical Change, The Review of Economics and Statistics, Vol. 48, No. 4 (Nov., 1966), pp. 444-448

IN the May, 1964 issue of this REVIEW, R. S. Eckaus presented estimates of general and specific education and training requirements by industry.1 For the analysis of projected demands on the educational system, it may be more useful to have such data on an occupational basis as technological change is not usually conceived of as neutral with respect to the component occupations of an industry. It is the purpose of this article to present such data and examine some of their deficiencies. There are substantial reasons to seek education and training requirements data on an occupational basis. If estimates can be Sbtained of the amounts of various types of training required to fill a certain job, then projections of changing occupational patterns will yield predictions of requirements of the educational and training system. Such predictions could tell us not only what specific occupations to train for, but the amount of teaching time and other costs required to train a work force in the new pattern. Further, educational and training requirements should be related to mobility characteristics of occupations. Presumably a higher level of formal or general education will be associated with a greater degree of occupational mobility, with the reverse probably being true with regard to level of training for a specific job.

Giorgio Basevi, The United States Tariff Structure: Estimates of Effective Rates of Protection of United States Industries of United States Industries and Industrial Labor, The Review of Economics and Statistics, Vol. 48, No. 2 (May, 1966), pp. 147-160

T HAS long been recognized that a good economic forecast should consist of several components. In addition to predicting turning points, a forecast should theoretically include some statements about the timing of the and the amplitude and duration of the subsequent movement. If the forecaster makes quarterly quantitative estimates of GNP, he is, in fact, estimating all of the aforementioned components. However, when forecasters use other types of predictions, they usually do not provide estimates of the timing or amplitude. This is especially true when analysts speak of the forecasting behavior of the leading series and/or the rate of change methods. While has been considerable discussion about the success of these methods in forecasting turning points, I very little is known about other aspects of their forecasting behavior. It has generally been concluded, that, in practice, the leading series and rate of change methods predict every turning point of a predictand such as the Federal Reserve Board's Index of Industrial Production, but they also display a large number of false leads. As for their other forecasting characteristics, Moore2 has concluded that some information about the amplitude of a recession could be obtained about six months after the movement first began. Finally Wright and Okun have attempted to estimate the dates of turning points, I but no attempt has been made to attach probabilities to the predicted dates of turning points. Our paper will present one method for attaching probabilities to the turning point forecasts which are obtained from using the leading series and diffusion indexes. The probability must refer to the likelihood of the predictand's occurring in a given time interval. Statements such as there will be a turn or there is an X per cent chance of a turn are tautologies, for sooner or later will be a turn. Thus to have any usefulness, the probabilities must be attached to specific time periods. In the following section we shall outline the methodology of the study, discuss the data to which this methodology was applied, and finally present the results.

This paper is not directed to the question of whether the Treasury should or should not practice in the public sector what the Clayton Act prohibits in the private sector. The paper is concerned exclusively with the theoretical question of whether the Treasury would necessarily receive higher prices by employing price discrimination than it could get by selling the issues at a single price. From a theory of bidding under uncertainty, which seems to apply naturally to the Treasury auction, it will be shown that buyers may be expected to enter lower bids under price discrimination than they would for a simulated competitive auction. If this analysis is accepted, it suggests that the Treasury may actually get less revenue from a given bill offering under price discrimination than under a competitive auction.

IN THE school year 1963-1964, according to the National Education Association, the total expenditures to educate 41.7 million pupils of the Nation's public schools exceeded 21 billion dollars. This expenditure figure shows a significant increase from 15.6 billion dollars in 19591960 and 5.8 billion dollars in 1949-1950 which were spent, respectively, for 34.2 million and 24.1 million pupils. In view of the magnitude of the resources involved and the rapid growth of their amounts, inquiry into scale economies in public education has not received adequate treatment by researchers. The main reasons for this seem to be (1) the difficulty of determining the quality of various schools, and (2) varying opinions regarding the importance of the implications of such a study. The cost per pupil may reflect differences in the quality of education among schools, unless this quality differential is somehow taken into account. Then, if a study indicates an economic advantage for large size schools, there is a question of how this fact should affect policy decisions when there are other factors to be considered. The United States Office of Education, for many years, has been making surveys of public school costs in cities of varying sizes. Their results in general show higher per-pupil costs for schools in larger cities. In the year 1958-1959, the cost per pupil in cities with a population of less than 10,000 was 312 dollars. The cost in cities with populations ranging from 10,000 to 24,999 was 305 dollars. In cities with populations from 25,000 to 99,999, it was 321 dollars, and in cities of over 100,000 people, 361 dollars.1 In 1939-1940, the equivalent figures were 80 dollars, 87 dollars, 102 dollars and 127 dollars, respectively.2 The surveys obviously were not intended for analysis of economies of scale in school operation. Although large schools are typically in large cities and small ones in smaller cities, city population is hardly a suitable index of school size. Also these surveys do not account for differences in the quality of schools among size classes. The first serious inquiry on the subject was made recently by Werner Z. Hirsch.3 In his analysis, which employs multiple correlation and regression techniques and uses an elaborate device to distinguish quality differences among schools, he finds no significant economies of scale. He thus concludes that consolidation is unlikely to solve the fiscal problems of public schools. Hirsch uses a school district as the unit of observation. A study based on school districts undoubtedly has its merits, but schools, by and large, operate independently within a district. Thus, a more meaningful analysis of the size-cost relation, as Hirsch also implies, should be based on individual schools. Of the 27 St. Louis public school systems included in his study, all but six had enrollments of more than 1,500. To test the validity of a conjecture that significant scale economies exist over a relatively low size-range into which the nation's great majority of schools fall,4 we need a sample with a larger number of smaller units. Schmandt and Stephens, in a rank order correlation analysis, offer the conclusion that

Tacitus believed that the chief office of history is to prevent virtuous actions from being forgotten. That these few pages perform this office depends on the self-evident proposition that actions in support of economic knowledge are, in their nature, virtuous. In the history of economic thought the lineage of specific current doctrine or method at times takes on the tenuousness of a finely frayed thread that frustrates all efforts to distinguish the fibers comprising it. It often happens, in that circumstance, that the thread is knotted at some point short of its ultimate wanderings by a tacit agreement to recognize one or a few persons as the originators of the method or doctrine in question. When that happens, earlier efforts fall beyond the bounds of present memory. On occasion, however, it becomes possible to retie the knot somewhat farther back in the past. That is the function of the present note. currently accepted view 1 holds that the first recorded index number appeared in the work of G. R. Carli, an Italian who used a modified form of the simple average of relatives index number in 1764.2 This view probably originated with Wesley Mitchell, who named Carli as the inventor of the index number.3 In point of fact, this honor might be placed nearly a century earlier than Carli's effort, and certainly 25 years before it, depending on how strictly one chooses to define the term index number. If we give the term the broad meaning of a method or device which allows one to measure changes in aggregate price levels, we must consider a small book published by Rice Vaughan in the year 1675.4 Vaughan, an Englishman, was concerned with the rise in prices which had occurred in his native land over the preceding century. He wished to separate the influence on this price rise of the debasement of currency trom the intiuence of the heavy influx of gold and silver into Spain from the East and West Indies. In order to undertake this task, he required a measure of the general price rise which had occurred in that country. Vaughan relied on historic records of the wages of labor for his standard of measurement of price changes. Two considerations prompted his use of wages as a surrogate variable. First, labor carries with it a constant resultance of the Prices of all other things which are necessary for a Man's life. . Second, records of wages were more accessible than price data since statutes were readily available which always direct [ed] the rate of Labourers and Servants to be made with a regard of Prices of Victuals, Apparel, and other things necessary to their use. 6 Vaughan accordingly compared statutes setting wage rates for such labor as threshing grain and carpentry in the reign of Edward III with similar statutes of the period in which he wrote. On the assumption that these statutes reflected the costs to the laborer of his provisions, they served as ready-made index numbers. conclusion supported by these comparisons was that prices had risen to six or eight times their level of a century earlier.7 Those readers who insist that an index number must make explicit use of the prices to be measured are asked to consider the work of another Englishman of a slightly later period. In 1707, William Fleetwood, Bishop of Ely, published a defense of the fellows of a certain whose annual income from inheritances or pensions ran to more than five pounds.8 When the college was founded in the fifteenth century, its founders stipulated that a fellowship could be granted only to those students whose annual income from such sources was not in excess of that amount. A student of Fleetwood's acquaintance whose fellowship was in jeopardy appealed to the bishop. It was the student's contention that, in view of the past record of rising costs, an interpretation in the spirit of the regulation, rather than the letter, was more appropriate. student was perspicacious in his choice of * author is Assistant Professor of Economics at the University of Missouri. 1See, for example, John E. Freund and Frank J. Williams, Elementary Business Statistics: Modern Approach (Englewood Cliffs, New Jersey: Prentice-Hall, 1964), 77. 2Del Valore e della Proporzione de' Metalli Monetati con i generi in Italia prima delle Scoperte dell' Indie col confronto del Valore e della Proporzione de' Tempi nostri, in Custodi, Scrittori Italiani de Economia Politica, Parte Moderna, XIII, 297-366. 'Wesley C. Mitchell, The Making and Using of Index Numbers, Bulletin of the United States Bureau of Labor Statistics, 284 (Oct. 1921), 7. 'Rice Vaughan, A Discourse of Coin and Coinage (London: Th. Dawks, 1675). 5 Ibid., 107. 6 Ibid., 108. 7Ibid., 117-124. 8 William Fleetwood, Chronicon Preciosum: or, an Account of English Money, the Price of Corn, and Other Commodities, for the last 600 Years (London: Charles Harper, 1707).

ONE of the attractive aspects of the Harrod-Domar model is the magnificent simplicity of its variables. This is especially true of the incremental capital-output ratio (ICOR). It has served as a magnet for economists (including the present writer). Many have been unable to resist employing it as a major element in their attempts to understand economic growth. But are ICORs really helpful in understanding growth? How are ICORs ' and growth rates really related? In a recent paper, Ohkawa and Rosovsky2 presented a graph that showed growth rates and ICORs for Japan from 1890 to 1931 (sevenyear moving averages were employed). The remarkable thing immediately apparent from the graph is the inverse relation between the growth rates and the ICORs. In the few cases where this relation does not hold, the changes in growth rates are very small. Is this relation a curiosity that holds only for or is it likely to hold for other countries? I want to show both on the basis of theory and of empirical evidence that the latter is what we should normally expect. We should expect an inverse relationship between observable ICORs and growth rates, in most cases, for the following reasons: (1) the investment rate is a more stable variable than are other variables affecting growth; (2) the significance of non-capital inputs is greater than that of capital inputs; (3) changes in the level of employment of all inputs affect growth more than investment; and (4) some outputs are related probablistically to inputs. On purely a priori grounds, we can say nothing about these relationships. It is possible to invent hypotheses that would lead to the conclusion that ICORs and growth rates are not inversely related. However, it is also possible to reason plausibly, but not necessarily, that ICORS and growth rates are inversely related. It is this type of plausible reasoning that I wish to undertake. We know on the basis of studies by Solow, Aukrust, Fabricant, and others,3 that increases in capital contribute only a small proportion to total growth. The proportion is probably somewhere between ten and 20 per cent. As a consequence, most of the growth rate is accounted for by non-capital inputs. The main burden of the argument is that investment is a much more stable variable than the non-capital inputs. First we will examine the consequences of this assumption, and then argue why it is likely to be so. Consider the case in which output is explained by the Cobb-Douglas production func'On a priori grounds one can distinguish three types of ICORs. Elsewhere, I have made the distinction between the net incremental capital-output ratio and the adjusted incremental capital-output ratio. By the net incremental capital-output ratios (NICORs) I mean the incremental capital-output ratios as they would be on the assumption that the supplies of all other factors are held constant. By the adjusted incremental capital-output ratio (AICOR) I mean the capital-output ratio as it would be if it were adjusted to a given increase in the supply of other factors -for example, a one per cent increase in the labor force. In practice, however, neither of these concepts are actually employed. Instead, we use the actual increase in the capital stock as a ratio of the actual increase in income. In principle, we should not expect that the actual or observable ICOR would behave similarly to the somewhat purer and more restrictive NICOR and AICOR concepts. But the actual ICORs are much easier to employ statistically and have been used to a great extent. Therefore, their behavior is of great interest to us. In the case of both the NICORs and the AICORs we should expect a clear-cut positive relationship between capital and output. That is, as capital increases we should expect output to increase also. In addition, in both these cases we should not expect the capital-output ratio to vary in any special way with the growth rate. However, for practical work we use actual ICORs and it is these that are under consideration in this paper. See the author's Backwardness and 178. See also the excellent discussion in Gerald M. Meier, Leading Issues in Development Economics (Oxford University Press, 1964), 101 ff. 2 Ohkawa and Rosovsky, Economic Fluctuations in Prewar Japan, Hitotsubashi Journal of Economics (Oct. 1962), 24. 'R. Solow, Technical Progress and the Aggregate Production Function, this REVIEW XXXIII (Aug. 1951). See also R. Solow, Investment and Growth, Productivity Measurement Review, No. 19 (Nov. 1959); Odd Aukrust, Investment and Growth, Productivity Measurement Review, No. 16 (Feb. 1959); and S. Fabricant, Basic Facts on Productivity (New York: National Bureau of Research, 1959).