3. Methods of Calculating Index Numbers

Nearly all the attempts that have hitherto been made to solve the problem of measuring the objective exchange value of money have started from the idea that if the price movements of a large number of commodities were combined by a particular method of calculation, the effects of those determinants of the price movements which lie on the side of the commodities would largely cancel one another out, and consequently, that such calculations would make it possible to discover the direction and extent of the effects of those determinants of price movements that lie on the monetary side. This assumption would prove correct, and the inquiries instituted with its help could led to the desired results, if the exchange ratios between the other economic goods were constant among themselves. Since this assumption does not hold good, refuge must be taken in all sorts of artificial hypotheses in order to obtain at least some sort of an idea of the significance of the results gained. But to do this is to abandon the safe ground of statistics and enter into a territory in which, in the absence of any reliable guidance (such as could be provided only by a complete understanding of all the laws governing the value of money), we must necessarily go astray. So long as the determinants of the objective exchange value of money are not satisfactorily elucidated in some other way, the sole possible reliable guide through the tangle of statistical material is lacking. But even if investigation into the determinants of prices and their fluctuations, and the separation Of these determinants into single factors, could be achieved with complete precision, statistical investigation of prices would still be thrown on its own resources at the very point where it most needs support. That is to say, in monetary theory, as in every other branch of economic investigation, it will never be possible to determine the quantitative importance of the separate factors. Examination of the influence exerted by the separate determinants of prices will never reach the stage of being able to undertake numerical imputation among the different factors. All determinants of prices have their effect only through the medium of the subjective estimates of individuals; and the extent to which any given factor influences these subjective estimates can never be predicted. Consequently, the evaluation of the results of statistical investigations into prices, even if they could be supported by established theoretical conclusions, would still remain largely dependent on the rough estimates of the investigator, a circumstance that is apt to reduce their value considerably. Under certain conditions, index numbers may do very useful service as an aid to investigation into the history and statistics of prices; for the extension of the theory of the nature and value of money they are unfortunately not very important.