Knowledge that Transforms

of the explanation for the unexpectedly low level of consumption in I95I and 1952. 4. The formula assumes that the behavior of large aggregates of individuals is reasonably stable. Unless this assumption is made no prediction is possible and the limits within which any economic speculation is valid becomes doubtful. Absolute stability of behavior cannot be expected, and to the extent that behavior is unstable the formula will fail. 5. There are without doubt other variables affecting consumption which have been ignored in the formula. Controls and wartime shortages of consumers' goods are two examples. Campaigns to induce consumers to save and buy bonds, and waves of speculative excitement are others. Changes in the distribution of incomes might also be expected to have some effect on consumption. 6. The statistics of disposable income and consumption may need some adjustments. Disposable income, for example, is a net figure after deducting depreciation calculated mainly on an original cost basis. Consumers, however, may well behave as if depreciation were calculated on a replacement cost basis. 7. The measurement of wealth is subject to conceptual and statistical difficulties which make it particularly elusive. The measure may moreover need to be adapted to the purpose for which it is being used. For example, Goldsmith has included the structures and durable equipment of corporations at their current values. In assessing the influence of investments in corporations on current consumption it may be that the market value of the common stock and the bonds issued by the corporations would give a better measure. Further investigation may make it possible to allow for some of these disturbing elements. To make allowance for instability of behavior will be more difficult but may be possible. Nevertheless, in view of these uncertainties the question naturally arises, can any formula be expected to give a reasonable guide to the consumption habits of individuals? The answer will be found only through the success or failure of some formula, such as the three considered in this paper, to explain consumption for a sufficient number of years. The closeness of fit of all three formulas at least holds out some promise that a useful guide can be found in this way. After reviewing the circumstances in which any formula of this kind might be expected to fail it is impressive to find how well all three formulas do in fact predict the behavior of consumers.

A RECENTLY published analysis of the structure of United States foreign trade concludes that widely held opinion that as compared with the rest of the world the United States' economy is characterized by a relative surplus of capital and a relative shortage of labor proves to be wrong. As a matter of fact, the opposite is true (p. 343). Conflicting as it does with so many current notions, this unequivocal conclusion is highly provocative. It would seem to imply that the economic pressures of the American economy operate in the direction of population emigration and capital inflow. It appears to be inconsistent with other empirical evidence: the performance in the United States by machine of tasks undertaken by hand methods abroad; the low portion of the American labor force employed in agriculture, as contrasted with allegedly widespread concealed underemployment in many agricultural areas overseas; even the use of labor-saving consumer durables in middle class American households but employment of domestic servants by comparable families in poorer countries. Is a major re-shuffling required in our preconceptions about relative factor endowments, or has this new study somehow gone astray? Specifically, the study purports to demonstrate the following argument: if the total volume of exports were reduced one million dollars, while holding the proportional composition the same as in I947; if competitive imports were similarly cut by one million dollars; and if the foregone imports were obtained instead from domestic import-replacement industries; then more domestic capital and less labor would be required to produce the imports at home than had been incorporated in the former exports. The relevant data, which provide the basis for Figure i of the published study (pp. 34041), are plotted on the scatter diagram. When the capital-labor ratio is taken as the independent variable, the predominance of labor-intensive goods among the export items and of capital-intensive goods among the imports is by no means as clearly discerned (p. 346) as one is led to expect. The overwhelming bulk of the points cluster closely about the line of zero net trade. Any measure of the relation between capital (labor) intensity and imports (exports) therefore tends to be dominated largely by a few points with strong net export or net import positions, and more particularly by a single extreme point near each end of the scale. The following are the sectors which, in the base year, contributed more than $25,000 net exports or net imports (per million dollars of United States exports and of imports):

TEN YEARS have passed since publication of Haavelmo's first article on simultaneous-equations approach.' These years have produced an abundance of theoretical literature and have greatly increased capital requirements of those who would engage in measurement of economic relationships. Measurement without theory has (quite properly) been drummed out of journals. However, measurement with theory has been painfully slow come forward. This may be due in part a sort of natural selection, in that those who have been most forehanded in acquiring new methodology have (with few exceptions) been chiefly interested in methodology per se. For them personally, empirical applications of new may be even less inviting than research using simpler methods. For, paraphrase Haavelmo,2 economists will have revise their ideas as to not only the level of statistical theory and technique but also the amount of tedious work that will be required, even for modest projects of research. There is no point in lamenting division of interest between methodologists and applied workers. But it appears that burden of testing new econometric tools under operating conditions must be taken up by latter group. Specific cases of breakdown or evidence of poor design may then direct attention of methodologists toward improving their product or modifying their claims for it. My own experience suggests that advertising has been much too derogatory of a long-established competitor. During past few years my work in United States Department of Agriculture has involved a considerable amount of statistical demand analysis. The object of this work has almost invariably been obtain numerical results which made sense in terms of commodities and classes of economic agents involved -that is, results of structural significance. In all but a few cases I have used singleequation methods for estimating desired coefficients. I accept proposition that many economic phenomena must be explained in terms of two or more simultaneous relationships. However, single-equation methods appear be both practically and theoretically appropriate for estimating many structural relationships in field of food and agriculture. The first section of this paper is an appraisal of applicability of single-equation methods statistical demand analysis for farm products. The second section deals with an older and simpler problem in structural analysis. This is adjustment of least-squares results for effects of measurement errors in independent or predetermined variables, object being obtain best estimates of coefficients of reversible (hence, structural) demand functions. The common element in two sections is emphasis upon estimation of coefficients or parameters of reversible demand relations. The usefulness of single-equation methods for predicting future values of a variable (given unchanged structure) has not been disputed by proponents of simultaneous-equations approach. Their applicability structural analysis has, I believe, been underestimated during past decade, and some reaffirmation of their value in this area is needed.

This argument would only be confused by expanding the notation into one involving separate terms and fractions involving determinants. Diagrams cannot help here and a prose translation would presumably have to cover an explanation about the inversion of matrices and the meaning of determinants. This argument, that AY = S-1(AJ) or something even more elaborate, is in principle involved whenever one wishes to find the effect of a given disturbance on a position of equilibrium involving many simultaneous conditions. Marshall himself insisted on the fact that economic variables are interconnected and determined in just this way.7a The difficulty in making AY = S-1(AI) intelligible to persons who have not found time to learn about matrices is therefore a main obstacle in getting them to understand the ramifications of any change involving three or more interdependent variables. A set of numerical examples is probably the best available substitute for matrix algebra in cases of this kind, but it is a very poor substitute indeed. Whilst the axioms and the results should be fully translated into prose, only minor concessions should be made to the semi-mathematician in the exposition of the proof itself. But there remains one further subject that is very much the concern of the non-mathematical reader. This is the possible effects of relaxing the simplifying assumptions. Usually the writer can only guess at such effects by using his mathematical judgment. Only the mathematical readers will be able to pronounce an informed verdict on the worth of such guesses. But the non-mathematical reader will be very interested in precisely these effects and it is therefore essential that any such guesses should be accurately translated into language which both he and the mathematicians can understand. Editors may ask their contributors to bear such precepts as these in mind when compiling articles on economic theory. But they are no more than a guide, and the editor who insisted on literal obedience to them would be unlikely to publish much in this field.