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V. On the Use and Misuse of Mathematics in Presenting Economic Theory

The Review of Economics and Statistics 1954 36(4), 369
Articles on economic theory are usually intended to explain to the reader what results may be expected to follow various policies or disturbances in given circumstances. The task of explanation is made difficult by the varying capacities and demands of the readers. If the theory is to be realistic, the given circumstances must reflect a great many of the complications of a real-world situation: an exhaustive account of these, whilst necessary for logical completeness, would be intolerably lengthy and boring for the reader who is well informed about the situation to which the theory is intended to apply. He can supply for himself, as obvious, many of the underlying assumptions about institutions and psychology which justify the reasoning in good non-mathematical articles on economic theory. But some readers will lack the experience or the docility to do this, and will either attempt to apply the theory to inappropriate circumstances, or will attack the writer for not giving an exhaustive account of his assumptions. Since proof is not always the most effective method of explanation, many writers are content to sketch their ideas in a manner which will enlighten sympathetic readers without attempting to convey complete conviction to anybody. The cautious economic theorist, whose overriding ambition is never to appear wrong and yet to appear in print at all, has little scope beyond the discussion of economic models. These are shadows of the real situations so drastically simplified that they can be completely described and many of their workings exactly portrayed within the compass of a single article. The logic leading from the assumptions about the model to the conclusions about how it will behave can now be made rigorous and independent of the reader's knowledge of the real world. Such models serve the useful purpose of making it possible to reach complete agreement within reasonable time: occasionally a study of them will reveal that earlier disagreements have been entirely due to a difference of intuitive assumptions about the real world. Unfortunately for the cautious theorist, his economic models will be judged according to the degree in which they appear to be relevant to the real world; so that in avoiding the appearance of being wrong, he may yet appear silly by publishing a long article whose relevance to any practical issue seems to be superficial. This danger of manufacturing mere toys is especially great since the assumptions which are most convenient for modelbuilding are seldom those which are most appropriate to the real world. Many would regard as the best and most important articles on economic theory those which reveal keen observation and judgment in choosing assumptions which accord well with facts and which are yet able to demonstrate fairly convincingly powerful conclusions of a simple nature, which suggest important analogues in the real world. They would regard the rigor of the logic and the exactness of the descriptions of the assumptions as secondary matters relating to their style rather than to their importance. The ability to judge the relevance of an economic theory and its conclusions to the real world is but rarely associated with the ability to understand advanced mathematics. An important article on economic theory is therefore likely to be wasted unless it can be set out in prose supported by the most elementary mathematics. It is obvious that there is no room in economics for long trains of deductive reasoning, 4 so that those economic models which are realistic and yet sufficiently simple to allow

The Wartime Labor Force in Major Industrial Areas

The Review of Economics and Statistics 1945 27(3), 133
ONE of the most troublesome statistical I shortcomings at the outset of World War II was the lack of pertinent data on the behavior of the labor force under conditions of exaggerated demand. The exertions of the last war had been of much lesser magnitude; moreover, they had been inadequately and imperfectly recorded. There was little to serve as a guide in appraising manpower resources or in determining the most fruitful and feasible channeling of pressure and persuasion. The statistical record of this war will be much more complete. Not only are we better supplied with current information on the development of the nation's wartime labor force, but we also have become more fully aware of the necessity of attacking our manpower problems on an area basis. The geographical distribution of the stresses and strains accompanying the war effort has been far from uniform. An appreciation of the extent to which the population has met the increased demands, through mobility of workers and through the recruiting of persons who normally would not work, and of the practical limits of the expansibility of the labor force may be obtained in part by an analysis of some of the boom areas in which war production has been concentrated. In the spring of I944 the Bureau of the Census, in cooperation with the President's Committee for Congested Production Areas, conducted a census of ten boom areas, to secure data about the wartime population.' This census yielded information on the size of the labor force, the relative contributions of the various population groups to each area's labor supply, the part played by migrant workers, the length of the work-week, and other significant items. When compared with the benchmarks provided by the Decennial Census of Population four years previously, just before the beginning of the defense boom, these data furnish a graphic description of the dynamics of labor supply in wartime.2 Each of the designated areas was so defined as to include not only the center of industrial activity but also the surrounding territory in which many of the workers and their families live and in which many large new war plants have been built. Each area comprises a county or a group of contiguous counties, embracing a critical war production center. The areas and the counties which they comprise are as follows: