It is certainly true to say that the present situation is unfortunate -the situation with respect to the use of mathematics in economic science -and improvement may be obtained as a consequence of a clearer understanding of the functions of mathematics. I very much welcome the attempt made by Dr. Novick, although I am inclined to put things somewhat differently. To what extent there is between us only a difference in wording and to what extent one of substance, I do not quite see. Therefore let me give my own view in my own words. The functions of mathematical treatment in economic research may perhaps best be discussed on the basis of a breakdown into various elements of a complete piece of econometric research. Not all pieces of important economic analysis are by necessity also complete: sometimes certain elements are absent, as a consequence of the special features of the problem handled. I do not want to say therefore that every contribution to economic science should show all the elements to be enumerated; but the function of mathematics becomes clearer if we consider this complete set of elements.

Philip J. Bourque, The Domestic Importance of Foreign Trade of the United States, by Producing Regions, Manufacturing Sector, 1947, The Review of Economics and Statistics, Vol. 36, No. 4 (Nov., 1954), pp. 401-408

THE United States, through her policy of economic assistance, first in the form of the Marshall Plan and since I952 in the form of Mutual Aid, has helped many friendly countries to recover from the ravages of war without any appreciable reduction in living standards. Had the United States not come to the rescue, a highly developed area like Western Europe would have been forced to adjust herself in one way or another to hard economic circumstances. In the process she would surely have had to suffer a decline in living standards productive of social unrest and possibly of communal strife sufficiently violent to have brought into power in some countries political parties of extreme doctrines and hostile toward the United States. If that danger has been avoided, it is by no means over. Though production in the rest of the world, and in Western Europe in particular, has recovered and advanced beyond its prewar standards, there is still some evidence of a dollar shortage suggestive of a structural disequilibrium which is unlikely to be solved with the mere passage of time. The question naturally arises what further measures might be undertaken by the interested countries to promote the expansion of world trade on a multilateral basis. If we agree that in the immediate future the prospects of a substantial contribution to this end by West European countries are rather poor, our main concern will be to reconsider the efficacy of those policies by which, it is frequently alleged, the United States might further contribute toward its realization. First, however, let us appraise briefly the existing imbalance. From June I95I to June I952 the United States current account had a surplus of $4,I00 million.' From June I952 to June I953 the current account surplus was roughly $68 million. One concludes the United States surplus on current account is tending to disappear completely, a conclusion which has promoted some cautious optimism. But optimism is warranted only if the situation has been brought about without further trade restrictions; in the present situation, that would be largely by an expansion of the value of to the United States in a way which would be unlikely to prove merely temporary. Glancing at the figures we discover that, of the reduction in the surplus from $4,I00 million to the present insignificant figure, the in to the United States accounted for less than $I,400 million. Of this increase in exports to the United States, about $500 million was an in United States government expenditure on purchases by its personnel abroad, and an estimated $250 million was on offshore purchases. Of the reduction in from the United States of close to $2.6 billion, a small part was accounted for by an in the output of coal in Western Europe and by better harvests abroad. The remainder is attributable largely to the effects of a further of import restrictions abroad in late I95 i and in I952. If these import restrictions are considered temporary, then the potential deficit is still very large. It would be larger still if the political situation were other than it is. For then the United States item imports of government services, which provided some $I,900 million in the period I952-53, would be reduced to a fraction of this sum. As a final damper to the optimism, it may be pointed out that should the high level of economic activity in the United States recede, even slightly as in I949, to the United States would fall off rapidly. At any event it must not be assumed that as soon as the surplus in the United States balance This figure results when we include government of services (largely on its military personnel abroad), offshore purchases both for the United States forces stationed abroad and NATO forces, and private remittances, and when we exclude all military-aid (in the form of goods and services).

U NINCORPORATED businesses comprise an interesting lacuna in the empirical knowledge of our economy, not to mention the unsatisfactory nature of theory which fails to account for the intertwining of household and firm behavior of those individuals who do not even have the legal structure of incorporation to separate their personal from their business activities. Lacking basic sources for statistical data on unincorporated business analogous to corporate income tax returns and accounting statements, economists have relied on scattered bits of information to piece together an incomplete picture of this sector. In this paper we shall examine data gathered from business respondents in past Surveys of Consumer Finances, conducted by the Survey Research Center for the Federal Reserve Board, to see what light can be shed on the structure of unincorporated business. As is well known, the Surveys of Consumer Finances are designed to give a statistical picture of the household or consumer sector of the economy and, in doing so, to provide in a rounded fashion various types of information on those households who have a whole or part interest in businesses. We have re-examined the questionnaire schedules from the I949-52 Surveys to extract as much information as possible on aspects of unincorporated business. The technical problems of using these schedules for the purposes at hand are taken up below. In each year's survey of 3,000-3,500 spending units, there are only 250-300 owners of unincorporated businesses, too few for most detailed analyses. In order to inaugurate work in this field on the basis of materials now available we have adopted, in many computations, the inadequate procedure of pooling the respondents from three or four surveys. We thereby get samples somewhat larger than 750 or i,ooo cases. The present phase of the study is, however, exploratory and preparatory to the ultimate conduct of a survey with a questionnaire tailored to our purposes and including an adequate number of cases for analysis. A motivating force behind this study of unincorporated business is the apparent existence of behavioral differences between business and other groups in the population. Statistical savings equations estimated from sample survey data indicate a hierarchical pattern in both marginal and average propensities to save: farmers are the highest savers; businessmen rank next; and non-entrepreneurial households are lowest. Various explanations have been advanced to account for the observed differences, and we shall consider these in some detail. The crucial issue is whether the differences are due to the savings and income concepts used or to alternative motivational forces and behavior patterns.' A by-product of this type of analysis is a contribution to the question whether the theory of behavior of businessmen can be compartmentalized into a theory of household behavior and a theory of firm behavior. If the compartmentalization is not possible, we are confronted with the necessity of developing a pooled theory of behavior. From the point of view of behavioral studies it may well be asked why we limit ourselves to unincorporated business. The reasons are largely pragmatic. The unincorporated sector is more of a terra incognita than either the farm or corporate sector. Legal differences in corporate organization carry some weight in distinguishing this type from unincorporated business, although it must be admitted that closely controlled small corporations may behave much like unincorporated enterprises of a comparable size. Many special features attached to farm enterprise, such as geographical location, government support, involvement in organized world markets, and so forth, lead us to exclude this sector from our present investigations.

textabstractSerie "Contributions to Economic Analysis", No.1. In Spanish: Ensayos de Teoria Economica, Coleccion de Ciencias Sociales No. 42, Tecnos, Madrid, 1965, 71 p.