5^4 



NATURE 



[June 23, 1921 



same whatever year be used as base, and this is 

 not the case if the arithmetic mean be used. 

 Jevons's calculations were not maintained, but his 

 work on this point of method has been fruitful. 



Sauerbeck, 3 having- regard to the unsatisfactory 

 character of the old Economist number, con- 

 structed in 1886 a fresh index, using forty-five 

 quotations. His base-period was the eleven years 

 1867-77, and he again used the simple arithmetic 

 average for his mean. The calculation of the 

 index-number was maintained, and it has now 

 become the index-number of the Statist. In some 

 ways this number also is no longer entirely satis- 

 factory ; foreign meat, for example, is not in- 

 cluded, nor rubber. 



The Board of Trade * in 1903 constructed an 

 official index-number of wholesale prices in which 

 a weighted arithmetic mean of the individual 

 index-numbers was used, weights being given by 

 the estimated values consumed. It was not a 

 satisfactory number. The correct method of 

 weighting does not seem to have been realised, 

 and the weights actually used were based on a 

 period different both from the reference year first 

 employed (1871J and from that used later (1900), 

 with the result that two widely divergent series of 

 figures have been given. Very rightly the Board 

 has decided that the old number should now be 

 entirely dropped and a fresh index constructed on 

 a new basis. This basis was fully described in 

 a paper by Mr. A. W. Flux,^ of the Board of 

 Trade, read before the Royal Statistical Society 

 for discussion in January last. So many as 150 

 quotations are used for the new number, and the 

 geometric mean is employed, thus freeing the 

 results from any influence of choice of reference 

 period, and obtaining a completely consistent 

 series of averages. No actual weights are used, 

 but, as in the case of the Economist and the 

 Statist index-numbers, there will be an approxi- 

 mate weighting by assigning more quotations to 

 the more important commodities. It must be 

 noted also that this number is really devised to 

 answer a question different from that faced by 

 Newmarch or Jevons — the effect, not of currency 

 on prices, but of prices on currency. In the case 

 of dutiable commodities the duty will therefore 

 he included in the price ; prices will not be quoted 

 duty-free as in the case of the other wholesale 

 numbers. The number, the first figures for which 



* Journ. Stat. Soc , vol. xlix., 1886 ; subsidiary pnpers and annual reviews 

 since. 



* Report No. 321, 1903, and later Labour Gazette or " Annual Abstract of 

 Labour Statistics." 



' Journ. Stat. Soc., March, 1921. The paper has also been separately 

 rinted. 



NO. 2695, VOL. 107] 



have been published in the Board of Trade 

 Journal, represents a great advance. 



All the above index-numbers are essentially 

 index-numbers of wholesale prices, and deal pre- 

 ponderantly, though not wholly, with raw 

 materials. Clearly this is not what is required 

 for an index-number of "cost of living." But 

 what do we mean by that very elastic phrase? 

 As soon as we endeavour really to analyse the 

 term, it becomes extraordinarily difficult to say. 

 The clearest definition is "the cost of purchasing 

 year by year the same schedule of commodities 

 and services." It is nearly a century since Joseph 

 Lowe^ attempted calculations on this basis for 

 the change in "cost of living" between 1792, 

 1813, and 1823 for a country labourer, a town 

 mechanic, and a middle-class family, using esti- 

 mated budgets of normal expenditure as his 

 foundiation. He also suggested the voluntary 

 regulation of wages and salaries on such a basis. 



It cannot be said that we have advanced much 

 beyond this work of a century ago so far as 

 regards method. The Board of Trade, soon after 

 the beginning of the war, began the publication 

 of an index-number of retail prices in the Labour 

 Gazette, afterwards maintained by the Ministry 

 of Labour. At first it was termed an index- 

 number of "cost of living," but, very judiciously,, 

 that phrase was afterwards dropped, and it is 

 now referred to only as a measure of changes in 

 retail prices. It is to be regretted that not only 

 members of the public, but also members of the 

 Government themselves, still, nevertheless, con- 

 tinue to refer to it as an index of the "cost of 

 living." The process of calculation was fully 

 described in the Labour Gazette for March, 1920. 

 A fixed schedule of foodstuffs was taken, based 

 on the pre-war consumption of a working-class 

 family, and the total cost of this schedule at the 

 prices of the day compared with the prices of 

 July, 1914, gives an index-number for food; 

 index-numbers for working-class rents, clothing, 

 fuel and light, and miscellanea (ironmongery,, 

 brushware, and pottery; soap and soda; tobacco 

 and cigarettes ; fares and newspapers) are deter- 

 mined by other inquiries, and these several 

 group-indexes are combined into a general 

 average on the basis of weights determined from 

 pre-war expenditure. 



The number is thus based entirely on the con- 

 ception of purchasing a fixed schedule — the mam- 

 tenance of a fixed mode of life. But when prices 



6 "The Present State of England" (London, 1822, and second edition^ 

 1823). 



