CHART IV. Percentage Distribution of Business Cycles in Various Countries and Various Periods According to their Approximate Duration in Years.-(Continued)

The first six figures in the chart deal with the five countries for which we have annals covering relatively long periods. The peculiarities of the American distribution stand out clearly-the pronounced mode, almost a "spike," at three years, and the relatively slight dispersion, indicated by a standard deviation and a coefficient of variation which are respectively the lowest and next the lowest in the list. In the English distribution, there is a curious predominance of cycles lasting 2, 4, 6, 8 and 10 years over cycles lasting 3, 5, 7 and 9 years. In view of the small number of observations (only 22), it is uncertain whether this result is significant. However that may be, the irregularities in the American and English distributions compensate each other for the most part, so that Figure C is more regular than either of the arrays from which it is made.

Next, the French, German and Austrian observations are combined with the English and American. Advantage is taken of the larger number of cases to compare earlier with later cycles. By using 1873 as the dividing point, we get two groups each of which contains 47 observations. From 1873 to the end of the late war, the business fortunes of these countries, particularly of the European countries, ran more similar courses than in earlier years. That is, the observations in the later period are less independent of each other than the earlier observations-a fact which may explain the lesser regularity of Figure E as compared with Figure D. As a test of this suggestion we have made a distribution of the cycles in the four countries in our list which seem to have the closest business ties with each other for the period in which we have annals for all four. The results, shown in Figure G, constitute one of the least regular distributions in the whole twenty-four. As a companion piece we have made up a random group of similar size from observations which must be nearly independent of each other, taking English cycles in 1793-1825, American cycles in 1825-57, German cycles in 1857-90, Canadian cycles in 1888-1924, and Russian cycles in 18911925. In this comparison the 38 independent observations (Figure H) yield a much more regular distribution than the 39 observations which are inter-correlated with each other. Indeed, the contrast in regularity is more striking than we would expect from other comparisons of the sort.

There follow ten figures in which all of the observations are broken into parts on the basis of four criteria. First, the countries

are grouped according to the average duration of their business cycles as given in our annals. Figure I shows the observations from countries with relatively long cycles, Figures J and K the observations from countries with relatively short cycles (excluding and including the United States), and Figure L the observations from countries with cycles of medium length. The latter group contains part of the observations used in Figure I and part of those used in Figure J. Second, the European and non-European observations are presented separately in Figures M and N. Third, the observations from five English-speaking and twelve non-English-speaking countries are shown. Fourth, Figure Q gives all the non-American observations for comparison with the American distribution of Figure A. Figure R sums up the whole body of data.

The final section of the chart is confined to recent cycles-those occurring since about 1890. Again the data are divided into groups: observations from European and non-European countries, from industrial and non-industrial countries; from all countries except and all including the United States.

When we review the whole array of distributions, we see that the diagrams and the differences among the diagrams are of a sort common in studies of social phenomena. As usually happens in such work, the small samples, especially when they contain inter-correlated observations, are rather irregular. But with increase in the size of the samples and in the independence of the observations, the distributions grow fairly regular, though not symmetrical.

The materials appear to be homogeneous, with the important exception already noted-the distribution of American business cycles in respect to length differs from the distribution of cycles in other countries. This difference stands out most sharply in the contrast between Figures A and Q. It is responsible for the double modes, separated by a lower point, in Figures O and X, and for the relatively high coefficients of variation in most of the groups combining American and foreign observations. In the samples drawn solely from foreign countries, the diagrams usually have a rounded top quite unlike the spike of Figure A. Combining the American with foreign observations generally produces an unambiguous mode at three years, but twice (Figures O and X) it produces the double mode already spoken of.

Barring out the twelve distributions into which American observations enter does not reduce the variety in the position of the crude modes. Two of the remaining dozen figures have modes at three years (G and P); two at three and four years (M and Q); and eight at 4, 5, or 6 years, if we may include here one double mode at 5 and 7 years (Figures T). By way of generalization we can hardly be more specific than to say that two thirds of the foreign cycles are concentrated in the interval three to seven years.

All of the distributions have rather high coefficients of variation (the standard deviations expressed as percentages of the arithmetic means). In other words, the observations do not cluster closely around their averages. These coefficients are least in the two distributions confined to single countries (Figures A and B), and greatest in the distributions made from American, British, French, German and Austrian observations since 1873 (Figure E). But the difference between the lowest and highest coefficients (39 and 48 per cent) is not great, and 14 of the 24 round off at 45, 46 or 47 per cent.

All the distributions are skewed positively. The range runs farther above the arithmetic mean than below it in every case, and in every case but Figure T the range also runs farther above the crude mode than below it. Moreover, the crude mode is less than the arithmetic mean in 16 cases, about equal to it in 7 cases, and clearly higher than the mean only in Figure T. One of the most significant distributions, Figure W, which includes all cycles since about 1890 in countries other than the United States, approaches symmetry; but the very broadest groups, Figures X (all recent cycles), Q (all foreign cycles), and R (all cycles) are decidedly, though not extremely, skewed.

Before attempting to interpret these frequency distributions, it is advisable to consider the relative duration of periods of prosperity and depression in business cycles, and the bearing of long-period trends of wholesale prices upon our problem.

4. THE RELATIVE DURATION OF PROSPERITY AND DEPRESSION.

Dr. Thorp has made a special study of the annals to determine as accurately as possible how many months of the record for each country can be classed as prosperous and how many as depressed. Need

less to say, this task involved the continuous exercise of personal judgment.

As pointed out in the comparison between the annals and certain statistical indexes of business activity, contemporary observers are always influenced by recent experience in their use of the terms depression and prosperity. Hence, no rigid criterion of what constitutes business prosperity and depression can be evolved from, or read into, our sources. But that fact does not obstruct, it really facilitates, the task in hand. For we seek to compare the duration of the prosperous phase with that of the depressed phase within each cycle treated as a unit. That the prosperous phases of successive cycles in the same country and of synchronous cycles in different countries attain different degrees of intensity is a matter of deep interest, both practically and theoretically; but it is beside the present point.

Dr. Thorp's chief difficulty was that his sources seldom date the transitions from one phase of a cycle to the next phase. In trying to supply that omission in every case, he had to rely upon indications which are often faint. In detail his decisions must be subject to a wider margin of error than his measurements of the durations of whole cycles, since the recessions on which the latter measurements are based, are the phases which have attracted most attention. Hence it will be advisable to confine attention to his averages, covering several or many cycles, and to draw only broad conclusions.

Table 6 shows the form and drift of Dr. Thorp's tabulations. It

TABLE 6

RELATIVE DURATION OF DIFFERENT PHASES OF BUSINESS CYCLES IN SEVENTEEN

appears that the phases of recession and revival put together make up rather less than one-quarter of the duration of recent cycles. But in view of the difficulty of saying just when revival has blossomed into prosperity, and just when recession has merged into depression, this conclusion should not be stressed heavily. However, if these