It seems to be taken for granted that, when we can show a reason why each price should have varied in the direction actually observed, we are thereby debarred from inferring a general displacement due, in the phrase of Mill, to 'causes that operate on all goods whatever.' But this assumption is quite erroneous. The meteorologist may be able to assign the reason why between morning and noon each particular day there has been a rise or fall of the barometer. But the mathematician is not thereby precluded from extricating by the theory of probabilities a mean variation between those hours." 1

Referring last year to this criticism Professor Laughlin complains that I have "wholly misunderstood" his argument.2

I am very sorry to have unconsciously misrepresented the argument which I was disputing. I can only console myself by reflecting that no amount of care on my part could have averted the mistake, since even after Professor Laughlin's explanation I am unable to discern any appreciable difference between the position which he takes up and that which was the object of my attack. He explains :—

“ .

"I at least never contended that in order to prove a general fall you must prove a fall in every article.' Accepting the fact of a decline in prices, my contention was solely that the cause of the decline could not be scarcity of gold; since, if there was a single cause for the fall then this cause should show itself in all,3 or nearly all, the commodities quoted." 4

Now my contention was and is that, though there be a common cause it need not "show itself in all or nearly all the commodities quoted."

To take a new example, for which the data happen to be ready to hand suppose that the average height of a regiment of 1000 Italian recruits selected indiscriminately from all the provinces was returned as half an inch in excess of the average height of the whole army; one might infer with certainty that the difference was due to a real cause (as distinguished from chance); and that cause might well be "single," such as the circumstance that the men in the regiment were (contrary to the general practice) measured with their shoes on. But it does not follow

1 Quarterly Journal, Vol. III (1889) p. 107.

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2 Journal of Political Economy (Chicago), Vol. II., p. 279. His former words (above quoted) are it is quite necessary. . . that the fall should be universal"; excusing, I think, my expression "a fall in every article." But I am quite willing to substitute" all or nearly all” for “ every."

▲ Loc. cit.

that this cause should show itself-by excess above the average of the kingdom-in a large majority. The proportion of men above the general average might be about 57 per cent., 570 out of the 1000.* Is that "all, or nearly all"?

Say the standard deviation for the national stature is 2.6 inches (Yule, Theory of Statistics). The coefficient for the mean height of the regiment would be 08; less than a sixth part of the observed difference! If h is the average height of the army, h+5 that of the regiment, the proportion of the regiment above h would be about 57 per cent. (2.6 being the S.D.).

(K)

PIERSON ON SCARCITY OF GOLD

[THIS is the first of two articles in which I deal with writings of the great Pierson relative to index-numbers. In this article, published in the ECONOMIC JOURNAL, March 1895, I have nothing but praise for Mr. Pierson's treatment of the subject.]

The Bimetallic League ought to translate and circulate an article on Scarcity of Gold which has lately been contributed by the eminent ex-professor, and ex-minister, Mr. N. G. Pierson, to the Dutch periodical De Gids. Lessons of caution and moderation might be accepted from such a teacher. For Mr. Pierson owns to a certain sympathy with the Bimetallist party. Indeed, he has ranged himself on that side unequivocally in his wellreasoned communication to the Gold and Silver Commission (second Report), in the course of which he says:

"It is considered a mere truism in this country [Holland] to say that Bimetallism, though highly objectionable if applied in a small country, is the best system imaginable if applied by an international agreement in a large number of civilised States. We thoroughly believe that it would be a great boon to all nations if this system were adopted by the principal countries of Europe and America."

Mr. Pierson in the article before us proposes two questions: I. Has there been a rise in the purchasing power of gold? II. If so, is the cause connected with gold or goods, or both?

I. The first question involves a consideration of the method of index-numbers. Mr. Pierson prefers the arithmetic to the geometric mean; not without a certain deference to the "feeling" —rather than the arguments-of Jevons, in favour of the geometric mean. Distinguishing the simple average of relative prices from that which is weighted according to the importance with respect to some human interest of different commodities, Mr. Pierson very properly ascribes a certain validity to the simpler

and more objective mean, for its own sake, and apart from the circumstance that as a matter of fact the two procedures are likely to differ little in result.

As to the period which should be taken as the base of standard, it is a matter of complaint that the advocates of Bimetallism frequently select the "inflation period" of 1870-75. If the period 1861-70 be taken as base, the period 1881-83 compared therewith shows no fall of prices; according to the index-numbers of Soet beer and Dr. Kral, based respectively on 114 and 265 commodities. It is true that Mr. Sauerbeck's index-numbers do point to a fall of prices in the interval considered. But this discrepancy is due to Mr. Sauerbeck's not having used a sufficient number of data. For observing that thirty-five of Mr. Sauerbeck's articles-or rather forty-one, as six of Mr. Sauerbeck's articles are duplicated-are common to Soetbeer, let us substitute the prices of those articles used by Sauerbeck for the prices used by Soetbeer in his index-number; and that index-number for the period 1881-83 compared with the period 1861-70 will not be appreciably affected. The discrepancy between the two results is found to be mainly due to the seventy-nine articles which Soetbeer has, and Mr. Sauerbeck has not. Accordingly it would seem that Soetbeer's result is the better founded. paring, according to his method, the level of prices in the period 1885-91 with that of 1861-70, we find a rise in the purchasing power of gold of only some 16 per cent.; whereas it is usual on Bimetallist platforms to speak of a greater rise.

Com

II. Coming to his second question, Mr. Pierson claims against both parties the right to use the term appreciation in the sense of a rise in the purchasing power of gold due to causes affecting gold primarily. He seems to convict a leading monometallist organ of using the term inconsistently. His difference with the Bimetallist leader, Professor Foxwell, is rather about things than words. Mr. Pierson controverts the argument that the depression which has prevailed during recent years must have been due to monetary disturbances: for that there are no other adequate causes for it. There have been many other causes, replies Mr. Pierson, and the cause assigned is not adequate.

To take the latter point first: the Bimetallist in his gloomy picture of the evils of contraction is apt to leave out of account the classes who are benefited by a fall of prices. These are not only creditors not engaged in active industry, but also certain classes of producers. Consider the series of instruments and materials conducive to the production of goods ready for consump

tion-the goods of the second or higher orders in the phraseology of the Austrian economists. Suppose that a fall of prices occurs first in the goods which are of the highest order, and is propagated downwards. Each class of producers, while his expenses of production are diminished, and until the price of his finished product falls, pending the restoration of economic equilibrium, is benefited. Who shall say that the fall of prices is not as likely to move in the direction which has been described as in the opposite direction? Thus Mr. Pierson is unable to accept Mr. H. H. Gibbs's dictum-that contraction is a greater evil than inflation. In this connection and with respect to other assertions of unfashionable opinions, Mr. Pierson refers with approbation to Professor Marshall's masterly and impartial evidence before the Royal Commission on the relative values of the precious metals.

The allegation that monetary disturbance is the only adequate cause of the recent depression of trade Mr. Pierson meets by assigning other causes the very dislocation caused by improvements in production, the Protection which became rampant in the 'seventies, the fall of prices consequent upon recent improvements in transportation and upon the enormous increase of goods which has occurred in so many departments of production-augmentations which Mr. Pierson, following in the steps of Mr. David Wells, exhibits in imposing detail. It is true that some of these causes, especially the last, operated at earlier periods, but not, Mr. Pierson seems to think, in the same degree. Perhaps he has hardly considered the difficulty of proving such a difference in degree.

Mr. Pierson however concludes with confidence that the level of prices did not fall till after 1883, and that the fall is due to causes connected with goods, not gold. But while thus cutting away one of the principal planks of the Bimetallist platform, Mr. Pierson does not attach himself to the opposite party. He makes a distinction between the creed and the propaganda of the Bimetallists. He believes in an international arrangement for steadying the relative value of gold and silver. But this arrangement need not involve the principle of unlimited coinage at a fixed ratio.

One practical difficulty in the application of that principle may be stated in the form of a dilemma as follows. If the ratio adopted is considerably different from 15 (silver): 1 (gold), say 25 to 1, then the expense of introducing the change would be enormous in view of the depreciation of the existing stocks of silver current at the rate of 15: 1. "If I reckon rightly," says

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