Knowledge that Transforms

THE long-run development of the terms of trade is a recurrent subject for economic analysis in which a succession of theories has been put forward.' It was once believed that the terms of trade would inevitably turn in favor of primary products and against manufactures because the extractive industries were subject to diminishing returns, manufacturing to decreasing costs. This view gave way to another, that world investment moved in large cycles, and that the terms of trade favored primary products when investment expanded, manufacturing when contraction set in. A third hypothesis suggests that productivity increases about equally in primary products and manufactures, but that with the growing real income it brings, Engel's law leads to smaller increases in demand for agricultural products than for manufactures and services, so the terms of trade will favor the latter. Lately the same shift of the terms of trade against countries producing primary products has been discerned by Singer2 and Prebisch 3 but attributed to monopolistic practices on the part of industrial countries. The most recent discussion bearing on the subject was initiated by Hicks,4 who suggested that the terms of trade are affected by differences in the rate of productivity increase between the leading industrial country and all other countries. The leader's terms of trade will turn in its favor or against it depending on whether its innovations are import biased or export biased. Hicks considered that British innovation in the nineteenth century was export biased, but that United States innovation currently tends to be import biased. His theorem has been criticized 5 mainly in relation to the equilibrium mechanism in the balance of payments, with only limited attention to the factual connection between innovation and the terms of trade, though attempts have been made to forecast the terms of trade between manufactures and primary products for I960, and once for I975.6 My contention is that few generalizations on the terms of trade between world manufactures and world primary products are valid but that they tend to turn against underdeveloped and in favor of developed countries.

Robert E. Baldwin, The Commodity Composition of Trade: Selected Industrial Countries, 1900-1954, The Review of Economics and Statistics, Vol. 40, No. 1, Part 2. Problems in International Economics (Feb., 1958), pp. 50-68

FROM the early days of input-output analysis its practitioners have recognized the importance of the aggregation problem and the fact that the results of the analysis depend upon the particular aggregation procedures used to combine industries. Recently, an increasing number of writers have become interested in theoretical as well as practical aspects of the problem.' The potential user of input-output analysis often needs to reduce a given table to smaller size. table say 200 by 200 or even 50 by 50is cumbersome for many purposes. The theorist finds it too detailed to understand, and the forecaster finds it too extensive to use in making further numerical computations. Of course some information is always lost by aggregation. But the considerations that lead to the computations of averages and index numbers also lead to the consolidation of inputoutput tables: ease of comprehension and economy of manipulation. The following question has been posed in the literature: 2 given a detailed input-output table in which many industries appear, and given the desire of the research worker to have only a few large industries to deal with, when is it possible to consolidate the small industries into industries, and still obtain the results of the analysis or predictions as would have been obtained by using the many small industries in the first place? The answer to this question has been shown to be almost never. The special cases where it is possible have indicated the type of conditions needed for what might be called good aggregation procedures meaning procedures which give approximately the same results as given by the detailed model. The need to develop criteria for good aggregation has been recognized, but few specific suggestions have been made.3 The purpose of this paper is to suggest specific criteria and procedures for good aggregation of a given input-output table. First, reasonable criteria are developed, based on the usual objectives of input-output analysis and on some special assumptions concerning final demand. Some approximations to these criteria are then proposed that are closely related to previous suggestions to aggregate on the basis of similarity of coefficients or homogeneity of input structure. The criteria are then illustrated and the usefulness of the approximations tested by numerical experiments involving a * The author gratefully acknowledges the assistance given him by the Social Science Research Council, which awarded him a Faculty Research Fellowship; the Bureau of Research of Kansas State College; Professor William A. Neiswanger, of the Department of Economics of the University of Illinois; Professor Thomas E. Hull, of the Department of Mathematics of the University of British Columbia; Patricia Kollman, graduate research assistant in the Department of Economics and Sociology of Kansas State College. 'J. B. Balderston and T. M. Whitin, in the Input-Output Model in Oskar Morgenstern, ed., Economic Activity (New York, I954), 79-I28; Tibor Barna, and in Input-Output Analysis in Tibor Barna, ed., The Structural Interdependence of the Economy (Proceedings of an International Conference on Input-Output Varenna, I954), ch. 7; John C. H. Fei, A Fundamental Theorem for the Problem of Input-Output Analysis, Econometrica, xxiv (October I956), 400-I2; M. Hatanaka, Note on Consolidation Within a Leontief System, Econometrica, xx (April 1952), 30I-303; Mathilda Holzman, of Classification and Aggregation in Wassily Leontief, ed., Studies in the Structure of the American Economy (New York, I953), ch. 9; John McCarthy, in the Open Leontief Model (paper presented to the Econometric Society at Cleveland, Ohio, December 1956); M. McManus, General Consistent in Leontief Models, Yorkshire Bulletin, vIII (June I956), 28-48; Edmond Malinvaud, Problems in Input-Output Models in Tibor Barna ed., op. cit., ch. 8; Oskar Morgenstern and Thomson M. Whitin, Comments in National Bureau of Economic Research ed., Input-Output Analysis: An Appraisal (Studies in Income and Wealth, Vol. i8, Princeton, I955), I28-35; Herbert A. Simon and Albert Ando, of Variables in Dynamic Systems (paper presented to the Econometric Society at Cleveland, Ohio, December I956); H. Theil, Linear in Input-Output Analysis, Econometrica, xxv (January I957), III-22. 2See works cited of Balderston and Whitin, Hatanaka, Malinvaud, McManus, Theil. 3Some preliminary suggestions have been made by McCarthy and by Simon and Ando in their papers cited.