## William Stanley Jevons Statistical Sciene

William Stanley Jevons and Statistical Sciene

Jevons's pioneering efforts in utility analysis were more than matched by his efforts in empirical and statistical science. In 1862, after publishing early works on scien­tific meteorology, Jevons set out to apply scientific principles to commercial statis­tics.3 His first paper, entitled "On the Study of Periodic Commercial Fluctuations," was forwarded along with his earliest theoretical paper to the meeting of the British Association in 1862. In it Jevons analyzed variation in the following variables: av­erage rate of discount, 1845 to 1861 and 1825 to 1861; total number of bankruptcies, 1806 to 1860; average price of government bonds, 1845 to 1860; and average price of wheat, 1846 to 1861. Jevons presented his data diagrammatically, and con­cluded that data should be arranged in such a way as to best elucidate the most in­teresting aspects for the purposes of the investigator. As an early discoverer of sea­sonal fluctuations, Jevons noted:
Every kind of periodic fluctuation, whether daily, weekly, monthly, quarterly, or yearly must be detected and exhibited, not only as a subject of study in itself, but because we must ascer­tain and eliminate such periodic variations before we can correctly exhibit those which are ir­regular or non-periodic, and probably of more interest and importance (Investigations, p. 4).
Thus Jevons offered various explanations for the seasonal fluctuations in his vari­ous data, applying the process of scientific abstraction used in his theoretical work.

Price Series and Index Numbers

One of Jevons's most important statistical papers was "A Serious Fall in the Value of Gold Ascertained and Its Social Effects Set Forth" (1863). In it Jevons wished to apply the general proposition "that an article tends to fall in value as it is supplied more abundantly and easily than before" to the then-recent gold discoveries in Aus­tralia and California. The French economist Michel Chevalier had predicted such a fall, but others, including Newmarch and McCulloch, had doubted that it would occur. In order to understand Jevons's achievement better it must be recognized that econ­omists of this period had only vague and ambiguous notions of what a fall in value was. Thus Jevons had to begin with an introductory lesson in logic applied to sta­tistics. He had to explain the meaning of an average rise of prices, and, most im­portantly, the method of constructing price indices. In this latter effort, he was clearly a pathbreaker. He discussed at length the compilation of price tables, computation of arithmetic and geometric means, the problem of weighting, and the selection of the sample commodities. Then with statistics gathered from various periodicals, in­cluding The Economist, the Gazette, and The Times, Jevons constructed an average annual price of thirty-nine commodities for the years 1845 to 1862. After assessing the statistics and painstakingly plotting them, he concluded:

It is hardly necessary to draw attention to the permanent elevation of prices since 1853... . The lowest average range of prices since 1851 has indeed happened in the last year 1862; but prices even then stood 13 percent above the average level of 1845-50.. . . Examine the yearly aver­age prices at any point of their fluctuations since 1852, and they stand above any point of their fluctuations before then within the scope of my tables. There is but one way of accounting for such a fact, and that is by supposing a very considerable permanent depreciation of gold (In­vestigations, pp. 44-45).

Jevons also discussed the depreciation of silver and the rate of fall in the value of gold, relating the total fall in gold value to the quantity in use.

Finally, Jevons investigated the effects of gold depreciation (price increase) on debtors, creditors, and various other classes. Throughout he displayed a keen prac­tical knowledge of credit institutions and commerce. He concluded that creditors, those injured by gold depreciation, have no equitable claim to compensation, but he failed to discuss the distributional effects of gold depreciation. He recognized, however, the indirect effects of gold discovery, such as the creation of new colonies, the dissemination of the English people and language, and the reanimation of com­merce.

Several years later Jevons continued and expanded his statistical study of price movements in "The Variation of Prices and the Value of the Currency Since 1782," published in the Journal of the Statistical Society of London (June 1865). In this paper Jevons expanded his index number methods by reducing data from Tooke and New-march's History of Prices into price indexes of all commodities and individual classes of commodities. He evaluated the theoretical foundations of all commonly used price indexes, favoring the geometric mean over Laspeyres's arithmetic mean and the harmonic mean. On the merit of these alternative calculations, Jevons ob­served, "It is probable that each of these is right for its own purposes when these are more clearly understood in theory" {Investigations, p. 114). The geometric mean pre­sented some calculational advantages, such as the facility to correct results by the continual use of logarithms. Also, Jevons wanted a ratio that would underestimate variations by comparison with Laspeyres's arithmetic mean.

As in his previous paper, Jevons meticulously explained his construction of the index from Tooke's data, including methods for "correcting" the data over various intervals and for the classifications of commodities. For example, the price data be­tween 1800 and 1820 had to be corrected to reduce prices and their variations to a gold standard, because the Bank of England sponsored a paper standard during this period. The quality of Jevons's study, in short, was extremely high, and the results, multiple price indexes between 1782 and 1865, mark the most im­portant early attempt at systematic price indexing in economic literature. Jevons's instinct for order and his readiness to raise questions concerning the quality of his raw data and his statistical methods make his contributions to price-index construc­tion not only above the level of his time but considerably in advance of it.