Volume 52 - Article 15 | Pages 445–478  

On the momentum of pseudostable populations

By Gustav Feichtinger, Roland Rau, Andreas J. Novák

Abstract

Background: Keyfitz introduced in 1971 the “population momentum” – 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.

Objective: We wanted to find analytical results for the momentum of pseudostable populations – that is, populations that relax the strict assumptions of the stable population model and allow fertility reductions at a constant rate.

Methods: The formal methods to analyze pseudostable populations are similar to those used in classical stable population theory. Numerical simulations, based on data from the United Nations’ World Population Prospects, show that the simplifying assumptions of our formal methods – rectangular survival and childbearing at a single age – do not affect the qualitative nature of our findings.

Results: The pseudostable population momentum 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 childbearing. 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.

Conclusions: Pseudostable populations describe the transition from a very young to a very old population. By deriving the population momentum for pseudostable populations, we are extending the analytical understanding of population dynamics for models that are less restrictive than the canonical stable population model.

Contribution: Some countries in Latin America experience a fertility transition that closely resembles the assumptions of pseudostable populations. Our analytical results could contribute to the understanding of population dynamics in these countries.

Author's Affiliation

• Gustav Feichtinger - Österreichische Akademie der Wissenschaften, Austria EMAIL
• Roland Rau - Universität Rostock, Germany EMAIL
• Andreas J. Novák - Universität Wien, Austria EMAIL

Other articles by the same author/authors in Demographic Research

The optimal transition to a stationary population for concentrated vitality rates
Volume 50 - Article 6

Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data
Volume 38 - Article 29

How many old people have ever lived?
Volume 36 - Article 54

Taylor's power law in human mortality
Volume 33 - Article 21

Minor gradient in mortality by education at the highest ages: An application of the Extinct-Cohort method
Volume 29 - Article 19

The reproductive value as part of the shadow price of population
Volume 24 - Article 28

Keeping a learned society young
Volume 20 - Article 22

Placing the poor while keeping the rich in their place: Separating strategies for optimally managing residential mobility and assimilation
Volume 13 - Article 1

Seasonal mortality in Denmark: the role of sex and age
Volume 9 - Article 9

Most recent similar articles in Demographic Research

Data errors in mortality estimation: Formal demographic analysis of under-registration, under-enumeration, and age misreporting
Volume 51 - Article 9    | Keywords: age misreporting, data errors, formal demography, mortality

The Average Uneven Mortality index: Building on the ‘e-dagger’ measure of lifespan inequality
Volume 50 - Article 44    | Keywords: exponential distribution, formal demography, lifespan inequality, mortality age-pattern, mortality plateau

Standardized mean age at death (MADstd): Exploring its potentials as a measure of human longevity
Volume 50 - Article 30    | Keywords: formal demography, life expectancy, mean age at death, mortality, standardization

How do populations aggregate?
Volume 44 - Article 15    | Keywords: aggregation, formal demography, harmonic mean, length-biased sampling

How many old people have ever lived?
Volume 36 - Article 54    | Keywords: elderly, formal demography, people ever lived, population aging