ON MEASUREMENT IN ECONOMICS

1. INTRODUCTION

The present has been termed "the inductive era" in economics. Whether the phrase be strictly justified is perhaps a matter for question, but certainly the emphasis on the factual aspect of economic study is every year more pronounced. For the economist of today facts constitute not only the ultimate test of theory but, probably to a greater conscious extent than formerly, facts constitute the raw material from which theories are to be cast.

This study of specific facts has been accompanied by an increased use of quantitative methods. The modern economist enumerates, measures, weighs. He seeks that accuracy and precision in dealing with facts, that power of exact description, which the ability to measure conveys. "When you cannot measure what you are speak ing about, when you cannot express it in numbers," said Lord Kelvin, "your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of a science, whatever the matter may be." The attempt to measure has been made in almost every field of economic interest. Precise methods have been developed for measuring changes in the general level of prices. By means of index numbers of various types changes in such varied and complicated phenomena as wage levels, the volume of production, the volume of trade, stock prices, and the cost of living are expressed in quantitative terms. These diverse applications have fully demonstrated the fruitfulness of quantitative methods, both for the testing of hypotheses and for the inductive derivation of new generalizations. The future development of economics as an effective instrument of social control will undoubtedly be conditioned largely by the use made of these tools.

The extensive employment of quantitative methods in economics, involving as it does the application to economic data of tools developed in other fields for other purposes, calls for some consideration of the logical assumptions involved in the use of these methods, the validity of applying them to the data of economics, and the precise significance of the results secured. The present paper is con

cerned with certain logical problems arising from the application of these methods in economic research, with particular reference to the nature of our knowledge of economic events, the nature and significance of economic generalizations, or "laws," and the possibility of deriving such laws by processes of quantitative induction. This may be considered as merely a preliminary discussion of many of the points raised. The main purpose in mind is to call attention to the practical importance of certain problems which must be faced if economics is to secure a sound quantitative foundation.

2. THE STATISTICAL CHARACTER OF USEFUL KNOWLEDGE

No discussion of method is significant unless it proceed from a consideration of the nature of the matter to be manipulated. As a mechanic chooses a tool adapted to his material, so the economist must adapt his methods to his data. What are, then, the data of economics? What is the character of the materials of economics, and what is the nature of our knowledge of them? If we can answer these questions, we shall be in a position to consider the instruments of measurement which may be employed.

Clerk Maxwell, the physicist, has set up a classification of scientific knowledge and of scientific method, a classification elaborated by Josiah Royce, which has particular significance for the economist. The division, essentially as explained by Royce, is as follows:

All scientific knowledge may be catalogued as historical, mechanical or statistical. That knowledge is historical which has as object the individual event-a solar eclipse, a sunrise, a single physical fact, or any single act of an individual. The historical method is one which concerns itself with single events, which studies individual organisms, the history of individual organisms, or the sequences of individual events. That knowledge is mechanical which deals with "the invariant laws to which all individual events of some field of inquiry are subject." The mechanical method concerns itself with such unchanging laws, and with individual events which are completely predictable from knowledge of such laws. Statistical knowledge is that having as object "not the single event and not the invariant law, but . . . the relatively uniform behavior of some average constitution, belonging to an aggregate of things and events, and the probability that this average behavior will remain, within limits, approximately, although always imperfectly uniform." The statistical method is that which deals with assemblages or groups in

1 "The Mechanical, the Historical and the Statistical,” Science, N. S. xxxix, No. 1007, April 17th, 1914.

terms of the averages by which they may be described, and which deals with relations which are not described by unchanging laws but by generalizations couched in terms of approximation and of probability.

Our knowledge of nature is of which of these types? To this fundamental question both Clerk Maxwell and Royce give an unequivocal answer.

"Our actual knowledge of concrete things," writes the former, "is of an essentially statistical nature." We cannot, from the very nature of the case, trace the path of a molecule, or identify it at different times. "Hence those uniformities which we observe in our experiments with quantities of matter containing millions of molecules are uniformities . . . arising from the slumping together of multitudes of cases, each of which is by no means uniform with the others." If knowledge of individual things and events is impossible when dealing with fundamental material units, invariant mechanical laws obviously cannot be applied to them. Purely mechanical as well as purely historical knowledge is, therefore, in practice, unobtainable. "The scientific view of nature is thus . . . neither purely historical nor purely mechanical, it is statistical." As a proof of the practical validity of this view Clerk Maxwell developed the atomic theory of gases, a theory derived from the logic of probabilities as applied to the velocities and the collisions of millions of hypothetical molecules.2

Josiah Royce goes even farther than Clerk Maxwell in stressing the dominant importance of the statistical view of nature. The three fundamental conceptions of this view (that of an average, that of approximation, and that of probability), he says, "are indeed not the only fundamental categories of our thought, but they are conceptions which go down to the very roots of our intelligence as well as of our voluntary activity. go down to the roots of that nature of things which our sciences are studying." 3 "Not the mechanical but the statistical form," he concludes, "is the canonical form of scientific theory."

They

...

The implications of this view are far-reaching. It means that,

1 Campbell and Garnett; Life of Clerk Maxwell, quoted by Merz, History of European Thought in the Nineteenth Century, II, 600-601.

2 "The distribution of the molecules according to their velocities is found to be of exactly the same mathematical form as the distribution of observations according to the magnitude of their errors, as described in the theory of errors of observation." Clerk Maxwell, Theory of Heat; quoted by Royce, loc. cit., 560. 8 Loc. cit., 559.

practically, knowledge of individual things and events in nature is impossible, that we must perforce deal with averages, and with "the total effects produced by an immensely large number of singly imperceptible events." Whether we are concerned with matter and the physical problems relating thereto or with social and economic events, the coarseness of our senses and the limitations of our intelligence prevent us from perceiving and dealing with individual things or occurrences. We deal with composites, aggregates, groups. We do so, moreover, not only because precise knowledge of individual units is impossible, but also because it is not the individual but the aggregate of things or events, as known through their combined effect, which has scientific significance for us. The ultimate constituents of matter-electrons, atoms, molecules are of interest to us only in the way in which, in combination, they affect our senses. We seek to understand their nature for the light it will throw upon their behavior in mass, as that behavior affects the matter with which our senses deal. The innumerable events which, in aggregate, constitute a social phenomenon are neither individually known to us nor individually of interest to us.1

All this is a matter which concerns us not as a problem in epistemology but in its practical relation to current scientific questions. Certain aspects of this view of nature should be emphasized because of their bearing upon economic problems.

One point of sharp contrast between the mechanical and the statistical views relates to the existence of individual variation in nature. The mechanical conception involves the notion of sameness, of the precise identity of all the things or events described by a given law. The statistical view assumes no such similarity of the individual objects constituting the aggregates which are of interest to us. We treat them as statistically similar, but recognize the existence of individual differences. The importance of variation in organic forms has been acknowledged; the failure to perceive differences, and the persistence of the mechanical view as applied to other forms, may be due merely to the inadequacy of our powers of discrimination. 'Absolute sameness, says Karl Pearson," is a purely conceptual notion which is not in human experience, but which has been extracted from that experience in the same manner as other conceptual limits." 2 Whether this concept of variation be

1 The limitations of statistical knowledge, as regards individual objects or events, have been emphasized by Raymond Pearl, Modes of Research in Genetics, 73-100.

2 The Grammar of Science, 3rd ed., 153.

valid as applied to the final constituents of matter need not concern us. In dealing with social and economic phenomena the existence of variation and the consequent inapplicability of the mechanical method must be recognized.7

If there be no sameness in nature except that which is due to our own limited powers of discrimination, if our knowledge be limited to knowledge of aggregates and of mass phenomena, there can be no certainty in our knowledge of nature and in our generalizations about the relations between things and events in nature. Our knowledge of the individual event must always be inadequate and incomplete; uncertainty and doubt can never be dismissed from our minds. An element of probability must be present in all our reasoning. "Perfect knowledge," Jevons writes, "alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. Therefore we content ourselves with partial knowledge, knowledge mingled with ignorance, producing doubt." This conception of uncertainty and probability in our knowledge of nature is an essential accompaniment of the statistical view, and here again it is at odds with the mechanical concept. The latter assumes perfect knowledge and no variation. "The equations of dynamics completely express the laws of the historical method as applied to matter, but the application of these equations implies a perfect knowledge of all the data." Where we come nearest to securing such complete knowledge, as, perhaps, on the subject of planetary motion, practical certainty is attained and the element of probability in applying the equations of dynamics may be ignored. A solar eclipse may be foretold with a negligible margin of error. Such certainty, however, represents but a limit, and a limit never attained in our actual knowledge of social phenomena, though we may approach it in our knowledge of the physical world.

Since our knowledge of nature is primarily statistical, and therefore "mingled with ignorance," and since generalizations of the mechanical type imply a perfect knowledge of all the data, which is seldom, if ever, to be had, we are confronted with a question as to the validity of all generalizations purporting to explain sequences or relationships. May such general statements be made in a world in which all knowledge is accompanied by doubt? And if made, how shall we determine their reliability, how measure the degree of doubt attaching to a given generalization? Problems of vital interest to the economist are raised by these questions.

1 Clerk Maxwell. Quoted by Merz, loc. cit., 602,