(N) PROFESSOR WESLEY MITCHELL ON INDEX NUMBERS [IN this paper, published in the ECONOMIC JOURNAL, 1918, under the title "The Doctrine of Index-Numbers according to Professor Wesley Mitchell," the plurality of conceptions attached to the term change-in-the-value-of-money, the variety of purposes subserved by an index-number for prices, is urged once more and with more confidence than before. That an index-number may be more than a register of a change in the value of certain specified articles, that there is an average trend of prices which may be expressed by methods other than those of a commercial account— this view is more acceptable now than it was thirty-five years ago. It is recognised in theory by Professor Mitchell, and realised in practice by Mr. Flux.] The problem of which the object is to measure changes in the value of money has long exercised economists and statisticians. Thirty years have elapsed since the British Association appointed a committee for the purpose of investigating the best methods of ascertaining and measuring variations in the value of the monetary standard. The wording of this instruction may serve to remind us of the tremendous magnitude which the phenomenon to be measured has since the outbreak of war assumed. No one would now set out to ascertain the fact of a change in the value of money-a fact which in the peaceful eighties of last century could be disputed by sturdy mono-metallists without obvious absurdity. But though the fact now stares us in the face, the measurement of its magnitude is still important; perhaps more important than ever. For it can hardly be doubted that as the war goes on, and during the period of so-called "reconstruction," there will be required careful measurements of change in the purchasing power of money, with a view to the adjustment of wages and of other payments. And not only for practical purposes, but also in the interest of monetary theory, will such measurement be urgently required. In the controversies which will probably flourish in the early part of the twentieth, as in that of the nineteenth, century concerning the management of the currency during a great war, reference will certainly often be made to the index-numbers which represent the change from time to time in the level of general prices. If, as may be expected, the quantity theory of money is appealed to, it will be proper to construct another kind of index-number showing changes in the volume of trade. And other index-numbers there are which may be required in the course of reconstruction; in particular, those which measure wages nominal and real. Coincidently with the increased demand for the use of indexnumbers it is opportune that there has appeared a singularly comprehensive and lucid treatise on this species of measurement.1 It is true that Professor Wesley Mitchell's monograph on indexnumbers of wholesale prices does not cover all the ground which we have here in view. But the methods appropriate to the general problem can mostly be learnt from his discussion of a particular but leading case. That discussion is so complete and thorough that it almost dispenses the student who is not a specialist from the trouble of consulting the earlier literature of the subject. Within a limited but considerable and representative province Professor Mitchell has explored every inch of the ground. He has traced the many-branching paths which perplexed most of his predecessors. He has added clear directions showing where each of the paths leads. The last-mentioned task is more difficult and important than may be supposed. It is a peculiarity of the problem that much thought must be expended in order to find the meaning of the question before you begin to answer the question. The practical man intent upon making or spending money does not suspect the ambiguity lurking under inquiries about its value. He asks what is the equivalent in our currency of the guinea in Charles II.'s time, and expects an answer as pat as if he had asked what is now the bank rate, or what the price of wheat. It is true that where the distance between the epochs compared is not so enormous, in the more usual comparisons of price-levels, the definition of the question is not so important; much the same answer may be given to different varieties of the question. The relation is like that between ethical theory and good conduct; if Bishop Butler and other moralists are right in thinking that 1 Index-numbers of wholesale prices in the United States and foreign countries (Bulletin of the United States Bureau of Labour Statistics, 1915; whole number 173). VOL. I. со much the same conduct may follow from first principles so opposite as rational benevolence and rational self-love. When this analogy was suggested to Sidgwick, on the occasion of a meeting of the above-mentioned British Association Committee, the author of the Methods of Ethics made reply to the effect that, while frequently different methods might be adopted without obvious difference in practice, yet occasionally at critical turning-points the difference between opposite first principles would make itself felt decisively. We surmise that in like manner monetary distinctions which are otiose in ordinary times may have become significant under present conditions. All the greater is the debt of the economist to Professor Mitchell for having made the distinctions clear. Consider, for instance, Professor Irving Fisher's index-number in which each article is weighted in proportion to the number of times it is sold; quite properly, as Professor Mitchell points out (78),1 with reference to Professor Fisher's purpose. In ordinary times there would probably be little difference between this number and that which is obtained by using the same commodities in the same quantities without taking account of the number of turnovers (Mitchell, loc. cit.).2 But in war time, methods of business being considerably altered, it is possible that the distinction corresponds to a real difference.3 The same may be said about another variety which Professor Mitchell thus distinguishes. "If the aim be merely to find the differences of price fluctuation characteristic of dissimilar groups of commodities, or to study the influence of gold productions, or the issue of irredeemable paper money upon the way in which 1 The numerals in brackets refer to pages in Prof. Mitchell's treatise. Cp. Memorandum British Association Report, 1889. Professor Foxwell's method, above, p. 261. The subtlety of these distinctions deceives even experts. Thus the reviewer in the Economist (for January 12, 1918) criticising a recent publication in which it was held not to be proved, upon the lines of Irving Fisher, that money rather than goods was responsible for the rise of prices, observes triumphantly: "There can be no question that the increase in currency has been very much more rapid than the increase in the production of goods, unless we are to assume that this country, with four or five millions of its best men withdrawn into the Army, has been able to increase its production by more than 50 per cent." But the four or five millions have not been withdrawn from the production with which we are concerned in this inquiry. They (with their dependents) make, primâ facie, at least as great a pull as before upon the currency. Again the increase of women's and old men's paid work swells the denominator, which Irving Fisher calls "T." But then, asks the reviewer, why have prices risen? Quite conceivably, we reply, not so much because the quantity of money has increased out of proportion to the quantity of "goods" (in the sense here relevant), as because the circulation of the goods is less rapid (as suggested in the work criticised [cp. Lehfeldt, ECONOMIC JOURNAL, Vol. XXVIII. (1918), p. 111]). That is not inflation" in the sense of causation on the side of money. prices change, it may be appropriate to give identical weights to all the commodities" (78). Again, the consumption standard, as based on family budgets, or more generally on the expenditure of the citizens in the way of consumption for the sake of personal or sympathetic satisfaction, exclusive of their collective expenditure on munitions for the satisfaction of patriotic motives, may well differ in war time from an index-number like that of Professor Irving Fisher, if there is included in the work which the currency has to do the payments by the Government for munitions. Conceivably, however differently from present experience, the momentum (price x velocity) of currency in relation to the "volume"—or, rather, the momentum, or flow-of goods, including munitions, might remain constant; while the prices of all the goods consumed by the citizen, exclusive of munitions, rose considerably. Our readers are perhaps beginning to feel that they have had enough of this concept-splitting. Yet there remain certain varieties of index-numbers which we cannot pass over : two mentioned by Professor Mitchell and two which it did not come within his subject, more narrowly defined than ours, to mention. There is first the index-number intended to serve as a business "barometer" (66). If the aim be to construct a business barometer, the data should be prices from the most representative wholesale markets, the list should be confined to commodities whose prices are most sensitive to changes in business prospects and least liable to change from other causes, and the weights may logically be adjusted to the relative importance of the commodities as objects of investment. Professor Mitchell also directs attention to what he calls a "general-purpose" index-number, not adapted to any special end and in practice applied to very various purposes, of which more than a dozen are enumerated (26). Professor Mitchell is no doubt right in thinking that "the day has not come when the uses of index-numbers are sufficiently differentiated and standardised to secure the regular publication of numerous special-purpose series." Till then " the users of indexnumbers must put up with figures imperfectly adapted to their ends" (26). 1 Cp. British Association Memorandum, 1887, section viii. : "Determination of an Index-number irrespective of the quantities of the commodities." • Cp. Memorandum, 1887 (above, p. 255), "mixed modes, compounding the ends or means or several distinct methods " "the most comprehensive . . purporting to be a compromise between all the modes and purposes-the method if practical exigencies impose the condition that we must employ one method, not many methods." Another conception of the end, another definition of the value of money, is derived from Ricardo's axiom that "a commodity which at all times requires the same sacrifice of toil and labour to produce it is invariable in value." Professor Marshall has countenanced this view of our problem. In his evidence before the Precious Metals Royal Commission of 1888, speaking of the appreciation of gold,1 he said: "When it is used as denoting a rise in the real value of gold, I then regard it as measured by the [increase] 2 in the power which gold has of purchasing labour of all kinds—that is, not only of manual labour, but the labour of business men and all others engaged in industry of any kind.” It has been said that changes under this head are sufficiently reckoned with when the changes in average incomes are noted. This, however, may be questioned in time of a war involving enormous changes in the quantity of labour employed in production, additions here and subtractions there. Nor can we pass over in silence Professor Nicholson's indexnumber based on capital. It is remarkable that the conception which lies at the root of this method should have been that which, under a different aspect, first presented itself to Professor Lehfeldt in his independent and original investigation of the " absolute price of gold." 4 Professor Lehfeldt's second definition, referring to a redistribution of effort of production" on the supposition of "the total of effort being unchanged," savours of the labour standard which we mentioned just now. 66 When we have decided what is the end at which to aim, we may go on to consider how the data are to be shaped to that end, and what data are to be sought. The step which is last in the analysis, as Aristotle would say, is first in the order of practice. The initial operation of collecting the original quotations of price requires more care and labour than might be supposed. “To judge from the literature about index-numbers, one would think that the difficult and important problems concern weighting and averaging. But those who are practically concerned with the whole process of making an index-number from start to finish rate this office work lightly in comparison with the 1 Appendix to Final Report [C 5512] Question 9025. Quoted in the British Association Memorandum of 1889, p. 161. 24 Diminution has been substituted for "increase" in the original by an obvious misprint. 3 Described in the British Association Memorandum, 1887, section vi., above, p. 230. ECONOMIC JOURNAL (March, 1918, p. 108). |