Knowledge that Transforms

FROM the standpoint of the physical volume of production, the year I926 was one of extraordinary growth. Actual output of both manufacture and mining established new high records for all time and agricultural production, the largest in the past 6 years, has been exceeded only in 1920 (Tables A and H). In each of these major lines of activity, the increase in the volume of production from the level of the preceding year was larger tl' an that normally to be expected even in a growing country like the United States. Such is the record as presented in graphic form on Chart i and in tabular form in Table B. Moreover, both mineral and industrial production, as

TN this REVIEW for January I926 we brought together some of the results of our studies of the relationship between money rates and speculation in the business cycle. There we stated our general conclusion that substantial quantitative changes in money rates, regardless of the length of time during which those changes take place, have been, in general, highly significant for security markets.' This general conclusion resulted from our statistical studies of the cyclical fluctuations of monthly average rates on prime commercial paper, duly adjusted for seasonal variation, on the one hand, and of monthly average industrial stock prices, monthly average railroad stock prices, monthly average prime railroad bond prices, and monthly average miscellaneous bond prices, on the other hand. The periods studied were I884-I925 for money rates and stock prices, and I890-I925 for money rates and bond prices. For these periods both the magnitude of fluctuations of the series, and their sequence in time were examined to ascertain whether systematic and simple relation between the money market and the securities could be proven to exist. In making this examination it was found convenient to divide the periods into the following four sub-periods: i884-i896, a period characterized by declining commodity prices, agitation for free silver, and difficulty in maintaining the gold redemption fund for greenbacks; I897-I9I3, a period of rising commodity prices, unquestioned maintenance of the gold standard, and comparative freedom from nonbusiness disturbances; I9I4-I8, a war period of large gold imports and abnormally low money rates followed in I9I7, after the entry of the United States into the war, by a money market controlled with reference to the exigencies of war finance; I919-25, a period characterized by, first, continued control of money rates with reference to the government's post-war financing, second, the withdrawal of control, for government purposes, of the money market and, third, paper inflation and deflation in Europe, unprecedented gold imports into the United States, and abnormally low money rates in this country. When we undertook the search to find some systematic and simple relation between the money market and the securities markets we did not expect to discover, nor did we in fact discover, a constant mathematical relation between money rates and security prices holding invariably in war as well as in peace, in times when the gold standard was threatened (such as I895-96) as well as in times when its permanence was not questioned, and in times of abnormal international gold movements (such as I92225) resulting from non-business influences as well as in times of movements resulting from fluctuations in trade. No one with the slightest familiarity with business and economic affairs would expect to find that security prices were in constant mathematical relation to money rates certainly not for such a long and varied period as I884-I925. Although an unvarying function was neither expected nor discovered our studies had led us to expect that a systematic and simple relation between money rates and security prices might be found to hold during the normal cyclical fluctuations of business from depression to prosperity and back to depression. Disturbances of a non-business nature were fewer and less pronounced during the interval of I7 years from I897 to I9I3 than during any other interval of equal length in the last 40 years. In fact the Spanish War was the only momentous non-business disturbance during these i 7 years, so far as money rates in the United States are concerned. Consequently, the investigation began with a study of the period I897-I9I3. For this test period the conclusion was reached that the simplest and most unvarying relationship of any discovered, between changes of money rates and subsequent levels of stock prices was given by the table showing (i) the rise (or fall) of I4 per cent and (2) the level of stock prices for the month immediately following the rise (or fall) mentioned.2 For the levels of bond prices,

CURVE A, speculation, now appears in the index of general business conditions, substantially as developed in the I923 revision.' The curve is obtained by averaging cycles for bank debits in New York City and for the DowJones average of industrial stock prices. It did not appear in I923 that any secular trend was present in these two constituents; and, although the accumulation of data since that time has rendered the presence of an upward secular trend in each series increasingly evident, it is only recently that we have become confident of the possibility of measuring even approximately such trends. In Curve A as it has been appearing, therefore, no correction for trend has been made; and, for each constituent, the actual items are expressed as per cent deviations from assumed horizontal lines. These deviations are then used in determining the cycle figures. In the case of the'New York bank debits an adjustment is necessary because of the presence of seasonal variation.2 The seasonal correction for the bank debits figures allows not only for annually recurrent fluctuations which are essentially seasonal in character, but also for the effect of extraordinary financial transactions which take place quarterly. It is believed that the present Curve A gives a substantially accurate record of the short-time fluctuations of the speculative type since the war. The fact, however, that this curve is not corrected for secular trend accounts for its extraordinary elevation during the last three years, and leaves room for a misunderstanding of the current position of the curve because of its apparent extreme departure from a supposed horizontal normal. It is therefore desirable to revise the curve by making due allowance for secular trend, so far as it is now possible to measure such trend. Moreover, it has now become apparent that Curve A can be improved by excluding from it the series for New York bank debits. Finally, it is desirable to replace the Dow-Jones average of industrial stock prices by new averages which rest upon a wider sampling of market transactions. It is the object of the present article to discuss these several changes by which the revised Curve A is substituted for that heretofore used in the index chart.

mHE economist is concerned with determining the and prospects of society. I In a more restricted, but nevertheless important, aspect of his work, he is concerned with determining the condition and prospects of business enterprise. The economist who is investigating problems relating to business is interested principally in the economic cycle, because our economic welfare is subject to the vagaries of this phenomenon. The data that exhibit economic cycles are of statistics. Methods for determining the correlation of are therefore fundamental to the investigation of economic cycles. The purpose of this paper is twofold. The first object is to describe a theory of correlation of that is particularly suited to determining the laws of economic cycles; the second is to introduce a practical application of the theory by means of a study of cycles in interest rates and in wholesale prices. Those wishing to obtain an idea of the theory here presented without going into the mathematics of the subject should limit their attention to Sections I, II, IV, VIII, and IX, on general theory, the correlation equation and the system factor, the economic indexes, forecasting, and the nature of the elements in the economic structure. Section III on solution for the system factor Y and, perhaDs. Darts of Section II will be of interest only to ose who may wish to apply the theory. Those interested in the practical results obtained by applying the method to a study of the relation between interest rates and wholesale prices will find Sections V, VI, and VII of primary interest. The type of statistical array called a series2 is one in which the items are ordered in a sequence that is fixed with respect to time. Annual, quarterly or monthly data of wholesale prices, interest rates, trade activity and rainfall are examples of important The difficulties encountered in applying the classic theory of correlation to are recognized by a number of statisticians. These difficulties are inherent in the problem, and are due to the fact that the fundamental propositions of random sampling do not apply to data that are definitely ordered with respect to time. We require, therefore, a more general theory, one that explicitly recognizes the possibility of mutual dependence between the successive items in the The essential idea of the theory proposed is that the correlation of presents a problem of multiple correlation, in which each item in one may depend upon not only the concurrent, but also upon the preceding, items in another The method of simple correlation, which is adequate for deducing the relation between of other types, is not sufficiently general to apply to series, because it considers only the relation between concurrent items in the series, and ignores the possible influence of preceding items. If, in a particular case, the preceding items are actually without influence, this fact can be demonstrated only by applying the more general theory. An intrinsic part of the theory is the concept of a system. Where two trains of events of different kinds are so related that each event of one kind exerts a definable effect upon the later events of the other kind, a systematic phenomenon is acting. A system is conceived to be an arrangement of connections and constraints 1When the Statistical Society of London was organized in I834, five years before the American Statistical Association, the prospectus announced that its functions were to 'procure, arrange and publish facts calculated to illustrate the condition and prospects of society' (presidential address by Warren M. Persons at the eighty-fifth annual meeting of the American Statistical Association). 2 The term is unfortunate, because, in mathematical usage, commonly refers to the sum of a number of quantities: thus, I+2+5+3, not I, 2, 5, 3. The data referred to as time series throughout the paper are sequtences of numbers that give the values of a variable at discrete, equally spaced intervals of time. They are, therefore, functions of time, in the way that function is understood in the calculus of finite differences. It has been suggested, therefore, (by Mr. John R. Carson of the American Telephone and Telegraph Company) that time sequences would be better than time series. The latter term is used so extensively in the literature of the subject, however, that I have refrained from introducing a new term.