Pollard Decomposition
Also known as: Pollard's Method, Pollard Life Expectancy Decomposition, Continuous Age Decomposition of Life Expectancy
Pollard's decomposition breaks a difference in life expectancy between two populations into additive contributions from each age, showing exactly how much of the gap is due to mortality differences at infancy, in midlife, or in old age. John Pollard derived a continuous-age formula expressing the life-expectancy difference as an integral of the age-specific mortality-rate difference weighted by life-table functions. Because the contributions sum exactly to the total gap and can be further split by cause of death, the method is a standard tool for explaining why one population outlives another.
Key highlights
- Decomposes a life-expectancy difference into age-specific contributions that sum exactly to the total gap.
- Extends naturally to a simultaneous decomposition by cause of death, attributing the gap to ages and causes together.
- Provides a continuous-age formulation with a clear analytic weight function, complementing discrete stepwise methods.
- Widely applicable to differences between countries, sexes, periods, or socioeconomic groups using only two life tables.
Intuition
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How it works
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When to use it
Use Pollard's decomposition when you have two life tables and want to explain a difference in life expectancy — between countries, sexes, periods, or social groups — in terms of the ages (and, with cause data, the causes) driving it. It is the appropriate continuous-age complement to Arriaga's discrete stepwise decomposition. Assumptions: accurate age-specific mortality for both populations, and that decomposing into a smooth age profile of mortality differences is the goal. Do NOT use it to attribute the gap to changes in population age structure — it decomposes the mortality (life-table) difference only; and be aware that, like all such methods, the exact age contributions depend slightly on the chosen weighting convention, so report which variant was used.
Strengths & limitations
- Decomposes a life-expectancy difference into age-specific contributions that sum exactly to the total gap.
- Extends naturally to a simultaneous decomposition by cause of death, attributing the gap to ages and causes together.
- Provides a continuous-age formulation with a clear analytic weight function, complementing discrete stepwise methods.
- Widely applicable to differences between countries, sexes, periods, or socioeconomic groups using only two life tables.
- It decomposes only the mortality component and does not address differences arising from population age structure.
- The precise age contributions depend on the weighting convention chosen, so different variants give slightly different splits.
- Cause-specific decomposition requires reliable cause-of-death coding, which is weak in many settings.
- Like other one-dimensional decompositions, it describes rather than explains causes, offering no causal mechanism.
Common pitfalls
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Applications
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Frequently asked
How does Pollard's decomposition differ from Arriaga's?
Both attribute a life-expectancy difference to ages, but Pollard's is a continuous-age, integral formulation with an explicit analytic weight function, while Arriaga's is a discrete stepwise method that separates direct, indirect, and interaction effects across life-table age intervals. The two give very similar results and are often used interchangeably; the choice is largely one of formulation and convenience.
Can Pollard's method decompose by cause of death?
Yes. Because each age contribution is proportional to the difference in the total force of mortality at that age, and the force of mortality is the sum of cause-specific forces, the age contribution splits additively into cause-specific pieces. This yields a simultaneous decomposition of the life-expectancy gap by age and by cause, with all pieces summing to the total.
Why does the choice of weighting matter?
The weight function combines life-table functions from the two populations, and there is more than one symmetric way to do this (for instance which population's survivorship and which one's remaining expectancy to use). Different conventions distribute the gap slightly differently across ages, though they all reproduce the same total. Reporting the convention ensures comparability across studies.
Sources
- 1.Pollard, J. H. (1982). The expectation of life and its relationship to mortality. Journal of the Institute of Actuaries, 109(2), 225–240.
- 2.Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell.ISBN 9781557864512
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ScholarGate. (2026, June 22). Pollard Decomposition. ScholarGate. https://scholargate.app/demography/pollard-decomposition