Knowledge that Transforms

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.

to a movement of five points in a high-priced stock as to a five point change in one selling at a low figure, more serious error tends to creep into the picture whenever some of the companies whose stocks are used as a basis for calculating the average price level issue rights to subscribe to additional stock or declare stock dividends, either in terms of their own shares or through the distribution of shares in subsidiary companies. Any change in the character of the equities represented, affects the validity of charts based on the average market quotations of a list of stocks. Those whose concern it is to protect investments in common stocks, need some more reliable measure of changes in the value of common stock equities, and it was with the purpose of establishing such a measure that the present studies were undertaken. As a result of

T HE index numbers of prices here presented in monthly form for the period I795 to I824 were constructed as a part of a study of the financial history of the United States during and immediately following the War of i8I2.1 To students of international trade, government finance, and money, banking, and prices, the developments of a hundred years ago are of interest because of the similarity between that period and the recent war and post-war period. It is hoped that the index numbers of commodity prices at wholesale may be of service to students of the history of these years. Such series provide a continuous record around which non-quantitative data may be organized, and, being sensitive barometers of economic life, they enable us to say something concerning the timing and the magnitude of the effect of the forces at work. A description of the construction of the indexes of prices in the United States from I795 to I824 is given in Part I below. Three indexes of prices in the Boston marketone of the prices of domestically produced goods, one of imported goods, and one of domes'tically produced and imported goods (the all commodities index) have been computed by months for the 30 years. In this section also indexes of prices of domestic goods quoted in the markets of New York, Philadelphia and Baltimore, from i8io to I8I9, are presented. In Part II the index numbers for the years i802-2o,have been examined to find out when business recessions and crises occurred, and some non-statistical material has been quoted which helps to explain the movements of prices in this period. Our conclusions concerning the causes of fluctuations in prices must necessarily be tentative, for the data upon which our judgment must be based are fragmentary.

THE accompanying chart presents a bimonthly index of general business conditions for the period I875-I9I3 consisting of three curves representing, respectively, speculation, business, and money (Chart i of the insert).' For the interval I903-I3 the index is that published in this REVIEW in January I924.2 For the interval I875-I902 the index is here published for the first time. The purpose of the present article is to describe the method of construction of the index for the earlier period, to discuss the relations existing between the fluctuations of its constituents compared with the relations found to exist between the curves for the i i years immediately preceding the war, and to make a brief survey of the period I875-I902 in the light of the new index. This index, like the one for I903-I3, is based upon corrected statistics. That is to say, the constituent statistical series of the three curves of the index of general business conditions have been adjusted for secular trend and seasonal variation. The following discussion relates to the fluctuations of the adjusted and not the actual series, unless otherwise specified.

T HE methods followed in the original construction of our index of business conditions were fully set forth in this REVIEW for April I919; and such changes as have been found necessary since I919 have been explained, as occasion offered, in subsequent numbers. Our methods of interpreting the index have never been presented so exhaustively', because in part they have developed out of our experience in handling current data and have been presented only in our Weekly Letters as occasion required. It has therefore happened that our interpretation of the index has not always been fully understood; and misunderstanding is easy unless any particular passage is interpreted not only with reference to its immediate context but also with reference to what has gone before. present article is devoted partly to various matters concerning which we sometimes receive inquiries, and partly to certain criticisms which have been offered recently, particularly those of Mr. Karl G. Karsten in his paper on The Harvard Business Indexes -A New Interpretation in the Journal of the American Statistical Association for December I926.

THE comprehensive and representative character of bank debits -bank clearings, before the commencement of reports for debits as a measure of business volumes is becoming more fully recognized with accumulating experience. There is, to be sure, some difference of opinion concerning the adequacy of debits as a measure of the physical volume of business.' Concerning the fitness of debits as a measure of the money volume of business, however, there is no considerable controversy; and the doctrine that debits furnishes the best single measure of the aggregate value of business transactions lacks little of being fully established. Moreover, it is now generally held that the fluctuations of debits in New York City reflect speculative movements in addition to business variations; and it is therefore customary to use debits New York City as more truly indicating the business transactions incident to industrial and commercial operations. That some portion of the variation in cities outside New York is speculative cannot be doubted, and that a large part of the variation in New York City arises from purely business transactions is also evident. The effect of speculative operations on outside debits is less clearly apparent than in New York, however, and a record of such debits may be accepted as a general measure of business activity. With the growing emphasis, in the study of business conditions, upon prompt information concerning brief developments, it becomes desirable to trace weekly figures for outside bank debits. The interpretation of such figures, with a view to appraising current tendencies within a particular phase of the business cycle, encounters serious obstacles. These obstacles are not identical with those which impede the use of aggregate monthly bank debits.2 For monthly data, the principal difficulties include: the making of allowances for holidays, the adjustment of figures for months having five Sundays, and the allocating of weeks which extend from one month into the following. Of these, only the first is of consequence in the study of weekly data: the irregular number of reporting days per week due to the very existence of holidays, the lack of uniformity in the observance of holidays in different cities, the uncertain effect on business volumes (both as respects extent and timing) of the observance of holidays, and the possibility that a particular holiday may at times fall within the same week as some other date (such as the first of the month) having a peculiar effect upon debits all these facts help to explain the effect of holidays upon the weekly figures. There are difficulties met with in the analysis of weekly data not encountered at least directly in the study of monthly aggregates. Chief of these arises in the custom for certain payments to be made on or about particular days of each month, with the result that there are considerable temporary expansions and contractions in debits at more or less regular times within the month. The fact that a particular day of the month does not fall on the same day of the week in each of several years implies an annual shifting of the weekly manifestations of these expansions and contractions. The effect upon the actual weekly figures for debits is most perplexing. It should be noted, moreover, that this intramonthly variation is not uniform for the twelve months of the year. In one month it is relatively intense, in another relatively slight; and this lack of uniformity is emphasized by the existence of certain large-scale financial transactions which distort the debits figures in particular months of each year. A further special difficulty encountered in the analysis of weekly data is due to the very detail sought in the weekly picture. The monthly aggregate marking the peak whether cyclical or seasonal in debits does not disclose the location of the peak within that month. This location becomes of moment in the study of weekly series; and the possibility that the peak effect as a whole is distributed, in unknown and perhaps unknowable proportion, between two adjacent weeks constitutes a serious obstacle in the analysis. 1 See Carl Snyder, this REVIEW, October I924, p. 256, and April I926, p, 85, for presentation of the case for the deflation of debits in order to measure physical volumes of business. 2 See this REVIEW, April 1926, p. 66.

STUDIES that have been made of land sales by the national government in the pre-Civil War period -among others those of Donaldson, Treat, and most recently Hibbard have presented the general course of the movement. Such statistics as these writers have advanced indicate that there were three occasions when the volume of sales reached particularly great heights. These occasions were the years preceding the crises of I8I9, I837, and I857. At these several times, speculation was rampant and the rush of purchasers to the local governmental agencies was so great that feverish activity of any sort came thereafter to be commonly described as doing a land-office business. But these accounts of land sales fail in several respects to give as full a picture of this important phenomenon as could be wished. Based on annual data, they do not show the timing of the speculative movements with a closeness desirable for the study of business cycles. As the course of commodity prices and other statistical series has been exhibited, or will shortly be exhibited, upon a monthly basis, there is reason for wishing the course of this speculative series of land sales to be available upon at least a quarterly basis.2 Secondly, since previous studies have presented data only for the country as a whole, little is definitely known as to the course of sales in the several sections of the country, especially as to the particular areas in the nation most affected at the different periods of speculative buying. Fortunately there exists in the records of the General Land Office material which makes possible a thorough study. The books of this Office give data by quarterly periods of the moneys received and deposited in the Treasury by the numerous local land offices, as shown by accounts submitted by such periods to the General Land Office in Washington. These data extend as far back as i8oi, but before i8i6 they are not full enough for our purpose except for particular areas since the reports do not become regular by quarters until this later date. However, covering the 45-year interval i8i6-6o, they embrace the occasions of the chief speculative activities, as far as land sales are concerned, and, indeed, the important periods of general speculative activity in the decades before the Civil War. Moreover, these financial items can be supplemented and tested by statistics of the quantity of land sold appearing in the annual reports of the Commissioner. These data also apply to the several land offices and are presented first I820 to i845 as single annual data, but later after i845 by half-yearly periods. By means of these two sets of figures, one can ascertain not only the significance in money terms of total land sales by the relatively short periods of quarter-years, but also receipts by each land office for similarly brief periods and the acreage sold office by office each year or half-year. For the interpretation of cyclical movements in the sale of public lands and for the determination of the sectional variation in these sales, such detailed statistics are invaluable. In the analysis here made of the new data, some simplification of the material has been thought advantageous, and this has been accomplished by grouping together the statistics relating to the land offices located in each of the several states, and by employing only the summations of moneys received or acreage sold in each group of offices for the various time periods. Since the boundaries of land districts (over each of which a single land office had control) usually did not extend over state lines, this method of operation serves merely to divide the country