¹ This paper was presented at the annual meeting of the Canadian Political Science Association in Ottawa, June 15, 1957. It is based on research supported by the Skelton-Clark Foundation at Queen's University and by the Institute for Economic Research, Queen's University. Valuable advice and criticism were obtained from A. W. Beckett, E. J. Chambers, D. J. Daly, F. A. Knox, D. W. Slater, M. C. Urquhart, and members of the staff of the Royal Commission on Canada's Economic Prospects.

² Report of the Royal Commission on Dominion-Provincial Relations (Ottawa, 1940), Book I, 125–6.Google Scholar

³ Ibid.

⁴ “The Effects on Canada of Industrial Fluctuations in the United States,” this Journal, V, no. 3, 08, 1939, 373–86.Google Scholar

⁵ Ibid., 384.

⁶ Ibid., 386.

⁷ See, for example, Walton, E. A., “The Vulnerability of the Canadian Economy,” this Journal, XX, no. 1, 08, 1954, 10–18.Google Scholar

⁸ Canadian Bank of Commerce, Commercial Letter, 01, 1957, 7, col. 1.Google Scholar

⁹ In the economist's sense of a ratio of percentage changes.

¹⁰ The elasticity of total output with respect to exports is equal to the export multiplier, multiplied by the ratio of exports to total output.

¹¹ Exports and imports need not, of course, be equal at any given time. But if, over a period of time, a high proportion of domestic resources is devoted to exports, there must be a good many domestic demands that can only be met by imports.

¹² Taylor, K. W. and Michell, H., Statistical Contributions to Canadian Economic History, II (Toronto, 1931), 4.Google Scholar It might be argued that my interpretation reads more into Taylor's statement than he intended. In any case, however, there appears to be little doubt that the point is a valid one.

¹³ This sentence is based on conversations with D. J. Daly, A. W. Beckett, S. S. Reisman, and others. They are not, of course, responsible for the interpretation I have placed on their comments.

¹⁴ I am indebted to Mr. D. W. Slater for suggesting this point.

¹⁵ In the Great Depression of the 1930's, income from wheat farming appears to have fluctuated more, relatively, than income from manufacturing, and this relation strongly influenced the thinking of the Rowell-Sirois Commission. But on the average, over a number of business cycles, income from wheat probably fluctuated less than income from manufacturing. See Mitchell, W. C., What Happens During Business Cycles (New York, 1951), Table 42.Google Scholar

¹⁶ See Appendix A.

¹⁷ Mitchell, , What Happens During Business Cycles, 6.Google Scholar

¹⁸ Mitchell and his associates rejected the use of a single aggregative series for the dating of business cycles because “We could find no series … that summarized the cyclical fluctuations of its economy in a way we could trust over the periods we wished to cover. While the concept of general business activity is fuzzy, it has the advantage of adaptability to differences in the composition of national economies and to changes in composition that occur in each of them.” (Ibid., 12.) When they found it necessary to measure the amplitude of fluctuations in “general activity,” however, Mitchell and his collaborators had recourse to aggregative series. See Burns, A. F. and Mitchell, W. C., Measuring Business Cycles (New York, 1947), pp. 402–3.Google Scholar See also National Bureau of Economic Research, Thirty-Sixth Annual Report (New York, 1956), 25–6.Google Scholar

¹⁹ A description of the series and their sources is given in appendices B and C.

²⁰ See, for example, Moore, G. H., Statistical Indicators of Cyclical Revival and Recession (New York, 1950), 4, 7, 10, 11, 64 Google Scholar; Hultgren, T., American Transportation in Prosperity and Depression (New York, 1948), 1-7, 19–28 Google Scholar; Federal Reserve Bank of New York, Selected Economic Indicators (New York, 1954), 9–11.Google Scholar

²¹ The failure of Canadian manufacturing production to match the slight U.S. decline in 1939 is of course due to the earlier impact of the war in this country. The Canadian series reflecting volume of freight traffic did not rise in 1952-3 because of their high sensitivity to agricultural recession.

²² The single exception is manufacturing production after the Second World War, which shows a stronger trend of growth in the United States than in Canada.

²³ Report of the Royal Commission on Dominion-Provincial Relations, Book I, 126.

²⁴ See Burns and Mitchell, Measuring Business Cycles, chap. VI.

²⁵ Gross Revenues actually fell from 1921 to 1922.

²⁶ Net National Income actually fell by 1 per cent between 1928 and 1929. See Dominion Bureau of Statistics, National Accounts, 1926 to 1950 (Ottawa), Table 1.Google Scholar

²⁷ In Canada the G.N.P. actually does not turn down but only “slows down” in 1948-9, whereas ton-miles turn down in 1947 and carloadings in 1948. In two instances (car-loadings in 1948, and ton-miles in 1952) the Canadian downturn follows the corresponding U.S. turn by a year, owing, perhaps, to the difference in trend.

²⁸ All time series used in this study have been corrected for seasonal variation. Most of the U.S. series have been corrected by the National Bureau of Economic Research or the Federal Reserve Board and have been obtained from published sources or from the National Bureau. Most of the Canadian series have been corrected by electronic computer at the U.S. Bureau of the Census, where this work is done on a contract basis. For the most recent period some seasonally corrected Canadian series have been obtained from Mr. S. Rubinoff at the Dominion Bureau of Statistics, and some have been published in the Canadian Statistical Review. Thanks are due to Mr. Rubinoff, and to Mr. J. Shiskin at the U.S. Bureau of the Census, for their assistance. The use of the electronic computer for seasonal correction has led to a dramatic decline in the cost of this operation, with far reaching implications for the range of analytical work that can be undertaken by an individual research worker with limited means. See J. Shiskin and E. Eisenpress, “Seasonal Adjustments by Census Methods I and II,” paper presented at a meeting of the American Statistical Association and the Econometric Society, New York, Dec., 1955, revised Jan., 1956 (mimeo.). See also references given in that paper, especially the paper by Morgenstern, O. in Morgenstern, O., ed., Economic Activity Analysis (New York, 1954).Google Scholar

²⁹ Measuring Business Cycles, 56-66.

³⁰ The use of three-month averages follows the method of the National Bureau of Economic Research. (See Measuring Business Cycles, 132, but note the modifications of the procedure discussed there. These modifications have not been adopted in our study.) The measurement of amplitude, however, differs from the National Bureau's procedure. We express the difference between terminal peak or trough and initial trough or peak of a swing as a percentage of their average. The National Bureau expresses the difference as a percentage of the average standing of the series over the full cycle.

³¹ Compare the rules for matching “specific cycle” turning points with “reference dates” in Measuring Business Cycles, 116-28. Note the refinements described on pp. 120-5 which are not adopted here.

³² See Table III. Many of the contractions shown there are in the range of 3 to 10 per cent.

³³ For a general description of the f-test see any textbook on statistics. For the test applicable to the present problem, f was computed as follows: t=D÷✓R. Here D is the difference between the average deviations of two time periods and R is computed as follows: R = (S.P-D ²)÷(n-3). Here S is the sum of squares of all deviations in the regression, n is the total number of observations, and P is computed as follows: P = M-(T ²÷V). Here M is the sum of the numbers of observations in the two periods being compared, divided by their product, T is the difference between the average values of the independent variable (United States amplitude) for the two periods, and V is the sum of squares of the deviations of the values of the independent variable from their mean, for the regression as a whole. The number of degrees of freedom applicable to this test is n-3.

The significance levels indicated by this test should be treated as approximate, since the assumption that the chance variables concerned are normally distributed may not be strictly realistic. Moreover, the tests for expansions and contractions combined are probably biased, since one would expect the chance variable for a contraction to be correlated with that for an adjacent expansion. The importance of this factor can be tested by means of the deviations. For example, in the case of manufacturing production, rank correlation of the deviations for contractions with those for the succeeding expansions yields a (Spearman) correlation coefficient of 0.88, while rank correlation of the deviations for contractions with those of the succeeding contractions yields a coefficient of zero (- 0.01). The low probabilities recorded in Table VI for “all fluctuations” may reflect in part these serial correlations.

³⁴ That is, differences as large as those found would arise with a probability of less than 1 per cent if the time sequence of deviations were the result of random forces.

³⁵ The findings relating to prices, stock prices, and other series will be discussed in a later paper. The methods of analysis are similar to those used here.