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  • Title: A model of numbers of births in three countries, with persistent forty-year cycles.
    Author: Marshall AM.
    Journal: Math Popul Stud; 1995; 5(2):171-82, 183. PubMed ID: 12290054.
    Abstract:
    This paper describes a model which relates fertility to partner availability, an aspect of relative cohort size. Partner availability is affected by the tendency for males to reproduce at a later age than females. For women born at a time of rising birth rates, there is a shortage of slightly older men as potential partners. Women born when birthrates are falling enjoy a surplus of older men from which to choose. This model is believed to be the first non-linear demographic feedback model involving feedbacks through marriage squeezes in which empirically estimated values of the parameters imply persistent limit cycles. The deterministic model makes births in each five-year period a function of births in previous five-year periods. The form of the function is chosen to model the effect of partner availability upon entry into reproductive relationships, and therefore on age-specific fertility. Marriage rates are not modeled directly. The model was developed from data for more than a century from England and Wales, New Zealand, and the US. The demographic transition is modeled with a logistic function and age-specific fertility rates are estimated using lognormal distributions. The stepwise inclusion of a partner availability estimate in the model showed that it accounts for 29% of otherwise unexplained variance. Projected future births stabilize in sustained or limit cycles with periods a little longer than 40 years, and amplitudes of at least 7% of the mean. The necessary conditions for cycle persistence are outlined on a graph of maximum and minimum fertility parameters.
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