Readings in Money and Banking / Selected and Adapted

by Chester Arthur Phillips

CHAPTER VIII

INDEX NUMBERS

[30]Index numbers are used to indicate changes in the value of money. The objects for which this measurement is undertaken are thus well stated by Sir R. Giffen (Second Report of the committee appointed for the purpose of investigating the best method of ascertaining and measuring variations in the value of the monetary standard. Report of the British Association, 1888): (1) The fixation of rents or other deferred payments extending over long periods of time, for which it has been desired to obtain a currency of a more stable sort than money is supposed to be. (2) To enable comparisons to be made between the value of money incomes in different places, which is often an object of great practical interest; not only individuals contemplating residential changes, but also governments and other large spending bodies, spending money in widely distant places, having to consider this question. (3) To enable historians and other students making comparisons between past and present to give an approximate meaning to the money expressions which they deal with, and say roughly what a given fine, or payment, or amount of national revenue or expenditure in a past age would mean in modern language. To which some would add: (4) To afford a measure of the extent to which trade and industry have been injuriously affected by a variation in prices; and of the correction which it would be desirable to apply to the currency.

An index number is constructed by combining several items, each of which is a ratio between the price of a certain article at a particular date under consideration (e. g., last year or month) and the price of the same article at a period taken as base or standard (e. g., 1867-77, in the index number constructed by Mr. Sauerbeck, Journal of the Statistical Society, 1886 and 1893). These ratios are generally expressed as percentages. E. g., the percentage for flour in 1885, as given by Mr. Sauerbeck, is 63; meaning that the price of flour in 1885 is to the average price of the same article in 1867-77 as 63:100. The term index number is sometimes applied (e. g., by Mr. Sauerbeck, op. cit.) to each of these items, as well as to their combination.

The percentages are usually compounded by taking an average of them. But a result of equal generality may be obtained by taking their sum. One of the best-known index numbers, that of the Economist, is thus constructed. Twenty-two articles having been selected, the price of each article at the current date compared with its price at the standard period (1845-50) is expressed as a percentage; and the sum of these percentages is put as the index number. Thus the Economist index number for the year 1873 is 2947; such a sum is easily reduced to the form of an average by simple division (e. g., 2947 ÷ 22 = 134). Accordingly in what follows it will be sufficient to consider the latter form only.

The construction of an index number presents the following problems: (a) What are the commodities of which the prices are to be taken? (b) How are the prices to be ascertained? (c) How are the ratios between the prices of each article at the current and the standard dates to be combined?

The answers to these questions vary according to the purpose in hand.... As appropriate to the first purpose, a standard of deferred payments, two methods present themselves, viz., to arrange that the debtor should pay, the creditor receive, either (1) the same quantity of goods and services, the same amount of utility, so to speak; or (2) the product of the same quantity of labour—or more exactly effort and sacrifice.

Of these methods the former has been more generally accepted. It is adopted for instance by the British Association Committee already referred to, as par excellence the measure of the change in the value of the monetary standard. The former method is indeed more intelligible. However, in favour of the latter there are some weighty considerations and authorities. It seems to be the nearest possible approach to Ricardo's conception of a commodity invariable in value, "which at all times requires the same sacrifice of toil and labour to produce it." (Principles, iii. ch. xx., "On Value and Riches," cp. Mill, bk. iii. ch. xv., "On a Measure of Value.") "A standard," says Mr. Leonard Courtney, "should be something which as far as possible involves the same labour and the same sacrifice in obtaining it" (Nineteenth Century, March, 1893). Prof. Marshall, in his evidence before the royal commission on gold and silver, says, speaking of appreciation of gold: "When it is used as denoting a rise in the real value of gold, I then regard it as measured by the diminution in the power which gold has of purchasing labour of all kinds—that is, not only manual labour, but the labour of business men and all others engaged in industry of any kind" (Question 9625).

If the first method is adopted, the answers to the questions above set are as follows: (a) The commodities of which the prices are to be taken should be articles of consumption rather than materials and implements. Payments for personal services should be included, but not wages in general. (b) Retail prices should be used. (c) The proper combination of the ratios is an average of the kind technically called weighted.... The general principle according to which the weights are to be assigned is that they should represent the importance of each commodity to the consumer. But this idea may be embodied in different plans.