Knowledge that Transforms

an essential part of the theory and study of competition and monopoly. Second, in any industry or other meaningful group, the number of firms, an essential magnitude in Mr. Prais's system, is usually un-knowable with any precision.4 It follows that average size or growth rate is equally unknowable. In any case, Mr. Prais's definition of concentration, as he points out, is a member of the same family as the Gini coefficient (op. cit., 268), or what I called Lorenz-type concentration, and that type has been rejected implicitly by other students, and explicitly by me, again, not for reasons of internal consistency, but of relevance to economic analysis. Mr. Prais's system has the immense advantage (and prestige) of being an extension of the classical statistical system, with all the logical symmetry and practical aids this would imply since it is a sum of squares, for example, it is additive, and significance tests are directly applicable. By comparison, the concentration ratio is a very clumsy and imperfect sort of expedient; the nearest approach to a general theory is in a brilliant paper by Jiirg Niehans.5 It would be incorrect, however, to leave the reader with the impression that Mr. Prais's system is of no interest or use. First, it may be applicable to non-economic problems, or to economic data which neither of us has investigated. Second, we should be interested in differential growth rates as such. Stephen Hymer and Peter Pashigian presented a paper, Firm Size and Differential Growth Rates, to the I958 meetings of the Econometric Society; although they did not have occasion to use measures of Mr. Prais's type, it is conceivable that others could. Finally, it is not only helpful but essential to conceive of the operations of any industry as a general system of random influences which will cause firms to gain or lose position or market share. Tendencies toward greater or lesser concentration, or toward no change, must be fitted into or superimposed upon such a general framework, or else we hail every passing leaf as evidence of the prevailing wind. I do not think Mr. Prais's definition of concentration is of any help in this task, but this is perhaps secondary; it should stimulate thinking toward incorporating the notion of a statistical system into the analysis of industry situations. 4 Ibid., and see the chapter on The Business Population in the forthcoming revision of Historical Statistics of the United States. 5 Jiirg Niehans, Eine Messziffer fur Betriebsgrossen, Zeitschrift fur die Gesamte Staatswissenschaft, iII (I955), 529-42. It is to appear in English in a forthcoming issue of International Economic Papers.

intensive goods to countries other than the United States. This may be considered as supporting the generally held opinion that Japan's foreign trade is two-sided.10 We suspect that foreign trade might have a similar nature. If data were available on the capital-labor ratios for United States exports broken down by countries, then more conclusive findings might be expected about the position of the United States in the international division of labor.11 Another interesting fact is that the capital-labor ratio for United States exports to Japan is not only larger than that for the United States total exports but also exceeds that for competitive imports. This means that United States exports to Japan are more capital-intensive than United States domestic production for replacing its competitive imports from the rest of the world. This would seem also to demand more careful investigation into the so-called Leontief paradox. We would like to refrain from drawing any sweeping conclusions here. 10 Cf. Economic Planning Board, Survey of Japanese Economy (I956-57). ' According to A. Daniere, relative foreign inefficiency is less in the production of B than in the production of A, where A denotes manufactured goods and B raw materials (ores, oils, rubber, and other important United States imports), due to differences in material resource endowment. Since these raw material products, on the whole, require a high capital-labor ratio, the large raw material component of United States imports suggests, in agreement with the authors' view, that the Leontief capital intensiveness situation holds better in the trade with raw material areas than with industrial countries. See Andre Daniere, American Trade Structure and Comparative Cost Theory, Economia Internazionale, Ix (August, I956), 426.

EVER since Samuelson's I939 article in this REVIEW on the interaction of the accelerator and multiplier, business cycle theory has been concerned with drawing out the implications of a set of differential or difference equations. It was never assumed that these models adequately described the basic structure of the economy but it was felt that a better understanding of the forces producing cyclical movements could be obtained in this manner. The basic mechanism generating the movements of the system in the models of Hicks, Harrod, Goodwin, and Kaldor was an interaction of the accelerator and multiplier.' In whatever form, such an endogenous income-generating mechanism was the core of these cycle theories. In many cases, the implications of such a set of dynamic equations were then found by deriving an analytical solution for the system. By determining the nature and size of the roots of the characteristic equation, it was possible to determine the type of movements implied by the basic mechanism. The effects of changes in the structural constants were also studied and boundaries derived separating the various kinds of movements. Two additional elements were usually incorporated in these models. Some exogenous expenditure was included to take account of the fact that not all expenditures could be explained by economic factors. Various assumptions were then made about its behavior over time. Thus, Hicks assumed an exponential trend for exogenous investment, whereas Goodwin's more Schumpeterian approach assumed that exogenous investment would occur in wavelike patterns.2 In addition, two different types of constraints were added, limiting the values the variables could take. full employment ceiling was introduced in the form of a production function setting a maximum value for output. And since gross investment could never be negative, it was sometimes necessary to substitute the rate of depreciation for the accelerator during the downswing. As a result of these additions, drawing out the implications of such systems was no longer simply a matter of examining the roots of the characteristic equation. One can approach the econometric models of Klein, Tinbergen, Valavanis,3 and others in the same spirit and consider their studies to be more complex models of the trade cycle. By specifying in more detail the various factors influencing the different types of expenditure and income, these models can be thought of as more adequately describing the forces at work producing cycles or any other type of movement. In particular, the econometric model developed by Klein and Goldberger lends itself to such treatment.4 As with the cycle models just mentioned, it contains exogenous variables, technological constraints, and an endogenous incomegenerating mechanism. Of the many exogenous variables in the model, those representing the influence of population and government activity *The material contained in this article has been taken from the author's doctoral dissertation Implications of Some Dynamic Models (Harvard University, I958). While taking full responsibility for the work, the author would particularly like to thank Professor James S. Duesenberry, who suggested the topic and followed the study through all its stages. In addition, W. H. Locke Anderson advanced the work through criticism and assistance in programming. earlier draft of this paper was presented at the Philadelphia meetings of the Econometric Society on 30 December I957. 1J. R. Hicks, Contribution to the Theory of the Trade Cycle (Oxford, I950), Roy Harrod, Towards a Dynamic Economics (London, I948); Richard Goodwin, Econometrics in Business-Cycle Analysis, reprinted in Alvin Hansen, Business Cycles and National Income (New York, 1957); Nicholas Kaldor, A Model of the Trade Cycle, Economic Journal, L (March I940). 2Richard Goodwin, A Model of Cyclical Growth, The Business Cycle in the Post-War World (London, I955). 'L. R. Klein, Economic Fluctuations in the United States, I92I-I94z (New York, 1950); J. Tinbergen, Business Cycles in the United States, z9z9-z932, Vol. II (Geneva, I939); S. Valavanis-Vail, An Econometric Model of Growth: U.S.A. i869-i953, Papers and Proceedings, American Economic Review, XLV (May I955). 'L. R. Klein and A. S. Goldberger, Econometric Model of the United States z929-I952 (Amsterdam, I955). The estimates considered in this paper are for the original model. Their equations have been reproduced in the appendix with slight modifications. The num;bering is my own, and Klein and Goldberger's expression Y + T + D has been replaced by GNP.

FOR all the interest that attaches to constant-price (physical-volume) estimates of output, it remains uncomfortably true that the outputs of some sectors are effectively unmeasurable in constant prices, at least by direct means. While this difficulty can arise from several sources, it commonly arises under either of two circumstances: where the total number of to be covered is very large, or where produced in any given year have no exact counterparts in the base year, i.e., where the products problem is unmanageably large. The conventional recourse under these circumstances is to some indirect measure of outputs, and usually to an index derived in one way or another from input data. Construction is manifestly an industry in which both of these difficulties are severe. It is a custom industry, in which single are frequently unique, and in which, even for otherwise identical products, differences in site may produce differences in costs and in services yielded. In the face of these difficulties, constant-price estimates of United States construction have been derived from input rather than output data: Simon Kuznets' estimates for decade averages, I869-I9I3, are based on materials inputs; ' his annual estimates for I 9I3-43, and the Department of Commerce annual estimates, are both essentially, though with minor qualifications, current values of outputs deflated by indexes of prices of inputs.2 The purpose of this note is to report the results of an effort to compose a constant-price index of Soviet construction.3 The substitute for a true output index employed here is the same as that used by Kuznets for the earlier period, a materials-input index. The results of the study are shown in Table i. So far as the available data and some rather incautious estimating procedures permit, this is an index of materials actually consumed in Soviet construction, not of domestic output or total consumption of construction materials conventionally defined. It is intended to include materials absorbed in gross new construction of all kinds, whether completed or in progress, no matter by whom performed or financed, and in the entire de facto territory of the U.S.S.R. as of each date. It is composed from quantity series for 59 kinds or grades of materials, some of which, however, are included for a few years only while others for some years are estimated in combination.4 It is weighted by I937 ruble prices for state industries, at wholesale. The years I92 7/28, I928/29, and I929/30 are fiscal years, beginning on October i. The war years are omitted for lack of quantity data; I94I Plan is included because of the abundance of quantity data available for that year.