James W. Vaupel
Vladimir Canudas-Romo

http://www.demographic-research.org/volumes/vol7/1/

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Abstract
We present and prove a formula for decomposing change in a population average into two components. One component captures the effect of direct change in the characteristic of interest, and the other captures the effect of compositional change. The decomposition is applied to time derivatives of averages over age and over subpopulations. Examples include decomposition of the change over time in the average age at childbearing and in the general fertility rate for China, Denmark and Mexico. A decomposition of the change over time in the crude death rate in Denmark, Germany and the Netherlands is also presented. Other examples concern global life expectancy and the growth rate of the population of the world.

Author's affiliation
James W. Vaupel
Max Planck Institute for Demographic Research, Germany
Vladimir Canudas-Romo
Johns Hopkins University, United States of America

Keywords
components of change, decomposition, derivatives of averages, formal demography

Word count (Main text)
2296

Other Articles by the same author/authors (in Demographic Research)

	[19-35] An integrated approach to cause-of-death analysis: cause-deleted life tables and decompositions of life expectancy
	[19-30] The modal age at death and the shifting mortality hypothesis
	[14-7] The relative tail of longevity and the mean remaining lifetime
	[13-24] Lifesaving, lifetimes and lifetables
	[13-5] Changing mortality and average cohort life expectancy
	[13-3] Age-specific contributions to changes in the period and cohort life expectancy
	[8-7] Oldest Old Mortality in China
	[7-8] Life Expectancy at Current Rates vs. Current Conditions: A Reflexion Stimulated by Bongaarts and Feeney’s "How Long Do We Live?"
	[6-5] Dr. Väinö Kannisto: A Reflexion

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