In this paper a method to investigate the dependence of age structure and growth rate on a given sequence of fertility and mortality schedules under the conditions of unchanging mortality and absence of migration is discussed. The method consists in projecting an arbitrary population classified by age to the ends of successive periods assuming that a given age pattern of mortality will remain without change and that a given sequence of fertility schedules will repeatedly operate on the population in a cyclical fashion. It is shown that after a sufficiently large number of repetitions of the cycle, the shifts in age structure between the ends of successive periods and the changes in the growth of the different age groups from one period to the next show a cyclical pattern. Formulas are derived expressing the above changes in terms of a sequence of k growth multipliers, k being the number of schedules in the fertility sequence, and the survival rates in the mortality schedule. A numerical illustration of the theory is given using fertility data from Finland.
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Brauer, A. 1961. On the characteristic roots of power-positive matrices. Duke Mathematical Journal 28: 291–296.
Coale, Ansley J. 1965. Birth rates, death rates, and rates of growth in human population. In M. C. Sheps and J. C. Ridley (eds.), Public Health and Population Change. Pittsburgh: University of Pittsburgh Press.
—, and P. Demeny. 1963. Regional Model Life Tables and Stable Populations. Princeton, N. J.: Princeton University Press.
—, and M. Zelnick. 1963. New Estimates of Fertility and Population in the United States. Princeton, N. J.: Princeton University Press.
Goodman, L. A. 1967. On the age-sex composition of the population that would result from given fertility and mortality conditions, Demography 4: 423–441.
Keyfitz, N. 1964. Matrix multiplication as a technique of population analysis. Milbank Memorial Fund Quarterly 42: 68–84.
— 1968. Introduction to the Mathematics of Population. Reading, Mass.: AddisonWesley Publishing Company.
Lopez, A. 1961. Problems in Stable Population Theory. Princeton, N. J.: Officeof Population Research.
Murphy, E. M. 1967.A Generalization of Stable Population Techniques. Unpublished Ph. D. dissertation. Department of Sociology, University of Chicago.
Stolnitz, G. J., and N. B. Ryder. 1949. Recent discussion of the net reproduction rate. Population Index 15: 114–128.
United Nations. 1958. Recent Trends in Fertility in Industrialized Countries. New York: United Nations.
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Namboodirl, N.K. On the dependence of age structure on asequence of mortality and fertility schedules: An exposition of a cyclical model of population change. Demography 6, 287–299 (1969). https://doi.org/10.2307/2060398
- Matrix Operator
- Successive Period
- Cyclical Model
- Model Life Table
- Fertility Schedule