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Covariances, Roots, and the Dynamics of Age-Specific Growth

Robert Schoen and Young J. Kim
Population Index
Vol. 58, No. 1 (Spring, 1992), pp. 4-17
DOI: 10.2307/3643798
Stable URL: http://www.jstor.org/stable/3643798
Page Count: 15
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Covariances, Roots, and the Dynamics of Age-Specific Growth
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Abstract

Regularities in age-specific growth rates are explored over age and time, with regard to age-aggregated summary measures and with respect to the spectral decomposition of a population. Using a new approach to the differentiation of population functions, changes in many crude rates are shown to reflect the covariance between age patterns of demographic behavior and age-specific growth. For example, the marginal change in the crude birth rate is simply the covariance between the age-specific schedules of fertility and growth, indicating that the birth rate increases to the extent that ages with higher fertility experience greater growth. Age-specific growth is an important demographic variable because of its ability to relate observed changes to mathematical models of population dynamics.

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