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This study analyzes the important increase in the rate of profit which occurred in the United States during World War II. The gap between the predepression trend line, from 1900 to 1929, and the postwar line, from 1946 to 1989, is estimated as a shift of 15.8 percent in absolute terms (to be compared with an average of 29.0 percent over the whole period). Using a production function analysis, the authors demonstrate that this transformation can be explained by an acceleration in the rate of 'autonomous progress' between 1930 and 1945. They identify a sudden and nonneutral discontinuity in the process of technical change, characterized by an autonomous substitution of equipment for structures. Copyright 1993 by MIT Press.

THIS article will treat the logical problem of the significance of trend-cycle separation in the analysis of time series, and also the related practical problem of choosing the best secular trend representation for a particular economic series. The article will begin with a discussion of the various points of view which have been held regarding the meaning of secular trend. I. A problem in mathemcatical curve fitting. It might be urged that in establishing a representation for secular trend, closeness of fit of the curve to the data should be the criterion, and mathematical measures of "goodness of fit" might be set up, analogous to those employed for frequency series. A fundamental difficulty, however, immediately appears. In applying this principle to secular trends, we must "choose a curve which reproduces the underlying movement of the data without bending or twisting, itself so as to conform to the extreme sinuosities, and which at the same time gives a good 'fit' as judged by some arbitrary criterion say, the mean square error."' These two requirements, however, are mutually contradictory,2 and evidently exercise of arbitrary judgment is required in effecting a compromise between them. In a word, our difficulty arises from the fact that we wish to represent not the series itself, but the secular trend of the series, and we are consequently unable to place sole reliance on a mathematical test for goodness of fit. Additional criteria are required. 2. A problem in statistical description. The problem of secular trend might be thought of as a problem in statistical description. Just as we describe the essential characteristics of a fre, quency series by the citation of averages, standard deviations, and measures of skewness, so we might describe the general tendencies shown by a time series through the computation of a line of secular trend. The secular trend has in fact often been defined in some such language as the following: the gradual and persistent movement of the series over a period of time which, contrasted with the short run fluctuations of the series, is long. In fitting the trend line which is designed to furnish a statistical description of the fundamental movements of a particular time series, he decisions as to type of curve and trend interval are by no means matters of indifference. In particular, with reference to the trend interval it is patently inappropriate to combine segments from time periods which are clearly non-homogeneous as would be the case, for example, if the years 1910-22 were selected for a commodity price series. Furthermore, if intervals for trend fitting are chosen indiscriminately, the calculated line is likely to be distorted by the influence of the cyclical movements at the beginning and end of the computation period.3 It is clear, then, that .even though we may fully accept the view that the problem of secular trend is one of statistical description, we have by no means reduced the problem to a mechanical basis, nor have we done away with the necessity for careful examination of the characteristics, and in particular the economic characteristics, of the original data. With respect to the usefulness and validity of the concept of secular trend as a statistical description, there is possibility for contrary opinions. On the one hand, it may be asserted that such a statistical description can have little or no value unless the calculations are preceded by an extensive causal analysis of the forces behind the movements of the series such analysis to be obtained through a theoretical examination of the causal forces in question, or through historical investigation, or both; and still further, that in the absence of an exhaustive analysis of this sort, the determination and representation of secular movements should not be undertaken. The opposing opinion is that until such time as our knowledge regarding economic causation shall be greatly increased, there will still be room for 1Henry Schultz, Statistical Laws of Demand and Supply (Chicago, I928), p. 47. 2 " On the one hand we can obtain the curve which actually goes through the points here the sum of the squares of the errors is zero, but the curve is composed of perturbations or sinuosities. On the other hand we can obtain a perfectly smooth curve ... and we obtain a large mean square error."E. C. Rhodes, "Smoothing," Tracts for Computers, No. VI (London, I92I), pp. 43-44. 3 The commonly quoted statement to the effect. that in the fitting of a straight-line trend, the interval should "begin and end in the same cyclical phase" is inadequate. For a precise statement of the criteria, see W. L. Crum. and A. C. Patton, Economic Statistics (Chicago and New York, I925),. p. 3II .

THE course of commodity prices during World War II and the first postwar year has been generally inverse to the course of stock market prices, especially if each is considered in relation to its trend. A similar inverse relationship developed during and after World War I. The commodity price movements of i9i6-20 and I940-46 show roughly the same general pattern, and there is a general similarity between the broad movements of stock prices for the two periods. In each postwar year, i9i8-i9 and I945-46, stock prices advanced sharply, but turned down as commodity prices started rising sharply, and in each case commodity prices remained high several months after the peak in stock prices. These observations are based on the two sets of records in Charts i and 2. Chart i presents the monthly record of wholesale commodity prices from I940 to the fall of I946, and a similar record of industrial stock prices. In order to emphasize the differences in the rate of change in prices, trend lines have been drawn in. They, of course, have no particular significance beyond their aid to

IN the case of most statistical series the abnormal features of the war and early postwar years made extraordinarily difficult the calculation of a "normal" which could be projected into the future for forecasting purposes. In no other case, however, has this difficulty been so great as in the statistics of the building industry. Today, 7 years after the close of the war, we are still not only in the dark as to what the trend of the industry is likely to be during the next few years, but also equally confused, because lacking adequate standards of judgment, as to the significance of the intense activity of the recent past. In the present paper brief reference will be made to certain recent studies which have calculated or assumed a building normal for the purpose of estimating the extent to which the accumulated building shortage of the war and post-war years has been made up, and consideration will be given to the factors which will affect the building normal of the future. Most of the earlier attempts' to calculate a building "normal" followed the course of endeavoring, by the method of least squares, to fit a straight line to the data representing the annual value of building permits issued in a large number of cities over a long period of time. Because of the difficulties involved in determining a normal period of adequate length and of making allowance for the effect of changes brought about by the war, none of these studies have produced long-term trend lines which have been received with any large measure of confidence, especially for forecasting purposes. A second group of investigators have sought the elusive "normal" of the building industry by plotting building permits against population growth instead of solely against time. For instance, Mr. H. B. Byer of the United States Bureau of Labor Statistics has recently published the results of an investigation in which he assumed that " the line of population increase is the normal line of construction increase. "2 The validity of this assumption is to be considered later. At the present time it is sufficient to note that his investigation resulting in the conclusion that at the end of I924 construction had not only made up for the war shortage but was actually about four-tenths ahead of current needs is subject to the obvious criticism that the author used as the basis of his calculations the value of permits issued in a single, and by no means typical year, namely, I9I4. The same general assumption that building varies directly and proportionately with population is the starting point of another investigation into the building shortage by the research staff of the National Bank of Commerce.3 Starting with the more normal year, I9I3, as the base, this study developed "a trend of building requirements" or "a line of normal growth of construction" which was based simply on the annual population of the 66 urban centers selected. Incidentally, the conclusion reached was that at the end of I924, a building shortage of over 3 billion dollars still remained. Of this same general type was the well-known study of the building shortage made by Col. L. P. Ayres, in I922.4 His "normal" was found by fitting a line, by the method of least squares, to the data representing the annual value of building permits per capita of population for 50 cities for the period I900 to I9I6. It therefore assumed that building operations varied directly with population. The period chosen, moreover, was subject to the criticism that it began with a year of abnormally low activity and ended with one of fairly high activity. To the present writer the underlying assumption of this second type of investigation does

trade around the rising line of trend determined from the annual indexes. Crop production, Curve II, likewise advanced during the interval, but at a slower pace than industrial production and trade. Industrial and agricultural production combined, Curve III, follows the year-toyear fluctuations as well as the trend of industrial production and trade more closely than those of agricultural production. This is a result of the greater weight given to industry and trade than to agriculture because of the relatively greater importance of the former in our economic life. The percentage increases of the ordinates of the trend lines for I932, as compared with I899, for each of the three groups shown in Chart i are: (I) industrial production and trade, I 76 per cent; (II) crop production, 48 per cent; and (III) these combined, I32 per cent. The three years, I930-32, record a decline in physical production far exceeding that of any other period in the interval covered. Using the annual figures, the decline from I929 to I932 in the combined index is fully 4o per cent, as compared with a drop of less than I7 per cent from I920 to I92I, and ii per cent from I906 to I908. In other words, the most recent depression may be described as a major economic decline followed directly by another equally severe collapse. The, index of industrial production and trade, here presented, is constructed from series representing six major industrial groups: manufacture, wholesale and retail trade, railroad freight traffic, building construction, mining, and electric power production. Each of these series is presented in Chart 2 (next page), on a ratio scale in order to bring out rates of growth. Among the major groups, electric power production expanded most rapidly, while the volume of manufacture, wholesale and retail trade, railroad freight traffic, and mining grew more gradually. Building construction, on the other hand, exhibits no clearly defined trend, either upward or d wnward. We may rema k, however, that the index of building construction is based on estimates of the value of construction deflated by an index of building costs and the figures are less dependable, previous to I919, than those for any other series included in the present study. In fact, it is impossible to say, on the basis of available data for building construction, what the long time trend of construction actually was. The series is included, nevertheless, because reliable figures are available for I919 and after. Just as the industrial groups represented by the six constituents display divergent rates of growth of physical output, so their relative economic importance, measured in dollars, varies widely during the period covered by the index. 1 The index for total crops (agriculture) is that of Warren and Pearson, Prices, pp. 44-45. Although live stock is not included, feed crops as well as food and other crops are included, and the index measures agricultural production relative to the base period.

QNLY a few statistical series measuring the volume of business are available for a long enough period to make possible satisfactory comparisons of a considerable number of past cycles with the present. Monthly (or at least quarterly) figures are necessary, and most of the prewar statistics relating to business volumes are on an annual basis. For the measurement of physical volumes, a satisfactory series for pigiron output has been developed by Professor Warren M. Persons, going back as far as I877 in quarterly form, and to I884 in monthly form.' For the measurement of dollar volumes there is the series for bank clearings in seven selected cities outside New York City compiled by Doctor Edwin Frickey, and published in this REvIEw for May and August I930. These figures go back, on a monthly basis, to i875. For the postwar period, bank debits of certain selected cities (again excluding New York, and also certain other cities especially affected by speculative transactions) are used to measure the dollar volume of business. Fluctuations in bank debits paralleled very closely those in the clearing figures for the post-war years, and the differences between the two series are probably less than the inaccuracies unavoidable in comparisons of such series over a long interval of time. This discussion will give chief attention to the clearings or debits figures. Such statistics are, of course, only one way of measuring fluctuations in business activity; but they have the advantage of covering a great variety of payments and are expressed in dollars, in which we are accustomed to reckon business transactions. On the following page, there is presented a chart of the adjusted figures for clearings or debits during periods of business decline and recovery.2 The low points of the indexes have been plotted on the middle line of the chart; when more than one low point appears, the last low point falls on the middle line. The period of d cline (except for I875-79) is from the last significant high point of the preceding period of activity to the low point; the period of recovery, from the low point to normal (in most instances). In i888, and again in I89I, when the fluctuations were mostly or entirely above normal, six months of recovery are shown. In I895, normal wa not reached, though closely approached, on the recovery. The pre-war figures are corrected for trend (as well as seasonal movements). Consideration is now being given to the determination of a trend line (or normal) for the past few years. Until such a normal has been satisfactorily ascertained, it is necessary to show I929-30 without correction for trend. The years I92-22 are likewise shown without such correction. The application of trends would tend to increase the amount of declines, and decrease the amount of advances; but over the short periods for which the figures are shown, such periods embracing wide fluctuations, the correction for trend would form a small proportion of the actual movement. For the I922 recovery, the final point is approximately at normal. The curve for debits in I929-30 is placed on the chart to facilitate comparison with the two declines which appear to resemble its movement most closely those of I920-2I and I883-84. The high point is placed on a level with that shown for I883, and twenty months (the duration of the I920-2I decline) from the middle line. This placing of the curve is not to be regarded as an expression of opinion as to the precise extent of possible further decline, or the exact length of time until the curve turns up. The twenty-month interval is the longest shown on the chart except that of the late seventies, which is not regarded as comparable because of the peculiar movement of the clearing figures in these years, attributable at least in part to the