in Spanish America. Doubtless we might carry our observations further back in most of the seventeen countries which we have studied. But after we had pushed our investigations everywhere into the twilight zone where business cycles are doubtfully recognizable, we should still be dealing with relatively small numbers. The observations are not all independent of each other. We shall see presently that the duration of business cycles in every country influences, and is influenced by, the duration of business cycles in other countries. Moreover, the non-business factors which affect the duration of business cycles often produce uniform results in several countries. To cite one example: 7 of our 17 countries had a two-year cycle at the end of the World War. One hundred and sixty-six observations, many of which come in clusters, are likely to show a less regular distribution around their central tendency than would 166 observations strictly independent of each other. If we wish to find out what we can about the probable duration of future business cycles, we should discard observations upon cycles. whose duration has been determined by factors of a kind not likely to be influential in the future. If the data for any country show CHART III (Continued). Approximate Duration of Business Cycles, arranged in Chronological Sequence. White inset figures indicate approximate duration in years. unequivocal evidence of a change in the length of cycles, the later data are likely to be a safer guide to expectations than the earlier data, or the full array. But we have no warrant for discarding cases in which cycles seem to have been cut short or prolonged by wars, civil disorders, exceptional harvest conditions, or any other factor, unless we believe that such "disturbing circumstances" will not recur in the future as in the past. Even the man who has supposed that business cycles "tend" to have some standard period will probably conclude upon studying the present charts that he had better take the data as they come. In fine, our observations form a fairly satisfactory basis for studying the duration of business cycles. Like all observations, their accuracy is open to question; but they have been made with care and their number is sufficient to allow errors to offset each other in some measure. We should be glad to have a larger sample; but the present one constitutes an appreciable fraction of its "universe." We need not reject any of the observations on the ground that the duration of certain cycles has been affected by "disturbing circumstances"; for we are interested in actual cycles in the actual world where "disturbing circumstances" are always present. We might expect a more regular distribution if all our observations were strictly independent of each other. But once again, as the world is constituted, inter-dependence in duration is characteristic of business cycles in different countries. A complete array of measurements for all past cycles would resemble our sample in this respect, and future cycles seem likely to show increasing interdependence in duration. Perhaps we should conceive of our distributions as made from a number of independent measurements smaller than the nominal count, but with the use of "weights" which total 166. Many cycles are weighted by one, while other cycles, which began and ended on the same dates in countries with close business relations, or dominated by the same non-business factors, are weighted by numbers running as high as seven. To put our data in shape for analysis, we must disregard the chronological sequence of cycles of varying length, shown in Chart III, and rearrange all the cases in frequency tables of the sort already given for American and English cycles-tables which show the number of cycles of each recorded duration. That step is taken in Table 4. But the tabulations by separate countries have slight significance, except for England and the United States, because the number of cases is small (5-15 cycles). Hence Table 5 is made from Table 4, by combining the observations from single countries into various groups. To facilitate comparisons among the two dozen distributions here shown, all the samples are put in percentages. Chart IV is a graphic form of these percentage distributions. TABLE 4 FREQUENCY DISTRIBUTION OF BUSINESS CYCLES ACCORDING TO DURATION IN YEARS Data from Seventeen Countries. Various Dates to 1925. Based upon Tables 1, 2 and 3. Ger- Austria Italy Nether- Sweden Russia Duration England France in Years 1793- 1838 1920 1920 1848- 1866- 1888- 1891- 1892- 18911925 1922 1920 1920 1920 1925 " 4 i 10 11 :1212 United Canada Aus- South Argen- Brazil India Japan China 1 Total number 32 Average dura tion in years 4.0 2 .. 6 5.2 |