The Formal Demography of Populations with Declining Fertility

Gustav Feichtinger , Vienna Institute of Demography, Austrian Academy of Sciences
Roland Rau, University of Rostock
Andreas Novak, University of Vienna
Stefan Wrzaczek, International Institute for Applies Systems Analysis
Thomas Fent, Vienna Institute of Demography

The global fall in fertility led to concerns about its consequences such as population decline and changing age structures. Early results obtained by Coale (1972) who studied populations with fertility that declines steadily at a constant rate in a manner roughly analogous to stable population theory have been extended and used to analyse important issues as the demographic dividend and the momentum. Keyfitz (1971) derived his famous formula for the demographic momentum of a stable population - that is, the amount of further population growth (decline) if an instantaneous reduction (increase) of fertility to the replacement level occurred in a stable population. It turns out that the momentum of pseudostable populations is a monotonously declining S-shaped function approaching zero with increasing time. Maximum momentum converges to a theoretical upper limit defined by the ratio of life expectancy at birth and the mean age at child-bearing. We prove that the timing, when the momentum is one occurs when the net reproductive rate is already smaller than one – unlike in stable populations. The only way to cope with 'depopulation' is to increase fertility over time. While a fast increase leads to fluctuating age compositions, any delay of an increase in birth rates implies a further population decline. The appropriate population policy tool is provided by an intertemporal optimisation approach balancing between these two opposite targets with fertility as control variable.

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 Presented in Session P8. Demographic Trends, History, Data and Methods