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## 4. Wieser’s Refinement of the Methods of Calculating Index-Numbers

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.

• 3. On Falkner's method, see Laughlin, The Principles of Money (London, 1903), pp. 213—21; Kinley, Money (New York, 1909), pp. 253 ff.
• 4. See 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.
• 5. See Weiss, Die moderne Tendenz in der Lehre vom Geldwert, Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung, vol. 19, p. 546.