While index numbers have been largely restricted to price phenomena, this is by no means necessary. Any phenomenon extending over a period of time and expressed numerically may be put in this form, the only peculiarity being that its relative rather than its absolute aspect is exhibited. Index numbers of wages, of rents, of imports or exports, sales, or of any other phenomena may be constructed. Historically, pricę indexes were the first to be computed and to these our major attention is given, inasmuch as they are currently compiled and are those in which the business man and student of economics probably have most interest.

The purpose of an index number is to reduce to a common denominator the qualities of different factors or phenomena so as to allow comparison generally historically. It is to translate absolute into relative qualities in order that comparisons may be made. Moreover, index numbers are summaries direct or indirect of things having a common quality, as for instance, in the case of price indexes, a selling value. They represent this quality as an aggregate or average at different times for purpose of comparison. If they are aggregates of prices rather than averages of relative prices, they are no less averages. They represent divergent things, responding differently to conditions of price determination and occupying different positions in the economy of business. Being aggregates or averages, they do not in themselves reveal all the peculiarities of the things which go to make them up.1 If averages may be fictitious and unreal, it must be borne in mind that no index number corresponds to a real thing. It is not like the mean of certain observations in natural science such, for example, as those for measuring the distance between the earth and the sun of which any one may err, but whose average will point to a single specific fact. An index number points to no single fact. It gives, to repeat, only an indication of a general trend of prices. People often think and speak loosely on this topic, as if an index number told the whole story once for all. There is no one change in prices. There is a

giving no evidence of the characteristic features of their several parts, and it becomes necessary to study the parts in order to understand the aggregate; or, on the other hand, if they may be real in every sense of the word, inasmuch as they represent the mode or characteristic thing, without at the same time revealing it, so may index numbers be fictitious and unrepresentative for one use but well suited for another. Everything depends upon the purpose for which they are computed and the factors which are important in their makeup. Blindly to employ a consumer's index number in a problem relating to capital investment is a practice of the same sort as to use an average in blind indifference to the things which go to make it up. The same is true respecting index numbers of wages, of rents, or of any other thing. Realizing the importance of this truth and in consistency with what has gone before, a large part of this chapter is devoted to the principles of index number making.

III. THE USES AND COMPUTATION OF INDEX NUMBERS

In what has gone before emphasis has been put on plan and purpose in statistical study. These need to be insisted upon especially in connection with this topic, because, while most index numbers are of the "general purpose" type, they are given particular use.

are made to serve

"Few of the widely-used index numbers, one special purpose. On the contrary, most of them are 'generalpurpose' series, designed with no aim more definite than that of measuring changes in the price level. Once published they are used for many ends - to show the depreciation of gold, the rise in the cost of living, the alternations of business prosperity and demedley of many changes, different in direction and degree. All that we can hope to secure by averaging and summarizing is some concise statement of the general drift." Taussig, F. W., Principles of Economics, Vol. I, p. 294. (Revised Edition, 1915.) Macmillan, New York.

pression, and the allowance to be made for changed prices in comparing estimates of national wealth or private income at different times. They are cited to prove that wages ought to be advanced or kept stable; that railway rates ought to be raised or lowered; that 'trusts' have manipulated the prices of their products to the benefit or the injury of the public; that tariff changes have helped or harmed producers or consumers; that immigration ought to be encouraged or restricted; that the monetary system ought to be reformed; that natural resources are being depleted or that the national dividend is growing. They are called in to explain why bonds have fallen in price and why interest rates have risen, why public expenditures have increased, why social unrest prevails in certain years, why farmers are prosperous or the reverse, why unemployment fluctuates, why gold is being imported or exported, and why political 'landslides' come when they do." 1

Generally, however, two major purposes are distinguishable, so far as price indexes are concerned. First, that of measuring quantitatively change in price level from time to time, and second, that of interpreting the effect of change upon various types of people. The first index number (or use) is often called the Jevonian, because the English economist Jevons was among the first to attempt to measure the change in the purchasing power of gold. The second index number (or use) — hardly a type of index number, although the conditions of its computation are somewhat different from those which characterize the first is the so-called consumers'. Its purpose is to approximate the effect of price changes upon consumers. Of course, there might, with the same justice, be computed a "producers'" index number, the only difference being that emphasis would be placed on other commodities - those in which they are interested and which enter into their costs.

1 Mitchell, Wesley C., "Index Numbers of Wholesale Prices in the United States and Foreign Countries," Bulletin of the United States Bureau of Labor Statistics, Whole Number 173, July, 1915, pp. 25–26.

Inasmuch as few students or business men have the necessary time and organization to construct index numbers suited to their particular purposes, and because there are now currently published many price index numbers, the order in which our discussion has proceeded - that is, from definition of purpose to employment of data is reversed. The purpose for which index numbers may be used must be settled in the light of the peculiarities of the numbers at hand. This calls for detailed and intimate study, and must follow the lines suggested in this chapter.1

Professor Mitchell enumerates the operations involved in making a price number as follows:

"(1) Defining the purpose for which the final results are to be used; (2) deciding the numbers and kinds of commodities to be included; (3) determining whether these commodities shall be treated alike or whether they shall be weighted according to their relative importance; (4) collecting the actual prices of the commodities chosen, and, in case a weighted series is to be made, collecting also data regarding their relative importance; (5) deciding whether to measure the average variations of prices or the variations of a sum of actual prices; (6) in case average variations are to be measured, choosing the base upon which relative prices shall be computed; and (7) settling upon the form of average to be struck.

"At each one of these successive steps choice must be made among alternatives that range in number from two to thousands. The possible combinations among the alternatives chosen are indefinitely numerous. Hence there is no assignable limit to the possible varieties of index numbers, and in practice no two of the known series are exactly alike in construction. To canvass even the important variations of method actually in use is not a simple task."

112

1 Such a comparative study has been made by Professor Wesley C. Mitchell in "Index Numbers of Wholesale Prices in the United States and Foreign Countries," Bulletin of the United States Bureau of Labor Statistics, Whole Number 173, July, 1915. Acknowledgments are here made of the indebtedness of the writer to Professor Mitchell for much of the illustrative matter in this and the following chapter.

2 Ibid., p. 25.

1. Data from which Price Index Numbers are Made

In a study of prices attention must first be centered upon the commodities included and the conditions of price making. Distinction will have to be made between producers' and consumers' goods,1 between raw and manufactured commodities,2 between manufactured goods bought by consumers for

1"... there are characteristic differences between the price fluctuations of manufactured commodities bought by consumers for family use and the price fluctuations of manufactured commodities bought by business men for industrial or commercial use. Though consisting more largely of the erratically fluctuating farm products, the consumers' goods are steadier in price than the producers' goods, because the demand for them is less influenced by changes in business conditions." Op. cit., pp. 60–61.

2 "These several comparisons establish the conclusion that manufactured goods are steadier in price than raw materials. The manufactured goods fell less in 1890-1896, rose less in 1896-1907, again fell less in 1907-1908, and rose less in 1908-1913. Further, the manufactured goods had the narrower extreme range of fluctuations, the smaller average change from year to year, and the slighter advance in price from one decade to the next. It follows that index numbers made from the prices of raw materials, or of raw materials and slightly manufactured products, must be expected to show wider oscillations than index numbers including a liberal representation of finished commodities." Op. cit., p. 53.

"First, the list of commodities used by the Bureau of Labor Statistics includes 29 quotations for iron and its products, 30 quotations for cotton and its products, and 18 for wool and its products, besides 8 more quotations for fabrics made of wool and cotton together. On the other hand it has but 7 series for wheat and its products, 8 for coal and its products, 3 for copper and its products, etc. The iron, cotton, and wool groups together make up 85 series out of 242, or 35 per cent of the whole number. Similarly, cotton, wool, and wheat, or coal, or cattle, with their products, make 20 per cent of the series in the third index number.

"Does this large representation of three staples distort these index numbers particularly the bureau's series where the disproportion is greatest? Perhaps; but if so the distortion does not arise chiefly from the undue influence assigned to the price fluctuations of raw cotton, raw wool, and pig iron. For, contrary to the prevailing impression, the similarity between the price fluctuations of finished products and their raw materials is less than the similarity between the price fluctuations of finished products made from different materials. As babies from different families are more like one another than they are like their respective parents, so here the relative prices of cotton textiles, woolen textiles, steel tools, bread, and shoes differ far less among themselves than they differ severally from the relative prices of raw cotton, raw wool, pig iron, wheat, and hides. Hence the inclusion of a large number of articles made from iron, cotton, and wool

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