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By Root 1291 0

dates, its economics a collection of statistical data. No other objection is more often brought against economics by laymen than that there are no economic laws; and if an attempt is made to meet this objection, then almost invariably the request is made that an example of such a law should be named and expounded—as if fragments of systems, whose study demands years of thought on the part of the expert, could be made intelligible to the novice in a few minutes. Only by letting fall morsels of statistics is it possible for the economic theorist to maintain his prestige in the face of questions of this sort.

Great names in the history of economics are associated with various systems of index numbers. Indeed, it was but natural that the best brains should have been the most attracted by this extraordinarily difficult problem. But in vain. Closer investigation shows us how little the inventors of the various index-number methods themselves thought of their attempts, how justly, as a rule, they were able to estimate their importance. He who cares to go to the trouble of demonstrating the uselessness of index numbers for monetary theory and the concrete tasks of monetary policy will be able to select a good proportion of his weapons from the writings of the very men who invented them.

2 The Nature of the Problem

The objective exchange value of the monetary unit can be expressed in units of any individual commodity. Just as we are in the habit of speaking of a money price of the other exchangeable goods, so we may conversely speak of the commodity price of money, and have then so many expressions for the objective exchange value of money as there are commercial commodities that are exchanged for money. But these expressions tell us little; they leave unanswered the questions that we want to solve. There are two parts to the problem of measuring the objective exchange value of money. First we have to obtain numerical demonstration of the fact of variations in the objective exchange value of money; then the question must be decided whether it is possible to make a quantitative examination of the causes of particular price movements, with special reference to the question whether it would be possible to produce evidence of such variations in the purchasing power of money as lie on the monetary side of the ratio. [1]

So far as the first-named problem is concerned, it is self-evident that its solution must assume the existence of a good, or complex of goods, of unchanging objective exchange value. The fact that such goods are inconceivable needs no further elucidation. For a good of this sort could exist only if all the exchange ratios between all goods were entirely free from variations. With the continually varying foundations on which the exchange ratios of the market ultimately rest, this presumption can never be true of a social order based upon the free exchange of goods. [2]

To measure is to determine the ratio of one quantity to another which is invariable or assumed to be invariable. Invariability in respect of the property to be measured, or at least the legitimacy of assuming such invariability, is a sine qua non of all measurement. Only when this assumption is admissible is it possible to determine the variations that are to be measured. Then, if the ratio between the measure and the object to be measured alter, this can only be referred to causes directly affecting the latter. Thus the problems of measuring the two kinds of variation in the objective exchange value of money go together. If the one is proved to be soluble, then so also is the other; and proof of the insolubility of the one is also proof of the insolubility of the other.

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