The authors extend thanks to Professor Barry Poulson both for introducing us to a study of Kuznets cycles and for reading the manuscript and giving some helpful suggestions. However, all results are solely the responsibility of the authors.

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³ Thomas, Brinley, Migration and Economic Growth (Cambridge: The University Press, 1954).Google ScholarCairncross, Alexander K., Home and Foreign Investment, 1870–1913 (Cambridge: The University Press, 1953)Google Scholar; Isard, Walter, “A Neglected Cycle: The Transport-Building Cycle,” Review of Economic Statistics, XXIV, No. 4 (Nov. 1942), 149–58CrossRefGoogle Scholar; Kuznets, Simon, “Quantitative Aspects of the Economic Growth of Nations: I. The Levels and Variability of Rates of Growth,” Economic Development and Cultural Change, V (Oct. 1956), 44–51.Google Scholar A recent study concentrating on the identification of demographic cycles in the age distribution of different countries and their effects on various economic time series is given by Kelley, Allen C., “Demographic Cycles and Economic Growth: The Long Swing Reconsidered,” The Journal of Economic History, XXIX, No. 4 (Dec. 1969), 633–55.CrossRefGoogle Scholar

⁴ Moses Abramovitz, Statement in the United States Congress, Joint Economic Committee, Employment, Growth and Price Levels, Hearings (86th Congress, First Session), Part II (Washington: G.P.O.), 411–66.

⁵ Abramovitz, Moses, “The Nature and Significance of Kuznets Cycles,” Economic Development and Cultural Change, IX (April 1961), 225–48.CrossRefGoogle Scholar

⁶ Abramovitz, Hearings, pp. 412–14.

⁷ Kuznets, Simon, Capital in the American Economy, Its Formation and Financing, N.B.E.R. (Princeton, N.J.: Princeton University Press, 1961), ch. vii, viiiGoogle Scholar; also see Kuznets, , “Long-Swings in the Growth of Population and in Related Economic Variables,” Proceedings of the American Philosophical Society, CII, No. 1 (Feb. 1953), 25–52.Google Scholar The following N.B.E.R. Annual Reports under the Directorship of Solomon Fabricant: Richard A. Easterlin, “Long-Swings in the Growth of Population and Labor Force,” Annual Reports, 39 through 44, 1959–64; Manuel Gottlieb, “Long-Swings in Urban Building,” Annual Reports 42 and 43, 1962–63; Creamer, Daniel, Capital and Output Trends in Manufacturing Industries, 1880–1948, N.B.E.R., Occasional Paper 41, 1954Google Scholar; Ulmer, Melville J., Trends and Cycles in Capital Formation by United States Railroads, 1870–1950, N.B.E.R., Occasional Paper 43, 1954Google Scholar; Borenstein, Israel, Capital and Output Trends in Mining Industries, 1870–1948, N.B.E.R., Occasional Paper 45, 1954Google Scholar; Mintz, Ilse, American Exports During Business Cycles, 1879–1938, N.B.E.R., Occasional Paper 76, 1961Google Scholar; Abramovitz, Moses, Evidence of Long-Swings in Aggregate Construction Since the Civil War, N.B.E.R., Occasional Paper 90, 1964.Google Scholar

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¹⁰ Goldberger, Arthur S., Econometric Theory (New York: John Wiley & Sons, Inc., 1964), pp. 306–17.Google Scholar

¹¹ One illustrative example of this is the Klein-Goldberger model based primarily on Keynesian type theory. See Klein, L. R. and Goldberger, A. S., An Econometric Model of the United States, 1929–52 (Amsterdam: North-Holland Publishing Co., 1955).Google Scholar

¹² An estimating technique is currently being developed that will not only establish restrictions on the structural system (i.e. zero coefficients), but will also separate the multicolinear relations embodied in each equation of the structural system.

¹³ It is not presumed at this point that long cycles, however defined, do in fact exist. The only assumption involved in the above system is that economic changes over certain periods can be represented by a closed endogenous model. Thus, if such a self-enclosed system fails to indicate a long-swing pattern which is inherent in some of the original data series, then one can infer that long-swings in economic growth must be the result of accidental features in the course of economic history rather than any intrinsic economic mechanism, or the mathematical analytic model is not adequate to capture the phenomena.

¹⁴ Samuelson, Paul A., Foundations of Economic Analysis (New York: Atheneum Press, 1965), pp. 311–49.Google Scholar

¹⁵ Note that if the minimum lag in all equations is q then the first q predicted values of the system prediction process will be identical to those of the pointwise prediction.

¹⁶ The Janus quotient is presented in Wold, H. O. A. (ed.), Econometric Model Building (Amsterdam: North-Holland, 1964), ch. vGoogle Scholar, “The Janus Quotient: A Measure for the Accuracy of Prediction,” by A. Gadd and H. Wold, pp. 231–35. For the Theil coefficient see Theil, H., Economic Policy and Forecasts (Amsterdam: North-Holland, 1958).Google Scholar

¹⁷ Wold, Econometric Model Building, p. 235.

¹⁸ For example a regression over 41 points with 19 parameters giving an ESS of 0.0016 and an R² of 0.999985 over the E period, gave a Janus quotient of 2,380 as compared with an ESS of 1.88 and a Theil of 0.013 over an F-period of 20 years.

¹⁹ Theil, Economic Policy and Forecasts.

²⁰ The system referred to below as the “best” system, although it is chosen as the best of the alternatives examined statistically, should be considered as the best representative of a class of systems and not as an absolutely unique “best” system.

²¹ Abramovitz, Hearings, pp. 411–43.

²² Abramovitz, “The Nature and Significance of Kuznets Cycles,” p. 241.

²³ Ibid., p. 247.

²⁴ Ibid., pp. 242–43.

²⁵ Kuznets, Capital in the American Economy, pp. 316–60.

²⁶ S. Fabricant found evidence of long-swings in the productivity indices estimated by Kendrick. See Fabricant, S., Basic Facts on Productivity Change, Occasional Paper 63 (New York: N.B.E.R., 1959), pp. 37–41.Google Scholar

²⁷ Easterlin, Richard A., “Long Swings in U.S. Demographic and Economic Growth: Some Findings on the Historical Pattern,” Demography, II, 1965, 490–507.CrossRefGoogle Scholar

²⁸ Easterlin, Richard A., Population, Labor Force, and Long Swings in Economic Growth, the American Experience (New York: N.B.E.R., 1968), p. 47Google Scholar

²⁹ Ibid., pp. 42–74. The sustained downswing in economic activity is explained by similar interactions, except that decreasing rates are substituted for increasing rates.

³⁰ Fabricant, Basic Facts on Productivity Change, pp. 42–45.

³¹ Schmookler, Jacob, “The Level of Inventive Activity,” Review of Economics and Statistics, XXXVI (May 1954), 183–90.CrossRefGoogle Scholar See also Schmookler, J., “Economic Sources of Inventive Activity,” The Journal of Economic History, XXII (March 1962), 1–20.CrossRefGoogle Scholar

³² Samuelson, Paul A., “Interactions Between the Multiplier Analysis and the Principle of Acceleration,” Review of Economic Statistics, XXI, No. 2 (May 1939), 75–78.CrossRefGoogle Scholar

³³ Friedman, Milton and Schwartz, Anna J., A Monetary History of the United States, 1867–1960 (Princeton, N.J.: Princeton University Press, 1963), p. 682.Google Scholar

³⁴ Ibid., pp. 187–88; pp. 676–700.

³⁵ Abramovitz, Hearings, p. 432.

³⁶ Williamson, J. G., American Growth and the Balance of Payments, 1820–1913 (Chapel Hill, N.C.: University of North Carolina Press, 1964), pp. 89–188.Google Scholar

³⁷ Actually during the early part of the period between 1869 and 1914 the balance of payments was normally negative; thus, the upswing in the Kuznets cycle produced a progressively more pronounced negative level in the balance of payments.

³⁸ Adelman, Irma and Adelman, Frank L., “The Dynamic Properties of the Klein-Goldberger Model,” Econometrica, XXVII (Oct. 1959), 596–625CrossRefGoogle Scholar

³⁹ Yamane, Taro, Statistics, An Introductory Analysis (New York: Harper and Row, 1964), pp. 677–78.Google Scholar

⁴⁰ See Easterlin's, R. review of the Coale and Zelnik book in the Southern Economic Journal, XX, No. 2 (April 1964), 363–70.Google Scholar

⁴¹ Adelman, Irma, “Long Cycles—Fact, or Artifact?”, The American Economic Review, LX, No. 3 (June 1965), 446.Google Scholar

⁴² The series is taken from Easterlin, Population, Labor Force, and Long Swings in Economic Growth, pp. 204–09.

⁴³ The annual GNP series is taken from Kuznets, Capital in the American Economy, p. 555.

⁴⁴ The same technique was used to give an annual series of Gross Producer Durables and Cross Construction back to 1869.

⁴⁵ The crucial distinction between pointwise and systemwise prediction is defined and discussed in Section II.

⁴⁶ On the basis of the relative success of Variant VI, simple periodic lag shifts of the form (5–6–7–8) (9–10–11–12), etc., were examined for the purpose of discovering any simple periodicity of this nature. These trials were unsuccessful.

⁴⁷ One further line of investigation was to search for mixed-lag periodicities of the type (1–2–3–6–7–8), (1–2–3–4–12–13–14–15), (7–8–9–14–15–16), etc., but without acceptable results.

⁴⁸ Hacker, Louis M., The Triumph of American Capitalism (New York: Columbia University Press, 1940), ch. xxiv.Google Scholar Also see Hacker, L. M., The World of Andrew Carnegie (New York: J. B. Lippincott Co., 1968), pp. xxvii-xxxi.Google Scholar

⁴⁹ For a discussion of the socio-economic effects of the Civil War see Engerman, Stanley L., “The Economic Impact of the Civil War,” Explorations in Entrepreneurial History, III, No. 3 (Spring/Summer 1966), 176–99.Google Scholar

⁵⁰ Ibid., pp. 179 ff.

⁵¹ North, Douglass C., Growth and Welfare in the American Past (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1966), p. 26.Google Scholar

⁵² Historical Statistics of the United States, Colonial Times to 1957 (U.S. Department of Commerce, Bureau of the Census, 1961), p. 56.Google Scholar

⁵³ Easterlin, Population, Labor Force, and Long Swings in Economic Growth, pp. 60 ff.

⁵⁴ Professor Adelman generated undulations roughly similar to the long-swings observed in economic data by applying stochastic shocks to the Klein-Goldberger model. See Irma Adelman, “Lone Cycles—A Simulation Experiment,” pp. 152–81, in Hoggatt, Austin C. and Balderston, Frederick E. (eds.), Symposium on Simulation Model: Methodology and Applications to the Behavioral Sciences (Cincinnati: South-Western Publishing Co., 1963).Google Scholar

⁵⁵ Frisch, Ragnar, “Propagation Problems and Impulse Problems in Dynamic Economics,” in Readings in Business Cycles (Homewood, Illinois: Richard D. Irwin, Inc., 1965), pp. 155–85.Google Scholar

⁵⁶ Another study which closely simulates business cycles by applying stochastic shocks to the Klein-Goldberger model is Irma, and Adelman, Frank L., “The Dynamic Properties of the Klein-Goldberger Model,” Econometrica, XXVII (Oct. 1959), 596–625.Google Scholar