Wheat Prices and Rainfall in Western Europe Author(s): William H. Beveridge Source: Journal of the Royal Statistical Society, Vol. 85, No. 3 (May, 1922), pp. 412-475 Published by: Wiley for the Royal Statistical Society Stable URL: http://www.jstor.org/stable/2341183 . Accessed: 25/06/2014 03:22 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Wiley and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. http://www.jstor.org This content downloaded from 185.44.77.40 on Wed, 25 Jun 2014 03:22:47 AM All use subject to JSTOR Terms and Conditions 412 [Alay, WHEATPRICES AND RAINFALLIN WESTERNEUROPE. By SIR WILLIAMH. BEVERIDGE. [Read before the Royal Statistical Society, April 25, 1922, the President, Sir R. HENRYREw, K.C.B., in the Chair.] I.-INTRODUCTION. II.-CONSTRUCTIONOF PERIODOGRAMOF WHEAT PRICE FLiuCTUATIONS. (With chart.) I lf.-INTERPRETATIONOF PERIODOGRAM. The four tests of periodicity. Thc periods found. Summary and Review (with table). IV.-COMPARISONWITH EUROPEAN RAINFALL, 1850-1921. (With chart.) V.-CONCLUSION. APPENDIX.-Harmonic Analysis of Wheat Price Fluctuations. I.-INTRODUCTION. THE paper which I have the honour of reading to you to-night is ill substance a sequel and supplement to an article on " Weather " and Harvest Cycles," published in the Economic Journal of December, 1921. In that article (which I shall refer to here as " my former article ") I gave index-numbers of wheat prices in Western and Central Europe from 1500 to 1869 and the preliminary results of an analysis of these figures, by mathematical and arith- metical methods, with a view to discovering periodicity. I sum- marized my conclusions on this point " in three propositions of a "descending order of certainty ": First, the yield of harvests in Western and Central Europe from the middle of the sixteenth to the opening of the twentieth century has been subject to a periodic influence, or combination of such influences, tending to produce bad harvests at intervals of about 15-3 years, the first epoch falling in 1556. This proposition is about as certain as harmonic analysis can make it. Second, this period of 15*3 years, though corresponding to certain physical facts, is not a permanent one, but arises from a temporary combination of two or more shorter cycles. This proposition, though not certain, is in both of its branches highly probable. This content downloaded from 185.44.77.40 on Wed, 25 Jun 2014 03:22:47 AM All use subject to JSTOR Terms and Conditions 1922.] BEVERIDGE-Wlheat Prices antdRainfall, etc. 413 Third, the shorter cycles whose combination has given rise to the 15.-3- year period from 1556 onwards, and which are themselves more permanent than their combination. are those named above as = 4 -374 years, = 5 11 years, and (probably) = 2-74 years and = 3 71 years. This proposition is a speculation as to whose plausibility and truth different readers will take different views.* I had hoped to-night to undertake a three-fold task: first, to give a full account of the sources and construction of my index- numbers as justification of their value; second, to give the results of a complete harmonic analysis in place of the preliminary examina- tion made for me by Mr. H. T. Curwen; third, to call attention to the economic, as distinct from the meteorological, uses of my index-numbers, and the light thrown by them on the history of prices in different countries and in Europe as a whole. Considerations of time and space have compelled me to modify this programme. In effect, I must confine myself to the second of the above tasks. The gist of my present paper is the complete harmonic analysis of my index of wheat price fluctuations for about three hundred years from 1545 to 1844, involving a test of the figures for all possible periods between two and a half and eighty- four years in length, and for many periods below two and a half years. This is followed by an attempt to relate the results of the analysis to rainfall records from 1850 to 1921. In so far as this attempt proves successful, the need for justifying my index-numbers by describing their sources and construction will no longer remain. The value of the index-numbers will be proved in the best of all ways, by showing that theories founded on them explain the facts of meteorology. I may, however, summarize and add to the statement made in my former article, as follows:- The numbers used for harmonic analysis are based ultimately on lists of prices for long periods of consecutive years in nearly fifty separate markets or districts of Western and Central Europe, and on official averages for whole countries when these become available. There has been no selection of places or of years to be included: within the area taken, every list known to me and sufficiently continuous to be used has been used substantially for the whole period covered by it, or till it was superseded by a comprehensive list for a whole country.t There has been no artificial weighting: * To avoid confusion I have omitted the letters A, B, C, and D by which I formerly identified these periods. The discovery by my further analysis of so many new periods has compelled a change of nomenclature. ? Hardly a dozen eccentric figures altogether out of many thousand- chiefly from German towns during the Seven Years' or the Thirty Years' War -have been rejected. VOL LJXXXV. PART III. 2 F This content downloaded from 185.44.77.40 on Wed, 25 Jun 2014 03:22:47 AM All use subject to JSTOR Terms and Conditions 414 BEVERIDGE-Wheat Pricesand Raifall [May, each list has counted for one in the country from which it came, and each of the five countries or territorial divisions-Britain, Low Countries, France, North Germany, South Germany, and Austria-has counted for one. Finally, there has been no smoothing or averagingprocess which could favour the appearanceof periodicity in general or of a period of any particular length; with the one exception just to be mentioned, I have indulged in no averaging at all. The one exception is this: the index-numibersof wheat prices (as set out in Column 1 of the table appended to my former paper) showed a marked secular trend, correspondingto the depreciation of money; they grew from an average of 15 I for the decade 1500-9 to one of 222-6 for 1860-69. It was essential to eliminate this trend. Otherwise, the later observations with their high values would have had undue importance in the indication of periods: this form of weighting was most undesirable, in view of the known inconstancy of meteorological cycles. The trend was eliminated by calculating continuous 31-year averages, and showing the index-number for each year as a percentage of the average for the thirty-one years of which it was the centre (Column 2 of the table in my former article). These percentages thus record the deviation of the price for each year from the average of the neighbouringthirty-one years; they are described as the " indices " of wheat price fluctuation "; they are the numbers submitted to harmonic analysis in my former article and more completely analysed in my present one. Some distortion of the harmonics present in a sequence of observations is probably involved in any smoothing or averaging process whatever. Professor Schuster, in his original paper on the periodogram,issued a weighty warning against the use of such processesbefore applying harmonicanalysis: as a rule the harmonic analysis itself performs any justifiable smoothing effectively and without distortion. The particular process employed here is, I think, as nearly free from objection as possible. Inspection shows that all the peaks and depressions of the original figures are faith- fully reproducedin the percentages,and that the proportionsbetween neighbouring peaks or depressions are unchanged. Mathematical analysis of the precise effect of any averaging process is a difficult matter which must be left to competent mathematicians. So far as I can judge, from a formula preparedfor me by Mr. H. T. Curwen, the general effect of the particular process adopted here should be to leave harmonics up to thirty-one years of length practically untouched in amplitude as well as in phase, while those of greater This content downloaded from 185.44.77.40 on Wed, 25 Jun 2014 03:22:47 AM All use subject to JSTOR Terms and Conditions 1922.1 in WesternEurope. 415 length are steadily but slowly damped down, their phase remaining unaltered. This simply means that a lower intensity may be significantof a true period if it occurs at fifty years than if it occurs at twenty-five. There seems to be no selective bias in favour of particular periods. The errors due to leaving the secular trend uneliminated would almost certainly have been more serious.* II.-CONSTRUCTION OF PERIODOGRAMOF WHEAT-PRICE FLUCTUATIONS. In my former article the harmonic analysis of the indices of wheat-price fluctuation, undertaken for me by Mr. H. T. Curwen, was carried only to the point of covering all periods of a complete number of years from two to thirty-six, and a certain number of intervening periods consisting of complete half-years.