The problem of measuring the objective exchange value of money and its variations has attracted much more attention than its significance warrants. If all the columns of figures and tables and curves that have been prepared in this connection could perform what has been promised of them, then we should certainly have to agree that the tremendous expenditure of labor upon their construction would not have been in vain. In fact, nothing less has been hoped from them than the solution of the difficult questions connected with the problem of the objective exchange value of money. But it is very well known, and has been almost ever since the methods were discovered, that such aids cannot avail here.

The fact that, in spite of all this, the improvement of methods of calculating index numbers is still worked at most zealously, and that they have even been able to achieve a certain popularity that is otherwise denied to economic investigation, may well appear puzzling. It becomes explicable if we take into account certain peculiarities of the human mind. Like the king in Rückert’s Weisheit des Brahmanen, the layman always tends to seek for formulae that sum up the results of scientific investigation in a few words. But the briefest and most pregnant expression for such summaries is in figures. Simple numerical statement is sought for even where the nature of the case excludes it. The most important results of research in the social sciences leave the multitude apathetic, but any set of figures awakens its interest. Its history becomes a series of 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.

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 ratio1

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.

• 1[Following Menger, we should call the first of these two problems the problem of the measurability of the äussere objective exchange value of money, the second that of the measurability of its innere objective exchange value. See also p. 146 n. H.E.B.]
• 2See Menger, Grundsätze der Volkswirtschaftslehre, 2d ed. (Vienna, 1923), pp. 298 ff.

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.

Very recently Wieser has made a new suggestion which constitutes an improvement of the budgetary method of calculating index numbers, notably employed by Falkner.3  This is based on the view that when nominal wages change but continue to represent the same real wages, then the value of money has changed, because it expresses the same real quantity of value differently from before, or because the ratio of the monetary unit to the unit of real value has changed. On the other hand, the value of money is regarded as unchanged when nominal wages go up or down, but real wages move exactly parallel with them. If the contrast between money income and real income is substituted for that between nominal and real wages and the whole sum of the individuals in the community substituted for the single individual, then it is said to follow that such variations of the total money income as are accompanied by corresponding variations of the total real income do not indicate variations in the value of money at all, even if at the same time the prices of goods have changed in accordance with the altered conditions of supply. Only when the same real income is expressed by a different money income has the specific value of money changed. Thus to measure the value of money, a number of typical kinds of income should be chosen and the real expenditure corresponding to each determined, that is, the quantity of each kind of thing on which the incomes are spent. The money expenditure corresponding to this real expenditure is also to be shown, all for a particular base year; and then for each year the sums of money are to be evaluated in which the same quantities of real value were represented, given the prices ruling at the time. The result, it is claimed, would be the possibility of working out an average which would give for the whole country the monetary expression, as determined year by year in the market, of the real income taken as base. Thus it would be discovered whether a constant real value had a constant, a higher, or a lower, money expression year by year, and so a measure would be obtained of variations in the value of money.4

The technical difficulties in the way of employing this method, which is the most nearly perfect and the most deeply thought out of all methods of calculating index numbers, are apparently insurmountable. But even if it were possible to master them, this method could never fulfill the purpose that it is intended to serve. It could attain its end only under the same supposition that would justify all other methods; namely, the supposition that the exchange ratios between the individual economic goods excluding money are constant, and that only the exchange ratio between money and each of the other economic goods is liable to fluctuation. This would naturally involve an inertia of all social institutions, of population, of the distribution of wealth and income, and of the subjective valuations of individuals. Where everything is in a state of flux the supposition breaks down completely.

It was impossible for this to escape Wieser, who insists on allowance for the fact that the types of income and the classes into which the community is divided gradually alter, and that in the course of time certain kinds of consumption are discontinued and new kinds begun. For short periods, Wieser is of the opinion that this involves no particular difficulty; that it would be easy to retain the comparability of the totals by eliminating expenditures that did not enter into both sets of budgets. For long periods, he recommends Marshall’s chain method of always including a sufficient number of transitional types and restricting comparisons to any given type and that immediately preceding or following it. This hardly does away with the difficulty. The farther we went back in history, the more we should have to eliminate; ultimately it seems that only those portions of real income would remain that serve to satisfy the most fundamental needs of existence. Even within this limited scope, comparisons would be impossible, as, say, between the clothing of the twentieth century and that of the tenth century. It is still less possible to trace back historically the typical incomes, which would necessarily involve consideration of the existing division of society into classes. The progress of social differentiation constantly increases the number of types of income. And this is by no means simply due to the splitting up of single types; the process is much more complicated. Members of one group break off and intermingle with other groups or portions of other groups in a most complicated manner. With what type of income of the past can we compare that, say, of the modern factory worker?

But even if we were to ignore all these considerations, other difficulties would arise. It is quite possible, even most probable, that subjective valuations of equal portions of real income have altered in the course of time. Changes in ways of living, in tastes, in opinions concerning the objective use value of individual economic goods, evoke quite extraordinarily large fluctuations here, even in short periods. If we do not take account of this in estimating the variations of the money value of these portions of income, then new sources of error arise that may fundamentally affect our results. On the other hand, there is no basis at all for taking account of them.

All index-number systems, so far as they are intended to have a greater significance for monetary theory than that of mere playing with figures, are based upon the idea of measuring the utility of a certain quantity of money.5  The object is to determine whether a gram of gold is more or less useful today than it was at a certain time in the past. As far as objective use value is concerned, such an investigation may perhaps yield results. We may assume the fiction, if we like, that, say, a loaf of bread is always of the same utility in the objective sense, always comprises the same food value. It is not necessary for us to enter at all into the question of whether this is permissible or not. For certainly this is not the purpose of index numbers; their purpose is the determination of the subjective significance of the quantity of money in question. For this, recourse must be had to the quite nebulous and illegitimate fiction of an eternal human with invariable valuations. In Wieser’s typical incomes that have to be traced back through the centuries may be seen an attempt to refine this fiction and to free it from its limitations. But even this attempt cannot make the impossible possible, and was necessarily bound to fail. It represents the most perfect conceivable development of the index-number system, and the fact that this also leads to no practical result condemns the whole business. Of course, this could not escape Wieser. If he neglected to lay particular stress upon it, this is probably due solely to the circumstance that his concern was not so much to indicate a way of solving this insoluble problem, as to extract from a usual method all that could be got from it.

• 3On Falkner’s method, see Laughlin, The Principles of Money (London, 1903), pp. 213—21; Kinley, Money (New York, 1909), pp. 253 ff.
• 4See Wieser, “Uber die Messung der Veränderungen des Geldwerts,” Schriften des Vereins für Sozialpolitik 132 (Leipzig, 1910): 544 ff. Joseph Lowe seems to have made a similar proposal as early as 1822; on this, see Walsh, The Measurement of General Exchange Value (New York, 1901), p. 84.
• 5See Weiss, Die moderne Tendenz in der Lehre vom Geldwert, Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung, vol. 19, p. 546.

The inadmissibility of the methods proposed for measuring variations in the value of money does not obtrude itself too much if we only want to use them for solving practical problems of economic policy. Even if index numbers cannot fulfill the demands that theory has to make, they can still, in spite of their fundamental shortcomings and the inexactness of the methods by which they are actually determined, perform useful workaday services for the politician.

If we have no other aim in view than the comparison of points of time that lie close to one another, then the errors that are involved in every method of calculating numbers may be so far ignored as to allow us to draw certain rough conclusions from them. Thus, for example, it becomes possible to a certain extent to span the temporal gap that lies, in a period of variation in the value of money, between movements of stock exchange rates and movements of the purchasing power that is expressed in the prices of commodities.6

In the same way we can follow statistically the progress of variations in purchasing power from month to month. The practical utility of all these calculations for certain purposes is beyond doubt; they have proved their worth in quite recent events. But we should beware of demanding more from them than they are able to perform.

• 6See also pp. 213 ff. below.