Volume 49 - Article 37 | Pages 1021–1062  

Analyzing hyperstable population models

By Robert Schoen


Objective: Few methods are available for analyzing populations with changing rates. Here hyperstable models are presented and substantially extended to facilitate such analyses.

Methods: Hyperstable models, where a known birth trajectory yields a consistent set of age-specific birth rates, are set out in both discrete and continuous form. Mathematical analysis is used to find new relationships between model functions for a range of birth trajectories.

Results: Hyperstable population projection matrices can create bridges that project any given initial population to any given ending population. New, explicit relationships are found between period and cohort births for exponential, polynomial, and sinusoidal birth trajectories. In quadratic and cubic models, the number of cohort births equals the number of period births a generation later, with a modest adjustment. In sinusoidal models, cohort births equal the number of period births a generation later, modified by a factor related to cycle length.

Contribution: Because of their adaptability, structure, and internal relationships, hyperstable birth models afford a valuable platform for analyzing populations with changing fertility. The new relationships found provide insight into dynamic models and period–cohort connections and offer useful applications to analysts.

Author's Affiliation

Other articles by the same author/authors in Demographic Research

A dynamic birth-death model via Intrinsic Linkage
Volume 28 - Article 35

Age-specific growth, reproductive values, and intrinsic r
Volume 24 - Article 33

The metastable birth trajectory
Volume 21 - Article 25

A behaviorally-based approach to measuring inequality
Volume 19 - Article 49

Changing mortality and average cohort life expectancy
Volume 13 - Article 5

Age-specific contributions to changes in the period and cohort life expectancy
Volume 13 - Article 3

Intrinsically dynamic population models
Volume 12 - Article 3

A diminishing population whose every cohort more than replaces itself
Volume 9 - Article 6

Estimating multistate transition rates from population distributions
Volume 9 - Article 1

On the Impact of Spatial Momentum
Volume 6 - Article 3

Toward a General Model for Populations with Changing Rates
Volume 4 - Article 6

Most recent similar articles in Demographic Research

The big decline: Lowest-low fertility in Uruguay (2016–2021)
Volume 50 - Article 16    | Keywords: adolescent fertility, birth order, fertility, Latin America, ultra-low fertility, Uruguay

Cohort fertility of immigrants to Israel from the former Soviet Union
Volume 50 - Article 13    | Keywords: age at first birth, assimilation, cohort analysis, fertility, immigration, parity, religiosity

Fertility decline, changes in age structure, and the potential for demographic dividends: A global analysis
Volume 50 - Article 9    | Keywords: age structure, demographic dividend, demographic transition, fertility, migration, population momentum, working-age population

Ultra-Orthodox fertility and marriage in the United States: Evidence from the American Community Survey
Volume 49 - Article 29    | Keywords: age at first marriage, American Community Survey (ACS), fertility, Judaism, marriage, religion, total fertility rate (TFR), Ultra-Orthodox Judaism

Variable-r in sex ratios: Formulas in honor of Jim Vaupel
Volume 49 - Article 26    | Keywords: cohort analysis, growth rate, sex ratio, variable-r method

Cited References: 19

Download to Citation Manager


Google Scholar

Article ID