Stabilization, birth waves, and the surge in the elderly*

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Abstract
Substantial regularities characterize the transition to stability that follows a shift from one set of vital rates to another. The new vital, rates interact with the population's initial age composition and generate birth waves whose amplitude and attenuation depend on the ratio of ultimate to initial growth and on the new pattern of stable net maternity. A greater change in growth and a later stable net maternity pattern produce larger fluctuations in the number of births. Stabilization begins at the youngest ages and proceeds upward. Sixty years after the shift, the birth waves have largely disappeared and the proportion under age 15 approximates the stable level implied by the new rates. Those patterns are manifest in the stabilization of both observed and Coale‐Demeny model stable populations. When fertility falls, the new stable population has a larger fraction at all ages above (approximately) 30, with greater changes characterizing the extremes of life. Fifteen years after the fall, there is a trough in the number at ages 0–14. Sixty years after the fall, when the largest pre‐decline cohort is age 60–74 and the smallest post‐decline cohort is age 45–59, there is a surge in the relative size of the elderly population. Thus after two generations, the birth waves produced by a rapid decline in fertility accentuate the effects of population aging.

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