THE purpose of the present article is to clarify and suggest improvements in national income and product concepts as used particularly by the Department of Commerce. In developing the proposals, major problems of definition, duplication, and conceptual difficulty will be presented, together with a brief survey of the development of ideas, including some of the recent debates which focus attention on unsettled questions. Broad relations between the national income and product series developed by the Department of Commerce are indicated in Chart i, the various bars being drawn approximately to scale, as of I952.1 In national income accounting the emphasis on net value added by, or income accruing to, the various economic factors, as a result of productive services currently rendered, is well understood. On the whole this represents current money income (with some imputations), but it omits three important money income items: realized capital gains (losses), unproductive transfer payments, and government interest. It also omits one imputation of major significance: the value of housewives' services. Of the two main subdivisions of what are regarded as nonproductive government outlays, transfers and government interest, the latter was shifted from productive income in the official revisions of July I947. These conventions and changes, though generally recognized, are by no means universally accepted by specialists in the field. In fact, some of them are receiving renewed discussion in recent debates.2 All the factor shares on productive account are now entered in the Commerce national income totals before direct taxes are deducted. The addition of indirect taxes and depreciation or capital-consumption allowances raises these net totals to the Commerce gross national product totals, but this development has created confusion over the meaning of net product and the extent to which double-counting is involved in the gross totals.3 The Commerce Department also takes the national income as a base for developing its personal income series. By subtracting corporate profits (before direct taxes are deducted but after dividend allocations) and adding transfers and government interest (in the main), the Department secures a mixture of productive and nonproductive items of personal income and savings. Realized capital gains and losses are still omitted however.4

Dr. Novick has added his voice to the swelling chorus of exasperated voices protesting in a variety of ways, in rhyme 12 or with reason,13 the increasing use of formal language, constructs, and derivations in economic and statistical analysis, and the specialization that springs from this development. It is probable that the protest is not directed at the use of tools of long standing in economics, such as diagrammatic representation or simple calculus. Most of us, including the present discussant, have little knowledge of the battles over the usefulness of these tools, fought and decided long ago. It is rather the tools and concepts that have been brought into economics more recently, such as matrix algebra, set theory, difference equations, stochastic processes, statistical inference, and the axiomatic method, which are now the issue. There is a remarkable similarity between the present stage of economics and the situation which arose in physics in the I930's. intensive use of matrix algebra and group theory by the developers of quantum mechanics gave rise to strongly felt protests on the part of experimental, general, and even some theoretical, physicists. Alarm was expressed at the increasing tendencies to a formalism of which the function was neither generally apparent, nor even as yet fully visible to the developers of the new theories. However, since that time the clamor has abated and quantum mechanics has become an acceDted and fruitful Dart of physical theory. In fact, the headstart of physics over the political and social arts and has since become the major threat to contemporary civilization. There is nothing in the existing difficulties of communication between mathematical and non-mathematical economists-illustrated by the substantive contents as well as by the emotional overtones of Dr. Novick's comments that time and effort will not cure. Most of what needed saying on these matters was said eloquently, effectively, and wittily in the bargain, in two recent publications, by Professor Samuelson 14 and Professor Stigler.15 An equally thoughtful discussion in a more sober tone by Professor Allais 16 perhaps appeared too late to be taken into account by Dr. Novick. It is unfortunate, however, that Dr. Novick has not clarified his attitude, for instance, to Samuelson's arguments, on those points where his views appear to differ from Samuelson's. Without this clarification, mathematics as a quantitative method as used in the applied natural and physical sciences still looks to me like just one case a rather successful one of mathematics as a language form. In some of his statements Dr. Novick appears indeed to attribute to reasoning (as applied to the physical world) a power to establish the validity of propositions without reference to a set of premises. In any case, he fears that the innocent reader of economics studies may impute such powers to argument in eco* I am indebted to several colleagues at the Cowles Commission for Research in and in particular to Professor Kenneth Arrow of Stanford University, for valuable comments on a draft of this discussion. responsibility for errors is mine. 'See, for instance, F. Waugh, Applicability of Recent Developments in Methodology to Agricultural Economics, Journal of Farm 35 (December I953). 's See J. M. Clark, Economists and Others: A Plea for Communicability, Econometrica, I5 (April I947). ' Paul A. Samuelson, Theory and Mathematics -An Appraisal, Papers and Proceedings, American Economic Review, 42 (May I952), 56-66. 16 George J. Stigler, The Mathematical Method in Economics, the fourth of Five Lectures on Economic Problems, delivered at the London School of Economics (New York, I950). 16 M. Allais, L'Utilisation de l'Outil Mathematique en Economique, Econometrica, 22 (January I954), 58-7I

Forty-six years ago when various social theories, pregnant with nineteenth century optimism, postulated a continuous increase in the rate of discovery and invention, a Swedish scholar noted that the annual number of patents issued by the principal industrial countries showed signs of leveling off.3 This retardation contrasted sharply with the rapid increase in patenting characteristic of the nineteenth century. Subsequent investigation disclosed that the number of patents issued per capita tended to level off and perhaps to decline for every nation after it had passed through the rapid industrialization phase.4 Whether the retardation in patenting reflected a genuine stabilization or diminution in the per capita rate of invention or merely in the proportion of invention which is patented is therefore a question which has perplexed social and physical scientists for some time.5 The issues raised by this trend in patenting in the western world are not merely academic, for if the possibilities enumerated by Kuznets many years ago are indeed correct, and patent statistics (for the period under review) reflect either inventive activity, changes in technical knowledge, or technical change,6 then the retardation in statistics of patents issued means that the growth rate of one or another of these fundamental phenomena has been declining. True, no retardation in the rate of technical change has appeared in other, more reliable indexes, such as output per unit of input, but the possibility exists that the data reflect a decline in

RECENT contributors 1 to the discussion of the effect of union bargaining power on labor's earnings have given only passing attention to one important facet of this problem: the influence of union pressure on the distributive share of income generated by industry that is paid to labor. While statistics have been gathered and studies made 2 of aggregate distributive shares, little attempt has been made to develop analysis around interand intraindustry comparisons of wage-income structures in the light of union growth. The purpose of this paper is to take one step toward a consideration of statistical data of the last two decades and test the hypothesis that where wage earners are strongly organized in trade unions, one might expect labour to succeed in obtaining a larger share of the product than elsewhere. 3