Knowledge that Transforms

IN SUCH fields of investigation as economics, psychology, and anthropology, where observations on several variables are taken into account simultaneously, it is at least as important to study relationships among the variables as to consider the variables separately. In fact, if there are significant relationships within a system of variables, a considerable part of the information furnished by the observations will be lost unless the relationships are taken into account. In general, very little is known a priori about such a set of variables, and hence our knowledge of them and their various interrelations must be inferred from observations. Questions relating to the problem of making inferences from observations resolve themselves into those of, (1) devising suitable functions of the observations for estimating parameters which characterize the hypothetical population of the variables and (2) determining frequency laws from which the degree of credibility to be placed in the departure of these functions from expectation can be evaluated. The more complicated the hypothesis concerning the interrelations of the variables, the more complex, of course, will be the functions of observations for measuring the relationships and testing the hypothesis. It frequently happens in multivariate analysis that a number of variables can be rationally classed into several mutually exclusive categories. For example, certain measurable traits of individuals may be classed as physical or mental. In the study of wholesale prices of farm products in a certain region over a certain period of time, the products may be classed as (1) fruits, (2) vegetables, or (3) dairy products, and the deviations of the prices of products within each group from seasonal and secular trends may be taken as the variables. When variables can be grouped in such a manner the question naturally arises as to whether or not there is any significant relationship between the groups of variables. That is, on the basis of the available observations, with what degree of credibility can we assert that the groups are mutually independent, so that knowledge relative to one of the groups gives us no significant information about the others? If they are significantly non-independent how can we measure the amount of dependence? It will become apparent as we proceed that statistical functions' and significance tests more general and comprehensive than I See R. Frisch, Correlation and Scatter in Statistical Variables, Nordielk

THE present investigation aims at basing the subject of Economic Dynamics on clear mathematical foundations as rigorous as those employed in any other branch of dynamics. It is shown that it may be based on postulates in complete formal analogy to those of ordinary dynamics. Economic Inertia and Economic Resilience (and Storage) are then defined and illustrated by examples. Differential equations involving these are next formulated for simple cases corresponding to the ordinary Dynamics of a Particle and it is shown how they enable us to plot curves of economic behavior as functions of time. Some of these curves are found to be oscillatory and others not. In Part II an endeavor is made to state the problem of economic dynamics in a sufficiently general form to permit of the immediate application of the modern methods of dynamical analysis used in physics. It is pointed out that, just as in radiation, we have periodic phenomena in economics, since most of our statistics show economic cycles. Our problem is essentially the same as the physicist's since both may be stated in the same words: Given a jumble of periodic phenomena, to find an interconnected dynamical system which will parallel the observed phenomena without departing at any point from what we can observe in other manners. An example is worked out illustrating our general dynamical system in a simple way, and the investigation closes with some general observations.

THE econometrician is often hampered by the absence of quantitative information, in spite of his efforts to restate problems of economic theory in such terms as will fit them for verification by actually existing statistics. The kind and amount of statistics available are thus very definitely limiting factors in some econometric works. But it may also be that the existing statistics invite theoretical enquiry, so that statistical information may occasionally be considered as a factor making for extension and progress of econometrics. For instance, whereas, in the field of cost theory, the state of statistical information is primarily a check on the progress of econometric studies, family budget statistics rather seem to be a branch of information which is full of promise. Dealing with some of the more terre a terre questions concerning family budget enquiries, an attempt will be made in the following to consider some of the many possibilities which this field of statistics seems to offer to the econometrician, provided he is patient enough to consider his assumptions carefully.