Intrinsically dynamic population models

Robert Schoen
Additional contact information
Robert Schoen: Pennsylvania State University

Demographic Research, 2005, vol. 12, issue 3, 51-76

Abstract: Intrinsically dynamic models (IDMs) depict populations whose cumulative growth rate over a number of intervals equals the product of the long term growth rates (that is the dominant roots or dominant eigenvalues) associated with each of those intervals. Here the focus is on the birth trajectory produced by a sequence of population projection (Leslie) matrices. The elements of a Leslie matrix are represented as straightforward functions of the roots of the matrix, and new relationships are presented linking the roots of a matrix to its Net Reproduction Rate and stable mean age of childbearing. Incorporating mortality changes in the rates of reproduction yields an IDM when the subordinate roots are held constant over time. In IDMs, the birth trajectory generated by any specified sequence of Leslie matrices can be found analytically. In the Leslie model with 15 year age groups, the constant subordinate root assumption leads to reasonable changes in the age pattern of fertility, and equations (27) and (30) provide the population size and structure that result from changing levels of net reproduction. IDMs generalize the fixed rate stable population model. They can characterize any observed population, and can provide new insights into dynamic demographic behavior, including the momentum associated with gradual or irregular paths to zero growth.

Keywords: dynamic models; population momentum; dynamic population models; eigenvalues; Leslie matrices (search for similar items in EconPapers)
JEL-codes: J1 Z0 (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.demographic-research.org/volumes/vol12/3/12-3.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:dem:demres:v:12:y:2005:i:3

DOI: 10.4054/DemRes.2005.12.3

Access Statistics for this article

More articles in Demographic Research from Max Planck Institute for Demographic Research, Rostock, Germany
Bibliographic data for series maintained by Editorial Office ().