**From the Preface**

This study is intended as a contribution to econometrics. It represents an attempt t0 supply a theoretical foundation for the analysis of interrelations between economic variables. It is based upon modern theory of probability and statistical inference. A few words may be said to justify such a study.

The method of econometric resesarch aims, essentially, as a conjunction of economic theory and actual measurements, using the theory and technique of statistical inference as a bridge pier. But the bridge itself was never completely built. So far, the common procedure has been, first to construct an economic theory involving exact functional relationships, then to compare this theory with some actual measurements, and, finally, "to judge" whether this correspondance is "good" or "bad". Tools of statistical inference have been introduced, in some degree, to support such judgements, eg the calculation of a few standard errors and multiple-correlation coefficients. The application of such simple "statistics" has been considered legitimate, while at the same time, the adoption of definite probability models has been deemed a crime in economic research, a violation of the very nature of economic data. That is to say, it has been deemed legitimate to use some of the tools developed in statistical theory without accepting the very foundation upon which statistical theory is built. For no tool developed in the theory of statistics has any meaning - except, perhaps, for descriptive purposes - without being referred to some stochastic scheme.

The reluctance among some economists to accept probability models as a basis for economic research has, it seems, been founded upon a very narrow concept of probability and random variables. Probability schemes, it is held, apply only to such phenomena as lottery drawings, or, at best, to those series of observations where each observation may be considered as an independent drawing from one and the same "population." From this point of view it has been argued, e.g. that most economic time series do not confirm well to any probability model, "because the successive observations are not independent." But it is not necessary that the observations should be independent and that they should all follow the same one-dimensional probability law. It is sufficient to assume that the whole set of say, n, observations may be considered as one observation of n variables (or a "sample point") following an n-dimensional joint probability law, the "existence" of which may be purely hypothetical. Then, one can test hypothesis against this joint probability law, and draw inference as to its possible , by means of one sample point (in n dimensions). Modern statistical theory has made considerable progress in solving such problems of statistical inference.

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