In preparing this study the author received significant research assistance from Richard H. Keehn. Comments on an earlier version of the study by Moses Abramovitz, W. D. Borne, Jack Dowie, R. A. Easterlin, Duane T. Kexel, Simon Kuznets, Peter Lindert, N. B. Ryder, and Jeffrey G. Williamson were also most helpful. An earlier version of this study was presented at the Fourth Congress of the International Economic History Association, Bloomington, Indiana, September 1968

¹ Controversy exists over the exact length of the business cycle. See Matthews, R. C. O., The Trade Cycle (Cambridge, [Eng.]: The University Press, 1959), ch. 12Google Scholar.

² For an excellent review of the Kondratieff cycle literature, consult Garvy, George, “Kondratieff's Theory of Long Cycles,” The Review of Economics and Statistics, XXV (Nov. 1942), 203–20Google Scholar.

³ Professor Kuznets describes long swings as follows: “By long swings we mean up and down movements extending over periods substantially longer than those associated with business cycles (i.e., four to eleven years). But these periods must be sufficiently brief so that these swings can be detached in series extending over secular stretches observable in social data—at most over a century and a half to two centuries. It follows that the duration of the swings so defined is limited to a range from over a decade to not much longer than a half a century.” Kuznets, Simon, “Long Secular Swings in the Growth of Population and in Related Economic Variables,” Proceedings of the American Philosophical Society, CII (Feb. 1958), 25Google Scholar.

⁴ An extensive bibliography of the long swing literature has been compiled by Easterlin, Richard A., “Economic-Demographic Interactions and Long Swings in Economic Growth,” American Economic Review, LVI (Dec. 1966), 1100–4Google Scholar.

⁵ Kuznets, Simon, Capital in the American Economy (Cambridge: Harvard University Press, 1961), ch. 7Google Scholar.

⁶ Abramovitz, Moses, “The Nature and Significance of Kuznets Cycles,” Economic Development and Cultural Change, IX (Apr. 1961), 225–48CrossRefGoogle Scholar.

⁷ Easterlin, “Economic-Demographic Interactions.”

⁸ For a particularly skeptical view of the “cycle” interpretation of the long swing, consult Adelman, Irma, “Long Swings—Fact or Artifact?,” American Economic Review, LV (June 1965), 444–63Google Scholar.

⁹ Losch, A., “Population Cycles as a Cause of Business Cycles,” Quarterly Journal of Economics, LI (Aug. 1937), 649–62CrossRefGoogle Scholar. See also Hall, A. R., “Some Long Period Effects of the Kinked Age Distribution of the Population of Australia 1861–1961,” The Economic Record, XXXIX (Apr. 1963), 43–52CrossRefGoogle Scholar.

¹⁰ The use of the term “self-generating” does not refer to amplitude considerations (i.e., whether the amplitude increases, decreases, or is constant over time); rather, it refers to an explanation of the turning points of cycles.

¹¹ Easterlin, “Economic-Demographic Interactions,” p. 1086.

¹² Ibid., pp. 1086–92.

¹³ A question may arise regarding the somewhat longer cycles implied by the model developed here when they are compared to the durations of long swings identified by Kuznets, Abramovitz, Easterlin, and others. Two points should be made. First, the concept of the cycles in this study is wholly consistent with Kuznets' and other researchers' boundaries of major waves denoted as long swings. Second, the distinction between “long swings” and “other” major cycles should, lie not in a single statistic summarizing their character but rather in their theoretical bases. Since a comprehensive model of the long swing has not yet been developed, a debate on cycle length cannot be resolved at this stage of the research.

¹⁴ Even though the male participation rate reaches its peak in the 35 to 50 cohort, the peak in the total labor force rate occurs sooner since the female rate reaches a maximum much earlier. The pattern of labor force participation rates depicted in Chart 1 was derived from the male and female rates for “semi-industrialized” countries, as compiled by the United Nations, Demographic Aspects of Manpower, Report I, Population Studies No. 33 (New York, 1962)Google Scholar.

¹⁵ For a detailed discussion of headship rates, together with an analysis of their role in residential demand in the United States, consult Campbell, Burnham O., The Housing Cycle and Long Swings in Residential Construction: A Statistical and Theoretical Analysis (unpublished Ph.D. dissertation, Stanford University, 1961)Google Scholar.

¹⁶ The rates shown in Chart 1 reflect those found for the United States by Campbell. Ibid., p. 407.

¹⁷ Ibid.

¹⁸ Optimal saving decisions rely on maximization of utility by appropriate discounting of expected future income and assets bequeathed, employing standard marginal equations. While the Modigliani-Brumberg formulation utilizes the assumption that the individual strives to maintain a constant standard of living over his lifetime, plausible modifications of this hypothesis which conform to age-specific, empirically determined consumption patterns would not alter the basic average savings pattern described in Chart 1.

The savings rates in Chart 1 are calculated from Australian age-specific earnings profiles using the assumptions outlined in the text. For a detailed discussion of the estimates, together with a review of the theoretical literature, consult Kelley, Allen C., “Demographic Change and Economic Growth: Australia, 1861–1911,” Explorations in Entrepreneurial History, V (Spring/Summer 1968), 256–60Google Scholar.

¹⁹ The demographic model producing the annual age-specific estimates of the Australian population is found in ibid., pp. 215–25.

²⁰ Ibid., pp. 228–46. Two individual sets of projected additions to the potential labor force were generated: the labor force inclusive and the labor force exclusive of all distributional changes. Each series was based on a pattern of age-specific labor force participation rates relevant to Australia during the period.

In computing the labor force series exclusive of changes in the age distribution, we used the age profile prevailing in 1881 and applied it to each year from 1861 to 1911. Experimentation with alternative age profiles did not provide results which differed significantly from those found using the 1881 series. The difference between the two labor force series represents additions to the labor force due entirely to shifts in the age distribution of the population.

An analogous calculation was made for changes in residential construction demand. Finally, for average household savings we experimented with a simplified version of the Modigliani-Brumberg model which uses information on Australian age-specific earnings profiles to generate a hypothetical average savings pattern for the economy as a whole.

The aggregate average savings ratio, APS(t), can be taken as the sum of age-specific savings ratios, S_x(t)/Y_x(t), each weighted by the proportion of total income earned at age x in year t, Y_x (t)/Y(t). Thus,

. This may be rewritten as

where,

APS_x(base year) is an age-specific average savings ratio for a base year;

P_x(base year) is the average labor productivity by age of the employed workforce in the base year;

and

WF_x(t) is the workforce of age x in year t.

Thus, for any time t, and any age distribution of the workforce WF_x(t), the aggregate savings ratio will be determined by the equation.

As a separate experiment we employed empirically determined life-cycle household savings rates to isolate the impact of age compositional changes on average savings. This measure is similar to that used to analyze labor force additions and residential demand. Both the Modigliani-Brumberg approach and the empirically determined rates produced similar aggregate savings patterns.

²¹ For example, if average household savings were 10 percent, a 40 percent variation would correspond to a range of 6 to 14 percent.

The experiments with the life-cycle model yielded savings with much greater cyclical amplitude than did the experiments using empirically determined savings rates. Since the savings data were available only in very wide cohorts, the resulting series contained considerable implicit smoothing. The savings rates in Chart 3 are thus likely to represent an understatement of the amplitude of the swings.

²² Kuznets places considerable emphasis on the role of long swings in “population sensitive” capital formation. His definition of the “population sensitive” components includes, among other items, investment-in railroads.

²³ Swings in the demand for education facilities lag behind those of residential construction by approximately one generation.

²⁴ “Other domestic saving” includes saving in the commercial, manufacturing, and agricultural sectors.

²⁵ It should be noted that the business and commercial sector may be subject to its own life cycle through the impact of replacement demand on investment and output.

²⁶ Kelley, Allen C., “International Migration and Economic Growth: Australia, 1865–1935,” The Journal Of Economic History, XXV (Sept 1965), 333–54CrossRefGoogle Scholar.

²⁷ A biobliography of data sources, prepared as an appendix, is available from the author upon request.

²⁸ Our observations for the United States apply to the period after 1870, since quinquennial population data were not available before this date. The impact of the heavy migration of the 1840's on the age structure of the population may have been partially offset by Civil War losses.

²⁹ Richard H. Keehn has identified “demographic shocks” due to migration’ in many of the newly settled states after 1850. He is also studying the speed with which the population approaches a “normal” age and sex distribution.

³⁰ Additionally, the Boer War had a major impact on the flow of migrants to South Africa.

³¹ Long swings in Canada before the turn of the century have been identified by Daly, D. J., “Kuznets Cycles in Canada,” a paper presented to the Canadian Political Science Association, March 13, 1962 (mimeographed), p. 16Google Scholar. The timing of the swings was quite similar to that found by Abramovitz for the United States. The major exception appears at the turn of the century when, as noted above, the role of demographic change may have entered more prominently into the Canadian long swing.

³² Taiwan represents another case of migration similar in many respects to the Israeli case. Unfortunately, data constraints preclude a quantitative examination of the impact of migration on Nationalist China.

³³ Furthermore, as Easterlin notes, the demographic pattern established by the postwar baby boom may emerge as an important influence on future secular variations of American economic performance.

³⁴ A model in which age-specific factors, births, and migration are endogenous is currently being developed by the author.