two bureau indexes because of its larger proportion of raw materials and smaller proportion of minerals. In fact it stands a shade lower, and the slight weight it assigns to the rapidly rising prices of forest products seems hardly sufficient to account for this result, since these products count for only 5 and 7 per cent of the totals in the two bureau series.

CRITICAL VALUATION

'A just evaluation of our seven American index numbers is not easy to make. For a comparison has little meaning unless it deals with all the important points at which the series differ. And since no one series is superior to the others at all points a verdict can not be rendered in a single sentence.

"In the publication of actual prices, the Bureau of Labor Statistics and Bradstreet's stand foremost. The contribution they have thus made to the knowledge of prices possesses great and permanent value over and above the value attaching to their index numbers. For, it is well to repeat, all efforts to improve index numbers, all investigations into the causes and consequences of price fluctuations, and all possibility of making our pecuniary institutions better instruments of public welfare depend for their realization in large measure upon the possession of systematic and long-sustained records of actual prices. And much of this invaluable material would be lost if it were not recorded month by month and year by year.

"Critical users of statistics justly feel greater confidence in figures which they can test than in figures which they must accept upon faith. Hence the compilers of index numbers who do not publish their original quotations inevitably compromise somewhat the reputation of their series. They compromise this reputation still further when they fail to explain in full just what commodities they include, and just what methods of compilation they adopt.1 In the latter respect the Annalist index number shares first honors with the Bureau of Labor Statistics' series. Any one who chooses to take the trouble can find what commodities are used, and how the final results are worked up from the raw material. Bradstreet's index number suffers a bit in comparison because readers are not told

1 Note omitted.

which 96 commodities out of the 106 of which prices are published are included in the index number, and because the method of reducing prices by the yard, the dozen, the bushel, the gallon, etc., to prices per pound is not fully explained. Dun's index number is more mysterious still, because neither the list of commodities nor the weights applied to each commodity are disclosed. And Gibson's present series also stands partly in the shadow because, while the list of commodities is known, the publishers state merely that these articles are weighted by Dun's system.

"With reference to weighting, Bradstreet's index number takes low rank, for the plan of reducing all quotations to prices per pound grossly misrepresents the relative importance of many articles. That figures made thus should give results in close agreement with the Bureau of Labor Statistics' series is a remarkable demonstration of the ability of index numbers to extract substantial truth even from unpromising materials. The agreement is all the more remarkable since the bureau's series is also badly weighted, though in a different way and in less degree.1 The revised bureau series is scarcely better than the original in this respect. It is better in substituting a single set of relatives for the articles of minor importance to which the original accorded several sets (for example, shirtings, sheetings, tools, window glass, etc.), but worse in cutting down the representation accorded to great staples (for example, pork, coal, pig iron, and leather).2 The Annalist index number follows the sensible, though rudimentary, plan of including two or three varieties of the most important articles, and only one of the less important. The like can be said in favor of Gibson's index number, both in its original and its present form, and in addition Gibson uses the Dun system of weights. The latter system is, in theory, the nearest approach to a satisfactory plan of weighting made by any American index number at present. Whether the practice is as good as the theory is doubtful, to say the least, for any one familiar with the deficiencies of American statistics of consumption must wonder whence the compilers derived their estimates of the quantities of 310 commodities 'annually consumed by each inhabitant.' Moreover, what little is known concerning the actual weights is not unobjectionable. Fifty per cent of the total is too large a weight to allow to foods in a wholesale-price 1 Note omitted. 2 Notes omitted.

series. Even in the great collection of budgets of workingmen's families made by the Commissioner of Labor in 1901 the average expenditure for food was less than 45 per cent of total family expenditure; and in wholesale markets, of course, many commodities that are never directly consumed by families have great importance.

Dun's index number is supposed to stand first in number of commodities included, but lack of definite information makes it impossible to judge whether its list is well balanced. The bureau's list also is long and contains samples of many different kinds of goods, manufactured as well as raw, consumed for all sorts of purposes and produced under all sorts of conditions; but the representation accorded to different parts of the whole system of prices is certainly far from equitable. Bradstreet's list, while less than half as long as the bureau's, seems better chosen. It is particularly strong in raw materials and rather weak in manufactured goods. The same remarks apply to Gibson's original list, though it suffers in comparison by being only about half the length of Bradstreet's. Finally, the present Gibson index number and the Annalist series are confined to foodstuffs, and make no pretense of representing prices at large.

"In the form of presenting results, Bradstreet's set an admirable example, which was wisely followed by Dun's. Their sums of actual prices can readily be turned into relatives on any base desired, and hence can be made to yield direct comparisons between any two dates. The other series, as averages of relative prices on the 18901899 basis, cannot be properly shifted without a detailed recomputation of the relative prices of each commodity, and force readers to make all their comparisons in terms of what prices were in the decade used as base.

"It is interesting, finally, to test the reliability of the several index numbers as 'business barometers.' Monthly figures would be much better than our yearly averages for this purpose; but since they are not to be had for most of the series during most of the period covered, we must do the best we can with the rougher gauge. In 11 of the 23 cases of changes from one year to the next the seven index numbers disagree as to whether prices rose, fell, or remained constant. In the following schedule these 11 years are represented by columns in which each index number is credited with plus one

1 Note omitted.

when its change accords with the character of the alteration in business conditions, debited with minus one in cases of disagreement, and marked zero when it recognizes no change in the price level.1 The net scores made by casting up the plus and minus entries indicate roughly the relative faithfulness with which these series have reflected changes in business conditions in the past. Of the index numbers regularly published, Bradstreet's makes much the best showing. Even the scores against it in 1895 and 1903, and its failure to show the reaction in business conditions in 1913, would be wiped out were the data by quarters and months used in place of the annual averages.

INDEX NUMBER

1891 1893 1895 1897 1901 1903 1904 1905 1908 1910 1913

NET

SCORE

1. Bradstreet's

2. Bureau of Labor Statistics, revised.

3. Gibson, original

4. Bureau of Labor

Statistics, orig

2 +1 +1 1+1+1

1+1+1+1+1

0+6

0+1+1+1+1+6

+1+1-1 0+1 0

0 0+1+1+1 − 1 + 1 + 1 + 1 0+5

"Each of these seven series, then, has its special uses, its merits, and its defects. Choice among them should be made in accordance with the particular purpose for which an index number happens to be wanted. But it seems feasible to construct an American series which would present a stronger combination of good qualities as a general-purpose index number than any now existing. The original quotations might be collected from the records of the Bureau of Labor Statistics and Bradstreet's, a list of commodities more complete than Bradstreet's and better balanced than the bureau's might be drawn up, the use of actual prices might be adopted from Brad

1 For a description of American business conditions in this period, see W. C. Mitchell, Business Cycles, Chapter III (Summary, p. 88).

2 Based on Bradstreet's original figures for 1890 and 1891, figures which are not used in the index number as currently published.

street's and Dun's, the several commodities might be weighted by physical quantities after Dun's fashion, but with the use of a criterion more appropriate to wholesale prices, and the whole process of construction might be set forth with the frankness characteristic of the Annalist and the bureau. Such a series might differ little from the figures now available; but, however it might turn out, its results would merit greater confidence than can properly be felt in any of the present index numbers as a measure of changes in the general level of wholesale prices."

IV. CONCLUSION

The collection of data, the development of plan and purpose, the use of statistical abbreviations in the forms of averages and aggregates, the association of means and ends are all admirably illustrated in index number making and using. With few statistical problems is it necessary to use so many data and to exercise so much care in the uses to which they are put, and yet these facts are not generally acknowledged by those who use index numbers and are likely to be given little weight unless the consequences of loose and indiscriminate use are pointed out. It has been the purpose of this part of the discussion briefly to develop the principles of index number making and to show their importance in respect to the leading American numbers. The application of statistical method is patent at every stage.